IFAC SYMPOSIA SERIES Janos Gertler, Editor-in-Chief, George Mason University, School of Information Technology and Engineering,

Fairfax, VA 22030-4444, USA

DHURJATI & STEPHANOPOULOS: On-line Fault Detection and Supervision in the Chemical Process Industries ( 1993, No.l)

BALCHEN et al: Dynamics and Control of Chemical Reactors, Distillation Columns and Batch Processes (1993,No.2)

OLLERO & CAMACHO: Intelligent Components and Instruments for Control Applications (1993,No3)

ZAREMBA: Infonnation Control Problems in Manufacturing Technology (1993, No.4) ST ASSEN: Analysis, Design and Evaluation of Man-Machine Systems ( 1993, No.5) VERBRUGGEN & RODD: Artificial Intelligence in Real-Time Control ( 1993, No.6) FUESS: Nonlinear Control Systems Design ( 1993, No.7) DUGARD, M'SAAD & LANDAU: Adaptive Systems in Control and Signal Processing ( 1993, No.8) TU XUY AN: Modelling and Control of National Economies ( 1993, No.9) LIU, CHEN & ZHENG: Large Scale Systems: Theory and Applications ( 1993, No.JO) GU YAN & CHEN ZHEN-YU: Automation in Mining, Mineral and Metal Processing (1993, No.J 1) DEBRA & GOITZEIN: Automatic Control in Aerospace (1993, No.12) KOPACEK & ALBERTOS: Low Cost Automation ( 1993, No.13) HARVEY & EMSP AK: Automated Systems Based on Human Skill (and Intelligence) ( 1993, No.14)

BARKER: Computer Aided Design in Control Systems (1992, No.J) KHEIR et al: Advances in Control Education ( 1992, No.2) BANY ASZ & KEVICZKY: Identification .and $ystem Parameter Estimation ( 1992, No3) LEVIS & STEPHANOU: Distributed"Intelligerice SysteJris. ( 1992, No.4) FRANKE & KRAUS: Design Methods of Control Systems ( 1992, No.5) . ISERMANN & FREYERMUTH: Fault Detection, Supervision and Safety for Technical Processes

(1992,No.6) TROCH et al: Robot Control ( 1992, No.7) NAJIM & DUFOUR: Advanced Control of Chemical Processes ( 1992, No.8) WELFONDER, LAUSTERER & WEBER: Control of Power Plants and Power Systems ( 1992, No.9) KARIM & STEPHANOPOUI.DS: Modeling and Control of Biotechnical Processes ( 1992, No.JO) FREY: Safety of Computer Control Systems 1992

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ARTIFICIAL INTELLIGENCE IN REAL-TIME CONTROL 1992

Selected Papers from the IFACllFIP/IMACS Symposium, Delft, The Netherlands, 16 -18June1992

Edited by

H.B . VERBRUGGEN Department of Electrical Engineering,

Delft University of Technology,

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Artificial intelligence in real-time control 1992: selected papen from the IFACJIFIPJIMACS symposium, Delft, The Netherlands, 16-18 June 1992/editcd by H.B. Verbruggen and M.G. Rodd. - ht ed. p. cm. - (IFAC symposia series; 1993, no. 6) ''IFAC Symposium on Artificial Intelligence in Real-Time Control 1992"-T.p. veno Includes index. I. Artificial intclligence-Cangresses. 2. Real-Time Cantrol-Cangresses. L Verbruggen, H.B. Il. Rodd, MG. m International Federation of Automatic CantroL IV. International Federatian for Infonnation Processing. V. Intematianal Association for Mathematics and Cooiputen in Simulation. VI. IFAC Symposium on Artificial Intelligence in Real-Time Control (4th: 1992: Delft, Netherlands) VIL Series. Q334.A7762 1993 629.8-dc20 93-33125

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Printed in Great Britain by BPCC Wheatons Ltd, Exeter

IFAC SYMPOSIUM ON ARTIFICIAL INTELLIGENCE IN REAL-TIME CON1ROL 1992

Sponsored by International Federation of Automatic Control (IFAC) Technical Committees on - Computers (COMPUT) - Manufacturing Technology (MAN.TECH) - Applications (APCOM) - Social Effects of Automation (SOC.EFF)

Co-sponsored by International Federation for lnfonnation Processing (IFIP) International Association for Mathematics and Computers in Simulation (IMACS)

Organized by Royal Institution of Engineers in the Netherlands

International Programme Committee M.G. Rodd (UK) (Chairman) K.J. AstrOm (S) L. Boullart(B) P. Bome(F) H.J. Efstahiou (UK) S. Franzen (S) A. Halme (SF) C.C. Hang (SGP) C.J. Harris (UK) G. Johannsen (D) I.G. Kalaikov (BG) V. Krebs (D) R. Lauber (D)

National Organizing Committee H.B. Verbruggen (Chainnan) J.M. van der Kamp L. Boullart P.M. Bruijn R.B.M. Jaspers A.J. Krijgsman Th . .Kristel

H.T. Li (PRC) I.M. MacLeod (SA) L. Motus (ESTONIA) S. Narita (J) Y.J. Pao (USA) L. Pun (F) A.G. Schmidt (D) S.O. Su (PRC) G.J. Suski (USA) S.G. Tzafestas (GR) T. Vamos(H) H.B. Verbruggen (NL) E.A. Woods (N)

PREFACE

This Symposium is a continuation of a series of three successful workshops in this field (1988 Swansea, U.K., 1989 Shenyang, PRC, 1991 Rohnert Park, CA, USA). It took place in the Department of Electrical Engineering on the Campus of the Delft University of Technology. This event was selected and sponsored by the University as one of its lustrum activities in honour of the University's 150th anniversary.

From nearly 100 extended abstracts and draft papers submitted, 57 were accepted after review by the International Programme Committee. Twelve colleagues were invited to organise invited paper sessions, and their enthusiasm and reputation led many authors to submit a paper. Finally, 48 regular papers and 65 invited papers were accepted. In addition, the organisers were happy to schedule 5 plenary paper sessions. This brings the total number of contributions to 112, of which 103 were acmally presented. It is regrettable that 9 papers could not be presented and discussed, as the authors could not come to Delft. However, the 92% of the papers presented was a relatively good score.

In spite of the currently unfavourable economic conditions and the ever-growing number of symposia and workshops in this field and related areas, the attendance at the Symposium can be considered very good with 181 participants from 25 countries.

The preprints of the Symposium contain 112 contributions printed in one volume of 750 pages.

The Symposium intended to:

investigate the state-of-the-art in the application of artificial intelligence techniques in real-time control,

bring together control system specialists, artificial intelligence specialists and end-users.

The main themes of the Symposium were:

The methodology of Artificial Intelligence Techniques In control engineering

• Neural Net Control

Knowledge-Based Control

Fuzzy Control

Qualitative Reasoning

Fault Detection and Fault Diagnosis

Genetic Algorithms and Learning

The application of ArtlftclaJ Intelligence Techniques In different areas of control

• Process Control

• Biotechnology

Robotics

Power Systems

Hardware and software requirements

• Temporal Reasoning • New Paradigms for Real-Time Control

Real-time Environments for Intelligent Control

During the plenary sessions, well-known scientists highlighted topics of this fast developing area in control engineering and artificial intelligence.

Of the plenary papers presented, the following two papers have been published in Control EngiMering Practice, Volume 1, Number 2 (Pergamon Press).

Autonomous controllers Astrom K.J. (S)

Toward intelligent control of mechanical processes Isermann R. (D)

In this volume the following two plenary papers have been inserted:

Knowledge-based control: selecting the right tool for the job Leitch R. (UK)

The functional-link net approach to the learning of real-time optimal control Pao Y.H. (USA)

The programme included 24 technical sessions, with three sessions taking place in parallel. The following regular and invited sessions were scheduled:

Neural Network Schemes

Knowledge Elicitation and Acquisition

Applications of Fuzzy Control

Temporal Reasoning

Analysis and Design of Intelligent Controllers

Applications of Neural Nets

Process Monitoring and Supervision

Fuzzy Control

Learning Control Schemes

Direct and Supervisory Knowledge-based Control

New Paradigms for Real-Time Control

Applications in Biotechnology I

Fault Detection and Fault Diagnosis I

Neural Nets and Simulation for Control

Qualitative Reasoning

Applications in Control and Measurement

Applications in Biotechnology II Applications in Process Control I

Fault Detection and Fault Diagnosis II

Genetic Algorithms and Learning

Real-Time Environments for Intelligent Control

Fault Detection and Fault Diagnosis ID Applications in Process Control II Development of Real-Time Al-Systems

Thirteen papers were selected for Volume 1, Number 2 of Control Engifll!ering Practice.

A selection of the remaining papers duly presented at the meeting was made by the editors for inclusion in the Proceedings.

About 35% of the papers presented reported on practical applications, 30% dealt with theoretical aspects and 35% had a mixed content of application-oriented and theoretical subjects.

Many of the professional engineers working in industry have the feeling that the gap between theory and practice in applying control and systems theory is widening rather than narrowing despite so many years spent on developing control algorithms. Much of this theory is heavily based on linear systems theory and on extensive mathematical models.

In practice, however, many systems are partly unknown and highly nonlinear, and an increasing number of people, confronted with real-life problems, feel that the elegant road paved by linear systems theory is leading a number of applications into a dead end. Instead of a mathematical description, an alternative could be a behavioural description based on qualitative expressions and on the experience of those actually working with the process.

This Symposium showed clearly that there are alternative possibilities for control based on artificial intelligence techniques, and in many ways this Symposium has provided a large-scale breakthrough for artificial intelligence techniques in control engineering.

In general, and according to the statements of many participants, this Symposium can be considered a very successful event which showed the importance of this new, developing area for control engineering.

The next event on the topic of Al in real-time control is planned for Valencia in 1994.

Prof.Ir. H.B. Verbruggen

Prof. M.G. Rodd

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

PLENARY PAPERS

KNOWLEDGE BASED CONTROL: SELECTING THE RIGHT TOOL FOR THE JOB

R. Leitch

Intelligent Automation Laboratory, Department of Electrical and Electronic Engineering, Heriot-Wall University, EdinburghEHJ 2HT, UK

Absract. We propose a classification of system models in terms of their knowledge classes and

characteristics, and relate these to existing approaches to the use of AI methods in Control. Such an classification is a necessary precursor to developing a methodological approach to identifying the most appropriate technique (tool) for a given generic class of applications (job).

Keywords. Systems Modelling, Qualitative Modelling, Expert Control, Model Based Control. Specification Methodology.

INTRODUCTION

Approaches to the utilisation of Artificial Intelligence (Al) methods for extending the range of automation continues to expand at an ever increasing pace. Each technique results in a number of new potential solutions. The result is that the practising Control Engineer is bewildered by the seemingly endless procession of techniques each offering some prospects of solving a given automation problem. But how does he choose what's best? Does he go for the latest Advanced Control method based on evermore sophisticated mathematics or is he seduced by the promise of Intelligent Systems using simple qualitative methods to produce flexible and effective systems. Or does he need both!

At present the Control community is not addressing this crucial problem of determining the most appropriate approach dependent upon the nature of the automation task and the characteristics of the system that is to be automated. Such a methodological approach is essential if effective use of both AI-based systems and 'conventional' control methods is to be established. A corollary to this is that we need to stop looking for a universally best approach, and put much more effort into understanding the assumptions and therefore the limitations of the various techniques. Only in this way can we select the right tool for the job.

1

APPROPRIATE MODELLING:

- that's the secret

These days the word 'model' is a heavily overworked term. In its most general form it can be used to mean any description of an entity. However what is crucial is to clearly understand the role of the model. Within engineering, models have long been used to predict the temporal evolution of the attributes of a physical system, often now called the behaviour of the system. However, recently, mainly stemming from the AI community, modelling techniques for reasoning about the topological properties or spatial position of objects and methods for representing and reasoning about the function qf systems have also been developed. Although these latter developments are interesting they have not yet impacted on Control Engineering. We will, therefore, restrict the subsequent discussion to models for the purpose of predicting behaviour, sometimes called behavioural models and descriptions.

Further, we must also consider the purpose (or task) for which the model is being developed. For example, it has long been recognised that models for open-loop and feedback control require different amounts of detail to achieve a similar performance. Now, with Control Engineering expanding its horizons to include other tasks, e.g. fault diagnosis, process monitoring, planning, training, etc., we must carefully consider the

relationship between task and model requirements. There will be no one model that is best suited to all tasks. This 'no best model' is fundamental to Engineering, whereas in Science, where the task of modelling is almost exclusively analytic - to describe the physical world as accurately as possible - the notion of best model may be valid. In Engineering, concerned with synthesis as well as analysis:

a model is correct if its satisfies its purpose.

Also, synthesis is usually expressed as a set of performance specifications for the system. So, even a best or optimal model can be difficult, and sometimes impossible to obtain. We are normally faced with a trade-off between some of the specifications. For example, accuracy of predictions and generality of the model can sometimes be conflicting requirements. Further, AI based approaches emphasise the need for 'understandability' or perspicuity of models as an

important specification requirement. In fact, many of the existing AI approaches and those under development, explicitly address this issue of enhancing 'perspicuity', sometimes at the notional expense of accuracy, so that the system can be more easily modified or extended. Therefore, in developing a model we have to consider the role (behavioural prediction), the task (control, diagnosis, training, etc.) and the performance specifications (accuracy, flexibility, generality, verifiability, perspicuity - and honesty).

Honesty! What has honesty got to do with modelling? Well, what has been under development within AI based approaches are techniques that allow the modeller to represent the available knowledge in a model at the degree of precision and certainty that is confidently known -no less and no more. That is, if the knowledge is uncertain, and perhaps even incomplete, we should provide representation and reasoning mechanisms to explicitly support such knowledge, and not require the modeller to make 'guesses' or estimates that he may not believe in for the model to become tractable. This last insight is particularly important and has resulted in an enormous interest in using AI techniques to develop altemative(qualitative or non-numeric) modelling approaches to cope with such issues (Weld, 1989; Davis, 1990; Leitch, 1990) a whole plethora of techniques based on a wide range of assumptions and normally developed for specific tasks. It is important that we now try to understand the relationships between such models and most crucially identify a methodology for

selecting the most appropriate technique for a

2

given purpose, task, specification and characteristics of the available knowledge.

APPROACHES TO MODELLING

The preceeding section argued that the approaches to developing models has expanded rapidly over the last few years. Unfortunately, most of these techniques have been developed in isolation, and partial ignorance, of other approaches and so very little understanding or taxonomic knowledge of the various approaches exists. This section makes an attempt to classify the existing assumptions behind the various approaches so that we can begin to understand the relationship between them. We first classify models into model classes and model types and then identify a number of dimensions for each. The former is used to classify the important assumptions that relate to the purpose of the model, whereas, the latter relates to the characteristics of the available knowledge.

Model Classes

This class of models reflects very fundamental assumptions about the model that are closely related to the purpose of the model. We identify three class dimensions: knowledge source, knowledge level and knowledge orientation. In fact, combinations of these dimensions lead to completely different approaches and research topics.

By knowledge source we mean where the knowledge that is used to build the model comes from. Two major sources of such knowledge have been identified (Leitch,1989) as empirical and theoretical. Empirical knowledge relates to that which is obtained directly from first hand experience. It attempts to capture knowledge that has been induced from direct observation of a particular system. As such it can be highly effective but is limited in its generality. Empirical knowledge has traditionally been omitted from control systems design, sometimes resulting in reduced performance, and hence requiring subsequent empirical tuning. However, the development of Expert Systems techniques has brought such knowledge to the fore and emphasised its importance and, more recently, its limitations. On the other hand, theoretical knowledge, that is knowledge of scientific laws and principles, has long been the basis of control system design. However, the use of such knowledge has, until fairly recently, been almost exclusively restricted to numerical descriptions usually in the form of differential or difference

equations. And, as discussed in the motivation, often there does not exist adequate knowledge to make use of the powerful methods associated with real-valued differential equations. The Artificial Intelligence community has, however, developed techniques that allow theoretical knowledge to be represented qualitatively and used to generate qualitative descriptions of the system's behaviour (Weld,1989; Leitchl990). Theoretical knowledge is, of course, general and is transferable from one application to another and, in fact, removes much of the knowledge acquisition problem associated with empirical knowledge. However, it can also be inefficient, and its very generality may mean that it is less effective. Clearly, theoretical and empirical knowledge are complementary; the best solution is obtained by a symbiotic combination of the two. However, such combinations are by necessity specific to a given application (Leitch, 1989) and care has to be taken to ensure that performance is indeed improved.

The second class dimension determines the subject of the know ledge. In Control Engineering terms we can have two options. We can represent the knowledge of the process itself, i.e. model-based approaches, or of the control algorithm, we term this object-level knowledge. Alternatively, we may choose to represent knowledge about the control design methods so that they can be modified on-line. We term this meta-level knowledge, as it reflects knowledge about the knowledge used to control rather than the modelling knowledge itself. Both approaches are actively being developed, both with AI-based techniques and 'traditional' control methods. For example, expert or intelligent control (Astrom,1986) can be described as a meta-level approach, usually with empirical knowledge at the meta-level and a conventional numerical controller(s) at the object level. In contrast, Fuzzy Logic Controllers (Mamdani,1976) can be regarded as object-level empirical knowledge (with uncertainty). Similarly, in the case of conventional control techniques, examples of object-level control are classical three term controllers or indeed an LQG derived state feedback control system. Adaptive control systems, are a common form of meta-level control as the performance of the system is monitored on-line, usually in the form of some performance index, and used to modify the (design) of the object level controller. This clear separation of meta and object level knowledge allows different techniques (models) to be used at each level, thereby greatly expanding the range of applicability of the control techniques. This distinction is fundamental in control applications, however, it is also valid within other

3

domains, e.g. diagnosis. We term this class dimension the knowledge-level.

A further distinction has to be made, and that is whether the knowledge represents an explicit model of the physical world to be reasoned about or whether it represents our procedures for controlling or diagnosing the world. In the latter case the model would be termed implicit. Explicit models relate system inputs to outputs in the same way as the real system. They can, therefore, have a causal interpretation (Iwasaki, 1986) associated with the structure of the representation. Conversely, implicit models effectively relate outputs (symptoms in the case of diagnosis) to inputs and are inherently acausal.

object

Figure!. Model Classes

In the former case, explicit models are currently being utilised as the basis for model-based reasoning, in particular for diagnosis, but control and training are equally important tasks. Explicit models are usually from a theoretical source, however, they need not be. In fact, much of causal modelling (Console,1989)takes its knowledge from empirical sources. Implicit models can also be obtained from both sources of knowledge. Conventional control algorithms are derived from theoretical models using some design procedure, whereas Fuzzy Logic Controllers utilise implicit models based on empirical knowledge at the object level. From Figure I , we can see that various approaches to control can be identified by appropriate combinations of the above dimensions. We believe that these class-dimensions provide an

important insight into the relationships between

many of the fundamental techniques currently under development. Model Characteristics

Whilst model class is determined by the purpose and task of the model, the properties of the available knowledge used to model the process determine the characteristics of the model that can be utilised. These characteristics are used to form dimensions along which models can be classified and hence used to identify the most appropriate model. It is in this area that AI is having the most significant impact. In fact, the issues here are exactly those that underpin knowledge representation issues within Al, and are, therefore, intrinsically fundamental to AI itself. Figure 2 illustrates the characteristic dimensions. We identify five dimensions that represent the principal assumptions for modelling and reasoning about the physical world; in other domains other characteristics may be more important.

A fundamental choice is whether to represent the dynamic evolution of the system or not. Until fairly recently most AI-based representation schemes were based on static models of the system assumed to be in equilibrium. Such models can, indeed, be useful especially in steady-state fault diagnosis. However, in (model-based) control and in diagnosing faults during the transient behaviour of a system, dynamic models are essential. Dynamic models require the representation of state and memory to reflect the energy storage, and hence delay, that occurs in the physical world. This is often confused, at least in AI circles, with temporal reasoning that reasons about the ordering of events in time. Static models can still have time-dependent variables, and even time-varying parameters, without being dynamic. Hence many temporal reasoning applications are based on static models. The choice of static or dynamic models fundamentally effects the representation language. In the former, algebraic equations will suffice whereas in the latter differential primitives are required.

One of the early insights to stem from AI work is the distinction between declarative and procedural representations. Declarative representations describe relationships between variables or attributes of the physical world. They do not imply a directionality in the relationship, only that a set of variables are related by the description provided. For example, Ohm's law states that the current through and voltage across a resistor can be related by an empirical constant (given real-valued descriptions of the current and the voltage, see later) called the resistance. It does not contain any

4

information about causality; that must be obtained from another source (Leitch,1987) This lack of directionality makes the representation very general but can also make the reasoning or inference mechanism inefficient. Conversely, if the available knowledge contains a strong element of directionality between the variables then a procedural language will be more effective. However, the directionality may be very specific to a given application or situation, and hence procedural representations tend to be highly specialised. The trend has been to make representations more and more declarative to increase generality and to cope with the resultant loss in efficiency by more computational power.

The third characteristic dimension concerns whether the system is considered to be continuous or discontinuous. In the continuous case, the system can only evolve through adjacent states whereas in the discontinuous case any state can follow a previous one, e.g. finite state machine. This leads to different techniques for generating the behaviour of the system. Continuity is clearly an important assumption in dynamic systems. However discontinuous dynamic systems can also be important.

An area of intense activity, now concerning both Control Engineering and AI researchers is Qualitative Modelling (Weld,1989, Leitch 1990). Although this will not be specifically discussed in this paper, it forms one of the main characteristic dimensions of models. This dimension concerns a spectrum of representations from purely quantitative models at one end and very weak

qualitative representation at the other. In fact, exploring novel representation techniques, e.g. order-of-magnitudes and fuzzy sets has been a major pre-occupation of qualitative reasoning research (Shen,1992a). The goal is to utilise a representation that 'honestly' captures the available knowledge whilst satisfying the performance specifications.

Finally, the fifth characteristic dimension is whether the knowledge of the model is uncertain or exact. Not to be confused with qualitative; a model can be qualitative and exact, and even honest! However, if the knowledge is uncertain then the representation should include some way of representing this. Two main forms of uncertainty have been recognised. The first, probability theory, concerns the situation when exact (deterministic) knowledge is not available and estimates based on the frequency of occurrence, represented by a probability density function, are used. It is essentially historically or

experimentally based. The second approach is to represent imprecision explicitly, i.e. vagueness is captured by a graded membership, a real number between (0-1), representing the degree of set membership of a particular item (Zadeh,1973). Whether probability or possibility is u800 does not concern this dimension, only that uncertainty is a characteristic of models that may be important, and, therefore, should be explicitly supported.

Figure 2 shows the five principle characteristic dimensions. In fact, each combination of choices on these dimensions represent a different 'type' of model. Some of these combinations represent very strong research areas, e.g. Qualitative, Dynamic, Declarative, Uncertain, Continuous, Models (Fuzzy Qualitative Simulation, (Shen,1991b) whereas others represent well established techniques, e.g. Quantitative, Dynamic, Procedural, Exact, Continuous, Models (differential equations). Still others, e.g. Quantitative, Static & Dynamic, Declarative, Continuous Systems have yet to be investigated.

I •

Static Dynamic

• • Continuous Discontinuous

. • Qualitative Quantitative

• • Declarative Procedural

• . Certain Uncertain

Figure 2. Model Characteristics

In this section we have proposed a classification of models into classes, reflecting their purpose, and characteristics, dependent upon the properties of the available knowledge. Our intention is that such work lays the foundation for a methodological approach that will provide, at least, a set of guide­lines to identify the most appropriate technique and associated model for a particular task and application characteristics.

5

EXTENDING THE SCOPE OF CONTROL ENGINEERING

Although modelling, in all its various guises, is intrinsically important, the real advantage comes when using these techniques for control applications. The last decade has seen a rapid expansion in the tasks or purposes for which Control Engineering knowledge or methodology has been applied. In this respect we take Control to mean interacting and reasoning about the real physical world for some specified purpose. The original tasks of Control: regulatory and servomechanism control by using feedback or feedforward techniques have been supplemented by a range of tasks including :- fault diagnosis, condition monitoring, critical event simulation, training etc. Each of these tasks uses some of the various approaches to modelling discussed in the previous section. However, so far there has not been a significant attempt to identify the 'best' approach to modelling for a given application. Such a methodological approach is now becoming crucial as both the classes and characteristics of models and the range of applications continually expand. What is required is a set of relations that will identify the most appropriate model, and the corresponding solution technique, for a given class of application, the class being determined by the characteristics of the domain. In this regard the model classifications presented in the preceding sections begin to form a basis from which such a methodological approach can be generated. In this section, we begin the process of attempting to identify particular solution techniques with generic problems appearing within the Control Engineering literature.

Coptrol Systems

One of the obvious approaches to the utilisation of Artificial Intelligence techniques within Control attempts to use Expert System techniques (Astrom,1986) as an adjunct to conventional methods. By placing an Expert System, usually using rule-based technology 'on top of an existing numerically based control system, the range of applicability of the controller can be extended by encoding into the Expert System rules for the adjustment of the control, either by modifying the control algorithm or by replacing it with another approach altogether. This essentially puts the Control Engineer on-line so that knowledge normally only used during the (off-line) design process is available during the actual operation. This approach is now being called Expert Control,

and represents a major actlVlty for Control Engineers wishing to become involved in Artificial Intelligence approaches. It is attractive in that it utilises existing techniques, and hence skills; we believe that the majority of Control Engineers have adopted this route. In terms of the model classification proposed in Section 2, this approach adopts an implicit empirical model at the meta­level (Expertise) and existing control methods which can be either implicit (feedback) or explicit (model reference) using either empirical or theoretical knowledge at the object-level.

The second approach uses AI techniques directly to model the system at a level of detail consistent with the available modelling knowledge and the task to be executed. Such approaches, sometimes called Qualitative Control, can be regarded as directly 'closing the feedback loop' by using AI methods. In this way qualitative representation of the control policy is used to compute the value of the control variable. This exposes a major shortcoming of qualitative methods for control applications: practical controllers still must output a numerical value. This requires that the qualitative value be 'approximated' by a numerical value; a symbol-to-signal transformation that is highly subjective. Fuzzy Logic Controllers are prime examples of this approach. They use implicit

Process

Expert System

Qualitative Control

empirical models at the object-level, with Fuzzy Sets to represent the inherent vagueness or uncertainty. This approach is appropriate whenever there is some inherent difficulty with conventional modelling (numerically-based) techniques. Further, in many cases it has been shown that equivalent control performance can be achieved, however, qualitative methods have a distinct advantage of perspicuity (Francis,1989). t

Meta-level control can also be used with qualitative controllers. A good example of this is again Self-Organising Fuzzy Logic Controllers (Linkens,1991) where self-organising rules are used to modify the fuzzy rule-base to improve the overall performance.

Awaiting development is the qualitative counterpart of Model Reference Control. In this case the techniques of Qualitative Simulation can be used to represent the 'reference model', i.e. the ideal model, and the control adjusted such that the observed behaviour approaches the predicted response. The comparison between behaviours will also require a form of symbol to signal transformation in order to identify real-valued adjustments to the controller. We are not aware of this work being reported or even pursued. In terms of the classification this approach would utilise explicit, theoretical models at the object- level

numerical controller

Expert System

Expert Control

FiKure 3 Generic approaches to Control

6

numerical controller

1---� qualitative model

discrepancy detector

Qualitative Model-Based Control Figure 3 <continued) Generic approaches to Control

Automated Fault Dia1mosjs

The most frequent task performed by AI techniques is fault diagnosis. An enormous literature has amassed on such techniques. Many parallels can be drawn with the previous discussion on control methods. For example, initial diagnostic systems utilised Expert System techniques to represent empirical knowledge of relationships linking symptoms (observations) with possible diagnoses (actions). This approach is now termed Classification-Based diagnosis and has many examples of successful implementations. However, the approach inherits the limitations of Expert Systems (empirical knowledge) in that only known or experienced faults can be diagnosed. It conforms to the use of empirical, implicit models at the object-level.

Another more general approach to diagnosis has recently been developing, based on the use of explicit models of the system to be diagnosed. Such methods are called Model-Based Diagnostic Systems (MBDS). The central idea of MBDS is the use of an explicit model of a system's structure and a simulation engine to generate the behaviour. Such a diagnostic mechanism determines some constituents of a physical system that account for the observed discrepancies, i.e. inconsistencies obtained from the model and driven by the observations.

The use of qualitative simulation techniques as the system model offers many exciting prospects for MBDS in that such developed diagnostic systems would allow the early detection of incipient failures (during the transient) and reduce the

7

requirement of accessibility of s�stem states by diagnosing over time. Within systems based on iterative search (Leitch,1991) diagnosis is performed as a refining process in the following way. Initiallised by observations, an inference engine predicts a system's behaviour based on the system's model of normal behaviour, and a discrepancy detector detects the discrepancies between the predictions and the observations. The resulting discrepancies direct an iterative search of the space of possible model variations, using the most likely dimension first, until a 'matching' fault model is obtained. This requires that the possible model dimensions be identified and characterised, for instance, a dimension with the modification of the functional relationships between system variables or that with structural changes due to physical effects. From a general point of view, this method can be seen as a generalisation of the conventional numerical approaches to MBDS. Actually, although it is a new approach to applying AI modelling techniques for diagnosis, it utilises the basis concepts of the traditional approaches to model reference reasoning in control and system identification (Landau,1979). An important property of this technique is that the diagnostic process will be robust in that the recursive nature of the iterative search will provide a reduction in the sensitivity of the modelling assumptions.

These examples give some indication in the possible diversification of applications now being pursued and which can quite reasonably be considered to be a natural part of the Control Engineers remit. Similar arguments can be

constructed for simulation and training as application domains.

Expert System

Classification Based Diagnosis

Process

1-----�1 qualitative model

discrepancy detector

candidate generator

Qualitative Model Based Diagnosis

Figure 4. Generic Am>roaches to Diagnosis

CONCLUSION

We have attempted to show that underlying a great part of what is currently being developed, both within the AI community and the Control Engineering community, is fundamentally concerned with generating a range of approaches to the modelling of physical systems. It is here that AI is having a very profound impact on Control approaches, if not yet on theory. We have presented a classification of approaches

8

to modelling based on model classes and characteristics. We believe that such a classification is a necessary precursor to establishing a coherent methodological approach to identifying the most appropriate tool for a given application. By extending the formal methods of reasoning to include the prediction of the qualitative evolution of a dynamic system we now have a much greater diversity of tools with which to more effectively tackle complex applications.

REFERENCES

Astrom K.J., J.J. Anton and K.E. Arzen. (1986) "Expert Control", Automatica ,Vol.22, No.3, pp277-286.

Console L. D. Dupre and P. Torasso. (1989) "A Theory of Diagnosis for Incomplete Causal Models", Proc. 11th Int. Joint Conf on Artificial Intelligenc.

Davis E. (1990) Representations in Common Sense Knowledge. Morgan Kaufmann, San Mateo, CA.

Francis C.F. and R.R. Leitch. (1989) "A Feedback

Control Scheme Based on Causal Modelling"Jnt. Journal of Engineering Applications of Artificial Intelligence , Vol.2 No.3, pp182-188.

Iwasaki Y. and H.A. Simon. (1986) "Causality in Device Behaviour", Artificial Intelligence, Vol.29, pp3-23.

Kuipers. B.J. (1986) "Qualitative Simulation", Artificial Intelligence, Vol.29, pp289-338.

Landau Y. (1979) Adaptive Control: The Model Reference Approach, Marcel Dekker.

Leitch R.R. (1987) "The Modelling of Complex Dynamic Systems", Proc. IEE, Part D, Vol.134, No.3, pp245-250.

Leitch R.R. and A. Stefanini. (1989) "Task

Dependent tools for Intelligent Automation", Int. Journal on Artificial Intelligence in Engineering, Vol. 14, No.3, pp126-143 ..

9

Leitch R.R. (1990)"A Review of the Approaches to Qualitative Reasoning of Complex Physical Systems", in Knowledge Based Systems for Process Control, McGhee J. Grimble M.J. and Mowforth P.(editors), Peter Peregrinus.

Leitch R.R. and Shen Q. (1991) "Finding Faults with Model Based Diagnosis", Proc. 2nd. Int. Workshop on the Principles of Diagnosis, Milan.

Linkens D.A. and S.B. Hasnain. (1991) "Self Organising Fuzzy Logic Control and its Application to Muscle Relaxant Anaethesia". Proc. IEEE, Part D, Vol.138, No.3, pp57-95.

Mamdani E.H. (1976) "Advances in the Linguistic Sythesis of Fuzzy Logic Controllers", Int. Journal of Man Machine Studies, Vol.8, pp669-678.

Shen Q. and R.R. Leitch. (1991a) "On Extending the Quantity Space in Qualitative Reasoning", To appear in The International Journal for Artificial Intelligence in Engineering.

Shen Q. and R.R. Leitch. (199 1b) "Combining Qualitative Simulation and Fuzzy Sets", Recent Advances in Qualitative Physics, B. Failings and P. Struss (editors), MIT Press.

Weld, D. and J. de Kleer, ( 1990). Readings in Qualitative Reasoning about Physical Systems. Morgan Kaufmann, San Mateo, CA, 1989.

Zadeh L.A. (1973) "Outline of a New Approach to the Analysis of Complex Systems and Decision Processes", IEEE Trans. Systems, Man, and Cybernetics, Vol.3, No.1 .,pp28-44.

Copyright @ IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

THE FUNCTIONAL LINK NET APPROACH TO THE LEARNING OF REAL-TIME OPTIMAL CONTROL

Yoh-Han Pao

Department of Electrical Engineering and Applied Physics, Case Western Reserve University, Cleveland, OH 44106, USA and Al Ware Inc., Cleveland, OH 44106, USA

Abstract. We present a strategy for learning optimal control. The approach uses functional-link neural network implementations which have several beneficial properties giving advantages over the more common generalized delta rule implementations. The learning task is decomposed onto three parts: identification and monitoring, one-step­ahead control generation and control path optimization. Each of these parts is accomplished with its own functional-link net and these are coordinated to provide the real-time learning of the optimal control path.

Keywords. Neural net control; functional-link net; real-time learning; optimal controls

INTRODUCTION

In this article we are concerned with neural-nets which can learn to control systems in accordance with a guiding intent and can also learn how to formulate that control strategy. The overall control task is viewed as being carried out by four component networks; these being the predictive monitoring net. the control action generator net, the objective function net and the optimization net.

A special type of artificial neural-net, the functional­link net is used for all four phases of this activity. It is the particular characteristics of the functional-link net which make it possible for us not only to support all four types of functionalities with nets of the same architecture but to do so in 'real time.' In view of this we begin with a brief discussion of the functional-link net itself.

The generalized delta rule net with hidden layer(s) and backpropagation of error training is widely used for learning functional mappings from one space, e.g. Rn, to another, e.g. R. Such a net is illustrated in Fig. la for the multi-input, multi-output case with a single hidden layer.

Such a net can be taught to learn a function. That is, training a neural-net may be perceived as a mathematical exercise, that of decomposing the prescribed mapping function into a body of simpler functions. In terms of the biologically motivated artificial neural-nets, these functions consist of a linear combination (the sum of scaled or weighted values) and a nonlinear transformation via the 'activation' function. The only nonlinear operation is that of the activation function.

11

However, neither our knowledge of biological systems or our knowledge of analog circuits suggest that such a restriction would be generally desirable.

Thus, instead of perpetuating the widely used back­propagation net (Fig. la), we investigated the possibility of generalizing the structure to include functional links, instead of exclusively linear links; the practical motivation for this modification being the possibility of significantly reducing the computational and structural complexity of such nets.

In real-time control the complexity of the training and retraining tasks need to be included in our consideration of computational complexity. It is not only the simple feedforward computations which are important. The generally iterative training task cannot be dismissed as an off-line, once-in-a-long­while task.

We now discuss the similarities and differences between the generalized delta rule (GDR) net and the functional-link net. The net shown in Fig. la is a GDR net with one hidden layer.

If we limit ourselves to the consideration of a single output, the linear link net computes the kth output according to Ok = fk(� where each fie is of the form

(1)

with Bj. A.j and bj different for each fk. The components of the vector A.j are Aji and all of the weights, Aj and Bj and the thresholds, bj, are to be learned. The function g is the nonlinear activation

function, a 'squashing' function such as tanh or a sigmoid function.

Hornik, Stinchcombe and White (1989) addressed the question of whether such a functional decomposition could approximate functions mapping RD to R with arbitrary accuracy. They demonstrated that for well behaved functions it could indeed do so as long as a sufficient number of nodes were used (Theorem 2.4 of Hornik, Stinchcombe and White, 1989).

In its simplest and most general embodiment, the functional-link net merely advocates the use functional links in lieu of the more restrictive linear links. In practice we found that the use of functional links almost always does away with the need for hidden layers. In particular we come close to obtaining a rigorous theoretical justification of the functional-link procedure by mapping the GDR net to the form shown in Fig. 1 b.

The net shown in Fig. lb is the random-vector, auto­enhanced version of the functional-link net. In this type of functional-link net the feedforward computations for the trained net are similar to that of the backpropagation net except that we do n.Q1 learn the weights A.j nor the thresholds bj. Instead we generate them randomly subject to some mild constraints. The weights, Bj. are learned and easily enable the random-vector, functional-link net to learn functions.

Sometimes researchers have the impression that the hidden layer provides a meaningful "internal representation". If this were really so then the functional-link net approach without the learning of the hidden layer outputs would constitute an impoverished representation of the solution. But it can be easily demonstrated that the so-called internal representation varies essentially randomly in the details with initial conditions and so specific meaning cannot be attached to it. This is why it is not surprising that the random vector functional-link net also functions well.

The functional-link net has no hidden layers. The net is a flat net and the training procedure consists of finding the minimum in a quadratic error surf ace, a procedure which is orders of magnitude more rapid than that of the training procedure in the backpropagation net.

This result is not to be misinterpreted to mean that all real neural-net systems, biological of otherwise, can be made 'flat'. Rather, introducing nonlinearity in the links is equivalent to the introduction of additional dimensions for the description of the mapping. In the new framework the computing task becomes linearly separable. It is this mathematical property of linear separability that is so useful in our use of the functional-link net for control.

In Fig. 2 we show a comparison of the learning rates which can be achieved with the backpropagation net and with two versions of the functional-link net; one with steepest descent update of weights and the other with conjugate-gradient descent updating of weights. These results are taken from an M.S. Thesis

12

(Dorney, 1992) and are typical of our general experience. Numerical comparisons are presented in Table 1 from the same source. The most important feature is that acceptable training can be achieved in a fraction of a second even with software simulations of such nets. This is in contrast to the (generalized) delta-rule procedure which requires tens of hours.

We now turn to neural-net control and to optimal control in particular. Our discussion will proceed in the following manner. At first, we will deal with the mechanistic aspects of the situation, namely given a system and means for observing it and means for controlling it, how do we learn how to control it so that it evolves in the desired manner? The next step is to ask how do we know what to specify as being the desired manner, in detail, in a mode which can be utilized in control.

There exist other perspectives on the first part of our subject matter and they can be perceived to be significantly different from the one advanced here. However, in our opinion, the present one is not only easy to understand intuitively, and suitable for dealing with noisy systems, but it is also conceptually compatible with the more analytical viewpoints conventionally accepted in the systems control community. It also leads naturally into our discussion of optimal control. Further details on such matters can be found in an article by Pao, Phillips and Sobajic (1992) which also contains a brief review of previous related work.

IMPLEMENTATION OF 'ONE STEP AHEAD' NEURAL-NET CONTROL

For linear discrete-time systems the one step ahead control provides a conceptually appealing approach to model based control design. By way of introduction we consider the generic nth order linear discrete-time plant described by the difference equation

y(t) + ai y(t-1) + ... + an y(t-n) = bi u(t-1) + ... + bn u(t-n). (2)

This is the deterministic auto-regressive moving average (DARMA) model in the language of Goodwin and Sin (1984) where we have assumed a plant with no direct feedthrough (bO = 0). The predicted output for such a plant would

y(t+ 1) = -a1 y(t) - ... - an y(t-n+ 1 ) + bi u(t) + ... + bn u(t-n+l). (3)

and the only difficulty would be to make sure that the an and bn values are known or can be determined accurately. With this closed-loop predictor the development of the one step ahead control law follows by solving the above equation for the control input, u, in terms of the past inputs and current and past outputs, with the predicted output, y, set to the desired output, Yd·

u(t) = l/b1( Yd(t+l) + ai y(t) + ... + an y(t-n+l) -b2 u(t-1) - . . . - bn u(t-n+l)) (4)

To describe a nonlinear plant with finite memory (order n) an nth order nonlinear difference equation is required. For this plant (without direct feedthrough) this equation is of the form

y(t+l ) = f(y(t), y(t-1), ... , y(t-n); u(t), u(t-1), ... , u(t-n)) (5)

where the function f represents a memoryless nonlinear function.

Neural-net control can be introduced at this point. Instead of Eq. 6 based on possibly intractable analytical functions and unknown coefficients, we train a neural-net to serve an a network representation of that function. The neural-net monitors the current and past plant inputs and outputs and adjusts its internal parameters until it can predict the next output of the plant. This is the prediction net which models and monitors the plant. It is illustrated in Fig. 3.

Actually what we have is but a set of data: measurements of the current and past plant inputs and outputs and one-step-in-the-future outputs. Instead of using a neural-net to learn the relationship expressed in Eq. 5, it is just as reasonable to train a net to learn the nonlinear counterpart of Eq. 6. In other words, it is equally reasonable to organize the data set so that a neural-net is given past controls (inputs) and the current, past and one-step-in-the­future outputs and learns how to 'predict' the appropriate current control. This net is illustrated schematically in Fig. 4. There is ample evidence that such nets can indeed be realized.

Although the one-step ahead controller is a very specific control design method, one of several, it is particularly well suited to the problem of the control of uncertain nonlinear systems. There are remaining issues which need to be considered in the use of this approach. Some of these are discussed in (Pao, Phillips and Sobajic, 1992). However in general this approach is practicable and works well indeed. We have demonstrated successful learning of processes under very noisy circumstances (Park, 1990) and even the learning of deterministic (near) chaotic processes (Pao, Zwingelstein and Sobajic 1990) and have implemented such control systems for practical control tasks.

With regard to system identification we digress briefly to exhibit some typical results which, though schematic, are nevertheless interesting and instructive.

In (Pao and Park, 1991) we showed what can be achieved when we train a neural net on a known input (input 1) to a nonlinear system and on the corresponding noisy output. Even though the true noiseless output was not available, we were able to learn a model of that nonlinear process very well so that in further operation we were able to estimate very well the actual noiseless system output. This is shown in Fig. 5.

To demonstrate that what we have learned is indeed the system (the process) rather than merely a model

13

of the output corresponding to input 1 , we feed a different input (input 3) to that same neural-net model of the process. In Fig. 6 we show that the estimated output is still very close to the true output. With regards to one-step ahead control, we display in Fig. 7 the controlled backing-up of a truck under challenging circumstances for which difficulties had been reported previously (Kosko, 1 992).

Having discussed the system identification (monitoring net) and the one step ahead neural-net control we move on to the central topic which is the learning of good control paths.

LEARNING OPTIMAL OR NEAR­OPTIMAL CONTROL PATHS

The neural-net control action generator described above is an optimal controller in the sense that for a specified new target system state to be attained in the immediate future, the control action generator net does indeed generate the control actions which will cause the system to move as close as possible to the target state in the prescribed time.

However, as is well-known, in general, a control task consists of more than driving the system to the next specified target state, in the immediate future. The real task is to know over what path is the system to be driven if a specified target state is to be attained after k time intervals in the future and if some objective function such as cost or energy usage is to be minimized.

In systems control, a typical task is that of evolving a system from one state to another over an optimal path, or reasonably near the optimal path. The path in question is optimal in the sense that an objective function (E) as evaluated over the � path has a minimum value and the path satisfies prescribed constraints. In practice the objective function might be chosen to achieve the new state in the minimum time, or with the least overshoot or with the lowest cost and so on.

Our approach to that task is consonant with the paradigm of learning control on the basis of delayed reward (Barto, Sutton and Anderson, 1 983; Werbos 1990) and reinforcement learning.

To implement our approach we use a functional-link net to learn a model of the objective function, E. That is we evaluate E(ll) for a meaningful set of control paths, 11. This is illustrated in Fig. 8. We note that the 11 in question now represents a sequence of control actions, each of which might be a vector. In general our u is now actually a sequence of vectors and might have been written as {11} but we refrain from doing so in the interest of clarity.

Having learned a network representation of E, we now evolve any initial sequence, u to the optimal control path .l.lopt by varying the control actions in the sequence until E attains a minimum value. It might be a local minimum in which case we would not have attained the optimal control but one that is reasonably near the optimal control.

The basis for the evolution of the individual control actions along the path is as follows. We take

or

� oc - aE cit OUj

oE dUj = - T) -OUj But the functional-link net allows us to write

and ()E = Pi + L Pj sech2 (Aj ll + bj) OUj

(6)

(7)

(8)

(9)

Therefore we can update the control sequence according to

Aui = - TlPi - T) L Pj Aji sech2 (A,; ll + bj) (10)

It is clear that

s1Ji = r. aE = - r. (�r dt i OUj i d

( 1 1)

and E decreases monotonically to a minimum.

The optimized 11 sequence is in fact the optimal control path.

The optimization procedure is similar to that of Hopfield and Tank and the net configuration used for that purpose is illustrated in Fig. 9.

We now describe an example to illustrate the optimization procedure.

We consider a simple system described in terms of a differential equation

x + t x + 2x = 2(t) (12)

where x is the single system observable and u is the control action.

The initial state is

x(o) = -1 x(o) = 0 (13)

and we want to drive the state to the final steady state described by

xss = 0 (implied) Xss = 0 (14)

Such a system is not without practical significance being, in fact, quite representative of some medication administration circumstances with x corresponding to the value of a monitored sensor reading and the u being the rate of drug administered.

If we wish to have x adjust as rapidly as possible to the final steady state, but without significant overshoot, then a suitable objective function might be

14

f<W = T + 5(ou)

where u is the control trajectory

( 15)

T is the rise-time, the time requested to attain 90% of the required change

ou is the overshoot

and Sou is the weighted overshoot

We carry out our computations in terms of a discrete time system approximation of the system described in Eq. 12.

We now proceed to learn a functional relationship between control action trajectories and the value of the objective function. For this purpose, we consider each trajectory as being a sequence of thirty (30) control action (u) values. Each such sequence constitutes a � and we generate forty-four (44) such trajectory patterns, each with it associated objective function value.

A typical control action trajectory and the corresponding system observable path are shown in Fig. 10. A number of such trajectories are shown plotted in Fig. 1 1 together with the corresponding objective function values.

We used functional-link net in auto-enhancement mode with seven (7) random vector enhancements to learn the relationship between the trajectories and the value of the objective function. That relationship is a mapping from 30-dimensional space to one­dimensional space and is not easily depicted graphically.

However we plot the objective function value against the id-number of the control trajectory in Fig. 12 in order to illustrate the idea that there might be a minimum and that we want to find that ll which corresponds to . that minimum. In this approach, as in all other such optimization procedures, there is no guarantee that we have the global minimum. Depending on the circumstances, there may be heuristics which could guide us in deciding whether to accept or reject any specific minimum obtained in this manner.

At any rate, using the functional relationship illustrated schematically in Fig. 12 and gradient descent, we determine the minimum in the objective function to be 1 .68 and the corresponding control action sequence and system response are shown in Fig. 13.

The procedure outlined in this paper can be used and has been used for the control complex linear and nonlinear systems. It is intelligent in the sense that the networks km:n how to exercise optimal control. However human insight and guidance are still required at this stage in any use of this technology in any specific application.

Summarizing, in this paper, we have concentrated on providing focus on a single coherent perspective on the use of neural networks for intelligent real-time control. We separate the entire task into two

separate but related subtasks. each of which has two components.

The first subtask is that of learning a monitor/predictor model of the dynamic system and learning ( one-step ahead) control action generator. The second subtask is that of learning a functional relationship between the control objective function and control trajectories. and then to find that trajectory which would yield the optimal control objective function value. That fmal component is not necessarily a neural-net computation task. However the use of functional-link neural-net computing enables us to start implementing this type of control as a practicable real-time conuol methodology.

REFERENCES

Bano. A.G .. R.S. Sutton. and C.W. Anderson (1983). Nemonlike adaptive elements that can solve difficult learning control problems. � Transactions Systems. Man and Cybernetics, SMC-13.5,834-846.

Domey, T.D. ( 1992). Learned adaptive environment control using artificial neural networks and fuzzy logic. M.S. thesis. Electrical Engineering. Case Western Reserve University, Cleveland, OH 44106. U.S.A.

Goodwin. G.C. and K.S. Sin ( 1984). Adaptive 5hering Prediction and Control. Prentice-Hall, New York. NY.

Hopfield. JJ. and D.W . Tank (1985). Neural computation of decisions in optimization problems. Bjologjcal Cybernetics, 52, 144-52.

Hornik. K.. M. Stinchcombe. and H. White (1989). Multilayer f eedf orward networks are universal approximations. Neural Networks, 2, 359-366.

Kosko. B. ( 1992). Neural Neiworks and fuzzy Systems. Prentice Hall. Englewood Cliffs. NJ, p. 347.

Pao, Y.H •• S. Phillips, and DJ. Sobajic (1992). Neural-net computing and the intelligent control of systems. To be published in the Iutematjonal Journal of Control Special Issue on Intelligent ContrQl.

Pao. Y .H., G.M. Zwingelstein, and DJ. Sobajic ( 1990). Analysis of transient on basis of identificatioo of signal generative structW"C: Even unto chaos. IEEE Annual International Conference on Neural Networks, San Diego, CA.

Park. G.H. ( 1 990). Svstem identification and noise cancellation with neural networks. M.S. thesis, Electrical Engineering. Case Western Reserve University. Oeveland. OH 44106. U.S.A.

Park. G.H .• Y.H. Pao, and DJ. Sobajic ( 1 99 1 ). Prediction. system identification and noise cancellation with neural networks. Submined for publication in the IEEE Transactions on Neural Networks.

Werbos, P.J . ( 1 990). A menu of design for reinforcement learning over time. N eura! Networks for Control. W.T. Miller, R.S. Sutton, and P J. Werbos (Eds.), MIT Press, Cambridge. MA.

(a)

(b)

5g. 1 . Comparison of the single bidden layer net and the function link net. (a) single hidden layer net; (b) enhanced input with no hidden layer, random vectors Aj and threshold hj.

Error

0 ...___.....,..�_ ........ ..,..,..�__.__,,...,.....,,---....._...,...,...� o 2.000 � .ooo 6,000 a.ooo lleration1

Fig. 2. Comparison of learning rates for delta rule. steepest descent and c onjugate gradient search techniques. (Fig. 5.23 of Dorney 1 992 reference) ( 'delta rule' s ign ifies backpropagation of error: steepest descent and conjugate gradient procedures were carried out with functional-link net)

15

u(l) -

u(t-n) Memoryless y(t+l) nonlinear

y(I)

y(t-n)

function

measurements y(t) • • • y(t-n) u(t) • • • u(t-n) prediction y(t+ 1)

Fig. 3. The modeller/predictor neural net

+ desired y(t l) -u(t·l )

u(t-n) Neural-net controller

y(t)

y(t-n) -

input to net : measurements u(t·l) • • • u(t-n)

y(t) • • • y(t-n) desired y(t+l)

output of net : conttol actioo u(t)

ll(t)

Fig. 4. The neural-net controllor action generator

Q.3 - --

Q.2 0.15

Q.1 Q.115

0 4115 ii

4.1 4.1-

IGOI

A

Sntem lcleoutlcabon llSlllC Mnnl llel · - - - - - "

fl A A

fl A A •

1 \ 1 ' \ / l \ /1 \I 'V "

I l I \j � v � �

_ .. _

fl 1 I I

I I I

v

-

Fig. 5. Estimated nonlinear system output for input 1 obtained with neural network trained on noisy measurements. (Figure 5-1 1 of P3rk 1991 reference: Input l consisted of a single sinusoid.)

o.•+.----..;;....------';.----li---l

44•-l..--------------------------.....i ,_ _ .. _

--- - · -- - · I -

Fig. 6. Estimated nonlinear systems output using neural net trained on noisy outputs with input #1 (See Fig. S). New input in this case ccosisted of dnee sinusoids instead of one but the nonlinear process was the same as before. (From Parle and Pao 1992)

_) o 10 20 311 • m so 10 ao 90 100

Fig. 7. Neural net control of truck backup (Pao and Park, unpublished results)

16

lj(JI) . canh<All + b;l

Fig. 8. Illustration of the net for learning the objective function

Updaled ll

� � I ,J

�

I I I I - . . . � I I • -. -' -

_, i' .... --1'1 111\ 1fr a u - · - I I - 1 l - I a ' ' ' H I

' w - - - -4111 4a .ii; Aut

�1 iu(U) 11(11) 12111) IJ{lll D ·11lli g2(1)

IJpdali!d ll -11� gj(I) .qi) fdU)

8,iiUV = A;isech2<Aj.11. + b_;) Fig. 9. Illustration of process for evolving control

path to optimum value

4 c: �i--...,..;:;;=:;ilil!=. _____ __

-0.% 1•\,'w.i:, -0.4 ll(O

-0.1

-0.1

. ,

' I •

Fig. 10. Typical control action and system response

I i·. . . ... • •• 1· \I · . ••• • \ 2 / ... ..2 -I � ,,

\ , \ ,

\ ,

·0.4 - .... ,"' z I I ···· 1

·0.1 -

Fig. 1 1 . Examples of control trajectories with corresponding objective function parameters

17

4 ] u .: ...... · ai;.o..

-.. / z

., \ �-··· ... _..-�;\ ... \..--. ..:···-···!\./\ .... / 1.1

18(1)1

11 ti H 21 H H - CO

Fig. 12. One-dimensional representation of the objective function f(u) and its component (rise-time and overshoot) in terms of coottol data sets

Fig. 13. Optimal control action and system response. Optimal criterion f(u*(t)) = 1.68

TABLE 1 Comparison of times taken to learn control task (from Table 5.1 of Dorney 1992

reference)

Leaming Computer Relative Scheme Jtcntions Tune/Iteration Comnarison

Delta 100,000 approx. 0.33 sec. 9.25 hr. rule

Quadratic 8,000 Approx.

approx. 1 .00 sec. 2.22 hr.

Conjuga&c 150 approx. 15.00 sec. 0.63 hr. gradient

Copyrigh\@ IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

METHODOLOGY OF ARTIFICIAL INTELUGENCE TECHNIQUES

NEURAL NETWORKS APPLIED TO OPTIMAL FLIGHT CONTROL*

T. McKelvey

Depart!Mnl of Electrical Engineering, LinlcOping University, S-581 83 Lin/Wping, Sweden

Abstract. This paper presents a method for developing control laws for nonlinear systems based on an optimal control formulation. Due to the nonlinearities of the system, no analytical solution exists. The method proposed here uses the 'black box' structure of a neural network to model a feedback control law. The network is trained with the back-propagation learning method by using examples of optimal control produced with a differential dynamic programming technique. Two different opti­mal control problems from flight control are studied. The produced control laws are simulated and the results analyzed. Neural networks show promise for application to optimal control problems with nonlinear systems.

Keywords. neural nets, optimal control, flight control

1 Introduction

The use of neural networks (NN) for different applications in control has recently emerged, see (Special issue on neural network in control sys­tems, 1990). The most interesting feature of a neural network is its capability to build an internal model of nonlinear functions, given input/output samples of the unknown function. The NN can be seen as a multivariable nonlinear function, parametrized with a set of parameters 8. Differ­ent parameters 8 give different functions. The key idea with NN is to fit the NN function to a set of known correct data by adjusting the parameters 8. In the next section this is further explained. In control of a fighter aircraft (AC) a wide range of optimal control problems arise. An interesting class of problems is control of the AC over a rela­tively long time period where the optimal criterias are given by different tactical goals. This type of control has typically been performed by the pilot

model would thus severely degrade the solution. The obvious solution is instead to use the nonlin­ear model in the optimization. A drawback with a nonlinear model is however the problem of finding an analytical feedback control. Unless the problem is very simple, only numerical solutions exist. The solutions obtained are also of an open-loop type, i. e. the solution only depends on time and the initial state. When applied in reality this type of open-loop control is sensitive to disturbances and instead the goal is to find a state-feedback control, using the current state to produce the control sig­nal which would give a closed loop control system.

The approach used in this paper to find a feedback controller is also used in (McKelvey, 1991). The method proposed use a neural network to model the unknown feedback control. The network is trained with examples of optimal control derived with a numerical method.

of the aircraft. The state equations describing the 2 dynamics of the AC are nonlinear. A commonly used method to deal with nonlinear systems is to linearize the state equations around a stable state. The optimal control problems studied in this pa-

Neural Network as a Mul­

t ipurpose Nonlinear Func­

tion

per usually includes a wide time horizon of 50-200 seconds. However during this time the state of the AC changes significantly. Using only a linear

*This work was partly sponsored by SAAB-SCANIA AB, Saab Aircraft division, Linkoping, Sweden.

A Neural Network is composed of many similar units called neurons. These units are usually or­ganized in layers forming an input layer, one or more hidden layers and an output layer. The in­put layer is not a real layer in the sense that it

19

Figure 1 : Feedforward neural network architec­ture.

does not include any parameters. Each unit in a layer is fully connected to all units in the previous layer, forming a set of cascaded layers (see Fig. 1) . Each input to a unit is scaled with a weight. The weighted inputs are added together with a thresh­old. The output of a unit is a nonlinear transfor­mation of the sum. This type of network architec­ture is called a feedforward neural network. Consider a NN with n inputs, two hidden layers and m outputs. The NN can then be seen as a function g : Rn x RP -+ Rm . The output Y E � of the network is then

Y = g(X, O) (1 )

where X E Rn is the input vector and 0 E RP is the parameter vector. Let us define [ tan� v1 ]

u(V) = .

tanh vn

(2)

where V is a vector with n components and tanh is the scalar function hyperbolic tangent:

ez - e-z tanh z = (3) ez + e-z Using (2) the NN can be described with the simple expression

Y = g(X, 0) = W3u(W2u(W1X + a1) + a2) + a3 (4)

where the matrices Wi contains the connecting weights between the units and the vectors ai con­tain the thresholds. All together they constitute the parameter vector 0. The dimensions of the ma­trices are defined by the number of inputs, outputs and the number of units in the two hidden layers. Theoretical results show that a NN with one hid­den layer can approximate any continuous func­tion on a compact set arbitrary well by using

complexity, i. e. the number of units in the hidden layers, is dependent on the amount of nonlineari­ties in the problem. Experimentation determined the number of hidden units in the networks used in this paper.

When the structure of the network is given, i.e. the number of units and layers, the network pa­rameters 0 have to be adjusted so as to give the best fit of the function g(X, 0) to the given data Z. This is referred to as training or learning in the NN literature. The data Z contain:; N samples of the unknown function f, given as input vectors xi and output vectors Yi , the index i indicating the different sam­ples. This gives the following relation: Yi = f(Xi) for i = 1 . . . N between the unknown function f and the data vectors. The output of the network depends on both the input vector X and the pa­rameters 0. The network error c for a given sample of Z and parameters 0 can be written

c(O, Zi) = Yi - g(X; , 0) (5) where

zi = [Yt, xTJ (6)

Z = [Z1 , Z2 , . . . , ZN]T (7)

To measure the network performance, a quadratic lossfunction V ( 0, Z) is introduced:

N V(O, Z) = L v(O, Zi) (8)

i=l

v(O, Zi) = c(O, zi? c(O, Zi ) (9)

The lossfunction V(Z, 0) is minimized using the well known back-propagation learning method (Rumelhart and McClelland, 1986). In back­propagation learning the parameters are changed in the direction of the negative gradient of the quadratic error v( 0, Zi) for each sample in the data Z as follows:

where k = 1 + ( i mod N) ( 1 1)

µi is gradually decreased during the learning to obtain a stable minimum. The learning process continues until the loss function V(O, Z) reaches a minimum. The initial vector o0 is initialized randomly with values in a limited range.

Aircraft Model an unlimited number of hidden units (Cybenko, 3 1989) . Empirical work has indicated that a NN with two hidden layers gives better performance compared to a NN with one hidden layer using The aircraft model is based on a modern fighter

aircraft. Using mass point dynamics with the the same amounts of units. The choice of network

20

states velocity v, climb angle /, horizontal posi­tion z, altitude z and the aircraft's mass m, the state equations are written as:

. Thr(z, M) - D(z, M, n) . v = - go sm 1

m

. go( ) 1 = - n - cos 1

v

X = V COS /

i = v sin 1

m = -Sfc(z, M)Thr(z, M)

with the constraint

( 12)

( 13)

( 14)

( 15)

( 16)

( 17)

where M is the Mach number, Thr is the thrust produced by the engine, D is the drag composed of induced drag and zero lift drag, g0 is the ac­celeration due to gravity, Sfc is the specific fuel consumption and n is the load factor on the wing which is used as the independent control variable. Thr, D and Sfc are functions based on a realistic model of a gel}eric fighter aircraft.

12.----.....---�--�-.....--�--�---,

10

J I 6

4

2

0 0.2 0.4 0.6 0.8 1.2 1.4 1.6

Mach

Figure 2: Simulated trajectories in the v - z plane from Example 1 . (Optimal trajectory: dotted line, neural network: solid line)

J The model can be summarized in the following ] standard form

x = f(z, u; t), z(to) = zo (18)

where z is the state vector, u is the control vector and t E [to , t J] is time.

o.5

0

............. ··

� � � � � � � � m n...-

4 Optimal Control Problems Figure 3: Load factor. (Optimal control: dotted line, neural network: solid line)

The problem formulations used in this section are the same as in (Jarmark, 1991). In the two prob­lem studied the loss function and the stop criterion can be described as:

V = F(z(t1 ) , t1 ) ( 19)

t1 = argt(<f>(z(t) ; t) = O) (20)

where the function V is to be minimized by choos­ing the optimal control, u*(t), t E [to , t J] . The problem can be solved numerically with a dif­ferential dynamic programming technique (DDP) (Jarmark, 1991). The solution obtained is given in an open loop format, i. e. , the control at any time t depends only on the initial state zo and the time t .

To obtain a feedback control solving the optimal problem a neural network is used to approximate the unknown feedback control function. The data Z used to train the neural network is composed of a wide range of correct solutions covering the state space of the problem. Using the DDP-technique,

21

optimal trajectories can be obtained from differ­ent initial positions. Putting together the state vector z along all the optimal trajectories with the control variable n forms our training set Z. The network structure is given by the number of states, used as inputs; the desired control as the network's output; and an appropriate number of units in the hidden layers.

4.1 Example 1 : Optimal Energy Climb

The first optimal control example is the classical energy climb (in flight mechanics) . The problem can be stated as:

V = -E1 (21)

t1 = given (22)

E1 = z(t1 ) + v(t1 )2 /2go (23)

where E J is the scaled sum of the aircraft's poten­tial and kinetic energy at the final time t J .

The task of the feedback controller is to produce the optimal control given the time to go, t- t J and the state variables velocity v, altitude z and climb angle 'Y. The horizontal position is not included since it is not coupled in the state equations and is not part of the optimization. The mass m of the AC is also neglected since the weight change is less than 5% during the optimization time. The final time t J is allowed to be in the range from 20 to 200 seconds to make the problem more realis­tic. This gives us the outer architecture for the neural network with 4 inputs and one output, the load factor n. Empirically 10 units and 5 units were included in the first and second hidden layer, respectively.

To produce the learning set Z the DDP-method in (Jarmark, 1991) was used to produce optimal tra­jectories with different initial states :z:(to) and final times t J . The initial states were chosen in order to distribute the optimal trajectories over the entire state space. Also the final times were distributed over the time range t1 E [20, 200] seconds. The learning data Z was composed of 40 different tra­jectories giving a total of 760 input/output pairs. The learning with the back-propagation algorithm converged to a minimum using a total number of 50000 iterations.

Figure 2 show the phase plane from a simulation when the neural network is used as a feedback controller. The trajectory produced by the neu­ral controller (solid) is shown along with the op­timal trajectory (dotted). Figure 3 show the cor­responding load factor n. The initial position was z(to) = 1 .5 km, v(to) = 240 m/s, 'Y(to) = 0 and the final time t J = 190 seconds. The optimal en­ergy is E0 = 18.97 km and the energy obtained with the neural network controller is 18.96 km, thus only a difference of AE = -0.01 km. Sim­ilarly excellent results were obtained using other final times and different initial states :z:o and the results from a set of simulations are shown in Ta­ble 1 . The initial states used in the simulations are different from the states used to produce the optimal trajectories in the training data Z.

4.2 Example 2: Reach a Launch Envelope in Minimum Time

This problem formulation models a mission for a fighter aircraft . The mission is to reach an enve­lope and launch a missile towards an approaching target. The target is assumed to fly straight at a constant velocity and altitude. The function to

z(to) km v(to) m/s t1 s E0 km A.E km 1 .5 240 190 18.97 -0 .01

2 1 10 150 16.61 -0 .01 3 300 70 14.32 -0.03 4 180 1 10 15 .70 -0.04 5 250 140 17.82 -0.03 6 200 20 10.08 -0.00 7 200 150 18.26 -0.04 8 250 200 20.57 -0.02

10 225 120 18.41 -0.02 10 300 50 16.94 -0.06

Table 1: Simulation results from Example 1 using initial states not included in the learning set Z

minimize is simply t J which gives the following:

t J = argt( </>(x(t) , z(t) , t) = 0) (25)

ef>(:z:(t) , z(t), t) = k1 (xt (to) - vtt - :z:(t))2 - z(t) + k2 (26)

Xt(to) - Vtt - :z:(t) > 0 (27)

where :z: is the horizontal position, z is the alti­tude, Xt(to) and Vt are the targets initial position and velocity, respectively. k1 and k2 are constants and 4> models the launch envelope, i.e. a curve, in the :z: - z plane. Thus the launch envelope moves together with the target towards the AC.

Here the task of the control law is to produce the time-optimal control given the state of the aircraft and the distance to the target. The inputs to the feedback controller are: the distance between the aggressor and the target :Z:t(t) - :z:(t) , the altitude z(t), the climb angle 'Y(t) and the velocity v(t). The output is again the load factor n . The neural network is thus composed of 4 input units and one output unit. The number of hidden units chosen and the method to obtain the learning set Z and to find the best parameter vector (} were the same as in the previous problem.

The results from a simulation using the neural net­work as a feedback controller is shown in Fig. 4-6. In Fig. 6 The phase-plot of z and :z: is shown to­gether with the launch envelope. The tick marks indicate the AC's position every 10 seconds. The initial state used is not part of the learning set Z. The performance is quite good and the aircraft· controlled by the neural network reaches the enve­lope only 0.3 seconds later compared to the opti­mally controlled aircraft. Simulations with other initial states and target positions give similar re­sults.

22

12

10

•

J 1 6

4

2

?.'.2 0.4 0.6 o.a 1.2 I.A !JI

-

Figure 4: Simulated trajectories in the v - z plane Example 2. (Optimal trajectory: dotted line, neu­ral network: solid line)

J ] 2

0

Tbm -.

Figure 5: Load factor. (Optimal control: dotted line, neural network: solid line)

5 Conclusions

In this paper neural networks have been used to develop nonlinear control laws solving optimal control problems. Due to the nonlinear proper­ties of the problem no analytical solution exists. The method described uses a differential dynamic programming technique to obtain a set of optimal trajectories which are used in the learning of the network. Two problems with different optimiza­tion criterias were examined. Simulations using the neural network as the feedback controller for the two problems give evidence that the proposed method is one way of solving this class of problems. Only a small network, with 15 neurons partitioned in the two hidden layers, 10 in the first and 5 in the second, was needed to give good results for both problems.

23

12 \ \ \ 10 \\

• �/''·,., J 1 6

2

0 0 s 10 IS 20 2S 30 3S "'° 45 Ilml

Figure 6: Simulated trajectories in the x - z plane. (Optimal trajectory: dotted line, neural network: solid line, Launch envelope: dashed line)

6 Acknowledgements

Part of this work was completed at SAAB­SCANIA AB, Saab Aircraft Division, Linkoping, Sweden as a master thesis at Dept of Automatic Control, Lund, Sweden, see (McKelvey, 1991). I also would like to thank my supervisors Bernt Jarmark and Soren Wickstrom both active at SAAB and Prof. K.J . Astrom, Lund, for their ideas and support .

References

Cybenko, G. (1989). "Approximation by Superpo­sitions of a Sigmoidal Function" . M athemat­ics of Control, Signals, and Systems, 2:303-314.

Jii.rmark, B . {1991). Various optimal climb pro­files. In AFM Conference, New Orleans, pages 124-130.

McKelvey, T. (1991). Neural networks applied to optimal flight trajectories. Master's thesis, Lund Institute of Technology, Sweden.

Rumelhart, D. and McClelland, J . (1986). Par­allel Distributed Processing: Explorations in the Microstructure of Cognition. MIT Press, Cambridp;e MA.

Special issue on neural network in control sys­tems (1990). IEEE Control Systems Maga­zine, 10(3) .

Copyright @ IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

ADAPTIVE NEURAL NETWORK CONTROL OF FES-INDUCED CYCLICAL LOWER LEG MOVEMENTS

S.H. Stroeve•, H.M. Franken•, P.H. Veltink* and W.T.C. van Luenen••

*Biomedical Engineering Division, Department of Electrical Engineering, University ofTwente, The Netherlands **Control, Systems and Computer Engineering Group, Department of Electrical Engineering,

University ofTwente, The Netherlands

Abstract. As a first step to the control of paraplegic gait by functional electrical stimulation (FES), the control of the swinging lower leg is being studied. This paper deals with a neural control system, that has been developed for this case. The control system has been tested for a model of the swinging lower leg using computer simulations. The neural controller was trained by supervised learning (SL) and by backpropagation through time (BIT). The performance of the controller with random initial weights was poor after training with BIT and fair after SL. BIT training of the neural controller with weights, which had been initialized by SL, resulted in good control. Training with BIT thus improved the performance of the controller that initially had been trained by SL. An adaptive neural control system based on BIT has been proposed and partially tested. The controller adapted relatively fast to the change of an important model parameter.

Keywords. Adaptive control; backpropagation through time; biocybemetics; functional electrical stimulation; neural nets; nonlinear control systems; self-adapting systems.

INTRODUCTION

Paralyzed limbs can be moved by electrically stimulating the appropriate muscles. Cyclical movements of the lower leg generated by stimulation of the knee extensor muscles (quadriceps) is being studied as a test case for control of cyclical leg movements induced by functional electrical stimulation (FES) (Veltink, 199 1). Figure 1 shows the situation considered. The torque that can be generated by the quadriceps depends in a nonlinear fashion on the angular position and velocity of the lower leg. Together with the nonlinear passive elasticities and gravitational force, this makes the relation between the movements of the lower leg and the stimulus of the quadriceps highly nonlinear. The quadriceps should be stimulated such, that the lower leg moves cyclically and reaches a maximum reference angle after each swing, during which disturbances may be present. This condition should be met, while minimizing muscle fatigue, so that the movement can be sustained as long as possible. The control system should adapt to changing system parameters, in particular to the maximum

25

achievable quadriceps torque, which decays due to fatigue.

Fig. 1 . Stimulation of quadriceps. The lower leg should reach tPmax,rcr·

METHODS

The electrical stimulation parameters are comprised in one stimulus variable u lying in the interval [O, l], '0' being no and ' 1 ' maximal stimulation of the quadriceps. A model that describes the relation between stimulus u and angular position and velocity of the lower leg has been based on literature (Davy and Audu, 1987; Winters and Stark, 1985, 1987; Yamaguchi, 1989). The model, which holds the nonlinear relations mentioned in the introduction, contains three state variables (activation of quadriceps N, angle ef> and angular velocity w), one input variable (stimulus u) and two output variables (angle ef> and angular velocity w). All model parameters will be assumed constant, except the maximum torque Mmax, which decays due to fatigue.

Cost Function

The quadriceps should be stimulated such, that the lower leg reaches a maximum reference angle after each swing, while minimizing muscle fatigue. This goal is comprised in the following cost function:

T

J = (cj>{7) - <Pmax.ref)2 + a. J u2 dt 0

(1)

, where T is the end time of one cycle, ef>max,rcf is the maximum reference angle and a is a factor which controls the ratio between the two cost components. It is assumed that fatigue is related to the time integral of the quadratic stimulus. The value chosen for ef>max,rcf is 45° .

Neural Network

The use of an artificial neural network (ANN) as a controller for this system has been evaluted. A two layer feedforward network with two inputs, 50 neurons in the hidden layer and one output has been used. No thresholds have been used. The transfer functions are sigmoid functions:

1'1 {�) = 0.3

1 + exp(-�) (2)

The angular position and velocity of the lower leg are input signals, the stimulus is output. The controller ideally generates the optimal stimulus (which results in minimal costs), that exists for each position-velocity pair. If the optimal mapping of a sufficient large part of state space has been captured by the controller, disturbances, which

26

250

I 200

150 f > 100 :I } 50

0

. . . . . . . · · · · · · · · · · · · · · · · · . . .

-40 -30 -20 -10 0 10 20 30 40 50

Ailgl• (del) Fig. 2. Optimal trajectories for a range of begin angles. Subsequent dots are 0.01 sec apart from each other. With each position-velocity pair corresponds one stimulus u.

cause a deviation from the undisturbed optimal path, can be compensated for in an optimal way. It follows from the model and the minimal stimulus restriction of the cost function, that no stimulus should occur during the backward swing. Therefore the neural controller needs only to be trained for positive angular velocities. The controller has been trained for trajectories with begin angles in the range -35° to -5° , so that disturbances resulting in deviations of approximately ± 15° from the undisturbed case are compensated for. Figure 2 shows the optimal trajectories for this range of begin angles. The controller should be able to generate close to optimal stimuli for position­velocity pairs in the dotted area of fig. 2. Two strategies have been used to train the network: backpropagation through time (BTT) and supervised learning (SL).

Backpropagation Through Time (BTT)

The BTT algorithm will be explained for a general discrete system and cost function:

,1(k+ 1) = Jf...I(k),ll.(k)) .I{O) = �

N-l 1 = t<.1<N>> + E g(.l(k),ll.(k),k)

k=O

(3)

(4)

, where ! is a n-dimensional state vector, !! a m­dimensional input vector and the costs are calculated after N timesteps.

Ordered derivatives. The concept of the ordered

derivative as stated by Werbos (1988), will be used here. The conventional partial derivative 8J/8xi(k) refers to the direct causal impact of xi(k) on J, while the ordered derivative a +J/8xi(k) (notice the plus sign) refers to the total causal impact, including both direct and indirect effects. Dynamic feedback is defined as the use of the chain rule for ordered derivatives, in order to calculate the derivatives of J with respect to the system variables. The following recursive relations hold for (3) and (4):

k=N: i=l. .n (5)

k<N:

<ri = ag�(k),u(k),k) + t < a+i . &"(k+l)

) &,(k) &,(k) q=l &q(k+ 1) ax,(k) a+J = ag(A(k),«(k),k) + t < a+J

. axik+l»

i3uik) auik> q·t ihik+l) i3uik)

i=l . .n; j=l . . m (6)

BIT algorithm. The BIT algorithm can now be summarized as follows: + + + + REPEAT

-a- Choose begin state. -b- Calculate trajectory for times k=O . . . N. -c- Calculate costs J of this trajectory. -d- Calculate the ordered derivatives

a +J/8xi(k) and a +J/8ui(k) for k=N . . . O using (5) and (6).

-e- Calculate the ordered derivatives of the costs with respect to the weights of the neural network ( a +JI a w) using backpropagation ( = dynamic feedback) of a +J/8u.

-f- Adapt weights using gradient information a +J/8w.

UNTIL Convergence + + + + The weights were adapted using the average of the ordered derivatives a +J/8w over N timesteps and the delta-bar-delta rule of Jacobs (1988).

Notice that when the costs only depend on the state !. and not on y, and no thresholds are used, the gradient information a +JI aw can also be calculated by forward propagating a +J/8xi(k) instead of backpropagating a +J/aui(k). This will not be further examined here.

Supervised Learning (SL)

The training set consisted of paired values of state (input) and optimal stimulus (output). The optimal

27

stimuli were calculated with an algorithm that resembles the BIT algorithm. After a certain constant begin state has been chosen steps b, c and d of the BIT algorithm were performed, followed by an adaptation of ui(k) in the negative direction of a +J/8u/k), until convergence was reached. After the optimal stimuli had been calculated for a range of states, the weights of the network were adapted by the following procedure: (1) back­propagation of 8J' I au, with J' = 1h(u-uopt)2 (u: actual stimulus, uop1: optimal stimulus), to calculate 8J' I aw for all weights of the network; (2) adap­tation of the weights following the delta-bar-delta rule. Notice that the main difference between SL and BIT is, that for SL firstly the optimal stimuli are determined (steps a-d) and secondly the weights are adapted (steps e-t), while in the case of BIT training and optimization are performed simultaneously (steps a-t).

RESULTS

Training

The neural controller was trained by BIT and SL. In case of SL the initial weights were randomly chosen, for BIT two cases were tested: random initial weights and initial weights computed by SL.

SL random. Supervised learning of a neural controller with random initial weights resulted in fair control. The total training set consisted of the position-velocity pairs shown in fig. 2 and the corresponding optimal stimuli . Each dataset consisted of five input-output pairs from the total training set. After 250,000 datasets the average costs had been reduced by a factor 10 and remained about constant. Figure 3 shows the performance of the controller after SL. It shows the costs in u (i.e. afu2dt) and the reached end angle for several begin angles. These data are also given for the optimal control case. The end angle is within 3 ° of the optimal end angle, stimulus u is too high for low begin angles and too low for high begin angles. The average deviation in the end angle from the reference angle is 1 . 83 ° . The average of the costs in u is 2.93 10·4, which is 3 % lower than the average of the costs in u for optimal stimuli (3.02 10'4). The average of the total costs is 10.6 10·4, which is 250% higher than the average of the minimal costs (3.05 10'4).

BIT random. Several simulations were performed in which neural networks with random initial weights were trained by BIT for a range of begin angles. In all these simulations the resulting networks performed badly. Stimulus u was high when it should be low and low when it should be

:!; I I Git

SI .s """ Col s e

0.60

0.50

0.40

0.30

0.20

0.10

0.00 -40 -35 -30 -25 -20 - U -10 -5

Bogin Anglo (dog) - + - a ·- + ·-· -- 6 - b ···· & ···· - o - c -- • -

Fig. 3. Performance of controller. The costs in u (non bold) and end angles (bold) for: (a) optimal control, (b) ANN, with random weights, trained by SL random, (c) ANN, with weights initialized by SL, trained by BTI.

0.30 .--------------, 10

0.20 / , � I

0.10

/ ' / \ \ 0

-5

0.00 L-.. __ ......_. __ � __ ___, -10 0.00 o.so 1 .00 t .SO

Time (see)

-- u --- -- Mq ----- Md

� .. .. � .. i � J

so 40 /"', I ' I ' I ' 30

I I I I 20 I I I I 10 I I I I I I

0 I I I , I , -10

I I I I I I \ \ I -20 \ I \ ,J -30

0.00 o.so 1.00

Time (see)

-- angle ----· velocity

200

100

0

-100

-200 1.50

I � � i

Fig. 4a. Cycle without disturbances (u: stimulus, Mq: quadriceps torque, Md: disturbance torque).

Fig. 4b. Cycle without disturbances (angle and velocity).

0.30 .----------------, 10

5

...... 0.20 ..:.. I �� I

0.10

0

-5

0.00 �--��-�--� -10 0.00 0.50 1 .00 1 .SO

Time (see)

-- u -- - -- Mq ---·-··· Md

Fig. Sa. Cycle with torque disturbance and low begin angle (u: stimulus, Mq: quadriceps torque, Md: disturbance torque).

28

.. .. � .!? 5

so .---------------, 200

40 --

30 / I I 20 I I I I 10 / I \ I \ I

0 \ I \ I \ I -10

\ I \ \ I ' --/ -20

.30 �--�--�--� -200 0.00 o.so 1.00 1.50

Time (eec)

angle velocity

I ! i

Fig. Sb. Cycle with torque disturbance and low begin angle (angle and velocity).

high. The costs were more than 2.5 times as high in comparison with a network which was trained by SL. Seemingly the network got 'stuck' in a local minimum of the cost criterion and was not able to find the global minimum.

BTT initialized by SL. Training with BTT of the controller, that had initially been trained by SL, improved its performance. The average costs decreased about a factor two after 76,000 iterations of BTT. Figure 3 shows that the end angle is within 1 ° deviation from the optimal end angle for begin angles from -30° to -5° . Only for a begin angle of -35° the deviation is more: 3° . For this begin angle the stimulus should be very small. Because of the averaging property of the neural network, the stimulus u is too large for this begin angle. The costs of the stimulus Ju are about equal to Ju.opt for begin angles larger than -25° and absolutely a little larger for lower begin angles. The average deviation in the end angle from the reference angle is 1 .00°. The average of the costs in u is 3.20 10-4, which is 6 % higher than the average of the costs in u for optimal stimuli (3. 02 10-4). The average of the total costs is 5 . 87 10-4, which is 90 % higher than the average of the minimal costs (3.05 10-4). The performance of the controller is satisfactory, since there is only a small deviation of the end angles from the reference angle and of the costs in u from the minimal costs.

Performance of Neural Controller

Figures 4 and 5 show two examples of the behaviour of the closed loop system, containing the controller and the model. The neural controller is deactivated (i.e. u=O) for negative angular velocities. The system response for one normal cycle without disturbances is shown in fig. 4. At the end of the cycle the starting point has again been reached. Figure 5 shows that the control system is well capable of compensating for an opposing torque during 0.5 second of the forward swing and a -10° deviation from the normal starting point. The maximum angle is only 3 ° smaller than the reference angle.

Network Adaptation to Changing Model Parameter

BTT after SL resulted in a better controller, at the cost of a longer training phase. Another advantage of the BTT algorithm is its ability to compensate for changing model parameters directly_ This is possible, since a model is used each iteration for the calculation of the gradients a +J/8w. In the case of SL a whole new training set would have to be

29

derived in order to account for changing parameters. In our application one parameter is known to vary significantly with fatigue: the maximum torque Mmax. The network adaptation with BTT after a change in Mmax was therefore investigated.

Step decrease of M"'"". Mmax was decreased 10% (from 50 to 45 Nm), which caused the average end angle to decline from 45.0° to 43.5° . After (only) 200 iterations the average costs had decreased 30 % and declined almost no more. The average end angle had increased from 43.5° to 44.8° .

Quasi ramp decrease of M"'"". Mmax was decreased with 1 Nm per 200 iterations from 50 to 25 Nm. Without adaptation of the controller the average end angle decreased from 45° to 36° . With adaptation the average end angle decreased from 45.0°to 43.5° .

Adaptive Neural Control System

Figure 6 shows a proposal for a configuration of an adaptive neural control system, that is based upon training with BTT. The system consists of two parts: ( 1) the control and parameter estimation part, (2) the weight adaptation part. The actual controller (neural network 1) is connected in closed loop with the lower leg. Angle information x is fed back to the input of the neural network. The stimulus u is input for both the lower leg and its modeL The parameters of model 1 are adapted in response to the difference between the output of the model and the physical system. In subsystem 2 neural network 2 is continuouly being trained by BTT for a range of begin states, so as to update the weights. Actual model parameters are frequently communicated from subsystem 1 to 2 and updated weights from subsystem 2 to 1 . The frequency may depend on the rate of change of the model parameters.

CONCLUSION

The computer simulations have shown, that the presented adaptive neural control system configuration, based on BTT, might be a very useful one. The neural controller was well capable of controlling the model of the lower leg for a wide variety of torque disturbances, after it had been trained sequentially by SL and BTT. The controller adapted relatively fast to a changing model parameter. Still for our purposes a faster adaptation is desired_ Therefore implementation of the weight adaptation process on transputers is being evaluated. The controller has not as yet been tested experimentally on a human leg.

error

Mo I 1 XII

_____ Neural Network 1 u

+ .___- Lower Leg x

Weights Parameters

, ------------------ ---------------------- ----------- "' �

.....--- Neural Network 2 u(k) Model 2

x(k) x(k+1) �----------------1Delay--___. Fig. 6. Adaptive neural control system. See text for description.

REFERENCES

Audu, M.L. and D.T. Davy (1985). The influence of muscle model complexity in musculoskeletal motion modelling. J. of Biom. Eng .• 107, 147-157.

Jacobs, G. (1988). Increased rates of convergence through learning rate adaptation. Neural Networks, l. 295-307.

Nguyen, D. and B. Widrow (1991). The truck backer-upper: an example of self-learning in neural networks. In W.T. Miller, R.S. Sutton and P.J. Werbos (Ed.), Neural networks for control. 1st ed. MIT Press, Cambridge, Mass. pp.287-300.

Veltink, P.H. (1991). Control of FES-induced cyclical movements of the lower leg. Med. & Biol. Eng. & Comput. , 29. NS8-NS12.

Werbos, P.J. ( 1 988). Generalization of backpropagation with application to a recurrent gas market model. Neural Networks, 1 . 339-356.

Winters, J.M. and L. Stark ( 1985). Analysis of fundamental human movement patterns through the use of in-depth antagonestic muscle models. IEEE Trans. Biom. Eng .• 32, 826-838.

30

Winters, J.M. and L. Stark ( 1987). Muscle models: What is gained and what is lost by varying muscle complexity. Biol. Cybem .• 55. 403-420.

Yamaguchi, G.T. ( 1989). A skeletal model for the normal walking gait. In Yamaguchi, G.T. , Feasibility and conceptual design of functional neuromuscular stimulation systems for the restoration of natural gait to paraplegics based on dynamic musculoskeletal models, PhD thesis, Stanford University, Palo Alto. Chap. 4, pp. 43-69.

Copyright @ IFAC Anificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

REGULARIZATION AS A SUBSTITUTE FOR PRE-PROCESSING OF DATA IN NEURAL NETWORK TRAINING

J. Sjoberg

Department of Electrical Engineering, LinlcOping University, S-581 83 LinlcOping, Sweden

Abstract. The great importance of pre-processing of data before the training of a feed forward network is emphasised by many researchers. This pre-processing is not always straightforward, and, further, the need of pre-processing makes the model "less black" . We show that regularization, besides its other positive effects, reduces the need of pre-processing.

Keywords. neural nets, regularization, bad start values, pre-processing

1 Introduction

Adaptive Neural Networks (NN) have recently been subject to substantial interest, see, e.g. , (Narendra and Parthasarathy, 1990) or (Special is­sue on neural network in control systems, 1990) . They are used in many different applications to approximate unknown functions.

Of particular interest for modeling and control is the NN's capability to describe the behavior of, possibly nonlinear, dynamical systems. From a modeling point of view a NN is just one particular parametrization of a nonlinear regression model for the system, like

y(t) = g (<p(t) , B) ( 1 . 1 )

see, e.g. , (Ljung, 1991 ) . Here y(t ) would be the output of the system and <p(t) would contain past inputs and outputs. The parameter vector B con­tains the weighting coefficients of the network and the mapping g( · , ·) is defined by the actual net. This means that the NN is used as a black-box model for the unknown system, i. e . , the NN is used to approximate the function characterizing the sys­tem.

Before the parameters ( "weights" ) in the NN are estimated ( "training of the NN" ) it is important to perform a preprocessing of the data. Without such a pre-processing there exists a risk that some of the units of the NN saturate. This means that the parameters in connection to this unit have no influ­ence on the output, or more precisely, the deriva­tive of the output with respect to these parameters

31

is zero. If this happens the parameters of the unit will not be adapted, and, hence, they will not con­tribute to a better model. These will be referred to as frozen parameters and frozen units.

Sometimes there is an obvious way to pre-process the data to avoid the problem of saturated units, but in many cases, e.g. , if the inputs to different hidden units are correlated in a tricky way, it can be hard to find a suitable pre-processing.

In Section 3 we will see how these frozen parame­ters can be melted, i. e . , we will see how the param­eters can be brought into a region where they can adapt to data and improve the model. This will be done with help of regularization which usually is introduced to avoid overfitting, see, e .g . , (Moody, 1992) , or (Sjoberg and Ljung, 1992).

When the parameters in a network are estimated, the start values are chosen randomly over some do­main. If these start values happen to come out bad, or if their domain of definition is badly cho­sen, there also exists a risk that some units will be frozen. Regularization will, however, solve the problem in the same manner as in case of tricky data.

Next section will introduce the considered network model, and Section 3 will show us the details of the effect of regularization. In Section 4 this will be illustrated by an example.

2 Neural Networks as adap­

tive models

Let us describe the NN modeling problem in the following way: Call the number of training data N, i. e. , N vectors of input values, X1c , sometimes called input patterns, and N corresponding out­put values, Y1c , sometimes called output patterns (in the case of regression, X1 = <p(t), Yt = y(t) , and t = k). That is, if f is the nonlinear function which we want to approximate then Y1c = J(X1c ) for k = 1 . . . N. Collect all weights and thresholds into a parameter vector 0. The network will then be expressed by a function, g( . , ·) , which is param­eterized by 0 and has current value of X1c as input. The resulting error obtained by the network, t:, can be written

t:(O, z,. ) = Y,. - g(O, x,.) where

(Yk , Xk) , (Z1 , Z2 , . . . ZN]r.

(2 . 1 )

(2.2) (2.3)

Input

Output

Figure 1 : A feed forward network with one hidden layer.

chosen so that the loss function,

N N 1 "" 2 VN(O, Z ) = 2N L..,, t: (0, Z1c ) ,

k=l

i s minimized.

(2.6)

A characteristic feature of NN models is that the dimension of 0 is quite high, often several hundreds. From an estimation point of view this should raise some worries, since it is bound to give a large "vari­ance error" , i. e. , the modeling error that origi­nates from the noise disturbances in the estima-tion ( "training" ) data set causes misfits when the model is applied to a validation ( "generalization" ) data set. To prevent misfit regularization can be used, i. e . , some kind of penalty of large parameter values is introduced in the loss function, (2.6) . The modified lossfunction can, for example, be chosen

Figure 1 shows a feed forward NN with one hid­den layer. In the first layer, the input layer, no computation is done. All the hidden units have identical structures, and consist of two parts. In the first part there is a linear, weighted, sum of the input values. Then, in the second part, this sum passes through a sigmoidal nonlinearity. The as output unit is just a weighted sum of the results from the hidden units. In order to obtain a more compact notation we write the weighted sums in the hidden layer as inner products. Then the NN can be expressed as

H

g(X,. , O) = L 02ju(OGXk ) (2.4) j=l

where H is the number of hidden units, 01j is a column vector containing the weights between the input units and hidden unit j. Similarly 02j is the weight between hidden unit j and the output unit and O" is the sigmoidal function chosen as

1 u(x) - --­- 1 + e-r (2.5)

The generalization into a feed forward NN with several hidden layers is straightforward. However, in this paper we only consider NN with one hidden layer.

The parameters which have to be estimated in the training procedure are the weights connected to the weighted sums.

The most common goal of the training is to obtain the Least Squares solution of 0, i. e . , 0 should be

(2.7) where 6 determines the degree of regularization. 6 = 0 reduces us to the former case without regu­larization. 0# is the parameter vector towards the regularization is done. If there is any prior knowl­edge of 0° , the "true" parameter vector, then 0# can be chosen to this value. We will set 0# = 0. However, other values are handled analogously.

There are several other ways to obtain regulariza­tion, e .g . , is the technique of weight decay equiva­lent to (2.7), see, e .g. , (Rumelhart and McClelland, 1986) .

The regularization has another effect which is the main topic of this paper; it reduces the importance of pre-processing of data.

32

0.9

0.8

0.7

0.6

o.s

0.4

0.3

0.2

0.1

0 -10 .. -6 ... -2 0 2 6 10

Figure 2: Typical sigmoidal function used in neural networks

3 Regularization instead of .

pre-processing

A well chosen tailor made model is always superior to a black-box model. It is, however, in many cases hard and time consuming to find a good, tailored model. In such cases a black-box model could be an alternative.

In most problems when a black-box model is chosen there is some prior knowledge, however not enough for a tailor made model. This knowledge should of course be used to make the modeling easier. Pre-processing of data is an example of such prior knowledge_

If there is no obvious way in which the transforma­tion of the data could be performed, then regular­ization could be an alternative to time consuming trial and error.

In our research, and to obtained the results pre­sented in the example later in this paper, we used a Gauss-Newton-based method (GN) , a second or­der descent method, to minimize the loss func­tion, (2.6 or 2.7). The most commonly used ap­proach is, however, backpropagation error algo­rithm (BP) which is a first order descent method and, hence, converges considerably slower than GN. More about BP and GN can be found, e.g. , in (Hecht-Nielsen, 1990), and in (Dennis and Schn­abel, 1983), respectively. Both methods are de­scribed by

The point is that the parameters will be updated proportional to Vfv , which consists of, among other factors, derivatives of the sigmoid function. With our choice, u'(x) = u(x)(l - u(x)) , and from Fig. 2 it is clear that when !xi � 0 then u'(x) � 0 and the corresponding component of VJ., is also zero, i . e . ,

(3.9)

for some z. This means that the corresponding weight , Bz , is not changed at all . We will now show this formally.

BP is a recursive steepest gradient method, i. e . , the gradient is computed for one input-output pattern at the time. The idea is that after several cycles through the data set, and if the step, µ, is small this should give a parameter change in the gradient direction of VN . The adaptation of parameter Bz , thus, becomes

a 0 -&2(0, Zk) k z - -µ 8Bz (3.10)

when the input-output pattern Zk is presented. Let us consider a parameter in the input layer of our NN model. Then, with help of (2 . 1 ) and (2.4) , equation (3. 10) becomes

(3. 1 1 )

where j is the label of the hidden unit t o which the parameters in 81; connect. The index i shows which component of 81; considered. If IB?jXk I � 0 for all k, then

(3. 12)

Notice that this equation is valid for all components of 81; . This clearly states that these parameters do not change, therefore, we refer to the hidden unit dependent on these parameters as frozen.

It is worth making the remark that we have not made any assumption about the output, Yk . Hence, the fact that a hidden unit is frozen has nothing to do with if the NN describes the system well or not.

If we introduce regularization, i. e. , instead of (2.6) the loss function (2.7) is used, then

W�(O) = VN{O) + 60. Specially, for the parameters to the former frozen hidden unit will be adapted according to

(3. 13) Here superscript ( i) indicates the ith iterate. The step size µ is determined by some search along the or indicated line. H, is a matrix that may modify the search direction from the negative gradient one, VJ,; 1 to some other one. In baekpropagation algo­rithm H = I, and in this theoretic work we only consider this case.

0·<'+1 ) _ 0-(i) £8

-<') _ (·i £)8

-<') lj - lj - u lj - - u lj . (3.14) From the last equation it is clear that 6 has to be chosen so that 0 < 6 < 2. The parameters

33

will be reduced every iteration until lflf}Xk l � 0 is no longer valid for at least some k. Then u'(O'[;Xk) # 0 , and we can switch back to the orig­inal loss function because (3. 12) is not true any more. However, the regularization may be kept to prevent overfit. In any case the goal is achieved, the unit is no longer frozen and the parameters can now adapt to the data.

4 Example

Let us now illustrate what has been presented with an example.

The goal is to model the dynamics of a hydrauli­cally controlled robot arm. The position of the robot arm is controlled by the oil pressure in a cylinder which can be controlled by the size of the valve through which the oil streams. The valve size, u(t) , and the oil pressure, y(t) are input and output signals, respectively.

We had 1024 samples available which were divided into two sets, the first 512 samples of the input- and output signal were used for the identification, and the last part of the samples was saved for validation of the model.

A NN with one hidden layer and four hidden units were chosen to model the behaivour of the robot arm. To predict next value of oil pressure

<p(t) = lOOO[u(t - 1) u(t -2) u(t -3) y(t - I ) y(t -2)] (4. 15)

was used as input to the network, i. e . , the network was given five input units. The goal is now to esti­mate the parameters so that the output comes as close as possible to y(t) , i. e. , to minimize (2. 1 ) .

To make the problem more tricky, and to get the effect of the regularization more obvious the input pattern is multiplied by 1000, i. e . , in this case there is an obvious pre-processing of the data: divide the input, (4. 15) , by 1000. However, we will instead of performing this pre-processing use regularization, and see how this will solve problem of frozen pa­rameters.

The start values of the parameters were chosen uni­formly random on the interval [-1 , 1] . The NN was trained 30 training cycles through the data, the first 13 without regularization, then 2 iterations with regularization, 6 = 0.5, and then another 15 iterations without regularization. In Fig. 3 and 4 the RMS error and the parameter values are shown versus the number of training cycles.

It is clearly seen that the parameters converge af­ter a few iterations. The error decreases very little during these iterations, and after these first itera­tions it does not decrease any more. At the 13th it-

34

RMS Em>r 1.6

1.4

1.2

0.8

0.6

0.4

0.2

00 10 IS 20 2S 30 35

Figure 3: During the first thirteen iterations some parameters are frozen, so optimization is done over a subset of the parameters. At the 13th iteration regularization is introduced and the frozen param­eters melt, hence, when the regularization is turned off, all parameters become available.

10.---�--�-�-�--�-�-�

·:::::::::::::.:·::::·::::·:::::::::::.:·:·:.:·::::::::::· ... _·\ '-� 0 - --------·-·················

==--====---==�--:,. .

-10

-JSL---�-��-�-___. __ _._ _ __. _ ___, o ro u 20 is 30 "

Figure 4: After that regularization has been used during two iterations all parameters are free to adapt.

eration the regularization is introduced during two iterations. At this point we have to accept that the error increases, because W N is now minimized in­stead of V N . After that the regularization has been turned of at the 15th iteration, however, we switch back to VN and the error decreases considerably.

This behaviour is explained by the theory in the previous section. As the input data are badly scaled some of the hidden units are frozen, and the model cannot use all its parameters to adapt to data. In Fig. 3 and 4 we see that there is no change of the parameters after iteration number 2 until the regularization is switched on at the 13th iteration. After two iterations with regularization the parameters have melt and the regularization is turned off again. This means that all non-frozen parameters have converged at the 2th iteration and

the frozen ones are unable to adapt. When the reg­ularization is turned off at the 15th iteration then the former frozen parameters are also free to adapt to data and there is a further decrease of the error.

5 Conclusions

Regularization is a necessary feature to avoid over­fit and in this paper we have shown that as a sec­ondary effect the regularization reduce the need of pre-processing of the data. The weights are auto­matically attracted towards the region where they have impact on the model. This means that less prior knowledge is necessary and, hence, with reg­ularization the Neural Network model structure is made "more black" .

References

Dennis, J . and Schnabel, R. ( 1 983) . Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Engle­wood Cliffs, New Jersey.

Hecht-Nielsen, R. ( 1 990) . N eurocomputing. Addison-Wesley.

Ljung, L. (1991) . "Issues in System Identification" . IEEE Control Systems Magazine. , 1 1( 1 ) :25-29.

Moody, J. ( 1992) . The effective number of param­eters: An analysis of generalization and reg­ularization in nonlinear learning systems. In Moody, J ., Hanson, S . , , and Lippmann, R. , editors, Advances in Neural Information Pro­cessing Systems 4. Morgan Kaufmann Pub­lishers, San Mateo, CA.

Narendra, K. and Parthasarathy, K. ( 1990). "Iden­tification and control of Dynamical systems using neural networks" . IEEE Trans. Neural Networks, 1 :4-27.

Rumelhart, D. and McClelland, J . ( 1986) . Paral­lel Distributed Processing: Explorations in the Microstructure of Cognition. MIT Press, Cam­bridge MA.

Sjoberg, J. and Ljung, L. ( 1992). Overtraining, regularization, and searching for minimum in neural networks. In Proc. IFAC Symposium on Adaptive Systems in Control and Signal Pro­cessing, Grenoble, France. To Appear.

Special issue on neural network in control sys­tems ( 1990). IEEE Control Systems Magazine, 10(3) .

35

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

NEURAL NETWORK MODELLING AND CONTROL OF A PLANT EXHIBITING THE JUMP PHENOMENA

G. Lightbody and G. Irwin

Control Research Group, Department of Electrical and Electronic Engineering, The Queen's University of Belfast, Belfast BT9 5AH, UK

Abstract. This paper focuses primarily on the modelling and control of nonlinear systems that exhibit gain discontinuities in their frequency plots. Structures and learning algorithms for neural network based nonlinear modelling are introduced and applied to the modelling and k-step ahead prediction of an example system. A nonlinear Internal Model Controller (IMC) is developed, based on the ability of the feedforward neural network to form nonlinear forward and inverse models. The results of simulation studies are given in each case.

Keywords: Neural Networks, Jump Phenomena, Modelling, Nonlinear Internal Model Control

INTRODUCTION

An important class of nonlinear systems, common in the field of servo-control, are those exhibiting the Jump Phenomena (West, Douce, 1954). Such plants exhibit a characteristic discontinuous jump in their gain Bode plot. It is usual that the frequency at which the gain jump occurs and its magnitude depend on the amplitude of the input signal and the degree of damping in the system. The modelling and control of such systems has received much attention, particularly using Describing Functions (Atherton, 1974) and more recently using linear ARMA modelling with variable-weighted-least-squares (Douce and Zhu, 1990). Such systems constitute a useful benchmark for demonstrating the potential of new nonlinear techniques, such as neural network modelling.

In an attempt to accurately model nonlinear systems, a variety of techniques have been developed, such as the Volterra series, Weiner series, the NARMAX method etc. A novel modelling technique, based on feedforward neural networks, has recently emerged, (Narendra and Parthasarathy, 1990), which allows for the modelling of nonlinear systems of partially known or unknown structure.

Feedforward networks, such as the Multilayer Perceptron, consist usually of many simple processing elements arranged in layers. Each element would take as input the weighted sum of all the outputs of the previous layer and passes this through a nonlinear function. The structure is feedforward in

37

nature, with no connections within layers or from outer layers back towards the input. Training of the network involves adjusting the weights of the network, using some form of learning rule, so that the network emulates the nonlinear mapping between input and output data vectors. This process clearly could be interpreted as system identification, (Chen, Billings and Grant, 1990). It is the nonlinear mapping property of feedforward neural networks which is central to their use in the modelling and control of nonlinear plants. Recent theoretical results (Cybenko, 1989; Funahashi, 1989) have in fact rigorously proven that most realisable vector functions can be approximated arbitrarily by a feedforward network with only a single hidden layer of nonlinear elements. Utilising the nonlinear vector function approximation capabilities of the feedforward neural network has offered many interesting possibilities for the modelling and the control of nonlinear and ill-defined plants common in industrial applications (eg. Willis, Di Massimo, Montague, Tham and Morris, 1991 ; Wu, Hogg and Irwin, 1992).

This paper illustrates the potential of feedforward neural networks for plant identification, through the use of a nonlinear second-order plant exhibiting the Jump Phenomena. It deals with the structures and learning methods for nonlinear system modelling and predictive modelling for this plant. A nonlinear Internal Model Controller, based on neural network forward and inverse models, is developed to control the plant.

THE JUMP PHENOMENA PLANT

A typical plant exhibiting the jump phenomena is given by the second-order servo-mechanism shown in Fig. 1 . Position and velocity are fed back to the controller, whose output is subject to amplifier saturation. This simple example shows the characteristic gain jumps and the nonlinear time responses that are typical of this class of system.

Fig. 1 The example Jump Phenomena system

The control input u(t) gives rise to the saturated input signal u*(t) defined as follows.

u * (t)=u(t)

u * (t)=+l .O

u * (t)=-1 .0

-1 .0<u(t) < +1 .0

u(t) � +1 .0

u(t) � -1 .0

(1)

There are two specific characteristics of this class of nonlinear systems. First, in the time domain, the step response for such a system will give progressively larger percentage peak overshoots as the amplitude of the input step increases, (Douce and Zhu, 1990). This can be seen in Fig. 2 which contains the time responses of both the nonlinear plant and the linear plant without saturation. The input signal to both systems is a Pseudo Random Binary Sequence (PRBS), whose amplitude is ramped from 0.0 to 3.0. It is apparent that for a small amplitude PRBS input both systems respond similarly. However as the amplitude of the input signal increases, the response of the nonlinear system diverges from the response of its linear counterpart.

-2��-��-��-�-��-�� o m � � � � � � � � �

time I a

- llnoar modol - nonllnoar plant

Fig.2 Responses of the nonlinear and linear systems

38

If a sinusoidal input of increasing frequency is applied to the nonlinear plant, a discontinuous jump in the Bode plot occurs whose magnitude and position depends on the magnitude of the input signal. It has been shown that these can in fact be predicted from Describing Function analysis, (West and Douce, 1954). Fig. 3 show the frequency response for the example nonlinear system determined using Fourier analysis, for increasing and decreasing input signal frequency. The amplitude of sinusoidal input signal is 3 .0.

1er9m�"------------------, 14 ··························· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·· · · · · · · · · ······················

12 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·······················•······

" ······ ······· · · · · · · · · · · · · · · · ······················· ········································

2 · · · · · · ·--+· · · · · · · ····························-�·-····················

0 0.08 0.28 0.45 0.85 0.85 t.08 1.25 1.45

frequency rad/a - 1ncrea1lng freq. - decr .. alng freq.

Fig. 3 Frequency response of nonlinear plant

NEURAL NONLINEAR MODELLING

The following difference equation model is widely used to represent a wide class of SISO discrete-time nonlinear systems:

yP(k+ l)=f(y P(k), . . y P(k-n),u(k), . . ,u(k-m)) (2)

Here the plant output yP at time k+ 1 depends on the past n output values and the past m values of the input u. This can be readily generalised to include a noise disturbance, , or to represent multivariable plants. The nonlinear function f(. ) is generally unknown, though some idea of its structure may be apparent. For example the plant output could be a nonlinear function of the past inputs only, added to a linear combination of the past plant outputs. Such knowledge of the plant structure is a useful first step in the identification of a nonlinear system model. General nonlinear modelling techniques have been studied, such as NARMAX, (Chen and Billings, 1989) for the identification of this nonlinear function.

Based on the theoretical results of Cybenko (1989) and Funahashi (1989), it has been suggested that feedforward networks, such as the Multilayer Perceptron, can be trained to form any realisable vector function f(.) and hence any nonlinear model. In fact, by correct expansion of the neural network equations (Billings, Jamaluddin and Chen, 1992), it can be shown that a general polynomial model results, similar to the polynomial version of the NARMAX series.

There are two general structures for the neural model of the nonlinear plant as described in equation (2). The series-parallel model, shown in equation (3), expresses the approximation of f(.) produced by the network in terms of the past inputs and the past outputs of the system being modelled.

yP(k+ l) =l(yP(k) , . . . y P(k-n),u(k), . . u(k-m)) (3)

With the parallel structure, the past outputs of the neural model are used instead of the plant outputs and hence there is feedback around the model. This can be best described by equation (4).

yP(k+ l) =l(yP(k), . . . y P(k-n),u(k), . . u(k-m)) (4)

If a static neural network is being used, the network must first be trained in the series-parallel form. After sufficient training has reduced the modelling error to a desired level, a parallel model is produced simply by replacing the plant outputs by their neural estimates. Dynamic or recurrent neural networks can also be used. These are trained directly as a parallel plant model but require more complex training algorithms, such as Back Propagation Through Time, (Werbos, 1988) and hence are usually computationally intensive. It should be noted also that the stability of identification, based on a parallel recurrent neural model, cannot be assured.

TRAINING ALGORITHMS

One of the major disadvantages of neural technology in control engineering is the extensive periods required to train the network. Initially the Back Propagation training rule was proposed, using gradient descent (Rumelhart, Hinton and Williams, 1986). However more sophisticated algorithms have been developed recently to help accelerate the learning process. These include the introduction of a momentum term, Stochastic Approximation techniques, (Sbarbaro and Gawthrop, 1990) or the use of more powerful off-line optimisation techniques such as the Broyden, Fletcher, Goldtharb and Shanno (BFGS) algorithm, (Shanno, 1978).

In order to accelerate the off-line training of series­parallel neural models, it was decided to investigate the potential of BFGS optimisation. Battiti and Masulli, ( 1990), demonstrated that this algorithm offered a significant acceleration of training for the Multilayer Perceptron. In our own simulations, based on the T800 transputer, it was found that the BFGS algorithm was on average four times faster than the conventional off-line batch gradient technique, (Lightbody 1991). To provide further acceleration of the learning process, a parallel BFGS algorithm was realised on an array of T800 transputers. Following Oglesby and Mason, (1989), this involved the

39

partitioning of the data space and distributing the various sections of the data to their respective processors. The gradient for each section of the data was first determined on separate processors and then combined to provide the batch gradient. Using this gradient value and the approximation to the Hessian matrix, a better direction for the update of the weights was be calculated obeying the Quasi-Newton condition. A parallel line search algorithm was then developed to accelerate the choice of the optimal step along this new update direction. It was found that the parallel BFGS algorithm could be implemented on an array of ten T800 transputers with a mapping efficiency of 99% and was approximately forty times faster than the batch gradient method on a single T800 transputer, (Lightbody, 1991).

NEURAL MODELLING

The basic structure for the neural network based series-parallel modeller is shown in Fig. 4, where a Multilayer Perceptron network is trained to provide the one-step-ahead estimate of yP, from the present and past two plant outputs, and present and past two plant inputs.

u(k)

DEi.AV UNE

DELAY UNE

NONLINEAR PLANT

MU' NEURAL

ORK

TRAINING ALGORITilll

Fig. 4 The neural series-parallel modeller

To train the network, it was first necessary to provide suitable data by exciting the system. Since a nonlinear system is being identified here, it is not simply a case of exciting all the dynamic modes but the full operating range must also be covered in such a way that the input space to the neural network is adequately spanned. In this case a hybrid excitation signal was employed, consisting of random steps in the range (-3.0, 3 .0], added to a higher frequency PRBS signal, with a random amplitude in the range (-0.5, 0.5] . The random amplitude, long duration steps are used to force the system output to cover the full operating range, with the PRBS present to excite all the modes and ensure that the record of inputs u is sufficiently dynamic. All data variables were then scaled so that they were in the range [-1 .0, 1 .0] and the vectors were randomised in the training set to ensure that there was no dynamic link between one

vector and the next when applied to the BFGS optimisation algorithm.

A nonlinear series-parallel model was then trained, using the parallel BFGS algorithm on 10 T800 transputers and a training set of 500 vectors. The network used was a (6, 15, 1) Multilayer Perceptron, with the nonlinear elements in the hidden layer being tanh(x/2) sigmoid functions. The sample time was 0.4 seconds. The response of the series model after one hundred iterations through the training set, taking approximately one minute, is as shown in Fig. 5. The responses of the series-parallel neural model and the jump-phenomena plant are indistinguishable.

output 2�-------------�

1.6 ················· . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.6

-o.s -1 · · · · · · · · · · · · · · · · . . . . . . . . . . . . . . . . . . . . . . . . .

- 1.6 '---'---'--__...__..___.L._�--'---'----'-----" o m ro � � � � ro � � � time / 11

- plant · · · · · Mural model

Fig. 5 Model response after 100 iterations

NEURAL PREDICTION MODELLING

The typical linear p-step-ahead predictive model, as used by Clarke, Mohtadi and Tuffs, ( 1987), for example is as given in equation (5), where P and Q are polynomials in the delay operator z·1 •

Based on this equation the following nonlinear p-step­ahead prediction plant model is proposed.

(6)

yP(k+p)=t(y P(k), . . y P(k-n),u(k+p- 1), . . u(k-m))

This network is then trained in the series-parallel structure, using present and past plant outputs, along with the present, past and the future plant inputs, to produce an estimate of the plant output, p steps ahead. Accurate prediction can be achieved over this range since the neural network has been trained to produce the full nonlinear model of the plant and not just a local linear approximation. A five-step-ahead predictor, represented by equation (7), was identified, based on a ( 10, 30, 1) Multilayer Perceptron neural network.

yP(k+5)=t(y P(k), . . . y P(k-2),u(k+4), . . . u(k-2)) (7)

The training set of 400 data vectors was produced

40

using the same hybrid excitation signal as before and the model was again trained, using the parallel BFGS training algorithm. After 400 iterations through the training set the model was tested using a hybrid PRBS signal. The sample time was 0.4 seconds. From Fig 6. the neural 5-step-ahead predictor provides accurate predictions of the plant output.

output u�---------------,

I · · · · ··················································

o.s

- 1

- u '---�'------'----'----"----'----'---"--� 0 � � � � � � ro �

time / 11

- plant ····· naural predlollon

Fig. 6 Neural 5-step prediction results

NEURAL INTERNAL MODEL CONTROL

Hunt and Sbarbaro, ( 1990), have suggested that neural networks could be incorporated into the Internal Model Control (IMC) structure proposed by Economou, Morari and Palson, ( 1986). The ability of the forward network to form accurate inverse and forward models of a nonlinear plant is utilised. However the problem in applying IMC to the control of the nonlinear plant in Fig. 1 , is that an inverse model relating the output of the plant to the input, does not exist. If the plant can be approximated by the less general structure of equation (8), where the nonlinearity is separable, then the full model inverse is no longer required and the inverse of the nonlinear function of the inputs would suffice.

yP(k+ l) =f(y P(k), . . . y P(k-n) +g(u(k), . . . u(k-m)) (8)

y (k+l) A f(k)+g(k) p

If the desired transfer function of the system over the full nonlinear operating range is chosen to be:

(9)

Then the system would follow this response, if g(k) was given as:

g(k) = C(z-1)(r(k) -yP(k))-f(k) (10)

The control u(k) could be calculated if the inverse of this function, g"1(.) was known:

u(k) = g-1(C(z-1)(r(k) -y P(k)) -f(k)) (1 1)

If good estimates of the forward plant sequence f(k)

and the inverse plant function g·1( .) are available then the following control law should provide the response of equation (9).

u(k) = g-'(C(z-1)(r(k) -yP(k)) -t(k)) (12)

The IMC structure of Fig. 7 was proposed for the control of the nonlinear plant. The forward model of the plant was provided by a neural network, consisting of two subnetworks connected to an output neuron. Once trained, the respective sub-networks would give estimates of the sequences g(k) and f(k). A second network was employed to provide estimates of the inverse function g·1(.).

output o.ar--'----------------,

-0.8 L____._ _ _,__,_ _ _.___--1._-'---'---"--'----'

o ro � � � � � ro � � -time /1 - nonlinear plant ----- deelRd r.apon••

Fig. 8 Response of system under IMC

..__�Y-,<kl FUTURE WORK

y (k) p

Fig. 7 The neural IMC structure

The neural network forward model of the plant, consisting of two (3, 15, 1) sub-networks connected to a linear output neuron, was trained using the parallel BFGS algorithm implemented on ten T800 transputers. The training set was generated using the hybrid excitation signal discussed previous! y. The inverse model consisted of a (6, 15, 1) neural network, which again was trained using the parallel BFGS algorithm. To provide the training set, in this case, a synthetic PRBS signal , u.(k), was input to both the plant and the forward model. The estimates of the sequence g(k) were then provided by the series-parallel model. This network was trained to relate the past three samples of the synthetic input u,(k) and the present and past two estimates of g(k) to the present synthetic input.

The desired response of the system was as defined by equation (13), from which the filter C(z-1) can be readily determined.

y (k+l) = 1 .8429y (k) -0.8521y (k-1) p p p

+0.00474r(k)+0.00449r(k-1) (13)

Fig. 8 shows how the nonlinear plant performs under neural Internal Model Control, for a random amplitude, PRBS setpoint sequence with a sample time of 0.4 seconds. The desired response of the system, described by equation ( 13), is also given. The nonlinear plant under IMC adequately follows the desired response.

41

It is proposed to investigate the possible use of Radial Basis Function networks for nonlinear modelling. Here the nonlinear optimisation problem of weight adjustment is then replaced by a linear one, which would provide the faster convergence required for on-line modelling and control. Likewise, it is thought necessary to develop recurrent neural network based modellers, along with an extensive analysis of their stability. Any further work would include also studying the effects of noise on neural models.

CONCLUSIONS

This paper applied neural network techniques to modelling and control of a particular type of nonlinear system which exhibited discontinuities in the gain Bode plot. It has been shown that feed­forward networks can be used to produce nonlinear models and predictive models for this system. A novel IMC structure was proposed, based on the ability of the neural network to form nonlinear forward and inverse models. It was shown that, using this control structure, the nonlinear example plant could be controlled to adequately follow a desired response.

ACKNOWLEDGEMENT

Gordon Lightbody would like to acknowledge the financial support of the Department of Education for Northern Ireland and the Institute of Advanced Microelectronics.

REFERENCES

Atherton, D.P. , ( 1974). Nonlinear Control Engineering. Van Nostrand Reinhold Company, London.

Battiti, R. and F.Masulli, ( 1990). BFGS optimisation for faster and automated supervised learning. Proc. Int. Neural Net. Conf. , Vol. 2, pp. 757-760.

Billings, S.A. , H.B. Jamaluddin and S. Chen, (1992). Properties of neural networks with applications to modelling nonlinear dynamical systems. Int. J. Control, Vol. 55, No. l , pp. 193-224.

Chen, S. , S.A. Billings and P.Grant, (1990). Nonlinear system identification using neural networks. lnt.J.Control, Vol.51 , No. 51 , pp. 1 19 1-1214.

Clarke, D.W. , C. Mohtadi and P.S.Tuffs, (1987). Generalised Predictive Control, Part 1 . The basic algorithm. Automatica, Vol. 23, No. 2, pp. 137-148.

Cybenko, G . , (1989). Approximations by superpositions of a sigmoidal function. Mathematics of Signals and Systems, Vol. 2, pp. 303-3 14.

Douce, J.L. and M. Zhu, (1990). Modelling a class of nonlinear systems. IEE Proc. D, Vol. 137, No. 6, pp. 385-389.

Funahashi, K. , (1989). On the approximate realisation of continuous mappings by neural networks. Neural Networks, Vol. 2, pp. 183-192.

Hunt, K.J. and D. Sbarbaro, (1991). Neural networks for nonlinear internal model control. IEE Proc-D, Vol. 138, No. 5, pp. 43 1-438.

Lightbody, G. (1990). A parallel BFGS algorithm. Queen's University Belfast, Dept. of Elect. Eng., Internal Report.

Economou, C.G. , M. Morari and B.O. Palsson, (1986). Internal Model Control. 5. Extension to Nonlinear Systems, Ind. Eng. Chem. Process Des. Dev. , Vol. 25, pp. 403-411 .

Narendra, K.S. and K.Parthasarathy, (1990), Identification and control of dynamical systems using neural networks, IEEE Trans. on Neural Networks , Vol . 1 , No. l , pp. 4-27.

Oglesby, J. and J.S. Mason, (1989). Dynamic scheduling for feedforward neural nets using transputers. Proc. First IEE Conference on Neural Networks.

Sbarbaro, D. and P.J. Gawthrop, (1990). Leaming complex mappings by stochastic approximation. Proc. Int. Joint Conf. on Neural Networks, January 1990.

Sbarbaro, D. , K.J.Hunt and P.J.Gawthrop, (1990). Connectionist representations and control structures. IEE Colloq .• Digest No. 1991/019.

Shanno, D.F, (1978). Conjugate gradient methods

42

with inexact searches. Mathematics of Operations Research 3 , pp 244-256.

Werbos, P.J, ( 1988). Generalisation of backpropagation with application to a recurrent gas market model. Neural Networks. Vol. 1 pp. 339-356.

West, J.C. and J.L. Douce, (1954). The frequency response of a certain class of nonlinear control system. British Journal Applied Physics. Vol. 5, pp. 204-210.

Willis, M.J. , C.D. Massimo, G.A. Montague, M.T. Tham and A.J. Morris, (1991). Artificial neural networks in process engineering, IEE Proc . • D,Vol. 138, No. 3, pp. 256-266.

Wu, Q.H. , Hogg, B.W. and G.W. Irwin, (1992). A neural network regulator for turbogenerators. IEEE Trans. on Neural Networks, Vol. 3, No. 1 , Jan 1992, pp. 95-100.

Copyright © IF AC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1 992

NEURAL NETWORKS (METHODOLOGIES FOR PROCESS MODELLING AND CONTROL)

G.A. Montague, A.J. Morris and M.J. Willis

Department of Chemical and Process Engineering, University of Newcastle, Newcastle upon Tyne, NEJ 7RU, UK

ABSTRACT

There are strong relationships between Artificial Neural Network and Radial Basis Function approaches to system modelling and representation. Indeed, the RBF representation can be implemented in the fonn of a two-layered network. This paper reviews the contributions that these two approaches can make to the process modelling and control. The development of dynamic system representations . is then examined in order to provide a basis for predictive control. Two alternative network modelling philosophies are considered: a time series approach and a network structure with embedded dynamics. Potential applications of the methods discussed are highlighted through studies of typical industrial process control problems.

Keywords. Neural networks, Radial Basis Functions, Dynamic Networks, Neural Network Predictive Control.

INTRODUCTION

System modelling and identification are fundamental problems in engineering where it is often required to approximate a real-world system with an appropriate model given a set of input-output data. The model structure needs to have sufficient representational ability to enable the underlying system characteristics to be approximated with an acceptable accuracy. For linear time-invariant systems model structure and identification problems have been well studied and the literature abounds with useful methods, algorithms and application studies. Widely used structures are the Autoregressive Moving Average (ARMA), the Autoregressive with Exogeneous Variables (ARX) and the Autoregressive Moving Average with Exogeneous Variables (ARMAX) representations.

In practice most systems encountered in industry are non-linear to some extent and in many applications non-linear models are required to provide acceptable representations. Non-linear system identification is, however, much more complex and difficult although the Nonlinear Autoregressive Moving Average with Exogeneous Variables (NARMAX) description has been shown to provide a very useful unified representation for a wide class of non­linear systems. Efficient parameter identification procedures are particularly important with non-linear systems so that the parsimonious model structures can be selected (Chen and Billings, 1990). The problem of identifying, or estimating, a model structure and its associated parameters can be related to the problem of learning a mapping between a known input and output space. A classical framework for this problem can be found in approximation rheory. Almost all approximation, or identification, schemes can be expressed as (mapped into) a network. For example, the well known ARMAX model can be represented as a single layer network with inputs comprising of lagged input-output data and prediction errors. In this context a network can be viewed as a function represented by the conjunction of a number of basic functions.

NEURAL NETWORK MODELLING

In developing a model which is representative of a systems behaviour, it is the topology of the network, together with the neuron processing function, which determine the accuracy and

43

degree of the representation. This paper concentrates on one specific topology which has probably been the most prevalent in ANN studies, the feedforward network. The power of the feedforward approach has been demonstrated by a number of workers (eg, Hect-Nielson, 1 989). A number of papers which have indicated that a feedforward network has the potential to approximate any non-linear function. Cybenco (1989) and Wang et al ( 1 992) have shown that the two-layered feedforward network can uniformly approximate any continuous function to an arbitrary degree of exactness - providing that the hidden layer(s) contain(s) a sufficient number of nodes. The ability of the network to approximate non-linear functions is dependent upon the presence of hidden layers. Without these only linear combinations of functions can be fined. The number of nodes in the hidden layer(s) can be as small or large as required. It is related to the complexity of the system being modelled and to the resolution of the data fit.

Approximation theory addresses the problems of interpolating or approximating a continuous multivariate function, f(x), by a selected function, F(x,w), having a fixed number of parameters, w. Given a function F, the problem reduces to identifying (or learning) the set of parameters w that provides the best possible approximation to f (according to apriori chosen criteria), when exposed to (or trained on) an 'example' data set. The representation problem relates to the selection of an appropriate approximating function F.

SIGMOIDAL FUNCTION NETWORKS

The feedforward artificial neural network (ANN) performs a non­linear transformation of input data in order to approximate output data. The number of input and output nodes is determined by the nature of the modelling problem being tackled, the method of input data representation chosen, and the form of network output required. The input layer to the network does not perform processing but merely acts as a means by which scaled data is introduced to the network. The data from the input neurons is propagated through the network via the interconnections. The interconnections within the network are such that every neuron in a layer is connected to every neuron in adjacent layers. It is the hidden layer structures which essentially define the topology of a feedforward network. Each interconnection has associated with it a scalar weight which acts to modify the strength of the signal. The neurons within the hidden layer perform two tasks; they sum the weighted inputs to the neuron and then pass the resulting summation through a non-linear processing, or activation, function. In addition to the weighted inputs to the neuron, a bias is included in order to shift the space of the non-linearity. For example, if the information from the ith neuron in the (j- l )th layer, to the kth neuron in the jth layer is I -_ 1 i· then the total input to the kth neuron in the jth layer is given by: J '

n

sj,k = bj,k + L wj-1 ,i,k 1j- l ,i i= l

:-vhere bj,k is a bias term which is associated with each interconnection and determines the co-ordinate space of the nonlinearity. The output of each node is obtained by passing the weighted sum, Sj,k• through a nonlinear operator. The most widely applied non-linearity is the sigmoidal function in the interval (0,+l ).

In situations where both positive and negative outputs are required the function can be re-scaled into the interval (- 1 ,+ I). The sigmoidal function has the mathematical description:

Oj,k = 1/(1 + exp(-Sj,k)]

Although this function has been widely adopted, in principle, any function with a bounded derivative could be employed (Rumelhart et al, 1986). Other alternative nonlinear activation functions are for example the monotonic forms - hyperbolic tangent, the saturation function, etc., and those based on Radial Basis Functions.

Process modelling using ANNs is similar to identifying the coefficients of a parametric model of specified order. Loosely speaking, specifying the topology of an ANN is similar to specifying the 'order' of the process model. For a given topology, the magnitudes of the weights define the characteristics of the network. However, unlike conventional parameteric model forms, which have an a priori assigned structure, the weights of an ANN also define the structural properties of the model.

The problem of determining the network parameters (weights) can be considered essentially a non-linear optimisation task. The simplest optimisation technique makes use of the Jacobian of the objective function to determine the search direction. A 'learning' rate term which influences the rate of weight adjustment (Rummelhart and McOelland, 1987) is used as the basis for the back-error propagation algorithm, which is a distributed gradient descent technique. In order to train the network with this approach, a representative process input data set is presented to the network. At each time instance, the input set is propagated through the network to give a prediction of output. The error in prediction is then used to update the weights based upon gradient information, in order to drive the cost function to a minimum. The error in prediction is thus in a sense back-propagated through the network lo update the weights. Such an approach to training is termed supervised learning since at any time instant both input and output data is available. The popularity of this learning technique can be judged by the commonly adopted, somewhat misleading, description of feedforward nets as backpropagation nets. There arc, however, a number of problems with the backpropagation approach. In common with other descent algorithms, difficulty arises when the search approaches the minima. If the surface is relatively flat in this region then the search becomes inefficient. Therefore, in most neural network applications, a 'momentum' term is added. The current change in weight is made dependent upon the previous

weight change by incorporating a scaling factor. In this approach, weights in the jth layer are adjusted by making use of locally available information, and a quantity which is 'back-propagated' from neurons in the (j+ !)th layer. Although this modification docs yield improved performances, in training networks where there are numerous weights, gradient methods have to perform exhaustive searches and are also rather prone to failure. Furthermore, in

adopting a down-hill search technique, the question arises as to whether the minimum is local or global. Although it could be argued that a momentum term may take the solution over a local minima, global optimality is not assured.

A more appealing method is that of Conjugate Gradients (Leonard and Kramer, 1990). Although quasi-Newton methods are usually more rapidly convergent and more robust than conjugate gradient

methods, they require significantly more storage. A Newton-like algorithm, which includes second derivative information, would treat the S matrix, in the optimisation procedure discussed above, as the inverse of the Hessian. An advantage of the conjugate gradient method, however, is that it relinquishes the need for second derivatives of the objective function whilst retaining convergence properties of second order techniques. A conjugate gradient

methodology is thus a well established contender for problems with a large number of variables such as the training of an artificial neural network. The basic philosophy is to generate a conjugate direction as a linear combination of the current steepest descent direction and the previous search direction. With this technique minimisation is initiated as with steepest descent. After this iteration a new direction of search is required. This direction is chosen so that it is conjugate with the initial search direction. Minimisation then proceeds in the newly defined direction. It should be noted, however, that when this technique is applied to non quadratic functions, the exact minimum will not be found in a finite

44

number of steps. Practical experience suggests that resetting the algorithm to the steepest descent direction every n iterations (where

n is the number of network weights) is superior to the repeated use of the conjugate gradient method.

An alternative approach (Bremermann and Anderson, 1989), attempts to avoid the solution becoming locked into a local minima.

Postulating that weight adjustments occur in a random manner and that weight changes follow a multivariate zero mean Gaussian distribution, the algorithm adjusts weights by adding Gaussian distributed random values to old weights. The new weights are accepted if the resulting prediction error is smaller than that from the previous set of weights. This procedure is repeated until the reduction in error is negligible. The procedure is referred to as the chemotaxis algorithm. During minimisation the allowable variance of the increments can be adjusted to assist network convergence and aid in the avoidance of local minima. The algorithm is of the graded learning type. Network outputs do not need to be available at every time instant, merely a measure of quality of fit needs to be given periodically. During minimisation, the allowable variance of the increments can be ad justed to assist network convergence and aid in the avoidance of local minima.

In network training one method adopted is to split the data, randomly, into training and test data sets. If the network approximation is adequate then the squared error between the training data outputs and network predicted outputs should be 'relatively' small and, more importantly, should be uncorrelated with all combinations of past inputs and outputs. Comparison of the

average error achieved on the training set with that achieved on the test data set can be used to indicate the adequacy of the model (network). For example, if the test data set error is significantly

larger then an over-dimensioned network is indicated. A number of model validity tests for non-linear model identification procedures have been developed, for example the statistical chi-squared test (Leontaritis and Billings, 1987), the Final Prediction Error Criterion (Akaike, 1974), the Information Theoretic Criterion (AIC) (Akaike, 1974) and the Predicted Squared Error criterion (Barron, 1984). The PSE criteria, although originally developed for linear systems, can be applied to feedforward nets providing that they can be approximated by a linear model.

Final Prediction Error (FPE) = (E/2N) (N + Nw)/(N - Nw)

Information Theoretic Criterion (AIC) = ln(E/2N) + 2 Nw/N

Predicted Squared Error (PSE) = E/2N + 2*( cr2)Nw/N

where cr2 is the prior estimate of the true error variance. These tests make use of functions that strike a balance between accuracy of model fit (average squared error over N data points, E/2N) and the number of adjustable weights used (Nw). Minimisation of these test functions results in networks (models) that are neither under nor

over dimensionalised. A procedure involving 'train - test - validate' experiments is used with different network dimensions to minimise a selected validation function. Final validation of the identified

network model should be acieved by checking its predictive qualities for both one-step-ahead and multi-step-ahead predictions. In addition it is also informative to plot the residuals.

Neural network model identification requires that the input data sequence must, at least, satisfy all the well known conditions associated with MIMO parameter identification - i.e. all the system 'modes' must be excited. However, persistent excitation alone is not sufficient. Random excitation is required with a magnitude covering the whole dynamic range and density that is sufficient to encapsulate the whole input domain of interest. The excitation required for good identification of an adequate model is closely related to the properties of the system being modelled and hence to the distribution of the training data set(s).

RADIAL BASIS FUNCTION NETWORKS

Recently there has been an increasing interest in Radial Basis Functions (RBF's) within the engineering community as powerful, technique for interpolation in multidimensional space. A RBF is a function which has an in-built distance criterion with respect to a centre. Functions like this can be used very effectively for interpolation (Powell, 1985) and for smoothing of data (Rippa, 1984). A recent application of RBF's is in the area of neural

networks where they can be used as a replacement for the sigmoidal transfer function. RBF networks have three layers namely an input layer, the hidden layer with the RBF non-linearity and a linear output layer. The function of the input layer of a RBF network is to distribute all inputs unaltered to each of the hidden layer nodes. The weights on the links between the input layer and the hidden layer are all set to 1 .0 and do not change during training. An RBF expansion with n-inputs and a scalar output implements a mapping according to:

N

f(x) = b0 + L Bi f(ll x - ci II)

i=I

where bi are the parameters or weights of ci, and ci are the RBF centres and N is the number of centres.

The functional form f(.) is pre-selected with the centres ci being some fixed points in n-dimensional space appropriately sampling the input domain. The RBF representation can be implemented in the form of a two-layered network. For a given set of centres, the first layer performs a fixed nonlinear transformation which maps the input space onto a new space. Each term f(ll x - ci II) forms the activation function in a unit of the hidden layer. The output layer then implements a linear combination on this new space. With the RBF centres regarded as adjustable parameters a network structure in feedforward form results. The most popular choice for f(.) is the Gaussian form and in this case the activation function in any hidden unit (H) becomes:

N

OH = exp [ - L f(xi - cH,il o? l i=l

where each Gaussian is characterised by the function centre cH i• and the function width oi.

'

In each node of the hidden layer the distance between the current input to the network and the centre of the RBF is calculated using:

where � is the vector of coordinates of the RBF centre. The result is then passed through the non-linearity f(.). The output generated by the hidden layer is fed into the output layer which then generates a weighted sum:

k

Yj = Bj + :E wij oi i=l

where Wi j is the weight on the link between output node j and hidden layer node i, Oi is the output generated by hidden node i, and k is the number of nodes in the hidden layer. The weights on the links between the hidden layer and the output layer are calculated by solving the equation AW = B.

Since the system of equations is overdetermined, an SYD-based generalised least squares minimisation procedure is used. RBF networks implemented in this way do not suffer from the problem of becoming locked into local minima as do the ANN's. There are two parameters in the RBF networks that determine the modelling capability of such a network, namely k and p, where k is the number of RBFs used in the hidden layer, and p is the parameter used to determine the spread oj of each RBF (cf. placement of RBF centres). To determine tlie spread the P-nearest neighbour method is used. This method selects for a particular cluster q a set of p clusters, whose cluster centres are nearest to cluster Ci. The spread oj is calculated using the relationship:

p (Jj = !JP * [ L D�i • �j) 10.5

i=I

where �i and �j are the cluster centre coordinates. The values of k and p are determined iteratively as part of the training procedure.

The predictive error is calculated using the jack-knifing method (Wetherill et al, 1991). This method can generate an unbiased estimate of the predictive error without making assumptions about the distribution function of the error. The method essentially splits

45

the training set in two partitions for training and for network testing. The error generated using the test partition, is stored for later use. After the newly trained network has been tested, the original training set is partitioned differently and the whole process is repeated. This continues until all examples in the original unpartitioned training set have been used for testing exactly once. Following this, the stored errors are averaged to form the estimate for the predictive error for a network with the chosen values of k and p. According to the theory of jack-knifing the best results are actually obtained when the cardinality of the test partition is I . However, for the sake of computational efficiency the original training set has only been partitioned 10 times, resulting in test partitions with a cardinality significantly larger than I . For the same reason the value of p has been limited to be either 2 or 3 although this might inhibit the modelling power of a RBF network.

At least two different methods of placement of the RBF centres have been reported. The first method is to position the RBF centres evenly spaced out along all dimensions of the input space which is usually a hypercube with coordinates in the interval [-1, l ] (Hunt and Sbarbaro, 1991). Although this method is simple, it has a few drawbacks, especially when the dimension n becomes large since the number of RBFs will go up exponentially. The second method actually clusters the network inputs in the training set and positions the RBF centres at the centres of each of the clusters. For this purpose K-Means Clustering is used (MacQueen, 1967). The second method does not suffer from the same problems as the first one since it will position RBF centres in those parts of the input space where there are actually data points. The K-Means clustering method used is not exactly as described in the paper by MacQueen since it does not allow for dynamic creation and deletion of clusters as described in that paper. Instead the number of clusters is determined beforehand. Initially K (where K is set equal to m, the number of nodes in the hidden layer) points are chosen at random from the training data set and used as provisional cluster centres. For each of the other points in the training set the distance to each of the cluster centres (D) is calculated and the point is added to the cluster whose centre is nearest. When all points have been assigned to a cluster, the new cluster centres are calculated by averaging each of the coordinates of all the points in a cluster. The whole process is repeated until no more changes are observed. This method has some randomness due to the use of a random number generator to choose the initial set of K cluster centres which may result in slightly different cluster configurations. Therefore, the clustering process and also the training process of the RBF network is repeated a number of times with the same parameters values for k and p and the network with the smallest predictive error is selected as being representative of a network with the given parameters.

All data in the training data set is preprocessed to have zero mean and unit variance. This step is necessary to prevent inputs with large average values in a certain dimension from overshadowing inputs in some other dimensions with a small average values which would otherwise have happened using the distance criterion D. This may introduce some artefacts into the training data and it may affect the results of the RBF networks. However, till now there has been no reason to assume that the RBF modelling capabilities have been negatively affected by this scaling process.

Because of the way in which the distance measure is incorporated into a RBF, it is impossible for RBF networks to selectively ignore certain inputs. Sigmoidal feedforward networks can be shown to selectively ignore inputs by considering the polynomial representation of the network nonlinearity. RBF networks do not have this capability and therefore care has to be taken with what data is presented to the RBF network. It is extremely important to only use inputs that have a fairly strong, not necessarily linear correlation with the outputs. Under no circumstance should totally uncorrelated data in either the linear or the non-linear sense be presented to a RBF network. In the next section results will be presented where this rule has been disregarded intentionally.

NEURAL NETWORK SOFTWARE SENSORS

Here sigmoidal function feedforward networks and RBF networks are briefly compared as difficult-to-measure-variable estimators (software sensors). Data from a large industrial penicilin fermentation process is used with the following measurements being

available: Fennentation age; Substrate feedrate; Dissolved oxygen (D02); co2 concentration in the offgas; Biomass laboratory assay. The biomass measurements are off-line measurements and are subkect to long and variable assay times. The biomass measure is known to be noisy and the noisiness tends to increase towards the end of the fennentation, which is reflected in the greater apparent swings of biomass levels as time progresses. More detailed studies on fennentation processes, as well as other industrial processes, are described in (Lant et al, 1990; Morris et al, 1991 ; Di Massimo ct al, 1991; Willis et al, 199 l a). It is interesting to compare these approaches with those based upon adaptive linear models (Tham et al, 199lb).

Of the many possible network inputs for bioreactor modelling only fennentation age and co2 are used in this study. In figures 1 and 2 the perfonnance of ANN models are presented, both with one hidden layer, a non-linear output layer and 5 and 60 nodes in the hidden layers respectively. The values on the axes have not been displayed for proprietry reasons. In each of the figures three runs of the fermenter have been displayed. The first two have runs been used for training while the third run has been used for testing. The results indicate that the ANN's are capable of representing the relationship between the input variables and the output variable adequately. They are definitely good enough to be used in control. It is also clear that the increase in the number of nodes in the hidden layer has not enhanced the modelling capability of the networks.

Figures 3 and 4 provide a comparison of the modelling capabilities of RBF networks with their ANN counterparts discussed above. The results shown in figure 3 have been generated by a network with 5 clusters, while the results in figure 4 have been generated by a network with 60 clusters. It is clear from the figures that a RBF with 5 clusters is just as capable of capturing the non-linear relationship between inputs and output as the ANN's. However, an increase in the number of RBF nodes has made a dramatic impact on the modelling capability of the networks. The RBF network with 60 clusters can follow the presented signal almost exactly, while for the test set it also has slightly bener results. This observation also raises a important question: if it is known that the process being modelled is noisy, is it necessary or even desirable to be able to match that observed process behaviour exactly. It is necessary to decide how close the model-process matching should be.

DYNAMIC NEURAL NETWORKS

The basic feedforward network provides a static representation of the data being modelled. The most straightforward way to extend this essentially steady state mapping to the dynamic domain is to adopt an approach similar to that taken in linear ARMA (Auto­Regressive Moving Average) modelling. Here a time series of past process inputs (u) and outputs (y) are used to predict the present process outputs. Important process characteristics such as system delays can be accommodated for by utilising only those process inputs beyond the dead time. Additionally any uncertainty in delay can be taken account of by using an extended time history of process inputs. Inevitably a significant number of network inputs result.

An alternative philosophy is to modify the neuron processing and interconnections to incorporate dynamics inherently within the network. In addition to the sigmoidal processing of nodes, the neurons (or transmission between neurons) can be given dynamic characteristics. For example, {exp(-std)•N(s)/D(s)}, where N(s) and D(s) are polynomial functions in Laplace operator s, and the time delay is represented by a second order Pade approximation (Willis et al, 199lb; Montague et al, 1991).

With an auto-regressive data input approach, the network model is required to predict y(t+n) from estimates of y(t+n-1). Errors in the estimate of y can accumulate as the prediction horizon increases. Since the dynamic network model is not autoregressive this problem does not arise and the predictions of process output are thus representative. The problem with the ARMA approach can be overcome by minimising the network prediction error during training not just for y(t) but also for all output predictions up to a prediction horizon.

NEURAL NETWORK BASED CONTROL

If the neural network model is of sufficient accuracy, tfien it is

46

possible to employ the model directly within a model based control strategy (Montague et al, 1991). A potentially useful algorithm is one which minimises future output deviations from the setpoint, whilst taking suitable account of the control sequence necessary to achieve this objective. This concept is common to most predictive control algorithms. However, the attraction of using the neural network instead of other model fonns within the control strategy is the ability to effectively represent complex nonlinear systems. Other approaches have also been proposed (eg Narendra and Parthasarathy, 1 990; Psaltis et al, 1988).

Since the early 1970's numerous model based control algorithms have been proposed, with the prime development objective being to increase performance and robustness of process regulation. A number of notable successes are those using model-predictive methods (eg Ricker , 199 1 ; Wilkinson, Morris and Tham, 1991). Algorithms such as Dynamic Matrix Control have been found to provide major cost benefits on many industrial systems with 'pay­backs' achieved in relatively short time scales. In almost all such control schemes a linear description of the process is assumed. If the system dynamics are relatively linear around the operating region, then the use of a linear model based control algorithm may lead to acceptable performance. However, in situations where the process is highly non-linear, the linearity assumption could well be detrimental to control system robustness. In this situation a common approach has been to adopt an adaptive control policy. Although the techniques for on-line adaptation are fairly standard, in a 'real' process environment the demands placed upon adaptive estimation schemes by everyday process occurrences can be extremely severe. Jacketing procedures are used to provide algorithm robustness. Whilst effective control system jacketing is essential, the consequences of failure in an adaptive scheme has resulted in their industrial application being far from common. In many situations a fixed linear model is used even if the system is known to be non­linear. As a result performance is sacrificed in order to maintain robustness in the face of process/model mismatch.

Neural Network Based Predictive Control The predictive control algorithm used is centred around an iterative solution of the perfonnance function:

N2,i Nu,i L [wi(t+n)-yi(t+n)]2 +L [qiDui(t+i)]2 }

i=O

where Yi(t), ui(t) and wi(t) are the controlled output, manipulated input and set-point sequences of control loop 'i' respectively. N 1 ,i and N2 i are the minimum and maximum output prediction horizons. Nu,i is' the control horizon and qi is a weighting which penalises excessive changes in manipulated input of loop 'i'. NL is the number of individual control loops. In the perfonnance function, the terms Yi(t+n), n = N 1 , ... , N2, represent a 'sequence' of future process output values for each respective loop, i= l , NL, which are unknown. Thus during minimisation, the sequence of process outputs is replaced by their respective n-step-ahead predictions. With the ability to predict the future outputs y(t+nlt), together with known future set-points, the future controls which will minimise the perfonnance function can be determined. In common with most predictive control strategies, beyond the control horizon, Nu, it is assumed that the control action remains constant. The optimisation algorithm therefore searches for Nu control values in order to minimise the perfonnance function.

Since neural network model is nonlinear, an analytical solution of the cost function is not possible. By adopting a numerical optimisation approach, a generalised solution technique results which can be used to provide a solution. Most optimisation algorithms employ some fonn of search technique to scan the feasible space of the objective function until and extremum point is located (eg Luenberger, 1973; Edgar and Himmelblau, 1989). The search is generally guided by calculations on the objective function and/or the derivatives of this function. The various procedures available may be broadly classified as either 'gradient based' or 'gradient free'. In an on-line situation, where process measurements are often corrupted by noise, the use of gradient based methods may not be feasible due to their susceptibility to discontinuities. A gradient free method is adopted (Powell, 1964; Fletcher, 1980) which enables the extremum of a function to be located using a sequential unidirectional search procedure. Starting from an initial

point, the search proceeds according to a set of conjugate directions generated by the algorithm until the extremum is found. Since control is based upon the prediction of future outputs obtained from a nominal model of the process, offsets may occur due to distulbances and plant-model mismatch. Following the concept of internal model control (IMC), the discrepancy between model and process responses can be estimated and used to 'correct' the predictions obtained from the model.

The process used to demonstrate the performance of the controller is a detailed nonlinear simulation of a binary distillation column. The 1 0 stage pilot plant column, installed at the University of Alberta, Canada, separates a 50/50 wt% methanol water feed mixture. The column is modelled by a comprehensive set of dynamic heat and mass balance relationships. Both the column and the nonlinear model have been used by many investigators to study different advanced control schemes (cg. Tham et al, 199la). The objective is to control the top and bottom product composition using the steam flowrate to the reboiler and reflux flow as manipulated inputs. The first step in the implementation procedure is the detennination of the process model. The neural network model used had 8 inputs, 2 hidden layers with 6 neurons in each layer and two outputs. The inputs to the network were time histories of steam and reflux flowrates and product compositions and the network was trained as a k-step ahead predictor.

The SISO control of bottom compos1uon was first investigated. Here the performance of the nonlinear predictive controller was

compared to both a fixed linear model based predictive control strategy and a conventional PI controller. The control objective here was to follow a series of setpoint changes in the bottom loop. Figure 5 illustrates the improved performance achieved by using a nonlinear process representation. This is especially evident in the comparison of the constrained predictive controller with both an averaged linear process model with the same algorithm but including a fixed nonlinear model.

The MIMO performance is demonstrated by the study of the servo response characteristics of the bottom composition loop and the resulting disturbance rejection properties of the top composition loop. The neural network based predictive controller pcrfonnancc was compared to that of a conventional PI regulator. The control objective was to follow a series of setpoint changes in the bollom loop whilst simultaneously maintaining top product composition at 95 wt% methanol. The integral of the absolute set-point tracking error (IAE) was used to quantify the performance characteristics of the two controllers. The control profiles shown in figures 6 and 7 arc characteristic of the respective control schemes. An important aspect of these results is the decoupling capabilities of the multivariable controller. Herc the ability of the network model to predict the effect of bottom loop disturbances on the output of the top loop facilitates more effective regulation of the top product composition. With the network based predictive controller an IAE of 22.24 was obtained on the bottom loop (compared to 3 1 .58 with PI control) and for the top loop an IAE of 3.0 was achieved (compared to 1 1 .52 with PI control). It is worth noting that the improvements gained over using a single-step ahead trained network (measured in terms of JAE) are 22% for the bottom loop and 18% for the top loop (results not shown). Experience suggests that in addition to the improved performance, increased control system robustness results from the reduced process/model mismatch.

CONCLUDING REMARKS

Artificial neural networks provide an exciting opportunity for the process engineer. It is possible to rapidly develop models of complex operations that would normally take many man months to model using conventional structured techniques. This paper has addressed RBF networks to estimation of process variables using industrial data. It has been shown that, given the availability of the right measurements, the RBF networks can be made to estimate more accurately than the feedforward ANN. The use of statistical methods like jack-knifing added to the reliability of the estimates generated by RBF networks and therefore its acceptability to the process industry.

The paper has also reviewed the dynamic modelling capabilities of artificial neural networks. However, care needs to be excecised.

47

This was highlighted by considering the consequences of using auto­regressive structures for dynamic modelling. A low error in single step ahead predictions can be deceptive as an indicator of 'quality' of the process model. This is an example of one of a number of essential considerations that need to be taken account of when modelling with artificial neural networks. Given that a representative dynamic model can be obtained then it is relatively straightforward to incorporate the artificial neural network model within an industrially acceptable multivariable control framework. As the control strategy solution is iterative in nature the approach may only be suitable for systems which are not time critical. It is believed that the artificial neural network approach to generic system modelling, if necessary coupled with inferential and predictive control appoaches, can provide improved process supervision and control performance without needing to undertake major model development programmes. Further discussions can be found in Willis et al ( 1 99 l b).

ACKNOWLEDGEMENTS

The support of the Department of Chemical and Process Engineering, University of Newcastle, and member companiies of the International Neural Networks Club are gratefully acknowledged. As also are the many enlightening discussions with colleagues in the Systems and Control Research Group.

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A.J. (1991), "Bioprocess model building using Artificial Neural

Networks". Bioprocess Engineering, 7, 77-82.

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Wiley.

Hecht-Nielson R., ( 1989), "Theory of backpropagation neural networks".

Proc Int. Conf. on Neural Networks, I, 593-6 1 1 , IEEE Press, New York.

Hunt, K.J., Sbarbaro, D. (1991), "Neural Networks for Internal Model

Control", IEE Proc.-D, Vol. 138, No. 5.

Lant, P., Willis, M.J., Montague, G.A., Tham, M.T. and Morris,A.J.,

( 1990), "A Comparison of Adaptive Estimation with Neural Network

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Control Conference, San Diego, USA, 2173-2178.

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methods for non-linear systems'', Int. Journal of Control, 45, 3 1 1 -341.

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Wesley

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Multivariate Observations'', Proc. of the Fifth Berkeley Symposium on

Mathematical Statistics and Probability, U.C. Berkeley Press, CA.

Montague G.A., Tham, M.T., Willis, M.J., and Morris, A.J., (1992),

"Predictive Control of Distillation Columns Using Dynamic Neural

Networks'', 3rd IFAC Symposium DYCORD+'92, Maryland USA.

Montague G.A., Willis M.J., Morris A.J. and Tham M.T. (1991),

"Artificial Neural Network based Multi variable Predictive Control".

ANN'91 , Bournemouth, UK.

Morris, A.J., Montague, G.A., Tham, M.T., Aynsley, M, Di Massimo, C.,

and Lant, P., (1991), "Towards Improved Process Supervision'', Fourth

International Conference on Chemical Process Control CPC IV, South

Padre Island, Texas, USA.

Narendra, K.S. and Parthasarathy, K., (1990), "Identification and Control of Dynamical systems using Neural Networks, IEEE Trans Neural

Networks, I , I, 4-27

Psaltis, D., Sideris, A. and Yamamura, A.A. (1988), "A multilayered neural network controller", IEEE Control Systems Magazine, April, 17-21 .

Powell, M.J.D. (1985), "Radial Basis Functions for Multivariable interpolation : a review", Proc. of the IMA Conference on Algorithms for the Approximation of Functions and Data, RMCS Shrivenham.

Powell, M.J.D. ( 1964), "An efficient method for finding the minimum of a function of several variables without calculating the derivatives", Comput J., 7, 155-162.

Ricker, N.L. (1991) "Model predictive control: state of the art". Preprints CPC IV, South Padre Island, Texas.

Rippa, S. (1984), "Interpolation and Smoothing of Scauered Data by Radial Basis Functions", M.Sc. Thesis. Tel-Aviv University, Israel.

Rumelhart, D.E. and McClelland, J.L. (1987), "Parallel Distributed Processing: Explorations in the Microstructure of Cognition", Vol. l , Chp. 8, MIT Press, Cambridge.

--- Biomass . . . Estimated Biomass

Figure 1 . State Estimation (ANN-5 Hidden Nodes)

--- Biomass Estimated Biomass

Figure 2. State Estimation (ANN-60 Hidden Nodes)

--- Biomass ... Estimated Biomass

Figure 3. State Estimation (RBF Network-5 Hidden Nodes)

--- Biomass ... Estimated Biomass

Figure 4. State Estimation (RBF Network-60 Hidden Nodes)

48

Tham, M.T., Vagi, F., Morris, A.J., and Wood, R.K., (199la), "Multivariable Multirate Self-tuning Control: A Distillation Column Case Study", Proc. IEE, Pt. D, 138, No. 1, 9-24.

Tham, M.T., Montague, G.A., Morris, A.J., and Lant, P., (199lb), "Soft­Sensors for Process Estimation and Inferential Control", Journal of Process Control, 1, 3-14.

Wetherill, G.B., Kelly, P.J. and Rowlands, RJ. (1991), Recent Advances in Data Analysis Methods, Internal Paper, ISRU, Dept. Chemical and Process Engineering, University of Newcastle upon yne.

Wang, Z., Tham, M.T., and Morris, AJ., (1992), "Multilayer Feedforward Neural Networks: Canonical Form Approximation of Nonlinearity", in press Int J. Control.

Wilkinson, DJ., Tham, M.T., and Morris, A.J., ( 1991), "Multivariable Constrained Predictive Control: with application to High Performance Distillation", Proc. American Control Conference, San Diego, USA, 1854-1859.

Willis, MJ., Di Massimo, C., Montague, G.A., Tham, M.T. and Morris, AJ., (199la) "Artificial neural networks in process engineering". Proc. IEE, Pt D., 138, No. 3, 256-266.

Willis, M.J., Montague, G.A., Morris, A.J., and Tham, M.T., (199lb), •Artificial Neural Networks: Pragmatic Solution or Panacea'', Proc. American Control Conference, San Diego, USA, 2337-2342.

100 200 300 Time (mins)

Net model IAE : S.7 Linear model IAE = 62.1 Pl Control IAE = 78.1

400

Figure 5. Set Point Control of Bottom Composition (SISO Controller)

soo

6.5 �---------------------.,

6

= .g 5.5 ·c;; 0 ! 5

§ 4.5 0 c::i 4

Figure 6.

II I \ , ,,

I ,1 1,

Net control PI control Set point

I 00 150 200 250 Time (Mins)

Set Point Control of Bottom Composition (MIMO Controller)

300

95.4 ----------------N-

e-

t-co

_n_tro_t �

95.3 � 95.2 .,_,

Pl control

Set point

g 95.1 ·c ·c;; 95 i....Jl,ll-A4....----!14.!.µ..l�--"�1.,U,..,....-,..J.,.fo.;>,-,,,._� 8. E 94.9 0 u 94.8 c. � 94.7

94.6 94·5 0 so 100 150 200 250

Time (Mins) Figure 7. Regulatory Control of Top Composition

(MIMO Controller)

300

Copynght @ IFAC Artificial Intelligence in Real-Time Control, Delfi The Netherlands, 1992

PARALLEL NONLINEAR DECOUPLING FOR PROCESS CONTROL - A NARMAX APPROACH

B.A. Foss and T.A. Johansen

Division of Engineering Cybernetics, Norwegian Institute of Technology, N-7034 Trondheim, Norway

Abstract: The contribution of this paper is twofold. First, we focus on the application of a particular NA RM AX (nonlinear ARM AX) model representation based on local models for adaptive decoupling. Second, in order to improve the robustness of the adaptive control algorithm we introduce a diagonal PI-controller in parallel with the adaptive decoupler. These controllers are separated in the frequency domain, such that the decoupler and PI-controller takes care of control actions at higher and lower frequencies, respectively. The parallel control structure supports incremental control design, in the sense that improved process knowledge is used to successively upgrade control performance. The concept is illustrated by a semi-realistic simulation example.

Keywords: Nonlinear Systems, Adaptive Control, Multivariable Control Systems, Process Control.

INTRODUCTION

The use of advanced control techniques for process control applications is often severely restricted due to limited process knowledge. It is, hence, important to construct controllers in such a way that prior process knowledge may be included in a reasonably simple manner. In addition, information on process characteristics, obtained during operation, should successively be made available for the controller. This gives rise to an adaptive controller in the sense that controller parameters, and in some cases structure, may change with time.

Given the above-mentioned problem two critical factors are the model used to accumulate process knowledge, and the control structure itself. Let us first present the rationale for the model concept we propose.

A process must work under varying operating conditions. A change in operating conditions may be caused by process nonlinearities, time­varying parameters, external disturbances, setpoint changes, startup and shutdown, component failure or process maintenance. This is illustrated in Figure I. Let 4> be the set of all operation points. A vector </> E 4> is a possible operation point for the process. A process will often operate in parts of 4>, say 4>o or 4>1 , and now and then enter other parts of 4>. Our approach (Johansen and Foss, I992a, I992c) is to use a set of simple linear local models to describe the process well in different parts of 4>, as shown in Figure I, and form a complete model

Fig. I: A typical situation. The set of possible operation points is 4>, but the process typically operate in the operating regimes 4>o and 4>1 . Several local models are used to cover all possible operation points in 4>.

49

by introducing smooth interpolation between the local models. This requires explicitly defined model validity functions for each local model. These functions indicate the validity of the local models as a function of the operation point, which is assumed to be known. During on-line identification, only the local models which have significant weight will be updated. Hence, information about other operating regimes will not be forgotten, and this information can be recalled instead of being relearned when the process re-enters an operating regime.

We will now turn to the second critical factor; the control structure. There exists a vast amount of literature on multivariable control de­sign. We will in this paper limit ourselves to output feedback inverse­based control. We consider only output feedback as state feedback is an unrealistic assumption for process control applications. Inverse­based control or decoupling is an efficient technique to design high­performance controllers for multivariable systems. The controller may, however, be extremely sensitive to modelling errors as shown by (Sko­gestad et al, I988). Another complication arises in conjunction with non-minimum phase plants. Internal stability prohibits the use of an ideal inverse-based controller. In the nonlinear case this condition is coupled to the stability of the zero dynamics of the controlled process, cf. (Byrnes and Isidori, I984).

Our approach is to use a parallel control structure consisting of di­agonal PI-controllers, and a decoupler. This gives a high degree of flexibility in the sense that it is possible to include a limited amount of decoupling action in the controller. Similar control structures are proposed in (Gj!llsreter and Foss, 1992) and (Wei et al., I989).

The continuation of this paper is organized as follows: First, the non­linear model representation is discussed. In conjunction with this, sim­ilarities to artificial neural network structures are presented. Second, the parallel control structure is reviewed in some detail. This gives the basis to present our multivariable adaptive controller. The properties of the controller is investigated through simulations on a semi-realistic model of an exothermic reactor. Some conclusions finalizes the paper.

NON-LINEAR MODEL REPRESENTATION

We will in this section, first, present the model structure which is applied. Thereafter, its learning capabilities, and its similarities to artificial neural networks are explored.

NARMAX Models Based on Local ARMAX Models

For linear systems, a popular family of models is the ARM AX models. In predictor form an ARMAX model can be written

y(t + n) = 0,P(t) + e(t)

with y(t) E �m•, u(t) E �m. , e(t) E � · , and ,P(t) E \). Here y(t) is the system output at time t, n is time delay, e(t) is the equation error at time t, 0 is a parameter matrix, and ,P(t) = [I�, y(t)T . . . y(t -nyfu(t)T · · · u(t - nuf e(t - If · · · e(t - n,ff is the information vector at time t. Here In, is a ny-dimensional vector with all elements equal to I . The NARMAX (nonlinear ARMAX) (Leontaritis and Billings, 1985), (Chen and Billings, 1989) model representation can represent a large

class of dynamical systems

y(t + n) = J(.P(t)) + e(t) ( ! )

Here f : I) -+ !Rm• i s a smooth nonlinear function. The problem is to represent this function. If we assume that our process know ledge is limited , a generic nonlinear structure for f is required. Among the alternatives are polynomials (Chen and Billings, 1989) and neural net­works (Chen et al. , 1990a, 1990b). A generic representation based on local models is proposed in (Johansen and Foss, !992a, 1992c), inspired by (Jones et al. , 1991). By definition, a local model is valid only within a limited operating regime. With the local model representation we try to reduce the problem of building a global model to the problem of building a set of local models. In order to integrate the local models into a global model, we use interpolation .

Assume that we have given a set of local models f; such that

y(t + n) = f;(,P(t))

To each such local model we associate a model validity function p; <Ii -+ [O, I] which, by definition, is close to I for those operation points <P where the model f; is a good model and close to 0 elsewhere. Hav­ing knowledge of this may seem like a strong assumption, experience shows however, that the choice of p; is not critical, (Johansen and Foss, 1992c). A typical choice for p; is a Gaussian function. We now define a set of normalized interpolation Junctions w; : <Ii -+ [O, I]

p;(</i) w;(</i) = °"N-1 · ( -'- ) i..JJ=O P1 'I'

(2)

By this definition we know that for any <P E <Ii, E��1 w1(¢i) = I . If we assume that the real system is given by ( ! ) , then the following identity will hold

y(t + n) N- 1

J(.P(t)) + e(t) = L J(,P(t))w; (</i(t)) + e(t) (3) i:O

Since w; is a normalization of p;, w; ( <P) is close to I for operation points <P where f; is assumed to be the best model, and close to 0 elsewhere. Hence, we can substitute f; for f on the right-hand side of (3) without loosing too much accuracy in the model. This leads to the proposed representation

N-1 y(t + n) = L f;(!/l(t))w;(</i(t)) (4)

i:O The local models can have different structures. We will in this paper limit ourselves to local linear models. This implies that f; in ( 4) is an ARMAX model. The structure, ie. model order, of each local model may vary. In practice this may be accomplished by keeping some local model parameters fixed to 0.

The operation point <fi(t) will typically be directly related to ,P(t), since this vector contains the inputs, outputs and in some cases the equation error. In most cases there will exist a mapping ,P(t) ...... <P(t), such that the operation point at any time can be calculated as a function of the information vector. This mapping will typically be a projection onto some subspace of the information space. In some cases it is not possible to find such a direct mapping. This is the case if some estimator is used to find quantities describing the operation points. Typically process knowledge about different operating regimes or the validity of the available local models will be used to define the validity functions p;.

An important property of (4) is that if all the local models f; are lin­ear in the parameters, the nonlinear model composed by interpolating the local models will also be linear in the parameters. In the simple case when we have uncorrelated noise, the global non-linear model can

50

be written in the linear regression forrµ y(t + n) = ()T 1P(t), where () contains all the parameters, and 1P(t) is a regression vector. The re­gression vector will contain products of w;(</i) and !/I, and may thus be non-linear in some of the components in ¢. Standard system iden­tification algorithms may, hence, be applied (Soderstrom and Stoica, 1988). The parameter estimation is based on the conventional least squares criteria. Only local models that have a weight above some limit should be updated, if forgetting is to be reduced. Another possibility is to only update the local model that has most weight. Using a model composed of several local models, and updating only the local models discriminates information, in the sense that a local model is adjusted only according to relevant data. Hence, there will be no forgetting about the operating regimes the process is not currently operating in. Since relearning because of changing operating regimes is generally not needed using this model representation, learning is only needed to compensate for variations in process parameters and disturbances. If these vary slowly compared to the process dynamics, the learning rate may be slow.

The model ( 4) can be viewed as a series expansion of the function f. Each term in the series expansion will be orthogonal to all other terms except those which have overlapping model validity functions. Informally, if the model validity functions do not overlap too much, a local model (corresponding to a term) will be "almost orthogonal" to most other local models. This supports the inclusion of a new local model without disturbing the other local models, except in the neighborhood of the new local model. Hence, the structure of the model representation ( 4) can be changed without loosing significant information. This also implies that the model accuracy may improve by adding new "almost orthogonal" terms (Johansen and Foss, 1992b).

Artificial Neural Networks

The model structure, (4), may be cast into the topology of an artificial neural network. There are at least two possible topologies, the first is shown for a SISO-system in Figure 2. We observe the forward structure of the network. In Figure 2 there are two types of nodes, one forming linear sums that represents an ARMAX model

nodef = 8T ,P(t) and the other forms a receptive field, which is used for interpolation

nodel = w;(</i(t)) Another possible topology would consist of a single hidden layer of homogeneous nodes, where each node is more complex. The dynamic properties of the model is obtained since each node contains a dynamic model. Each of the N hidden nodes has the output

node; = 8T ,P(t)w;(</i(t)) where ()1 is the parameter vector associated with local model i. This model representation has similarities to the approach proposed in (Willis et al., 1991) . The main difference is the fact that we use localized basis functions instead of the global sigmoid basis functions.

PARALLEL DECOUPLING

We will in this section first discuss the proposed parallel control struc­ture and show that it can be used to incrementally include process knowledge into the controller. Second, the decoupler part of the con­troller will be presented.

Fig. 2: Artificial Neural Network interpretation of the local model rep­resentation. There are separate nodes for computing the local model prediction and for computing the local model weight.

Incremental Control Design

A controller with a particular structure may be transformed into other structures. Seemingly equivalent configurations may, however, have very different practical applicability. There are two main reasons for this. First, in applications non-ideal effects will always appear. In such circumstances equivalence can be difficult to obtain. Second, the parameterization of a controller or model is important from an applica­tions point of view. Different configurations may support alternative parameterizations. As mentioned earlier, our approach is to use a parallel control structure consisting of diagonal controller, and a de­coupler. The control system is shown in Figure 3. Loosely speaking, the controller is essentially a diagonal controller when the gain of the diagonal part is much larger than the gain of the decoupler.

Before we continue, let us make the following observation:

Given a process which is to be controlled, the process knowledge is often inadequate in the sense that the use of an inverse-based con­troller is not viable. As time goes by process knowledge increases due to operation experience and experimentation on the process. Hence, decoupling may be included after some time. This will improve con­trol performance (while maintaining adequate robustness) compared to diagonal control. We denote this incremental control design. The proposed control structure may be used to accomplish incremen­tal control design. Initially, the diagonal controller is active. The controller is designed on limited process knowledge. The bandwidth will therefore be low.

As process knowledge is gathered the decoupler is activated. This is not a one-step procedure since the gain and the internal structure of the decoupler need not be static. This may be illustrated by the following example:

Step response tests may have been performed in some operating regime. We may utilize this information to include decoupling in this operating area. The local model representation supports such a scheme.

There may be interaction problems related to the parallel structure. Given an initial diagonal design, the inclusion of a decoupler will in­fluence the process as seen from the SISO-controllers, ie. the trans­formation from UP[ to y in Figure 3. This is easily seen in the linear case. If we use transfer functions and assign the following notation

H(s) CPI(•) CvE(s)

- process transfer function - diagonal controller part - decoupler part

the transfer function from Up/ to y is given by

_!_(s) (I - H(s)CvE(•W 1 H(s) Up/ In order to minimize interaction effects, the two controller parts should be separated in some sense. We employ separation in the frequency domain. The idea is to let the diagonal controller be dominant at low frequencies, and the decoupler to be dominant at higher frequencies. Initially, when only the diagonal controller is active, the bandwidth of the control system will be low. Activating the decoupler will increase the bandwidth.

The decoupler should include filtering so as to decrease it gain at high frequencies. This is important to minimize the effect of noise, and from a robustness point of view.

There is an interesting relationship between the parallel decoupler and sliding mode control systems, see (Utkin, 1992) for a comprehensive treatment of such controllers. A sliding mode controller can consist of two parts, cf. Chapter 2.4 in (Utkin, 1992); one part is a decoupler and the other is a stabilizing element containing a discontinuous function as shown below.

u(t)

us(t)

UDE(t)

us(t) + UDE(t)

Ksign(e(t) + :i;-1 ]_'00 e(t)dt)

decoupler

K and T; are constant diagonal matrices.

By using Lyapunov-theory, it is possible to show that us should be the dominant controller part in situations with large uncertainties in process knowledge. A sign-function will often be undesirable as it leads to chattering effects in the control. If it is approximated by a steep linear function with saturation, us is computed by a diagonal PI-controller in the linear region, and will then be equal to Up/ in Figure 3. We are then left with a controller very similar to the parallel decoupler. Hence, this gives a rationale for our reasoning earlier where we say that the decoupler is included as process knowledge increases.

5 1

Set oint Diagonal

PI

Decoupler

Process

Fig. 3: Parallel Control Structure.

The proposed control structure is not an optimal controller since it only allows weak d�coupling effects at low frequencies since the diagonal controller is dominant there. Hence, we sacrifice performance in order to minimize interaction effects.

Decoupler

Let us recall that the process is given by ( l ) . Solving this equation with respect to u(t) gives

u(t) tPinv(!)

r 1 (.P;,.. (1)) (5) [yT(t + n) YT(t) . . · YT(t - ny) uT(t - 1 ) · · · uT(t - nu) eT(t) - · · eT(t - n,)f

where 1- 1 has the following property

y(t + n) /(y(t), · · · , y(t - ny), r1 (,P;,.. (t)), u(t - ! ) , · · · , u(t - nu), e(t - !), · · · , e(t - n,)) + e(t)

A decoupler is, in essence, a function which computes a control input to satisfy certain future values of the controllers variables. The decoupler can be found in at least two ways. A model for (I) can be identified and the equation can thereafter be solved with respect to u(t). This is a straightforward task if f is linear in u(t). With local linear models, a sufficient condition for this is that ef>(t) does not depend on u(t). A more direct approach is to identify the inverse model (5), which can be used directly as a decoupler.

In general, there are several problems connected to inverse-based con­trol.

1. If the process has a time delay of n, a necessary condition for r1 to exist is that tPinv(!) contains y(t + n). This necessitates information on the future value of y. A natural choice for this is the future reference value.

2. The noise terms e(t) · · · e(t - n,) are not known. These may be substituted by the prediction errors.

3. Finding the inverse of the process may be an ill-conditioned prob­lem. This situation will arise if the influence of u(t) on y(t + n) in ( ! ) is small. This problem can be dealt with by redefining l/J;..v , for instance by extending the prediction horizon n. Ill-conditioning is a more serious problem if it is related to cou­plings in the process. This may be explained by viewing the linear case.

Assume that we have a process transfer function H ( s) with a high condition number and that this high condition number is caused by process interactions. A decoupler will be of the form

where H dfog(s) is a diagonal matrix.

We have to invert H(s). In the ill-conditioned case small changes in H(s) may change C(s) dramatically. Hence, the controller depends on an accurate process description. In this case it is advantageous to limit the ill-conditionedness of the controller. This may be accomplished by the parallel structure. At high fre­quencies where the decoupler is dominant, the PI-controller adds to the diagonal controller elements. This will decrease the ill­conditionedness of the controller.

To summarize, the parallel structure is beneficial since it is easy to limit the decoupling effect of the control, and since it supports the notion of incremental control design.

In this work we will integrate local linear decouplers based on the direct inverse model formulation (5) using the interpolation algorithm presented earlier.

INVERSE-BASED NONLINEAR PROCESS CONTROL

We will in the following show how the local model representation and the parallel decoupler may be integrated, and present in detail the controller which we will apply. The control system consists of two main parts; the controller and the identification part.

Controller

The parallel controller consists of two parts; the diagonal Pl-controller, and a decoupler. The control signal is

u(t) UPJ(t) + <WDE(t)

where 0 $ a $ I is a "de-tuning" parameter that may be time-varying. In particular we let a = 0 until the parameter estimator has found rea­sonable parameter values for the decoupler. After the startup phase, we let u(t) = UPJ(t) + "DE(t) . A diagonal PI-controller is realized using conventional discretization and anti-windup on the integrators. We observe that a reference model may be used to generate Yd by LP-filtering the setpoint y*. We will in the following assume that the system is deterministic. In accordance with the discussion above, a decoupling control can then be computed as

llDE(t) = r1 (yd(t+11), y(t), . . . , y(t- 11,), UDE(t- l), · · · , UDE(t-nu)) (6)

which is realizable when the future reference value Yd(t+n) is available.

The decoupler is based on local linear representations and an interpo­lation algorithm as discussed earlier. Each local decoupler may have different structure.

¢DE(t)

N - 1 L ern • . .PvE(t)w;(,P(t)) i=O [1�. YI(t + 11) yT(t) . . · YT(t - 11,) "bE(t - 1) · · · UbE(t - nulf

(7)

The interpolation implies that the decoupler is nonlinear even if the parameters 0inv, are constant.

Identification

The aim of the identification is to identify an inverse process model

UDE(t - 11) r1 (y(t), y(t - nJ, . . . , y(t - 11 - 11,J , UDE(t - 11 - 1) , · · · , UDE(t - 11 - nu))

An RLS-method based on the following criteria is used

1 T J = 2 L IJu(t - 11) - ilvE(t - n)ll� t:n Observe that (8) can be rewritten as

T J � L JluPI(t - 11) + (uvE(t - 11) - ilvE(t - n))il�

t=n

(8)

This means that both the "prediction" error of the decoupler and the PI-control action will be minimized. An alternative would be

- 1 T 2 J = 2 L Jl(uvE(t - 11) - ilvE(t - n))llA t:n

(9) where the PI-action is not directly minimized. If we use (9) we are essentially identifying the process including Pl control. This is sensible as the decoupler is optimized in relation to the chosen PI parameters. The approach is however, not viable initially since "DE = 0. Hence the control input u must be used. We have employed this strategy also after activating the decoupler. There are two reasons for this. First, the difference using the two indices was observed to be small. Second, the identification strategy is simplified by keeping to one control input.

The process is identified in closed loop. It is well known that the use of a low order linear controller can result in the identification of the controller instead of the inverse process, see (Gustavsson et al., 1977). Our controller is generally non-linear. The closed loop identification problem is therefore only of interest in the interval when only the diagonal Pl-controller is active.

52

Each of the local models are essentially identified one at the time. This limits the closed loop identification problem as it is the relative complexity of the process vs. the controller which is important. It is also important to identify the process when it is upset by external disturbances as this eliminates the closed loop identification problem.

On-line parameter estimation may provide integral action in the de­coupler. This can give problems as the decoupler operates in parallel with the PI controller. There are three ways of handling this

I . We may identify a high-frequency model as a basis for the decou­pling, ie. filter away bias terms. In this way the decoupler will not include integral action.

2. We may perform on-line parameter estimation using a recursive algorithm without forgetting.

3. The on-line estimator may be extremely slow, hence only adjust for long term changes.

If it is important to adjust to long term process changes, only alterna­tives I and 3 are viable. In the simulations we will use 3, and ensure that the parameter estimator is much slower than the PI-controller. To reduce forgetting, only the parameters of the model with weight w;(,P(t)) � 0.6 is adjusted at a given time instant. The de-tuned RLS­algorithm uses a conventional constant forgetting factor.

SIMULATION EXAMPLE - A CHEMICAL REACTOR PROBLEM

Here we present a semi-realistic simulation example, where the pro­posed control structure is applied to an exothermic CSTR where a !st order chemical reaction A -+ B takes place. The system is described by the following mass- and energy-balances

vicA dt d pcP Vdi_T

where the symbols are described in table I. In addition there is a dead-time r due to stirring dynamics, and 1st order dynamics in the heat exchanger providing Q and in the concentration sensor

Symbol Value

T 350-400 11 310 TR 350 CA ca..

CA ca.. 1 C,A.j ca.. 10 EA 70000 R 8.314 ko 0.042 p 1.0 Cp 4.0 v 10.0 C.Hr -90000 q; ca.. 50-500 90 ca.. 50-500 Q ca.. -6 - 3 Q ca.. -6 - 3 T 1.0 T<I 2.0 Tc,. 2.0 Tm 8.0 To 360-385 T. 360-385 CAo CA4 TA

Table 1: Symbols. Unit Decription

K Reactor temperature K Inlet tempera.ture K Reference temperature kmol/m3 Concentration of A in reactor kmol/m3 Measured concentra.tion kmol/m3 Inlet concentra.tion of A kJ/kmol Activa.tion energy kJ/(Kkmol) Gas constant 1/min Frequency factor kg/ I Ave. density in reactor

kJ / ( K kg) Ave. heat ca.pa.city in reactor

m3 Reactor volume

k J / kmol Reaction energy I/min Inlet flow I/min Outlet flow MW External power from

heat exchanger

MW Power setpoint to heat exchanger

min Dead time min

min

min

K K kmol/m3 kmol/m3 kmol/l

Time-constant in

heat exchanger Time-constant in temperatur sensor Time-constant in Reference Model Temperature setpoint

Reference Model Output Concentration setpoint Reference Model Output

Reaction rate

UPI

Disturbances

11* Decoupler

11 8

Fig. 4: Direct Multivariable Adaptive Control System for simulation example.

The control system consists of a diagonal PI-controller in parallel with an adaptive decoupler based on the proposed nonlinear model repre­sentation, see figure 4. The control objective is to keep CA constant, while T may be varied between different setpoints to control the pro­duction rate. The temperature setpoint typically varies between 360 and 385 K. We assume that we know T and CA , and can use Q and q; as control variables. The control vector is defined as u = [q; Qf and the output vector as y = [cA Tf. We use a diagonal PI-controller with gain Kp =

diag(6 . 10-s 1 .5 · 105) and integral time T; = diag(1 6 min 16 min). We further assume an ideal level controller, such that q. = q;, making V constant.

The structure of the decoupler is given by

liDE(t) = r1(UDE(t - ! ) ,yd(t + l) , y(t)) ( 1 0)

Motivated by the dead-time, sensor, actuator and process dynamics, a "prediction horizon" -r, = 3.5 min is chosen. This correspond to one time-step in ( 10). The sampling interval is 0.5 min for the decoupler while the Pl-controller is run continuously. Most of the nonlinearities in this system is due to temperature variations. Hence, we apply the simplest possible choice for the operation point, namely ef>(t) = T(t). The unknown function 1-1 is approximated by two local ARMAX models, one for each of the operation points ef>o = 360 K and 4>1 =

380 K. Gaussians with q = 10 K is used as model validity functions

Figures 5 show a simulation sequence when the temperature setpoint changes, and disturbances in inlet concentration CA; are simulated. Simulations using only the well-tuned PI-controller is shown for com­parison. Initially the curves are the same, since only the Pl-part of the parallel controller is active. When the decoupler is activated after 3.5 h, there is a small transient until almost perfect reference tracking in both T and CA is achieved. The activation of the decoupler may introduce unnecessary disruption in the control input. It is therefore important to include bumpless transfer in the control algorithm. This is done by adjusting the integral term in the diagonal controller when the decoupler is activated.

We see that the disturbances in CA due to process couplings caused by the temperature setpoint change is almost removed using the decou­pler. The variations in the control signal is smaller using the parallel controller that with only PI control. We also observe that after the parameter estimates have converged, the PI-action is close to zero, as would be expected from the index (8). However, when disturbances occur, the Pl-controller compensates. This is because the estimator is slow. It only responds to long-term variations in the process.

CONCLUSIONS

A multivariable adaptive controller has been proposed. It supports the notion of incremental control design. It is shown how the local model concept is an efficient way of building a non-linear model, and how it, together with a parallel control structure, supports the successive inclusion of process knowledge. This is highlighted by the simulation study.

53

ACKNOWLEDGEMENTS

This work was partly supported by the Royal Norwegian Council for Scientific and Industrial Research (NTNF) under doctoral scholarship grant no. ST. 10 . 12.221718. We wish to thank Ole Bj!llm Gj!lls!Eter for comments, and Knut Egil Pedersen, who performed a preliminary simulation study on this control structure in his Diploma-thesis.

REFERENCES

Byrnes and Isidori ( 1984). A Frequency Domain Philosophy for Nonlinear Systems with stabilization and Adaptive Control. IEEE Con/. on Decision and Control, Las Vegas pp. 1 569-73

Chen S. and Billings S. A. ( 1 989). Representation of Non-linear Sys­tems: The NARMAX Model.. Int. J. Control, 49, pp. 1013-1032

Chen S. et al. ( !990a). Practical Identification of NARMAX Models using Radial Basis Functions. Int. J. Control, 52, pp. 1327-1350

Chen S. et al. ( 1990b ) . Non-linear System Identification using Neural Networks. Int. J. Control, 5J, pp. 1 191-1214

Gj!lls!Eter 0. B. and Foss B. A. ( 1 992). Parallel Decoupling of a High Purity Distillation Column. Submitted to IEEE Con/. on Decision and Control, Tucson

Gustavsson et al. ( 1 977). Identification of processes in closed loop -ldentifiablity and Accuracy Aspects. Automatica, JS, pp. 59-75

Johansen T. A. and Foss B. A. ( 1992a). Nonlinear Local Model Repre­sentation for Adaptive Systems. Proc. Singapore Int. Conference on Intelligent Control and Instrumentation, 2, pp. 677-682

Johansen T. A. and Foss B. A. ( !992b). Representing and Leam­ing Unmodeled Dynamics with Neural Network Memories. Proc. A CC, Chicago, II.

Johansen T. A. and Foss B. A. ( 1992c). A NARMAX Model Repre­sentation for Adaptive Control based on Local Models. Modeling, Identification, and Control, JS, pp 25-39

Jones R. D. et al. ( 1991). Nonlinear Adaptive Networks: A little Theory, A few Applications, Tech Rep. 91-273, Los Alamos Nat. Lab. , New Mexico.

Leontaritis I. J. and Billings S. A. ( 1985). Input-output parametric models for Non-linear System. Int. J. Control, 4J, pp. 303-344

Skogestad S. et al. ( 1 988). Robust Control of Ill-Conditioned Plants: High Purity Distillation. IEEE Trans. Automatic Control, SS, pp. 1 092-1 105

Soderstrom T. and Stoica P. ( 1 988). System Identification. Prentice Hall.

Utkin V. I. ( 1992). Sliding Modes in Control and Optimization. Springer Verlag.

Wei et al. ( 1 989). Enhanced Multiloop Feedback Control. Int. J. Control, 49, pp. 1 1 95-1216

Willis et al. ( 1991). Artificial Neural Networks in Process Engineering. Proc. IEE, JSB, pp. 256-266

4-C>C>

3S>C>

3.SC>

3 :<C>

:2.C>C>C> 1 tSC>C> 1 60<:> 1 4C>C> 1 :2.C>C>

SC>C> <SC>C> 4C>C> 2-C>C>

1 ::2.C>C>C>

1 C>C>C>C>

SC>C>C>

..SC>C>C>

4C>C>C>

:::Z.C>C>C>

C>C>

2

\ \

--- T [K] with PI + adaptive decoupler T [K] with PI only Ta [K]

CA [kmolfm3] with PI + adaptive decoupler Ca [kmolfm3] with PI only cA, [kmolfm3]

:2.C>

CA; [kmolfm3] with PI + adaptive decoupler :2.C>

,

Q [MW] with PI + adaptive decoupler Q [MW] with PI only

.. - - - - - - - _ _ _,- - - - - - - - -"\... .. _ _ - -

--- QDE [MW] with PI + adaptive decoupler - - - - - - Qp1 [MW] with PI + adaptive decoupler

q; [Ifs] with PI + adaptive decoupler q; [Ifs] with PI only

2-C>

.. - - - - - - - - - - __ ... _ _ - -\.. .. -

- - - - - - - - ... - - - - -- - - - - -.. _ _ _ - --- - - - - - - - _ _ / ....... -- - - --

........... .. ... _ _

1 C>

Figure 5 : Simulation sequence.

54

q;0,. [Ifs] with PI + adaptive decoupler q;p1 [Ifs] with PI + adaptive decoupler

:2.C> time [h]

Copyrigbt @ IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

THE INFLUENCE OF TRAINING DAT A SELECTION ON PERFORMANCE OF NEURAL NETWORKS FOR CONTROL

OF NON-LINEAR SYSTEMS*

A.B. Bendtsent and Niels Jensen

The PDDC Group, .DeparttMnt of Chemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark

Abstract

This work is part of research aimed at us­ing artificial neural network models for real time process control over wide operating ranges where linear models either fail or must be adapted on-line. This paper discusses the influence on con­trol performance of different methods for selecting and randomization/ normalization of data used in estimating the weights in artificial neural network. The non-linear model system used comprises level control of a tank with non-vertical walls in which the level is controlled by manipulating out­flow and disturbances occures in the inflow. The simulation results show, that the con­trol performance of the network is consid­erably influenced by the way in which the data for weight estimation are generated. A small randomized data set gives perfor­mance comparable to a data set sequential in time, which is many times larger. The performance of the trained artificial neural network in controllin.g the level of the tank is also compared with that of an IMC-PID controller. Results clearly demonstrate the advantage of the artificial neural network over the IMC-PID tuned at a nominal operating. The artificial neu­ral network gives better performance over a wide operating range, because it accounts for the non-linear nature of the process.

1 Introduction

In advanced process control the control either di­rectly uses a model of the process to be con­trolled as for example model based predictive con­trol (MBPC) (Richalet and Tzafestas (1990)) or the design of the controller is based on a model of the process as with the frequency domain design methods (Maciejowski ( 1989)). Traditionally the model has either been differential equations derived

• Presented at 1992 IFAC/IFIP/IMACS Interna-tional Symposiwn on Artificial Intelligence in Real-Time Control, Delft, the Netherlands, June 16-18, 1992

t Present address: Centre for Food Research, Royal Vet­erinary and Agricultural University, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Denmark

55

from fundamental physical, chemical and thermo­dynamic principles or input-output models identi­fied from experimental data. In most cases the con­trol or the design of it is based on a linearized model of the form

dx dt

y

Ax + Bu + Dd

Cx

( 1 )

(2)

where x, u, d and y are state, input, disturbance and output vectors respectively, and A, B , D and C are constant matrices of appropriate dimensions. Models of this form are valid for a given operating point, but fail to account for non-linearities , such as reaction kinetics over changing operating condi­tions . There are controller design techniques, such as LTR (Niemann et al ( 1 990a and 1990b)) and H00-control (The Institute of Measurement and Control ( 1991) ) , that attempt to incorporate the uncertain­ties introduced by linearization and changing oper­ating conditions into the design of the controller.

An alternative approach would be to develop a non-linear model of the process covering all rele­vant operating regions and using this, either implic­itly or explicitly, to control the process. This paper discuss the use of artificial neural networks to con­trol non-linear systems over wide operating ranges. The quality of data needed to estimate the weights in the artificial neural network controller (NNC) is specifically adressed. This is done by a series of sim­ulations on a specific non-linear system. The per­formance of the artificial neural network controller is compared to that of an IMC-PID controller and the robustness of each is discussed.

2 NNC in Control of Non­

linear Systems

In this work the control of the level in a tank with slanted wall is used as a sample non-linear system. The manipulated variable is the output flow and the disturbance is the inflow. The tank is a regular pyramid which is standing upside down. A sketch of the system is shown in figure 1 . The volume of

Figure 1 : Diagram of tank with a neural network controller.

the tank is given by

v

where h is the height of the level in the tank and 4> is the angle of the tank wall with the vertical. The nominal volume in the tank is chosen to be 5 m3 , and the mean value of the steady state in and outflows are 1 m3 /hr. The angle of the tank walls with the vertical were chosen to be 30° . The tank model, representing the physical system, was programmed in C and interfaced to the commercial neural networks software " NeuralWorks Explorer" .

The neural network was initially configured with 4 linear input neurons , 18 hidden sigmoid neurons and 1 sigmoid output neuron. The inputs to the neural network were the present tank level , the tank level one time step into the past, the current outflow and the level setpoint. The output was the desired outflow. Experiments with the number of hidden neurons showed, that the number of hidden neurons could be reduced to 5 without loss of performance. Reduction af the neural network below 5 hidden neurons gave a significant loss of performance.

The performance of the NNC's could be measured by (Jensen ( 1990)) :

ds = S/eve1/m1evel Sinflow/minflow (4)

where ds is a measure of disturbance suppression, Si's are standard deviations and ffii 's are mean val­ues. However, in the statistical treatment, the sim­pler approach of using the RMS error between de­sired and actual level is used.

56

The weights of NNC's were estimated using six different approaches for generating the data: con­tinuous presentation, selective presentation with and without permutation, sequence presentation with and without permutation and short sequence presentation . In all cases more than one simulation was performed with different weight initialization to allow statistical treatment of the performance results. The performance of all NNC's were tested using the input signals and setpoint changes shown in figure 2 for continuous presentation.

2.1 Continuous Presentation

The weights of the NNC were first estimated by continuously feeding data from a simulation to the network. In the simulation the inflow was varied as a random number in the interval [0.3; 1 .7] passed through a first order filter with a time constant of 0.9 hours. The sample time, A.t = 1 hour, was se­lected to be large compared to the nominal time constant of the tank. This approach can be com­pared to implicit adaptive control with the adapta­tion on all the time.

The NNC's ability to control the level was tested using a series of four input sequences, each 500 sam­ples long. The first sequence was inflow variations in the interval [0.3; 1 . 7] m3 /hr passed through a first order filter with a time constant of 0.6 hours. The second sequence was step changes in inflow occur­ring with a probability of 2% and having a time con­stant of0 .4 hours. The third sequence combined the noise and step changes in inflow. Finally the fourth sequence consisted of noisy inflows, as in the first sequence, combined with changes in level setpoint generated as the changes in mean inflow in the sec­ond and third series . All networks were tested for control performance with these four test sequences.

The test results for the neural network controller trained by continuous simulation and presentation of training data resulted in overtraining around the nominal inflow and hence gave poor control if the mean inflow deviated from the nominal mean value as shown in figure 2. Suplementing the training us­ing other mean inflows did not improve the perfor­mance . This is because the weights of the NNC's after an initial period are adjusted to model the random noise in the estimation data. An adaptive controller behaves likewise during periods when the process is not sufficiently excited .

2.2 Selective Presentation

In order to avoid adjusting the NNC weights, based on random noise in the estimation data, a selec­tive data set representing 500 training points, cho­sen from a 25000 time step continuous simulation, was constructed. The construction method was a combination of stochastic selection, to ensure some connected samples and systematic control of group

... Level

0 u u u u en-:.. u u ,. 1�

Figure 2: Test of neural network trained by contin­uous simulation. The top curves are the level and the level set point, and the lower one the inflow. The different types of inputs are described in the text . The numbers under the inputs indicates the distur­bance suppression.

size, in order to obtain a more square distribution of inflows in selected data set . The selected estimation data were then presented to the neural network af­ter mixing. The NNC estimated in this fashion gave considerably better control of level for changes in mean inflow. This result was obtained whether the data points were mixed or not (i.e. presented in the sequence generated by the simulation) .

A comparison of weights in the NNC's, as (jS­timated by continuous presentation ( CP) and by selective presentation (SP), showed the latter had a more. even weight distribution. Continuous pre­sentation gives low weight on old outflow and also partly on old levels.

It is thus the distribution of the estimation data and not their sequence of presentation which is im­portant for the control performance of the NNC.

2.3 Sequence Presentation

A sequence of 500 data points from the continuous simulation was created and used to estimate the weights of an NNC, both in the sequence generated and perturbed. The non-perturbed presentation gave a performance similar to continuous presen­tation, but the perturbed presentation gave an im­provement in performance similar to the improve­ment obtained for selective presenation.

2.4 Short Sequence Presentation

In chemical systems a large amount of estimation data may not be available . Therefore was a short data sequence of only 50 data point generated, per­turbed and presented to the neural network many times. This gave the same control performance as the NNC estimated by continuous presentation, i .e .

57

NNC performance on test sequences 0.25

UCSP SPCSP

0.2 CP PSP USP PCSP

0. 1 5

0 . 1

0.05

0

Figure 3: RMS deviation between level and setpoint for all simulations and all types of inputs. Each group of four vertical bars represents test of a par­ticular NNC. Within each group each bar represents one of the four test sequences .

systematic deviation from the setpoint if the aver­age inflow is different from the nominal.

2 . 5 Statistical Evaluation o f Simula­tion Results

From the plots, of test result against time, is it diffi­cult to ascertain which method of data presentation is best. The RMS deviation between actual and de­sired level for all simulations and all types of inputs are shown in figure 3. This figure gives the gen­eral idea that, except for the unperturbed presen­tation of a sequence of data, all training methods are about equal . In order to discriminate a vari­ance analysis (Hicks ( 1982)) is performed on the test results. Table 1 shows the result of an analysis of variance (AN OVA) for the four different test se­quences and 4 different training methods: continu­ous presentation, perturbed selective presentation, unperturbed selective presentation and perturbed sequence presentation. This shows the control per­formance, as measured by the RMS deviation from setpoint, is significantly different for the four esti­mation approaches.

Since the unperturbed sequence presentation had too large an internal variance, an ANOVA would not be meaningful. Instead, a Wilcoxon test (Con­radsen ( 1984)) , showed that there was no significant difference in control performance between the neu­ral network controllers, trained by continuous pre­sentation and by presentation of an unperturbed se­quence. It did, however, show that the neural net-

Test Mean Std.Dev. F F-ratio N 0 . 1 187 0.0058 0 .0004 15 .70 s 0.0630 0.0296 0.0000 252.79 N+S 0 .0782 0.0265 0.0000 97.59 N+SP 0. 1697 0.0073 0 .0276 4.658

Table 1: Analysis of variance for the four different training methods shows the control performance is significantly different for the five different estima­tion approaches for all four test sequences (FjF­ratio) . N=Filtered noise, S=Steps, SP=Setpoint on inflow and desired level respectively.

# Cases Mean Std.Dev. Rank-Sum 3 0.0652 0.0064 6.000 4 0.0986 0.0189 22.000

Expected rank-sum 12.000 Actual rank-sum 6.000 Std .Dev .rank-sum 2.828

Table 2: Wilcoxon test for NNC's estimated from perturbed and unperturbed data sequences. This gives an absolute z-value of 2 . 1213, which is signifi­cantly greater than 0.0339. Hence the mean values are different.

work controller, trained by a perturbed sequence, was significantly better than that trained by an un­perturbed sequence. The data for comparing the RMS mean values for the NNC's as estimated either by the presentation of a sequence of data points or by a perturbed sequence of data points , are shown in table 2 for step changes in inflow. The NNC estimated from the perturbed data is significantly better.

A Newman-Keuls test (Hicks ( 1982)) is used to find the neural network controller with the best per­formance on the test sequences. The test is per­formed for each test sequence separately. For fil­tered noise on the inflow there is no difference be­tween the NNC, which is estimated from perturbed selected data, and that estimated from unperturbed selected data. The latter cannot be destinguished from the use of continuous data. The data for com­bined noise and step changes are shown in table 3.

These tests show, that for the three first test se­quences, the control performance of the NNC as es­timated by continuous estimation, was significantly worse than the others. The difference between per­formance of the NNC based on a perturbed selected presentation, and that based on unperturbed se­lected presentation is insignificant for all test se­quences. The selected presentation of data gives sig­nificantly better performance for the test sequences involving steps, with and without noise .

The Wilcoxon tests and the Newman-Keuls test

58

Mean Std. Distance to Least Signif. Higher Mean Distance

6 .07 0.27 0 .1 0 .9 6 . 16 0.27 1 .6 1 .6 1 .0 1 .2 7.71 0 .32 4.8 6.3 6.4 1 .0 1 .2 1 .4 12.46 0 .32

Table 3: The Newman-Keuls test for connected mean values based on tests of NNC's with com­bined noise and step changes in inflow. The rows are NNC estimated from perturbed selected data, un­perturbed selected data, perturbed sequence data and continuous data. Only the first two rows can­not be distinguished. NOTE: All numbers in the table have been multiplied by 100 .

leads to the following prioritisation , of the quality of the estimation data, based on the observed control performance on the test sequences:

1. off-line estimation based on perturbed or un­perturbed selected data with a square distri­bution.

2. off-line estimation based on perturbed sequen­tial data with a normal distribution.

3. off-line estimation based on unperturbed se­quential data with a normal distribution.

4. recursive estimation based on sequential data with a normal distribution.

In terms of model based and/or adaptive control this means that off-line estimation of a model, based on data covering the whole operating region equally, is best. This is followed by the off-line estimation based on data from a single operating point. Re­cursive estimation of a model in a single operating point gives the worst performance over a wide op­erating area.

3 NNC in Control of Systems

with Time Delays

In many industrial processes quality control is based on a laboratory analysis of a process sample. The analysis result is available for control with a long but approximately known delay, e .g.

delay � � * nominal time constant ± 30% (5)

Input to the neural network now includes informa­tion about the delay of the two level measurements in our model system. The weight estimation algo­rithm did not converge for random variations in in­flow . Hence the noise on the inflow was reduced and the mean value systematically changed from 0.6 to

... • Level

u u u u

1• 1• 1.4 I.I

02 o•

0 100 aao 400

... Level

...

Figure 4: Performance of NNC on system with de­lays at operating points with time constants 20% and 120% of design conditions.

1 .4 m3/hr, and convergence was achieved. The con­trol performance was, as expected, worse than for the system without delay. The performance of the NNC at levels different from the design conditions are illustrated in figure 4. The NNC is robust to­wards known variations in time delays and towards very large changes in system time constant .

4 Compartive Performance of

IMC-PID Controller

Robust controller designs based on the internal model principle have become increasingly popular in industrial applications . Here an IMC-PID con­troller is design for the nominal operating point based on the following linear transfer function for the system

H(s) 1 e-9• e-9•

U(s) = G(s) = - 3</>h2 -s- = I<p -s- (5)

The PID-controller parameters are given by

4 (7)

L.-l u 3

H u ... 22

2 1• 1• IA 12

I Flow u u

0.4 02

0

Figure 5: Performance of IMC-PID on system with delays at operating points with time constants 20% and 120% of design conditions.

(8)

(9)

The tuning parameter A was selected to be 2 based on a trial and error approach, since lower values gave unstable control and higher values sluggish control. The performance is better than the NNC for step changes in inflow and for step changes com­bined with noise , but significantly worse for random noise on the inflow or setpoint changes with ran­dom noise on the inflow. The performance of the IMC-PID controller at level setpoints different from the design conditions are shown in figure 5. For a reduction in level setpoint form 3m to 2m the IMC­.PID controller becomes unstable, while an increase in level setpoint, as expected, represent no problem. If the IMC-PID controller design is based on the op­erating point with the smallest time constant , the system remains stable , but the control is worse than the NNC.

59

5 Conclusions

It has been demonstrated , that NNC can be de­signed to control non-linear systems. This can be done using sample times, that are long, compared with the system time constant . For best control performance the NNC weights should be based on equal excitation of the system in the operating re­gion of interest .

The NNC can also be used to control systems with long, but known and uncertain time delays. The NNC gives better control performance over a wide operating region than a robust controller, such as an IMC-PID controller. This is attributed to fact, that the neural network contains a better non­linear model of the system, whereas the internal model represents a linearization in one operating point.

References

[1] Bendtsen, A.B. ( 1 990) : " Neurale Netvrerk i Regulerings¢jemed" (in Danish) , M.Eng. The­sis , Dept. of Chemical Engineering, Technical University of Denmark, Lyngby, Denmark.

[2] Conradsen, K. ( 1 984): "En introduktion ti! statistik" , Volume lB, IMSOR, Technical Uni­versity of Denmark , Lyngby, Denmark.

[3] Hicks , C.R. ( 1982) : " Fundamental concepts in the design of experiments" , 3. Edition, Holt, Rinehart and Winston Inc.

[4] Jensen, N. ( 1 990) : "SPC - Does it have a func­tion in control system design and monitoring for continuous processes?" , Preprints, Nordic CACE Symposium, Lyngby, Denmark, Novem­ber 15-16 .

[5] Maciejowski, J .M. ( 1989): "Multivariable Feed­back Design" , Addison-Wesley Publishing Com­pany, Wokingham, England.

[6] Niemann, H .H . ; S¢gaard-Andersen, P. ; Stous­trup, J . ( 1990a) : " Loop transfer recovery: anal­ysis and design for general observer architec­tures" , Report No. 1990-02, Mathematical Insti­tute, Technical University of Denmark, Lyngby, Denmark.

[7] Niemann, H .H . ; So gaard-Andersen, P.; Stous­trup, J . ( 1990b) : " H00 optimization of the re­covery matrix using the Q observer structure" , Report No. 1990-27, Mathematical Institute , Technical University of Denmark, Lyngby, Den­mark.

[8] Richalet, J . ; Tzafestas, S . ( 1990) : "Computer Integrated Design of Controlled Industrial Sys­tems" , Proceedings of the CIM-Europe Work­shop, Paris, France, 26.-27. April.

60

[9] The Institute of Measurement and Control ( 1991) : " Robust Control System Design using H00 and Related Methods" , Preprints of Work­shop at the University of Cambridge, 21 .-22. March.

Copyright @ IF AC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

PROPERTIES OF THE NEURAL NETWORK INTERNAL MODEL CONTROLLER

H. Kolvlsto, V. Ruoppila and H.N. Kolvo

Tampere University of Technology, Department of Electrical Engineering, P.O. Box 692, SF-33101 Tampere, Finland

Abstract. Nonlinear Internal Model Controller (IMC), realized with a multilayer perceptron neural

network, is studied in this paper. The neural networks for the process model and the resulting controller

are identified using the Recursive Prediction Error (RPE) method with the applied gradient calculation

procedure. Novel stability analysis and stability projection methods are also introduced. Both simula­

tion and laboratory processes are used in testing the control performance. Results indicate that the IMC

control structure provides robust performance and is clearly a good alternative for controlling nonlin­

ear plants. The real-time experiment addresses the very important question of implementing and gain­

ing practical experience with neural network controllers.

Keywords. Neural nets; nonlinear control systems; identification; control applications.

INTRODUCTION

Robust control of nonlinear systems is currently one of the

most active research areas in the control literature. There is

already strong evidence that neural network controllers

have many excellent properties required in practice, e.g.

Narendra and Parthasarathy (1990), Koivisto, Kimpimiiki

and Koivo (1991) and Psichogios and Ungar (1991) . What

has been especially lacking are use of efficient identifica­

tion methods and their analysis, and practical results (not

only simulation studies). This paper addresses both of these

issues in the framework of a neural network internal model

controller.

Chen, Billings and Grant (1990) applied well known recur­

sive Gauss-Newton algorithm for the identification of neu­

ral network based predictors. Their identification method is extended in this paper to handle the more general form of a

predictor. Methods for stability analysis and projection into

the stable region is discussed for the first time.

The Internal Model Control (IMC) principle is now well

known, see Morari and Zafuiou (1989). Economou and

Morari (1986) extended the IMC strategy to nonlinear sys­

tems. Hunt and Sbarbaro (199 1 ) have demonstrated that

neural networks can be applied straightforwardly in the

IMC framework.

The method used in this paper is to design nonlinear con­

troller, which minimizes the selected cost function. After

the design procedure the resulting controller is used in the

conventional IMC architecture. The stability analysis of the

control system is also discussed. Both simulation studies

and real-time experiments with the laboratory scaled heat-

61

ing process are used i n testing the control performance.

This paper gives also indication of practical implementa­

tion of neural networks in the real-time environment.

NEURAL NETWORK AS A PREDICTOR

Multilayer perceptron network (MLP) is the most widely

studied network architecture today. Multilayer perceptron

network represents a special form of parametric function

that performs a nonlinear mapping from an input space to

an output space (Rumelhart, Hinton and Williams, 1986).

Neural networks have been widely used in time series mod­

els and controllers. The neural network as a d-step ahead

predictor of the output y ( t + d) can be presented as a func­

tion

y ( t + d) = /( cp (t) , 0) (I) where the parameter vector 0 denotes the weights of the

network and cp (t) is the data vector at time t containing

past measurements y, past predictions y and past inputs u . The actual contents of the data vector cp will depend o n the

selected form of the predictor. Two common model struc­

tures are presented in Fig. 1 . Both the Nonlinear AutoRe­gressive with eXogenous inputs (NARX) model and the

Nonlinear Output Error (NOE) model are nonlinear exten-

uW :I 1w� y(t) : M : M u(!)�y(t+d) y(t+dll)

Fig. 1 NARX (on the left) and NOE predictors.

sioris of the corresponding linear time series models. In the

linear case both ARX and NOE models are commonly used

for controller design using the certainty equivalence prin­ciple. The difference between NARX and NOE models is

conceptually much bigger than in the linear case. Only

NOE model, which represents the deterministic part of the

system, should be used in the design of IMC like determin­

istic controller, as will be done in this paper.

MODEL IDENTIFICATION

In this section the Recursive Prediction E"or (RPE) method is used for estimating the parameters of nonlinear

stochastic time series model, in the context of neural net­

works. The background of RPE algorithm is given in Ljung

and Sooerstrom (1983) and Goodwin and Sin ( 1984). The

neural network application of RPE method is presented by

Chen, Billings and Grant ( 1990), whose results will be

extended to the identification of the NOE predictors.

Consider the overall cost function

I N VN ( 0) = 2 L (y (t) - y (t, 0) ) 2

I = I (2)

where the scalar y (t, 0) is the prediction of the measure­

ment y. The cost function is minimized recursively with

respect to the parameters 0 . Only the d-step-abead NOE

predictor

y (t, 0) = /(<p (t - d) , 0) (3)

cp (t - d) = [y (t - 1 ) . . . y ( t - n0)

u (t - d) . . . u ( t - d+ l - nb) ] T (4)

is considered, because the resulting model will be used for

the control design. The gradient of the predicted output

y (t, 0) is defined as [cry (t, 0) JT 'l' (t, 0) = a0

= g (cp (t) , 0) (5)

and is an n0-dimensional vector. The combination of the

equations (3) and (5) [ y (t, 0) ] = [/(<p (t - d) , 0) ]

'I' ( t, 0) g (<p (t - d) , 0) (6)

is referred as the extended network model by Chen, Bill­

ings and Grant (1990). The stability of (6) is of vital impor­

tance in any implementation. The set of all 0 that each

produces a stable extended network model is denoted as Da . This results in the RPE algorithm [ y (t) ] = [/(<p (t - d) , � ( t- 1 ) ) ]

'l' (t) g (<p (t - d) , 0 (t - l ) ) £ ( t, 0) = y (t) - y (t)

0 (t) = S (t - 1 ) + P (t) 'I' ( t) £ (t)

P (t) = i [ P (t - 1) - P (t - l ) 'l' (t)

x l A. + 'l'T ( t) P < t- 1 ) 'I' < t) r1'l'T (t) P u - 1) 1

(7)

(8)

(9)

(10)

62

where £ ( t) is the prediction error, 0 ( t) is the estimate of

0 at time t and A. is the forgetting factor. In this paper the

numerically better DD-factorization algorithm is used

instead of equation (10) for updating the covariance matrix

P (t) (Biermann, 1977). The algorithm (7) ... (10) is the

proper RPE method only, if the dynamic nature of the gra­

dient is taken into account. Otherwise the algorithm is plain

recursive Gauss-Newton algorithm.

Due to the NOE structure, the previous estimates y and pre­

vious gradients 'I' are functions of the parameter estimate

0 ( t - 1 ) . Thus all predictions and gradients from 1 . . . t must be computed with the e ( t - 1 ) at each iteration t. By

expecting 0 ( t - 1 ) to be close to 0 ( t - 2) in the limit, a

reasonable approximation is (Goodwin and Sin, 1984)

y (t, 0 ( t - l ) ) =/(cp ( t - d) , 0 (t - 1 ) ) ( 1 1 ) A A T <p (t - d) = [ y (t - l , 0 (t - 2) ) . . . u ( t - d) . . . ] (12)

Similarly, the gradient 'I' is approximated by the equation [ df( <p ( t - d) , 0) J T "' (t) "' i.)0 • 0 = a1 _ 1

na [i.)/(<p (t - d) , 0) . ] + I a A ( t- . 0) w (t - 1)

i = 1 y 1' 9 = 01- 1

(13)

This equation has similar form as Narenda and Parthasar­

athy (1991) used with dynamic backpropagation algo­

rithm, although they did not state whether they considered

NARX or NOE model. They also motivated the algorithm

by the "sensitivity analysis networks". The derivation pre­

sented here produces closer analogy to the linear RPE­

method.

The convergence of the algorithm (7) ... ( 10) can be proved

by applying the differential equation method (Ljung and

Sooerstrom 1983). From the practical point of view, the

main assumption is that a projection is employed to keep

0 ( t) inside the stable region D0, i.e. the predictor is kept

asymptotically stable. The stability projection consists of

two separate procedures: instability detection and actual

projection method. In this paper we do not try to prove the

asymptotic stability, but to derive practical methods for

instability detection and parameter projection. It should be noted that any successful projection ensures the asymptotic

stability only with respect to the data used up to time t .

The results presented b y Zafiriou ( 1990), based on the well­

known contraction mapping principle, allows the develop­

ment of the conditions for stability. If the predictor is pre­

sented using a state space operator H (d = 1 for sim­

plicity)

x (t + I ) = H (x ( t) , u (t) , . . . , u (t + I - nb) ) ( 14)

where the state vector x = [ x1 . . . xn ] T, then the conver­

gence of the successive substitution l (t + 1 ) = H (x (t) )

implies stability of the nonlinear system. The term stability

is used in the sense of the global asymptotic stability over

the domain of H.

The operator H is a contraction in the domain DH only if (Zafiriou, 1990)

sup p (Vx H) < 1 x e DH

(15)

where p (B) is the spectral radius of B, defined as p (B) = max IA. (B) I, A. (B) being the eigenvalues of B. Instability condition is more useful: the system is unstable if p (VxH) > 1 .

In the SISO case this is equivalent to that each time step the time series model f is linearized near an operation point (not a steady state) and the stability of the resulting linear system is analysed using the characteristic equation

( -1) 1 -1 -na 0 A q = - a1q - . . . -an q = a (16)

where aj = at ( cp (t) ' 9 (t) ) 1a9 ( t- i) . The roots of A ( q-1) are exactly the same as those of the dynamic gra­dient equation (13) and the extended network model is sta­ble only if the predictor is stable.

If instability is encountered, the parameters 0 must be pro­jected into the stable region. We propose a simple projec­tion method: the characteristic polynomial A ( q -l) is multiplied with the parameter 0 < k < 1 so that

(17)

This moves all the poles of A ( q -l) towards zero. In the MLP network context, this means that all the weights leav­ing those particular input nodes are multiplied with { k, k2, . . . } . The parameter k can be solved analytically

for low order models, but it is used as a tuning parameter. More advanced methods for projection could be developed, but the calculation of the resulting network weights would be difficult

INTERNAL MODEL CONTROL

Hunt and Sbarbaro (1991) and Psichogios and Ungar ( 1991) have shown that neural networks can be applied straightforwardly to the IMC framework. Their results will be extended here.

The underlying idea of the IMC struc:ture is that a control­ler designed for a particular process model is also imple­mented so that it controls that process model - not the process itself. The mismatch between the actual process and the model is used to change the set point of that inter­nal model controller loop, which increases the robustness of the overall control structure.

In the IMC framework, the controller is normally designed to act as an inverse of the process model, resulting, in prin­ciple, in perfect control. This approach has some draw­backs, which are somewhat reduced by a more general approach presented here.

Our proposal is to derive nonlinear IMC controller without the assumption of the inverse feedforward controller. The key idea is to design the feedback controller for the model so that it minimizes the selected cost function. The general

63

structure of the controller gives more freedom to search the particular nonlinear control law.

The proposed generalized IMC method has useful features: 1) The existence assumption of the model inverse can be removed. 2) The asymptotic stability of the controller can be handled by projecting the parameters of the controller into the stable region. The second item is not limited to the proposed method. It can be applied also to the inverse model controller. However, after the possible stability pro­jection, the controller is not any more the exact inverse of the model and the perfect control can not be obtained.

The general nonlinear IMC structure is presented in Fig. 2, where the nonlinear operators denoted by P, M and C rep­resent the plant, the model of the plant and the controller, respectively. The operator F denotes the IMC filter. The primary reason for including the filter is to increase the robustness of the IMC structure by reducing the loop gain. In our proposal the IMC filter is moved to the feedback path, because the desired closed loop behaviour is taken into account during the optimization of the controller.

OPTIMAL CONTROLLER DESIGN

In this section a fixed parameter NOE model is used for controller design by minimizing the predicted d-step-ahead control error. The controller is also assumed to be NOE type, which remarkably affects the identification procedure and, as a consequence, the quality of the resulting control­ler. The controller is implemented using neural network and is of the form

u (t, 8) = a ($ (t) , 8) $ {t) = [ r (t + d) . . . r ( t + d+ l - mc)

y ( t + d - 1 ) . . . )) (t + d - ma>

u (t - 1 ) . . . u (t + 1 - mb) ]T

(18)

( 19)

where cl> is the data vector, 8 the parameter vector of the controller and r the reference input

The parameter vector of the controller is obtained by mini­mizing the cost function

1 N JN (8) = 2 L [ r (t + d) - y1(t + d, 8) ] 2

I = 1 N

+ I L .iu( t, 8)2 I = 1

u(t)

Fig. 2 Nonlinear IMC structure.

(20)

where

y1( t+ d, S) = [E (q-1) IE ( 1) J y (t + d, S) (21) du (t, S) = u (t, S) - u (t - 1 , S) (22)

The polynomial E ( q-1) specifies the desired closed loop

response (Goodwin and Sin, 1984) and y is the weighting

of the controller output.

The solving of the partial derivatives ayf(t + d) 1as and

ddu (t, S) tas, required by the RPE method, leads to the

same problem as in the model identification. Because the

model and the controller are assumed to be NOE type, the

recursive nature of the gradients is more complicated. The

notation u is used to emphasise the fact that also the previ­

ous inputs are the functions of the controller parameter esti­

mates.

Let us introduce the gradients

Using the same approach as in the model identification, the

recursive equations of the gradients can be derived. Some

notational simplifications are used compared to equations

( 1 1 ) ... (13):

cp (t) = [ r(t + d) . . . r (t + d+ l - mc) y (t + d- l ) . . . y (t + d - m0) u (t - 1 ) . . . u (t + l - mb) J T

u (t) "' a ( cp (t) , 8 ( t - 1 ) ) cp (t) = [Y ( t + d- l ) . . . Y (t + d- n0)

u (t) . . . u (t + l - nb) ] T y (t + d) =f(cp (t) )

'¥ (t) = [aa (cp (t) ) JT u as

+ � aa (cp (t) ) '¥ (t + d- i) i = 1 ay (t + d - i) Y mb

+ L aa <«l> < r> > '¥ <t - i) ; = 1 au (t - i) u

'¥ (t + d) ,,, I. df(cp (t) ) '¥ (t + d- i) y ; = 1 a9 < , + d - i) y

Introduce [[dyt<t + d) ]T '¥ (t) = as

[ JY dd:�t) J1 e (t) = [ r (t + d) -y1(t + d) -JYdu (t) JT

(24)

(25)

(26)

(27)

(28)

(29)

(30)

(31 )

(32)

(33)

64

The covariance matrix P ( t) and the parameters El are

updated after the calculation of equations (24) . . . (33) by

using equations (9) and (10) (S instead of 0). In practice

the covariance matrix is updated doing two successive

sweeps of the UD-algorithm, one for ay1( t + d) tas and

one for JY aM (t) tas (Bierman, 1977).

The convergence analysis of this RPE algorithm and the

stability analysis of the IMC structure is complicated. The

analysis consists of several parts:

• Convergence analysis of RPE algorithm.

• Asymptotic stability of the predictor (assumed).

• Asymptotic stability of the controller.

• Internal stability of the model-controller loop.

• Overall stability of the whole IMC structure.

The convergence of the RPE algorithm requires that a pro­

jection is employed to keep the controller parameters inside

the stable region D0 by projecting the extended network

model consisting of the update equations (24) ... (31 ) into

the stable region. This is a complicated task and waits for

further analysis. However, several remarks can be made

using similar framework as in the predictor identification:

1 ) The extended network model is asymptotically stable, if

the internal model controller loop (24 ) ... (27) is, because the

gradient equations have the same dynamics as the "linear­

ized" models.

2) A projection must be employed to ensure the asymptotic

stability of the controller. This is necessary, especially in

the case inverse-model controller, because the controller

tries to cancel the internal dynamics of the model. The

internal dynamics of the process model can be unstable due

to several reasons, causing the resulting controller to be

unstable or to have the ringing effect. The detection of the

possible controller instability and the projection is made in

a similar manner as in the case of the predictor.

3) The asymptotic stability of the predictor and the control­

ler does not necessarily ensure the asymptotic stability of

the internal model controller loop, although it increases the

possibility. The input-output stability of the internal loop

could be checked instead i.e. the loop gain of the model

controller loop is kept less than one by reducing the gain of

the controller, if necessary.

4) The input-output stability of the whole IMC structure

can be ensured by selecting the suitable IMC filter. One can always find a filter which reduces the loop gain of the over­

all control system, so that the input-output stability is met

(Economou and Morari, 1986).

SIMULATION EXAMPLE

Following simple example gives some insight to the prob­

lems in the design of the nonlinear IMC controller. Con­

sider the system

x1 = - co;x2 - 2conx1 sin ( 1tco;x2) + co; ( u - 0.5) Xz = Xp y = Xz + 0.5 (34)

model poles and zeros

-2

control signal

50

0 Re

100 ISO time [s]

(a)

controller pole

(d) -J.50 50 JOO 150

time [s]

Fig. 3 The analysis of the control system behaviour with­

out the stability projection.

where ron = 0.5 and 0 � u � 1 . The example system has a

linear steady state and a nonlinear dynamical behaviour.

The equation (34) is a second order system, where the

damping factor s = sin ( 1t ro�x2) i.e. the open loop poles

are on the imaginary axis if x2 = 0 and y = 0.5 . The uni­

formly distributed noise with variance 0.02 is added to the

measurement. The control interval is chosen as one second.

The NOE model structure with na = nb = 2 and d = l , and the controller structure with ma = 2 , mb = 1 and

m c = 2 is used. The model network consists of two hidden

layers with five hyperbolic tangent nodes and an one output

node with linear activation function. The controller has the

same network structure, except that the hidden layers have

ten nodes and the activation function of the output node is

hyperbolic tangent.

The cost function (20), with E(q-1 ) = l - 0.75q-1 and

y = 0 is minimized in 2000 iterations without the parame­

ter projection. The closed loop response is excellent, but

the control signal has severe oscillations. The controller is

redesigned with "( = 0.01 and the ringing effect is reduced.

The resulting control system is analysed by calculating the

poles and zeros of the "linearized" model and the controller

for a step-ramp type setpoint changes. The behaviour of the

poles and zeros of the model is displayed in Fig. 3. The

model has unstable zero dynamics in some regions, which

is somewhat cancelled by the controller and the controller

is unstable in some regions (Fig. 3).

The controller is again redesigned, now with the parameter

projection method with k = 0.9 and y = 0.01 . Because

mb = 1 , the projection can be made more precise i.e. the

only real "pole" of the controller is limited to [ -0.8, 1 ] . This not only ensures the stability, but also reduces consid­

erably the ringing effect of the control signal inside the sta­

ble region. It should be noticed that this can not be achieved

using only control cost weighting y.

The closed loop behaviour with the measurement noise is

shown in Fig. 4, which also presents the effect of the IMC

filter. When the filter F = 1 is used, the controller com­

pensates rapidly the load disturbances, which are generated

65

temperature ("C] 501 ,--�������-

40

50 1 00 control signal [%]

Fig. 5 The heating process and ·the measured open loop

response to the 30 min. ramp both up and down

(the ramp down is the mirror image w.r.t. the verti­

cal axis at 100 %).

by adding -0.1 to the measurement. The control system is

sensitive to the noise and ringing can be seen in the output

of the controller before t = 280. With the filter

F = 0.25/( 1 - 0.75q-1) the robust control with good per­

formance is achieved.

REAL-TIME EXPERIMENTS

The neural network IMC controller is tested in real-time

experiments with laboratory scaled heating process (Fig 5). The water flows into an uninsulated 0.4 litre tank through a

multidelay pipe. The water is heated by 1 .5 kW resistor ele­

ment and the temperature of the outlet flow is measured

with a Pt-100 transducer. The aim of the control is to drive

the temperature of the outlet flow to the desired value.

The process has four important characteristics for control

design: 1) The time-delay is 13 seconds and the dominating

time constant is about 100 seconds. 2) The dynamics is

very sensitive to the flow changes. 3) Noise is a function of

the temperature and the inlet flow. 4) The process has

extremely slow modes due to the lack of insulation.

setpoint --, measurement - and prediction error -

400

control signal

500 600 time [s]

00���--'10�0 �---'-2�00���30�0���

4�0-o��-s�oo��-.-J600 time [s]

Fig. 4 The behaviour of the overall control system during

load disturbances. At t = 280 the pole of the IMC

filter is changed from 0 to 0.75.

=�� W L

JO '--��---'-�-'-"""*"°"""�...,.�...._ --..-!::!:>o ..... ..-o......<J 0 B � � � = I� � I� � �

time [s]

·�� 0 B � � � = ID � I � I � � time [s]

Fig. 6 The behaviour of the control system and the predic­

tion error I y - yl + 10. The inlet flow is changed

40 % at t = 50 s and t = 380 s.

The temperature measurement and control signal (0-10 V

voltage of the thyristor) are AD/DA converted with a unit

controller which is connected to the HP 9000/425T work­

station via the RS232 bus. The software of the workstation

consists of the process simulator Simnon communicating

through tcp/ip sockets with the Planet/XNet neural network

software (Miyata, 1990). Simnon is used to store the meas­

urement data to a file and to communicate with the process.

The control signal itself is computed in XNet. Both soft­

ware packages are modified by adding communication pro­

cedures.

Exactly the same network structures are chosen both for the

model and the controller as in the simulation example. The

control interval is 3 seconds. The model structure with

n0 = nb = 2 and d = 5 , and the controller structure with

m0 = 2, mb = 1 and me = 2 is used.

The model is fitted in 2000 iterations to the input-output

data of the process. The controller is designed by minimiz­

ing the cost function (20) with E (q-1 ) = l - 0.7q-1 and

"( = 0.01 . After 2000 iterations, the parameters were fixed

and the prediction error feedback with the filter F = 1 is

added.

The behaviour of the controller in real-time experiment is

displayed in Fig. 6. At t = 50 and t = 380 the inlet flow

is changed. The response to the flow changes is sluggish.

This is due to the nearly integrating modes of the process,

which can be seen from the slow change of the prediction

error (Fig. 6) and the hysteresis-like response to the ramp

(Fig. 5). Thus the controller is not able to eliminate the

resulting control error faster. Koivisto, Kimpimiiki and

Koivo ( 1991) have demonstrated that the multistep predic­

tive controller, implemented by the neural network, has

better ability to cope with similar control situation. Overall,

the Th1C controller is robust and the desired closed loop

response is achieved over the whole domain of interest.

66

CONCLUSIONS

The design method for the neural network IMC controller

is presented in this paper. It is based on the minimization of

the selected cost function. The existence assumption of the

model inverse can be removed. Also a novel method for

ensuring the stability of the controller is given. The pro­

posed controller is successfully tested both in simulations

and in real-time experiments. The results demonstrate that

the good performance and the stability in the presence of

the model mismatch and disturbances are obtained by prop­

erly designed IMC controller.

REFERENCES

B ierrnann, G. J. ( 1977). Factorization Methods for Discrete Sequential Estimation. Academic Press, New York.

Chen, S., S. A. Billings and P. M. Grant, P. M. (1990). Non­

linear system identification using neural networks.

International Journal of Control, 51, 1 19 1-1214.

Economou, C. G. and M. Morari (1986). Internal model

control, 5. Extension to nonlinear systems. Ind. Eng. Chem. Process Des. Dev., 25, 403-41 1.

Goodwin, G. C. and K. S. Sin (1984). Adaptive filtering, prediction and control. Prentice-Hall, Inc., New Jersey.

Hunt, K. J. and D. Sbarbaro (1991). Neural networks for

nonlinear internal model control. IEE Proceedings-D, 138, 431-438.

Koivisto, H. (1990) Minimum Prediction Error Neural

Controller. 29th IEEE Conference on Decision and Control, Honolulu, Dec 1 -5, 1990.

Koivisto, H., P. Kimpimii.ki, P. and H. Koivo ( 199 1). Neu­

ral predictive control - A case study. IEEE Interna­tional symposium on Intelligent control, Arlington,

Virginia, Aug. 1 3-1 5, 1 99 1 .

Ljung, L., and S. Si:iderstri:im ( l 983). Theory and practise of recursive identification. MIT Press.

Miyata, Y. ( 1990). A user's guide to Planet version 5.6. Computer science department, University of Colorado,

Boulder, 1990.

Morari, M., Zafiriou, E. (1989). Robust Process Control. Prentice-Hall.

Narendra, K. S. and K. Parthasarathy ( 1 990). Identification

and control of dynamical systems using neural net­

works. IEEE Trans. on Neural Networks, l, 4-27'.

Narendra, K. S. and K. Parthasarathy (1991). Gradient

methods for the optimization of dynamical systems

containing neural networks. IEEE Transactions on Neural Networks, 2, 252-262.

Psichogios, D. C., and L. H. Ungar (1991). Direct and indi­

rect model based control using artificial neural net­

works. Ind. Eng. Chem. Res. , 30, 2564-2573.

Rumelhart, D. E., G. E. Hinton, and R. J. Williams (1986).

In D. E. Rumelhart and J.L. McClelland (Ed.) Parallel Distributed Processing: Explorations in the Micro­structure of Cognition Volume 1: Foundations. M.I.T.

Press, Cambridge, MA. Chap. 8, pp. 318-362.

Zafiriou, E. (1990) Robust Model Predictive Control of

Processes with Hard Constraints. Computers Chem. Engng, 14, 359-371 .

Copyright @ IF AC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

A TARGET-DIRECTED NEURALLY CONTROLLED VEHICLE

H. Herbstreith, L. Gmeiner and P. Preu6

Institulfiir Innovation und Transfer, Fachhochschule Karlsruhe Moltkestrafle 4, 7500 Karlsruhe I, Germany

Abstract An investigation of a neurally controlled vehicle in a computer-simulated parcours with dynamically changing obstacles is presented. The purpose was to judge the applicability of commercially available neural net shells in process control and automation. The chosen shell provides capabilities for associative memories by un­supervised learning, and for supervised learning by means of the back-propagation algorithm. This algorithm is furthermore enhanced by the functional link approach of Pao ( [Pao89]). The vehicle and its environment are displayed graphically. The task for the vehicle is to find its way from a user-defined starting point to an en­ding point. The neural net is responsible for control of the alternating behaviors of target-orientation and obstacle avoidance. We use ten input neurons, nine re­presenting sensors that deliver information about the distance from non-passable areas in any direction. The tenth sensor is responsible for locating the target in a compass-like way. Three output neurons determine one out of seven possible steering directions. The network was trained off-line, with patterns generated schematically by a program. The results are discussed and further refinements proposed. Keywords actuators, adaptive control, artificial intelligence, automation, computer applications, neural nets, optimal search techniques, robots, signal processing, simu­lation

INTRODUCTION AND RELATED WORK

The search for intelligent systems in process con­trol and automation, the innovative results in neurocomputing and the availability of neural net shells motivated applied researchers like us to ex­periment with the new instruments. We wan­ted to determine if those systems prove flexible and suitable enough when faced with real world problems. The selection of an appropriate case­study was influenced and finally determined by one of our industrial partners, who was involved in the ANNIE project, sponsored by the European Community.

To document the progress, a prototypical appli­cation was designed, in which a simulation of a mobile robot controlled by a neural net roamed through an arbitrary environment without colli­ding with obstacles. The results of this work are reported in [HGZ90].

In a second phase, we added an essential func­tional part, the target-bound behavior. This was achieved by changing some vehicle characteristics and enlarging the input layer of the net.

67

In some situations this approach proved insuffi­cient, and a conventional algorithmic solution to optimize the behavior has been overlaid.

Our work emphasizes on the control of autono­mous mobile systems, as in the following contri­butions:

Gla91 Guiding the arm of a robot through an obstacle space, by testing possible collisi­ons, following the forms of an obstacle if recognized, and generating random interim targets when caught in a minimum. In con­trast to our work, the complete obstacle space must be known a priori. No new obstacles can be learned, and the track is not optimal.

PT91 The robot is guided by a reference track, which attracts the vehicle to the target. Each obstacle has a potential field, which exerts a repulsive force. These two forces guide the vehicle around an obstacle. Here, the driving ground must also be known, and this method can lead to a local minimum.

MT90 An optimal path in an obstacle space is sought by an unsupervised learning neu­ral net. Unlike in our investigation, the obstacles are known, and replanning follows the emergence of new objects .

Our approach ([HGP92]) combines neural and conventional techniques in the following manner:

• control of two different behaviors by one net, avoiding obstacles when necessary, i.e. driving towards the target when appli­cable,

• independence from a given obstacle space and target, which can be dynamically chan­ged by the user during the consultation.

SYSTEM DESIGN

In this section, the functions of the vehicle in its logical and technical (hard- and software) context are introduced.

Simulation Interface and Vehicle

The simulation environment is graphically gene­rated within a window, in which a parcours can be created by editing simple objects. In Fig. 1 the basic forms of the obstacles are indicated. They are quadratic, rectangular (horizontal, ver­tical and inclined) or circular.

It includes a coordinate system, whose public data can be accessed from anywhere in the pro­gram.

Within this parcours, a starting and ending point which must be passed by the vehicle, are set up by the user. Furthermore, the menu allows the changing of vehicle parameters , like movement step size, the steering mode, and starting and ending points.

The vehicle possesses ten virtual sensors, from which nine are ultrasonic, and one is target­searching. Their position and number have been determined experimentally.

The ultrasonic sensors measure the distance to an obstacle. Each sensor monitors an area which is divided into seven equidistant concentric seg­ments. Contact with an obstacle activates all sec­tors up to the the one where the point nearest to the vehicle is located. In Fig. 1 the active, high­lighted areas of the sensors can be seen. The vehicle is now heading towards the upper border The target lies in the top left corner .

The tenth sensor calculates the target from the position of the vehicle, and the angle between

68

the heading vector and the direction of the tar­get (target-vector) from the angle between the vehicle's longitudinal axis (heading-vector) and the y-axis of the coordinate system. The gradua­tion of the angle is in steps of 15 degrees, like the possible steering directions of the vehicle, map­ping them to a further net input.

The periodically recorded sensor data are trans­formed by the neural net into steering commands. The vehicle can move in seven directions, three to each side, and one forward. The length of its steering steps is 15 degrees. Driving can take place either in place, or while going forward.

Processing Architecture

In the following, a hierarchical architecture of the vehicle's behavior is established (Fig. 2).

All levels of perception are involved during the exploration phase. Ensuing from the flow of in­formation, points delivered locally by the sensors are joined to lines. They represent obstacles on the world-level. The final task of the perception after the exploration is to structure the lines to a map. This is done off-line. The procedure re­structures a homogeneous mass of expressionless information blocks related to the mission, into few, heterogeneous, rich information pieces.

During the consultation phase, the vehicle percei­ves and usually transmits local points, i.e. pos­sible distance values and the target direction. Because of the steady adjustment with stored points, all layers up to the world layer are in­volved.

Only the local planning level is involved during the exploration phase; the vehicle responds to lo­cal sensor values with an avoidance tactic.

The vehicle interprets the lines, also off-line, as restrictions to optimization of the missions tar­get. By dividing the whole task into several parts with specific subgoals, the mission can be stored as a sequence of target directions. These are pas­sed one after another, defining a route as the way to the next target.

In this hierarchy the directions are specified with increasing immediacy, to be transformed finally into steering instructions.

Hard- and Software

The system runs on two workstations. First, a VAXstation 3100 with VMS, running the neural net shell N-NET [Pao89], and the program, which manages the communication between N-NET and the vehicle simulation on the second station.

........ F--4 llrfu- .....

z

Figure 1 : The Vehicle in its Environment.

The second is a DECstation 2100 with Ultrix, carrying the graphical representation of the ro­botic vehicle, thereby showing the physical equi­valences of the net's input (sensors) and output (steering commands) .

These stations are linked together via DECnet. Communication takes place as follows: the si­mulation writes a string of integers, representing sensor values, into a mailbox. The net-interface polls this mailbox, loads the values, and feeds them into the net. The result is written back into the mailbox, where the simulation reads it, and takes the required action. This is a cyclic process.

The entire application is programmed in C, the graphics are based upon the X-Window System with the DECwindows widget set. The size is 290 kilobyte executables for the simulation, and 2200 kilobyte for the net (application and trained nets) . NEURAL TASKS

The neural net system consists of two kinds of neural nets: associative memory, which classifies a homogeneous collection of patterns during the training, and accumulates similar patterns in clu­sters. These clusters form the input to the second

69

learning stage, where they are trained separately by means of single back-propagation nets.

During the consultation, it assigns an incoming input pattern according to its characteristics to one of the existing clusters, resp. nets.

The approach of dividing the large mass of mixed pattern types into small classes of a single type makes learning more efficient, because no cont­radictory patterns exist in the input range of a single net.

The second kind of neural net is a back­propagation net, which consists of an input and an output layer. It is enhanced by functional links, thereby allowing faster and more accurate training.

At discrete points of time, sensors deliver data to ten input neurons, associating an output pattern which represents the suitable steering direction. These can move the vehicle towards the target, when no obstacle is in sight, or away from it, when the direct way is blocked by a barrier.

The described behavior has its origin in the dif­ferentiated teached reactions to patterns the ve­hicle has been taught. When the sensors show no obstacle in front of the vehicle, the direction

p e r c e p t i 0 n

I f

- - ( Mission 0 {:Mission � � ..-

._- r w� 0 .�- f f p I a n n i n g

+ - tj' Local � � ..-

Values-. r � o · -

Figure 2: An Architecture of the vehicle's behavior.

of the target is taken into account, and the stee­ring command, which corresponds best to the di­rection is generated. Should there be obstacles ahead, the value of the target sensor is unim­portant, only the command for turning away is selected.

The neural net system was trained off-line, with patterns generated schematically by a program. Each obstacle situation, in combination with the target direction, offers another typical pattern from the sensors. The task for the generator is to vary the values for each pattern class in certain bounds, so that they correspond closely to the ones offered in the actual simulation.

All parameters have been determined by exten­sive use of the trial-and-error method.

CONVENTIONAL ENHANCEMENTS

Furthermore, the procedure is enhanced by con­ventionally implemented optimization, contribu­ting a strategic component, in contrast to the me­rely tactical hide-and-seek of the net.

In a preliminary phase, the vehicle explores the terrain, and stores points of sensor-obstacle contact. After the user finishes the tour, the program eleminates redundancies, connects the points to obstacle lines, and thereby creates a map.

This map is taken as a basis for finding all possi­ble ways from a user-defined starting point to the target point in a concrete case. From these the shortest one is calculated. It splits up the route into several shorter interim goals. As an effect, the vehicle avoids local minima on its way. The algorithms are documented in [Die92) .

70

Should the vehicle encounter unknown obstacles on its way during the consultation, they are in­corporated into the map, and in the next run considered for optimization.

EXPERIENCES

The neural solution was first implemented. After a short time it became obvious, that the neural approach alone could not solve the problem com­pletely. The problems of local minima and an efficient route planning were therefore transfer­red to a conventional supervisor.

In the following, the neurally and conventionally motivated problems and deficiencies are descri­bed.

The pattern generator left out a special class of values, namely that none of the sensors is ac­tivated, except the target sensor. Because this pattern was underrepresented in the random dis­tribution of data from the generator, it could not be taught correctly, and therefore caused a wrong association. The missing patterns were then ad­ded by hand.

Near obstacles, the vehicle swings between two directions. When the target lies behind the obstacle, the vehicle tries to reach it, and bo­unces off the walls. When it has moved away far enough, the sensors again register the possi­bility for a target drive, and the movements are repeated. In the extreme case this leads to a lo­cal minimum, but with conventional planning the targets mostly lie right behind a corner, causing the vehicle to follow a zigzag path. When lear­ning new patterns, the vehicle must be influenced

in such a way, that when the sideward sensors re­cord an obstacle and the target lies behind it, the steering should continue to drive forward. When the obstacle is passed, the vehicle can again turn towards the target.

On the conventional side, the aspects are the fol­lowing: because learning the terrain takes place once, and depends furthermore on the user, remo­val of an obstacle is not recognized by the plan­ning component. Permanent learning is possible, but would slow down performance.

Learning of new obstacles during a target-bound drive is more complicated, because the vehicle swings in the way described above, and the sen­sor data for the same obstacle is interpreted dif­ferently for each angle of contact. A helpful ap­proach is to divide the terrain into a grid, and count the number of points in each quadrant. The obstacle lies along the line of the most points.

It was observed, that the vehicle is only able to recognize a relatively coarse structure of its envi­ronment. For this reason, only a portion of the actual parcours could be covered during the ex­ploratory phase. To compensate for this, the real structure of a complex terrain is taken from the model data.

CONCLUSIONS

The evaluation of the use of a neural net in a technical context was successful. The assumpti­ons found in the literature concerning flexibility, ability to generalize and real-time capabilities of a neural net were confirmed. The work requi­red to configure and train the net was less than expected.

The tool N-NET from AI-Ware prooved suitable for use in complex applications. Because of the functional link method, which enhances the gi­ven back-propagation algorithm, the net conver­ged quickly during training, or pointed out cont­radictions in the patterns in a short time.

A purely neural solution did not completely sa­tisfy our system requirements. Therefore the con­ventional enhancement was necessary.

REFERENCES

Bue90 Rolf Buerk. Erstellung einer X­Windows Benutzeroberflache zur

7 1

Darstellung eines mittels Neuro­naler Netze gefiihrten autonomen Fahrzeugs. Diplomarbeit, Fach­hochschule Karlsruhe, FB Informa­tik, 1990.

Die92 Matthias Dietrich. Simulation ei­nes zielgerichtet fahrenden, auto­nomen Roboterfahrzeugs unter X­Windows. Diplomarbeit, Fachhoch­schule Karlsruhe, FB Informatik, 1992.

Gla91 Berhard Glavina. 3DMP - Ein Programm zur schnellen Erzeu­gung von Roboterbewegungen mit sechs Freiheitsgraden. In Autonome Mobile Systeme, Pages 89-103, Karlsruhe, December 1991.

HGZ90 Heinrich Herbstreith, Lothar Gmei­ner and Bernd Zimmermann. In­telligente Systeme und ihr Ein­satz in der Automatisierung in mittelstandischen Industriezweigen. AbschluBbericht, Fachhochschule Karlsruhe, HT, March 1990

HGP92 Heinrich Herbstreith, Lothar Gmei­ner and Patrick PreuB. Intelligente Systeme und ihr Einsatz in der Au­tomatisierung in mittelstandischen Industriezweigen. AbschluBbericht, Fachhochschule Karlsruhe, HT, April 1992

MT90 J . del R. Millan and C. Torras. Reinforcement Learning: Discover­ing Stable Solutions in the Ro­bot Path Finding Domain. In European Conference of Artificial Intelligence. Pages 219-221 , Stock­holm, August 1990.

Pao89 Yoh-Han Pao. Adaptive Pattern Recognition and Neural Networks. Addison-Wesley, 1989

PT91 Ewald von Puttkamer and Rainer Trieb. Modellierung und Hier­archie der Steuerung des autono­men mobilen Roboters MOBOT-11!. In Autonome Mobile Systeme, Pages 73-87, Karlsruhe, December 1991 .

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

EMG PATTERN RECOGNITION BY NEURAL NETWORKS FOR PROSTHETIC FINGERS CONTROL

A. Hiraiwa, N. Uchida and K. Shimohara

NIT Human Interface Laboratories, 1-2356 Take, Y okosuka-Shi, Kanagawa, 238-03 Japan

ABSTRACT The cybernetic interface through which users can communicate with computers "as we may think" is

the dream of human-computer interactions. Aiming at interfaces where machines adapt themselves to users' intention instead of users' adaptation to machines, we have been applying neural networks to realize electromyographic(EMG)-controlled prosthetic members---a historical heritage of the cybernetics. This paper proposes that EMG patterns can be analyzed and classified by neural networks. Through experiments and simulations, it is demonstrated that recognition of not only finger movement and torque but also joint angles in dynamic finger movement, based on EMG patterns, can be successfully accomplished.

KEYWORDS : Cybernetics, Electromyography, Manipulation, Man-machine systems, Neural nets

I NTRODUCTION People usually use a keyboard, a mouse or

their voice in order to transmit their intentions to machines like computer systems. Is there any way of transmitting users' intentions to machines more directly and conveniently without any intermediate operations and/or procedures? One such interface utilize the users' biotic information, information which people naturally emit is the EMG-controlled interface. The EMG-controlled interface is based on the assumption that the extracted EMG signals reflect the person's desired muscular movements.

The idea to use surface EMG for controlling a prosthetic hand/arm was proposed by Winner --- an early advocate of Cybernetics. As matter of fact, several types of EMG-controlled prosthetic arms and/or hands have been developed. For example, the Boston Arm[l] , the Utah Arm[2] and the Wime Hand[3]. In those devices, surface EMG related to a movement is detected with electrodes, motors are driven according to the detected EMG, and then the desired movements of flexing and extending prosthetic arm/hand are achieved. They have been very useful tools to return to the user a function lost by accidents etc. for users.

However, in order for users to master the prosthesis, they have had to re-construct their own body images in their brains so that their muscles consistently generate the appropriate EMG needed to control the prosthesis. Usually it takes about one month for this, since individuals basically have individual muscular control ability. Moreover, the training to re-construct their body images, which was constructed over their entire life so far, often

73

requires both physically and mentally exhaustive efforts.

Hence, a number of studies employing systems that use user-indicated EMG patterns have been reported[4]-[6]. That is, if the system can identify the users' intentions through recognition or classification of EMG patterns, all that the system has to do is just to generate the control signals yielding the prosthesis movements that correspond to the users' intentions. In order to analyze and classify the EMG signals from surface electrodes, they employed learning mechanisms, such as the linear separation function[7] and the Perceptron. However, the linear separation function and Perceptron do not have sufficient tolerance to artifacts and variance in electrode positions, moreover, there remain difficulties in the areas of convergence performance and classification ability.

Neural networks have recently attracted attention as a possible breakthrough in the areas of analysis and classification due to their good trainability , adaptability, and non-linear separability. Neural networks are expected to learn the relationship between the extracted EMG patterns and the appropriate movements of prosthetic hands/arms. In other words, users can master the use prosthetic hands/arms by training the neural networks instead of themselves. Hence, we propose the new concept, the "Artificial Body Image". The idea is to make neural networks re­construct the body image instead of users by using the automatic learning ability of neural networks. Figure 1 shows the concept in action.

In this paper, we apply a typical neural network with the backpropagation learning

1 • Put DataGlove onto other hand & Perform{lmage)Finger Motion Symmetrically

2 . Training for Neural Network

3 • Take off the DataGlove & Put on Prosthetic Hand

Fig. I Concept of EMG controlled prosthetic hand by pattern recognition of neural networks

Surfac.EMG

Fig2.Block diagram describing surface EMG and classification by neural network

algorithm for the analysis and classification of EMG patterns. The pattern are related to 5 stationary finger positions, torque, and 10 joint angles of 5 dynamic finger movements. Through experiments and on-line simulations, it is confinned that neural networks have sufficient power to learn and recognize EMG patterns for driving EMG-controlled prosthetic members.

EMG PATTERN RECOGNITION EMG pattern analysis/classification problems

can be summarized as follows: 1) how to extract the speed and torque control

infonnation needed to perfonn single ann or hand motions with the EMG signals

2) how to classify EMG signals from multi­channel surface electrodes into control signals that can direct complex prosthesis movements.

Most ann/hand motions are generated by the cooperative movement of several muscles, which transmit different pulse signals. Therefore, EMG signals are observed as the summation of signals transmitted non-linearly and independently by several muscles. Thus, EMG signals from a surface electrode on one muscle can be degraded by crosstalk from other surrounding muscles. This obviously complicates the task of separating and classifying muscle-derived EMG signals.

Hence, when applying a backpropagation-type neural network for EMG pattern recognition, we FFT-analyze EMG patterns as input infonnation for the network in the following experiments. The

74

Fig3. Schematic diagram ofEMG classification system

Fig.4 FFT analized EMG pattern( ex. "I")

I-ex '

I-ex 5

I-ex 4

I-ex 3

I-ex l

I-ex I

=

�

-

0

x

• unit A • unit ! • unit M 13 unitT O unit N

0 0

0

0 o.o 0.2 o.• o.& o.e 1 .0

Fig.5 Processing unit firing rates(ex. "I'')

neural network thus learns the relationship between the FFT-analyzed EMG patterns and intended finger motions, torque or joint angles of fingers. Figure 2 shows the schematic diagram of the EMG classification system using a neural network as a learning mechanism.

Recogn ition of Stationary Finger Motions The EMG signals (band-width 50-3kHz) were

detected by surf ace electrodes on the subjects' flexor digitorum superficialis when the finger movements halted (frame length 20ms ). The signals were FFT analyzed with 1/3 oct , and transformed into FFT­analyzed patterns of 10 bands whose central frequencies are 63, 80, 100, 125, 160, 200, 250, 315, 400, and 500Hz. The FFT-analyzed patterns were given to a neural network as input data as shown in Figure3.

The backpropagation-type neural network we employed here consists of 10 input, 7 hidden, and 5 output units. The 5 output units correspond to the 5 categories of finger movements as follows, (A) flex all fingers, {I) flex only index finger, (M) flex only middle finger, {T) flex only thumb finger, and (N) relax all fingers. In the training phase, the right category related to a FFT-analyzed EMG

pattern is given to the network as the desired output, and then connection weights in the network are modified so that the error between the desired output and actual output is reduced.

After 1 ,000 training cycles for 30 data sets, 20 out of 30 new EMG patterns were successfully recognized as estimated from the magnitude of the unit's firing rates --- the recognition rate is 67%. Figures 4 and 5 shows the FFf-analyzed EMG pattern and the unit firing rates for examples of pattern ("I") recognition, respectively[8].

In the case of employing 2ch EMG, by adding another electrode on the extensor digitorum, the recognition rate increased up to 86% by applying the neural network with 20 input, 20 hidden, and 5 output units.

Recogn ition of Torque Muscle movement is originally executed as

torque control generated by the rivalry between flexor digitorum superficialis and extensor digitorum. We conducted experiments for torque recognition in the same way as the finger motion recognition. EMG signals were detected with a surface electrode pasted on the subjects' flexor digitorum superficialis, processed into FFr-analyzed patterns, and given to the neural network as input patterns as shown in Figure 6. In this experiment, five categories corresponding to five output units in the network were set for five kinds of torque, such as 0, 120, 240, 360, and 480 gf-cm, which were measured in the stationary state where the first joint angle was kept at 60 degrees. The network employed here had 10 input, 13 hidden, 5 output units. After 10,000 training cycles with 25 training data samples consisting of 5 kinds of torque in 5 sets, recognition results for 25 new data in the range in which differences from the desired outputs were within ±140 gf-cm, as shown in Figure 7. Figure 8 shows simulation results for 50 new data in the case that the same network was trained with 4 kinds of torque by 10 sets without data for 240 gf­cm torque. From Figure 8 we find that the neural network complements the lack of classifying ability for the unknown data.

, . ,,,, � . . .

Fig.6 Schematic diagram of EMG torque recognition system

75

J �m.------------(480gf · an) � 0.75 .j9.ll ..... ....+ll----llt--------­g (360) � 0.5 -19-1 ... f-H�-IM·•·i ff"J-------& (240) S 0.25 -19-tl-ffl-HHHiHI al (120) � 0 W.""".-Jl!o11¥,J¥!ljl, .�IJ.Jrl-l,,s,e.SrF.¥� 8 .. -0.25 +-:-_.!,---,-::::�--:::7::-'U--::-::::r---0:--a:

Bar : recognized toruque Line : error

(8-60deg)

Fig.7 Result of toruque recognition for unleamiing EMG pattem

(480 gf ..:..an)

..,, <?�)

� g � OJ ::i (240) I: .9 al ..,, N c (120) O> 8 .. a:

. -· .. -.- �·-

(8-SOdeg)

Bar : recognized toruque Line : error

Fig.8 Result of toruque recognition for unlearning EMG pattern complement

Recog nition of Joint Angles In Dynamic Finger Motions (1 ch)

In order to make a EMG-controlled system recognize dynamic finger movements for smooth control of prosthesis, it is necessary for the system to deal with and recognize EMG signals as continuous analog data.

In the experiments here, the subjects ,made continuous finger movements at random for a certain period, while EMG signals were detected dynamically and continuously as temporal sequence data. At the same time, joint angles during finger movements were observed with a DataGlove. To deal with the temporal sequence processing of EMG signals in a neural network, we employed the "moving window" method. That is, EMG signals observed in the window open to the stream of EMG signals were successively processed into an FFf­analyzed pattern, and given to the network as input in the same way. Joint angles obtained by the DataGlove were given to the network as the desired outputs. After sufficient training, the network was continuously tested for a new sequence of EMG patterns, and the recognition results in real-time and on-line manner were compared with the actual joint angle observed with the DataGlove .

Figure 9 shows the schematic diagram of this experimental system. A pair of electrodes were

Robot Hand or �rtualCG hand 1 20,--����������

Fig.9 Schmetic diagram of EMG dynamic recognition

O 0 J fc.h C g J 2ch 0

-----...

{O cm

Fig.10 Electrodes position

placed on the subject's flexor digitorum superficialisabout 10 cm from the subject's left wrist, see Figure 10. EMG signals with a band­width between 50 - 3kHz were sampled at 2.048 kHz, analyzed by FFf with 1/3 oct., frame­length:500 ms., and framing-cycle: 125ms., and transformed into the FFf-analyzed patterns with 10 bands whose central frequencies were 63, 80, 100, 125, 160, 200, 250, 400, and 500Hz. On the other hand, 10 joint angles for 5 fingers--the first and second joint angles per each finger--were sampled at 32Hz, and averaged over 16 sampling points so as to meet the frame-length of the FFT window, 500ms. The FFf-analyzed EMG was input to the network, and the averaged joint angles as the desired output to the network were both normalized before given to the network; angle 0 to 0, angle 120 degrees to 1 . The EMG patterns given to the network as training data were 2,400 patterns observed for 300 sec. The neural network was a backpropagation-type network with 10 input, 20 hidden, and 10 output units.

Figure 1 1 shows experiment/simulation results of the network after 1 ,000 training cycles. 200 EMG patterns, i.e. a sequence of EMG patterns for 25 sec detected from the same position of electrodes from the same subject were processed by the neural network. Recognition results for the first joint angle of index finger and the actual joint angle measured with the DataGlove are shown in Figure 8. Although there is some difference between the angles from the network and the DataGlove, the tendency for the subject to flex the f i r s t j o i n t o f i n d e x f i n g e r

76

O> "' "O

96

"' 72 !'! O> "' 0 �

U:·

0 0 6.25

- Recognized value ···-·· Desired value

1 2.5 1 8.75 25sec

Fig.1 1 Result of recognition of joint angles in dynamic fingers motion(lch)

96 Cl Q) "O Q) 72 � Cl Q) "O x Q)

;;:::: iii Q) a:

24 48 72 96 1 20 Recognized flex degree deg

Fig.12 Correlation diagram of recognized flex degree and real flex degree

is the same and easily understood. The same results were obtained from the second joint of index finger and joints of the middle and ring fingers. As for the thumb and little fingers, the same tendency was obtained but the recognition performance was worse. Figure 12 shows the correlation diagram between joint angles of the first joint in the index finger recognized from EMG patterns by the network, and actual joint angles observed by the DataGlove. 2,400 patterns for 300 sec. are plotted in Figure 12, and the correlation coefficient was calculated to be 0.691 .

Recognition of Joint Angles In Dynamic Finger Motions (2ch)

Next, we conducted an experiment using 2ch EMG signals for recognition of joint angles in dynamic finger motions, since 2ch EMG resulted in better performance than lch in the recognition of stationary finger movements. Almost all conditions were the same as those for lch except the frame-length was set to 500ms, and framing frequency to 250 ms due to the limited computation speed of this system. In this experiment, two pairs of electrodes were mounted on the plastic belt of a

1000 2000 3000 -

Fig.13 Relationship between the RMS error and the

training cycles

1 20

96

i I i i i , t ii f l

_ Recognized value ····- Desired value

�. , I

o i------�--......... ----1 O 1 U ��

Fig.14 Results of recognition of joint angles in dynamic fingers motion(2ch)

deg 1 20 .----------------,

Thumb MP - Index MP ::::: Middle MP ::::Ring MP

U�e MP

-1201--�-�-�-�-�--� O 25 50 75 100 125 150 175sec

Fig.15 Recognition error between the network output and the desired output for the MP joint angles of all 5 fingers

deg 120 ..----------------,

Thumb PIP ::::1ndexPIP ::::Middle PIP -Ring PIP

Little PIP

·120 o : 25 50 75 100 125 150 175sec

Fig. 16 Recognition error between the network output and the desired output for the PIP joint angles of all 5 fingers

77

Ill a> deg � 25 Cl Q)

"O al 20 N ·2 [ 1s

cc 0 10 � :J Jr 5 c: <II � 0

c.. 0 ::E 0 .t:l cc E :J F

0.. a: .t:l E :J F

c.. c.. :::? a: x x Q) Q) "O "O .E .E

c.. 0.. 0.. 0.. 0.. :::? a: :2 a: :::? Q) Q) Cl Cl Q) =a =a c c 5 "O "O a: a: � �

Fig.17 RMS error average of all joint angles

0.. a: Q) ::: �

wrist watch, and a subject wore the watch so that the pair of electrodes was placed against the flexor digitorum superficialis and another pair on the extensor digitorum, as shown in Figure 10.

The number of training data was 600 patterns observed for l 50sec. The neural network employed here had 20 input, 20 hidden, and 10 output units. Figure 13 shows the relationship between the RMS error and the training cycles.

After 2,700 training cycles, 100 EMG patterns, i.e. a sequence of EMG patterns for 25 sec., detected on the same position of electrodes form the subject, were given to the network as input. Recognition results by the network and the desired output by the DataGlove for the first joint angle of the index finger are shown in Figure 14. We confirmed that the neural network achieved good performance in recognizing EMG patterns. The same results were obtained for the first and second joint of the other 4 fingers.

Figure 1 5 shows the recognition errors, between the network output and the desired output for the first joint angles for all 5 fingers, for 600 EMG patterns when the subject continued finger actions at random for 150 sec. Also, Figure 16 plots corresponding data for the second joint angles of all fingers. From these figures, we see that most errors were around 30 degrees. Figure 17 shows the root mean square average of the errors for all joint angles. The root mean square error average is within less 25 degrees from the figure. Through this experiment, we confirmed that multi-channel electrodes are useful in the recognition of dynamic joint angles in finger motions.

Real Time Dexterous Man lpu latlon by 2ch E M G

We made a EMG controlled Sfingers 1 0 joints dexterous hand (Fig. 1 8). We succeeded for gripping a tennis ball (Fig . 1 9), and Playing a keyboard (Fig.20) by the EMG controlled dexterous hand.

D I S C U S S I O N During the experiment o f dynamic joint angle

recognition, we sometimes observed that there was

Fig. 18 The EMG controlled 5fingers 10 joints dexterous hand and user's hand with 2ch surface electrodes

Fig.19 Gripping a tennis ball by the dexterous hand

Fig.20 Playing a keyboard by the dexterous hand

78

Fig.21 Near future prosthes hand using FFr analyred EMG signals by neural network

some delay in EMG recogmt1on. There is, therefore, room for improving the method of inputting the desired output to the neural network. Moreover, the use of other neural networks with the potential to deal with temporal sequence processing is suggested as another way; we employed a rather simple neural network with the backpropagation learning algorithm this time.

Also, to enhance the recognition perfonnance of neural networks, the improvement of electrodes and means to cope with muscle fatigue must be considered. In particular, multi-channel surface electrodes with over 10 channels up to several hundreds, developed by Matsuda[9] for example, might be indispensable instead of one or two pairs.

Another discussion might address the application of neural networks for EMG pattern recognition, when considering a more practical prosthetic hand/ann: the case of employing one neural network with multiple inputs and multiple outputs, or the case of employing multiple neural networks where each network has multiple inputs and single output. Although we examined the applicability of a single neural network with multiple inputs and outputs in this paper, the means of partitioning the processing for a certain joint into a network with a single output, and integrating those multiple networks should be effective, especially for fast training.

Figure 21 shows a prosthesis system of the near future, that will implement the simple backpropagation-type neural network which we reported in this paper. There is room for improvements for the reported system; however, we confinned the possibility that users can control five finger movements dynamically and independently.

On the other hand, the cybernetic interface called "Virtual Reality," through which users can access the virtual world that computers create, has recently gathered attention, recently. Thus, it is expected that the infonnation channel between users and computers will widen more and more with new tools and devices. For example, glove-typed tools, such as the DataGlove, for inputting finger and/or hand movement to computer are becoming popular in this field. By using EMG pattern recognition, a new tool for transmitting finger/hand movement to

Radio Link

or Infrared Communication Link

\

} Surface electrodes pair

or Array

Fig.22 Concept of EMG recognized wrist watch

computers without a glove will be possible, in which electrodes and a VLSI chip for neural networks are mounted in a wrist watch(Figure 22).

CONCLUSION We applied neural networks for EMG pattern

recognition and examined their feasibility and applicability for EMO-controlled prosthesis---a historical heritage of Cybernetics. It was clarified that a simple backpropagation-type network has sufficient ability to classify stationary finger positions and recognize torque in finger motions. Moreover, we confirmed that neural networks have the potential to achieve unprecedented performance; joint angle recognition of 10 joints in 5 fingers with dynamic and continuous finger movements.

ACKNOWLEG EMENTS We thank Dr.Yukio Tokunaga and Takaya

Endo for their encouragement and support during this research project.

79

R E F E R EN C E S 1 . Mann R . , et.al., Kinesthetic Sensing for the

EMG Controlled B oston Arm, IEEE Transactions on Man-Machine Systems, March 1970, pp.1 10-1 15.

2. Kato I . , et.al. , The evaluation method of rehabilitation devices-Field testing of powered forearm prosthesis, WIME Hand, Proceedings of 6th International Symposium on External Control of Human Extremities, Dubrovnik Yugoslavia, pp.Sup.141-184,1978.

3. Jacobsen, S ., Development of Utah Arm, IEEE Transactions on Biomedical Engineering, vol.27, no.7, pp.249-269,1982.

4. Tani, K.,et.al., Gisyu-seigyo no tameno kinden patan no gakusyuu shikibetsu( Japanese), Biomechanism , no.5 , pp.88-95 ,Tokyo Univ.Press, 1980.

5. Hogan, N.,Myoelectric S ignal Processing: Optimal Estimation Applied Elctromyography­Partl: Derivation of the Optimal Myoprocessor, IEEE Transactions on Biomedical Engineering, vol.27, no.7, pp.382-385, 1980.

6. Suzuki, R., and Suematsu, T., Pattern Recognition of Multichannel Myoelectric Signals by Learning Method, Japanese Journal of Medical Electronics and Biological Engineering, vol.7, no.I , pp.47-50,1969

7. Sardis G., et.al., EMG Pattern Analysis and Classification for a Prosthetic Arm, IEEE Transactions on Biomedical Engineering, vol.29., no.6, pp.403-4 12, 1982.

8. Hiraiwa A., et.al.,EMG Pattern Analysis and Classification by Neural Network, Proceedings of 1989 IEEE International Conference on Systems Man and Cybernetics, pp. 1 1 13-1 1 15,1989.

9. Masuda T., and Sadoyama T., Topographical Map of Innervation Zones within Single Motor Units Measured with a Grid Surface Electrode, IEEE Transactions on Biomedical Engineering, vol.35, no.8, pp.623-628,1988.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

MONITORING AND CONTROL OF POWER SYSTEM VOLT AGE STABILITY USING AN ARTIFICIAL

NEURAL NETWORK

H. Mori

Department of Electrical Engineering, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki 214, Ja[Xln

Abstract This paper proposes a decentralii.ed method for monitoring and control of power

system voltage stability with an artificial neural network (ANN). One of the problems in

applying neural networks to power systems is how to cope with a lot of variables in real­

sii.e power systems. Most of the conventional ANN-based approaches suffer from the curse

of the dimensionality in power systems. As a result, it seems that the applications are far from

the real world. However, as far as voltage problems are concerned, they possess peculiar

local characteristics. It implies that the problem may be decomposed into subproblems. This

paper focuses on the characteristics and considers more realistic ANN applications. The

proposed method is tested in a 30-node system to demonstrate the effectiveness.

Keywords. artificial neural nets; decentralized control; monitoring; voltage control

INTRODUCTION

Voltage instability is a matter of great interest to power

system operators. The problem gets involved in the lack of

reactive power sources. In addition, it is influenced by

dynamic load characteristics. Voltage instability is

inclined to occur as power systems become heavy-loaded.

The problem has been studied from a standpoint of the

existence of the load flow solutions (Galiana,1975). In

particular, it has been found that a pair of multiple load

flow solutions gets closer to each other as power system

conditions get closer (Tamura and co-workers,

1980a, 1980b, 1981, and 1983 ). Also, voltage stability

indices have been proposed to take appropriate control

before power systems approach critical conditions

(Carpentier and co-workers,1984; Mori and Tamura, 1985;

Kessel and Glavitsch, 1986; Tiranuchit and Thomas, 1988).

Furthermore, methods for finding bifurcation or critical

points have been investigated (Alvalado and Hung, 1988;

Chiang and co-workers, 1989; Iba and co-workers, 1989;

81

Mori and Tsuzuki, 1990). Recently, dynamic models for

voltage instability have been developed (Sekine and

Ohtsuki, 1989; Begovic and Phadke, 1989; Chiang and co­

workers, 1989). This paper describes an artificial neural

network (ANN) based method for monitoring a voltage

instability index. As the index, the idea of VIPI (Mori and

Tamura, 1985) is utilii.ed to measure margin to the critical

conditions since it is more understandable in a sense that

power system conditions can be expressed in terms of the

angle of a quantitative measure.

TABLE 1 Oassification of ANNs

Feedforward

Supervised MLP Learning

Unsupervised KFM Learning

Feedback

Recurrent

Hopfield Net BM

At present, artificial neural networks (ANNs) have been

studied by researchers in all engineering fields as well as

biologists. The neural computing has several advantages

such as parallel computing, self-organization, feature

extraction, fault tolerance, etc. In particular, the

technologies are useful for solving the so-called complex

problems that are hard to solve. Typical ANNs are

feedforward multi-layer perceptrons (MLP), recurrent

multi-layer perceptrons, Kohonen feature mapping (KFM), Hopfield net, Boltzmann machine(BM), etc. TABLE 1

shows classification of ANNs. Above all, the MLP has

been widely used in system identification, estimation,

prediction, and classification problems. The KFM is used

to classify input patterns. The Hopfield network is useful

for solving combinatorial and associative memory

problems. The ANN comes from a spin-glass model. Also,

the BM has an advantage that a solution near a global

minimum is obtained. The basic idea is that the simulated

annealing technique is applied to the Hopfield net.

Concerning applications of ANNs to power systems, the

following problems have been solved: dynamic security

assessment (Sobajic and Pao, 1 989), static security

assessment (Aggoune and co-workers, 1989; Chen and

Hsu, 1990; Niebur and Germond, 199 1 ; Mori and co­

workers, 1991), alarm processing (Chan, 1989), harmonics

identification and detection (Mori and co-workers, 1989:

Hartana and Richards, 1990), fault detection (Tanaka and

co-workers, 1989; Ebron and co-workers, 1990; Kandil and co-workers, 1991), voltage control (lwan Santoso and Tan,

1990), harmonics prediction (Mori and co-workers, 1990a,

1992), load forecasting (Park and co-workers, 1 990),

topological observability analysis for static state estimation

(Mori and Tsuzuki, 1989, 1990b), and so on.

This paper presents an MLP based method for estimating

the voltage instability index so that the computational effort

is reduced. The index is based on a set of multiple load

flow solutions. One of the drawbacks on the index is that

the index calculation is quite time-consuming in finding

the closest pair of the multiple load flow solutions. On the

contrary, ANNs allow us speed up calculation of the index

through the pattern recognition. Also, a decentralized

scheme is presented to handle a lot of input variables so

that the curse of the dimensionality is alleviated.

82

REVIEW OF MULTIPLE LOAD FLOW

SOLUTIONS

This section describes multiple load flow solutions that are

used to estimate margin to the critical conditions of the

static voltage stability. Since the AC load flow equation is a

set of nonlinear equations, there exist multiple solutions.

Klos and Kerner (1975) undertook computer simulations to

verify the fact Afterwards, Tamura and co-workers have

shown that the number of multiple load flow solutions is

related to static voltage stability ( 1980a, 1980b, 1981 and 1983). In other words, the number of multiple solutions is

two before the critical conditions as power system

conditions get heavy-loaded. Fig. 1 shows the concept of

multiple load flow solutions, where vector a indicates the

critical conditions at Ys = Ya· In the figure, x2 designates

the counterpart of the operational solution x 1 under power

system conditions Ys although there exist three solutions

except x 1 . On the other hand, there are more than four

solutions under light-loaded conditions.

Now, let us consider a nonlinear load flow equation:

where

Ys = f(x)

Ys= specified value vector

x : bus voltage vector

f( • ): nonlinear load flow equation

(1)

I I I I I 'Heavy Loade�

I I I .. I I I

I Ys Ya

POWER SYSTEM CONDITIONS

Fig. 1 Concept of multiple load flow solutions

Consider a pair of the multiple load flow solutions, x 1 and

x2. The pair may be expressed as follows( Tamura and co­

workers, 1980b):

x1 := a + b

x2 := a - b

(2)

(3)

where, vector a is a singular vector in x-space (voltage

space).

Since the pair satisfies the same specified value Ys• we have

where

Ys = f( a ± b)

= y(a) ± J(a)b + y(b)

= y(a) + y(b)

= Ya + Yb

Ya := y(a)

Yb := y(b)

Ya : singular vector in y-space.

(4)

As power system conditions become heavy-loaded, x1 and

x2 approach singular vector a in x-space while power

system conditions Ys does singular vector y8 in y-space.

Fig. 2 shows singular vectors in x-space and y-space. Thus,

an index for static voltage instability in x-space may be

written as

90 : = cos-1 ---- [deg.] (5)

II •II: magnitude of vector •

The conventional methods for finding a pair of multiple

load flow solutions are based on the exhaustive search

(Tamura and co-workers, 1980a).

A N N - B A S E D M E T H O D F O R

M ON I T O R I N G AND C ON T R O L O F

VOLTAGE STABILITY

Estimation of Global Index

In order to reduce the computational effort in finding the

multiple load flow solutions , a three-layered perceptron is employed to estimate the global index given in Eqn. (5).

That is because the conventional methods are time-

consuming due to the exhaustive search. The ANN allows

us to estimate output variables with the nonlinear mapping.

The input may be expressed as power system conditions

while the output is the global index. Thus, global index 90

may be written as follows:

(6)

where

h( • ): nonlinear mapping

Fig. 3 shows MLP based estimation of the global index.

However, the direct application of an artificial neural

network to voltage instability has the following problems:

a) The method sufferers from the curse of dimensionality

11 x1ll• llx2ll as the system size gets larger. As a result, it takes a lot of

where computational time in the learning process and easily

x-Space y-Space

Fig. 2 Singular vectors in x-space and y-space Fig. 3 Estimation of global index with ANN

83

Fig. 4 System decomposition

Yst

Ys2

YsN

• • •

lss #N I

Fig. 5 Decentralized scheme for monitoring voltage stability

84

gets stuck in local minima.

b) The global index is not sufficient in examining which

areas are much weaker in terms of the static voltage

stability.

Therefore, more effective methods are required to handle

power system voltage stability problems.

Estimation of Local Indices This paper proposed a decentralized scheme for voltage

stability with an ANN. It is well-known that voltage

problems have local characteristics in power systems. Jn other words, it is possible to decompose the problem into

several subproblems. In this paper, a power system is

decomposed into subsystems so that the ANN-based

method alleviate the curse of the dimensionality. Fig. 4 shows decomposition of a total system into N subsystems(

SS# l - SS#N). Hence, the ANN is constructed at each

subnetwork to evaluate a local voltage index and

understand which subnetwork is closer to the critical

conditions. Similarly, the margin to the critical conditions

at each subnetwork may be expressed by the inner product.

The local index for subsystem k may written as

where

---- [deg.]

I I Xtkll• llx2kll

(7)

Xtk: voltage vector at subnetwork k corresponding to Xt

x2k: voltage vector at subnetwork k corresponding to x2

Local index 9Lk subsystem k is estimated by the

following equation:

(8)

where

Ysk: specified value at subnetwork k corresponding to Ys hk( • ): nonlinear mapping at subnetwork k

Fig. 5 shows a decentralized scheme for monitoring voltage

indices. Weaker subnetworks in terms of voltage instability

are identified by arranging the index in ascending order.

Control of Local Indices

Furthermore, the ANN estimates the optimal control variables to enhance voltage stability margin. The optimal control variables are given by minimizing the local index 9Lk . The problem may be solved with the nonlinear programming although it requires the computational time. The three-layered perceptron is constructed using the power system conditions and the optimal variables as the input and output data, respectively.

EXAMPLE

The proposed method for estimation of local indices has been applied to a 30-node system. The system was decomposed to three subsystem, SS#l, SS#2 and SS#3, which have the same number of nodes. Fig. 6 shows the decomposition of the 30-node system. TABLE 2 shows the global and local indices. From the table, it can be seen that SS#l has the smallest local index while SS#3 has the largest index.

The following system conditions were used: 1) The input variables are the specified value of the load

flow calculation. Thus, SS#l has 18 input units while SS#2 and SS#3 have 20 input units. As far as the number of the hidden units, the following experimental formula was used:

nh= 2 ..J ni + no

where nh : # of hidden units fii : # of hidden units no : # of hidden units

(9)

Thus, SS#l has 9 hidden units while SS#2 and SS#3 have 10 hidden units.

2)The backpropagation algorithm was used to determine the weights between units. The convergence criterion was 20000 iteration counts.

3) One hundred power system conditions was prepared as the learning and test data, respectively.

4)The teacher's signal was prepared by the off-line conventional method.

85

Fig. 6 30-node system

TABLE 2 Global and local indices at 30-node system

Total System Subsystems

SS#l SS#2 SS#3

Indices 13.1 1 3.501 5.860 20.97

The ANN at each subnetwork were evaluated to estimate the local index. The ANNs of SS#l, SS#2 and SS#3 have 2.7[%], 3.1 {%] and 3.5[%] of the average rms errors, respectively. Theses figures were acceptable as the approximate value obtained from ANNs.

CONCLUSIONS

This paper has presented an ANN based for monitoring and control of voltage stability in power systems. To alleviate the curse of the dimensionality in power systems, a decentralized scheme has been proposed. Estimation of local indices at subnetworks was tested. The simulation results indicated that the ANN-based method was acceptable.

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Copyright @ IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

MULTI-DIMENSIONAL LOCALLY GENERALIZING NEURAL NETWORKS FOR REAL TIME CONTROL

P.E. An and C,J. Harris

Advanced Systems Research Group, University of Southampton, Southampton, S09 5NH, UK

Abstract Based on the fast learning convergence properties of networks with lo­cal generalization (compared to multi-layered networks with global learning inter­ferrence and possible multi-minima), this paper reviews three locally generalizing neural networks: Radial Basis Functions (RBF), B-Splines (BSPL) , and Cerebel­lar Model Articulated Controller (CMAC). In specific, the learning performance of the CMAC network was evaluated using a non-linear time series with four inputs and two outputs, and compared to those using RBF (Chen, Billings (1991)) and B-Splines( Brown, Harris ( 1991)) . In relation to real-time control tasks, either the plant derivative (or jacobian) or an approximated version of the jacobian is required if the controller is adjusted based on an instantaneous tracking error (instead of the control error) . This way the controller becomes sensitive to the estimated plant jacobian. This paper also studies the ability of the CMAC network to approxi­mate a plant made of multi-sinusoids, and estimate the plant jacobian based on the approximated plant model.

Keywords Local Generalization, Receptive Field, Time Series Modelling, Deriva­tive Estimation.

INTRODUCTION.

Artificial neural networks are widely used in ar­eas of system modelling and control , and pat­tern classification because of their ability to ap­proximate an unknown complex mapping. These networks are non-linear both in space and time. This provides a richer degree of freedom in cap­turing the complex mapping, as compared to conventional adaptive control (only non-linear in ·time, with a chosen linear model) . The modelling capability of a neural network can be evaluated in terms of its convergence and its rate of con­vergence (towards approximating a desired func­tion), asuming that the network size (total num­ber of adaptable parameters in the network) is within practical limits.

All existing neural networks can be categorized as either locally generalizing or globally general­izing. The network generalization is global if one or more of the adaptable parameters in the net­work can potentially affect the network output at every point in the input space. On the other hand, the network generalization is considered local if only a small subset of adaptable parame-

87

ters can potentially affect the network output in a local region of the input space.

Networks with global generalization (e.g. Multi­layered Perceptron) have slow learning conver­gence (or require many training cycles because of the global learning interferrence ) , and slow nu­merical computation (because all adaptable net­work parameters are adjusted for each training sample). In addition, the network convergence (even for a single input) is not often guaranteed because of the presence oflocal minima in the ap­proximation error surface. While these networks might be useful for off-line learning applications (like classification/recognition), it is highly un­desirable to be used in any real-time control ap­plications ( unstability).

On the other hand, networks with local gen­eralization (e.g. Cerebellar Model Articulation Controller) have relatively faster learning conver­gence (or require fewer training cycles because the learning interference is no longer global) , and faster numerical computation (because only few adaptable network parameters are adjusted

for each training sample) . In addition, the net­work convergence is guaranteed because of the absence of local minima (due to the quadratic error surface) . Based on the chosen evaluation criteria (convergence, rate of convergence), net­works with local generalization are better suited in real-time control tasks. Three different lo­cally generalizing approximation networks were reviewed, and the learning performance of these networks were evaluated using a non-linear time series with four inputs and two outputs. These networks are:

1

• Radial Basis Functions (RBF)

• B-Splines (BSPL)

• Cerebellar Model Arithmetic Controller (CMAC)

Network Review

1 . 1 Radial Basis Function (RBF)

The RBF receptive field width is either fixed prior to learning, or made adaptable during learning based on the approximation error. The receptive field roll-off is commonly based on ei­ther a gaussian type (with non-compact local support) or a thin-plate spline type (z2log(z2) (global support) . Only the gaussian roll-off is considered here because of its inherent local gen-cx-;i>2 eralization property (fi(X) = ezp p• , where Pi is the ith field width and 'Yi is the ith cen­ter location). A multi-dimensional receptive field (Fi ) is formed using a product operator on fi in each input axis (Fi (X) = f.,1 ,i (X) · f.,2,i (X) ·

·f.,N,i (X)) . Four methods are commonly used in placing the receptive field centers. They are based on

• Data set. 'Yi is assigned to each of S data points. This method works well when S is a small number. When S becomes very large (with few receptive fields available) , 'Yi can be solved using the recursive least square method.

• Uniform randomness. "'(/s are as-signed randomly in RN . This method as­sumes the presence of an excessive number of available receptive fields in the network in order to achieve a statistically uniform field placement in RN. However, this method is highly undesirable when only a small num­ber of receptive fields are available.

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• Function approximation error. 'Yi is adapted (by means of the steepest descent method) based on the approximation error. This method only works well if the approxi­mation error surface ( E) is well defined (one global minimum) . In reality, the extra de­gree of freedom on Pi often introduces multi­ple local minima in the error surface, which is undesirable for any adaptation.

• Input distribution. 'Yi is adapted (by means of clustering method) based on the input distribution. That is, more receptive fields will be allocated to some region of RN (ZN) when the input data statistics in zN is higher. This method works well only if the input distribution in zN matches properly the local Fourier contents of the function to be approximated in zN.

With this set of attributes, the RBF output is a sum of L Fi weighted by its Wi (equation 1) , where L is the total number of network weights.

( 1 . 1)

Given a training sample (X1: , Y1: ) in the kth cycle, Wi is adjusted incrementally in the direction of steepest descent of the approximation error ( E1:) (LMS rule, equation l . la & l . lb ) . Details of RBF architecture can be found in Poggio, Girosi ( 1990) and Chen, Billings (1992) .

E1:(X1: ) = � (Yk - YRBF(X1: ))2

6W. = /3·E1:(X1: ) ·Fi(X1:)

( l .la)

( 1 . lb)

In addition to the LMS rule, Wi is commonly normalized with a summation of all active recep­tive field strengths (l:: Fl) . The resulting nor­malized LMS rule (NLMS) is shown in equation l . lc. The LMS rule and the NLMS rule become similar when the training input is close to any of the active receptive field centers. In cases where the training input is distant from all active recep­tive fields, the NLMS rule becomes particularly superior by speeding up the convergence based on the automatic scaling (l:: Fl).

(1 . lc)

In cases where Pi and 'Yi are to be adaptable, their corresponding updates are given as follows:

( l . ld)

c (3 E (X ) w. 8F,(X1o) a"'{;. = 2 . k k • i . a..,. where (3, (31 and f32 are learning rates.

1 . 2 B-Splines (BSPL)

( l . le)

The receptive field width in BSPL is fixed prior to learning. While there are many ways to con­struct the field roll-off (Ii) , this report focuses only on the recurrence relation method ( equa­tion 1 .2) suggested independently by Cox (1972) and de Boor ( 1972) . In equation 1 .2 , n is the width order of k When n is set to 1 , /;. becomes rectangular, and the network does not have any generalization (table-look-up). When n is set to 2, /;. becomes linearly tapered around the field center. Two closest fields now share 253 gener­alization (fig. 1) . This method provides a natu­ral extension to a smoother receptive field (with a stronger generalization) as n increases.

/n,t. (X) = ( ..,:�2;�: .. )/n-l,i-1(X)+

(..,);;_:+i )/n-1,t. (X), n > 1

/1,;. (X) = 1 , X E ht.-1 , 'Yt. ) = 0 , otherwise.

( 1 .2a)

( l .2b)

A multi-dimensional field ( F;.) is formed using a product operator on individual receptive fields (/n,i) in each input axis (same as RBF). This method gives rise to two desirable properties. First, the receptive field has a compact sup­port, which eliminates any global network inter­ferrence. Second, it gives rise to a normalized network field strength with respect to the input. That is, for any X, the sum of all Fn,i associated with X is always constant. This forces the net­work to be unbiased toward any inputs (assume no prior knowledge about :F is available).

Unlike RBF, the receptive field centers are nor­mally fixed at the cartesian grid points in RN . Although this allows the field placement to be uniform in RN , the number of receptive fields re­quired in the network grows exponentially with the input dimension. Therefore, BSPL is suitable only for a low-dimensionality approximation.

With this set of attributes, the BSPL output is a weighted sum of active receptive field strengths associated with X (the receptive fields in which X falls). Unlike RBF, only a relatively few re­ceptive fields (because of compact local support) are used for each training sample.

Given a training sample (X1: , Y1: ) in the kth cy­cle, W;. is adjusted incrementally in the direction of steepest descent of the approximation error

89

(E1:) (using NLMS or equation l . lc in RBF). Details of BSPL architecture can be found in Cox ( 1972), De Boor ( 1972) , and Brown, Har­ris ( 1992) , Brown, Harris (1991) .

1.3 Cerebellar Model Articulated Controller ( CMAC)

The receptive field width in CMAC is fixed prior to learning (same as BSPL). The standard recep­tive field roll-off (suggested by Albus) is a rectan­gular function though a linearly tapered function has widely been used. A multi-dimensional ta­pered field (F;.) is formed using a minimum op­erator on /;. in each axis. For an example, a two-dimensional receptive field is a pyramid.

The receptive field centers in CMAC are fixed prior to learning (same as BSPL). But unlike BSPL, the field centers are traditionally placed on a hyper-diagonal and also sub-diagonals in RN , rather than on every grid points in RN . An example of a two-dimensional field placement is given in fig. 2 .

The field placement can be constructed system­atically by decomposing the network into C lay­ers of receptive fields. These receptive field lay­ers are offset diagonally relative to each other, and each of these receptive field widths (uniform throughout the network) is set proportional to C. In doing so, a larger C implies more lay­ers of receptive fields, but on the other hand the field width is much coarser. Moreover, a larger C will result in less uniform field place­ment within a single receptive field. Therefore, a well-balanced network performance can only be achieved by choosing an appropriate C. But un­like BSPL, the number of active receptive fields is independent of the input dimension. Also un­like BSPL, the total number of receptive fields required in the network grows much slower than that of BSPL by about a factor cN- l , which is highly critical in terms of memory requirement constraint (especially for a larger C). Because of an efficient use of memory storage, CMAC can also be used for a high-dimensionality approx­imation. A potential trade-off of the efficient memory management is a larger approximation mismatch over the entire RN , especially when Y is dense everywhere (uniform frequency distribu­tion) in RN .

In order to improve the uniformity of the field placement, three heuristic constraints were sug­gested by An, Miller, Parks ( 1991) to restructure the field placement. First, the projected fields onto each axis must be uniform. Second, the hy­perdiagonal field distribution is forbidden in any subspaces. Last, the receptive fields are forced

to be widely apart from each other. These con­straints gives rise to a more uniform placement at the expense of a possibly larger C, especially in a higher dimensional input space.

With this set of attributes, the CMAC output is a weighted sum of active receptive field strengths associated with X (same as BSPL). The adap­tation of � is based on equation l .lb (same as RBF & BSPL). Details of CMAC architecture can be found in Albus (1972) and An, Miller, Parks (1991) .

2 Network Evaluation On Time Series Prediction

There are many ways to evaluate and com­pare the learning performance of these networks. Chen, Grant, Cowan ( 1991) evaluated the learn­ing performance of RBF based on a non-linear time series with four inputs and two outputs. Brown, Harris (1991) evaluated the learning per­formance of BSPL based on the same 40 non­linear time series, and compared the results using BSPL to those using RBF. In this paper, CMAC was evaluated using the same 40 non-linear time series so that a reasonable comparison among these networks can be made. RBF, BSPL and CMAC were all used in reconstructing the dy­namics of these non-linear time series. The cho­sen non-linear 40 time series without noise has an unstable fixed point at the origin, and a sta­ble limit cycle projected in both (Y1 ( t) , Y1 ( t - 1)) and (Y2 (t), Y2(t - 1)) (fig. 3 and 4, equation 2.1 and 2.2) .

Y1 (t) = (0.8 - 0.5e-y:(t- l )}Y1 (t - 1) - (0.3 + 0.9e-Y1(t-l))y1 (t - 2) + O . lsin(y2 (t - 1)) + ei ( (t)

(2 .1)

Y2(t) = 0 .6y2(t - 1 ) + 0 .2y2(t - l)y2(t - 2) + l .2tanh(y1(t - 2)) + ea (t) (2.2)

In Chen, Grant , Cowan ( 1991) , the RBF cen­ters were placed by means of the orthogonal least square method, and 50 RBF centers were chosen based on an off-line approximation error criteria (non real-time learning) . The basis function was a thin-plated spline (z2log(z2) ) , and the weights were adjusted by the recursive least square (RLS) method. 1 ,000 noisy iterated training data were used in which both white noise sequences (mu­tually independent) had a zero mean and 1 % variance (refer to equation 2.1 and 2.2) . After training, the iterated network outputs projected in Y1 (t) , Y1(t - 1) and Y2 (t) , Y2(t - 1) are repro-

90

duced in fig. 5 and 6.

In Brown, Harris ( 1991 ) , there were seven over­lapping piecewise linear splines in each axis, and altogether 2 ,401 splines in the four-dimensional input space. The physical spline width was 1 unit wide. The weights were adjusted by the stochastic NLMS method. 7 ,000 noisy iterated training data were used with identical noise char­acteristics as in RBF. After having 10 training cycles (the same 7,000 iterated training samples were used in each cycle), 650 weights were ac­tually used. 1 ,000 iterated network data were generated, and the network outputs projected in Y1 (t), Y1(t - l) and Y2(t) , Y2(t - l) are reproduced in fig. 7 and 8. Thejagged limit cycle was caused by the piecewise linear interpolation with the rel­atively small field width.

The CMAC receptive field was formed using a piecewise linear roll-off function and a su­perellipse operator (distance metric is defined as (X{ + Xi + Xi + Xt) t ) . There were fifty nine receptive fields in each axis, and altogether 480 receptive fields in the four-dimensional input space. The physical field width was 3 units wide. Each active field strength was normalized by a sum of all active field strengths for each train­ing sample, and the learning rate was set to 0 .1 . The identical set of training data (7 ,000 samples used in each cycle) applied to BSPL was used to train the CMAC network. After having one training cycle, 279 weights were actually used. 1 ,000 iterated network data were generated, and the network outputs projected in Y1 (t) , Y1 (t - l) and Y2(t) , y2 (t - 1) are shown in fig. 9 and 10 .

With relatively small set of weights, all three networks were able to capture the dynamics of the 40 non-linear time series (the unstable origin and the stable limit cycle in Y2(t) vs. Y2(t-l) and Y1 (t) vs. Y1 (t - l) . Among these networks, RBF used the fewest weights (see table 1) . Neverthe­less, no attempts were made in obtaining a min­imum set of weights and a minimum set of train­ing cycles for each of these networks based on the reconstructed the times series dynamics. For an example, any prior knowledge of the smooth de­sired function surface can be used in any of these networks to further reduce the size of the weight set.

3 Derivative Estimation

One of many useful applications on neural net­works is estimating a plant derivative. In fig. 1 1 , a feedforward controller is adjusted based on an instantaneous tracking error (E(i) = � (Yd(i) -Ynetwork(i) )2 ) (a feedback controller is commonly

used to provide a safety net for the learning con­vergence to be established, and is ignored in this example). The goal-directed adaptation is only possible if the plant derivative (Jacobian) is known, or its close approximation has been established (see equation 3 .1) . By using another neural network to model the plant (shaded blocks are neural networks) , the estimated plant jaco­bian can be recovered from a set of the interpo­lated weights, like any expansion series.

(3 .1)

This section evaluates the ability of the CMAC network to estimate the function derivative cg�) for a single input and a single output. The (SISO) function of interest (F) was sin(21rX) + sin(61rX) + sin(101rX), and was defined in [0, 1] . The desired function (F) and its derivative ( g�) are shown in fig. 12 and 13 respectively.

The resolution of the field placement was 0 .02 unit (the distance between the two closest field centers), and the physical field width was 0.2 unit (ten overlays of receptive fields) . The receptive field roll-off was chosen to be piecewise cosine. The training set was made of 50 number of sam­pled data points taken at the grid points in the input space. The network output was then given 5 ,000 training samples randomly chosen from the training set. After 5,000 trainings, fig. 12 shows the network was able to properly approximate F and fig. 13 shows the estimated derivative net­work output ( g;). (Further work needs to be done on a multi-dimensional input , which is a tougher problem for the CMAC network (due to sparsity of receptive fields).

4 Summary

In general, with RBF it is best to have a small­est set of weights so the on-line numerical com­putation for both the center adjustment ( adap­tive clustering) and the weight adjustment (RLS) can be minimal. In BSPL, both the total num­ber of network weights and the number of active weights for each training sample grow exponen­tially with the input dimension. This imposes a heavy memory requirement constraint on any real-time applications with high dimensional in­puts. In CMAC, the total number of network weights is much smaller than that in BSPL, espe­cially for a large field width. Also, the number of active weights is independent of both the training sample and the input dimension (which in turn is much less than the total number of network

91

weights) . A potential trade-off between CMAC and BSPL in terms of the memory requirement is the function approximation accuracy (which is highly dependent on the desired function surface itself) .

Acknowledgement.

This work is currently funded by the PROMETHEUS project. Professor Harris is supported by Lucas Aerospace.

References.

Poggio T. , Girosi F. ( 1990) , Networks for Ap­proximation and Learning, Proceedings oflEEE, Vol. 78, No. 9, p 1481-1497.

Chen S . , Billings S. ( 1992) , Neural Networks for Non-linear Dynamic System Modelling and Iden­tification, to appear in International Journal of Control.

Cox M. ( 1972) , The Numerical Evaluation of B­Splines, J . Inst. Math. Appl . , 10 , pl34-149.

De Boor C. ( 1972) , On Calculating with B­Splines, J . Approximation theory, 6 , p50-62.

Brown M. , Harris C.J. ( 1992) , B-Splines Neuro­controller, to appear in " Parallel Processing in Real Time Control" , Ed. E. Rogers, Prentice Hall.

Albus J .S. ( 1972), Theoretical and Experimental Aspects of a Cerebellar Model, PhD dissertation, University of Maryland.

An P.E. , Miller T.W., Parks P.C. ( 1991) , Design Improvements in Associative Memories for Cere­bellar Model Articulation Controllers (CMAC), pi International Conference on Artificial Neural Networks, Helsinki University of Technology.

Chen S . , Grant P. , Cowan C. ( 1991) , Orthogo­nal Least Squares Algorithms for Training Multi­Output Radial Basis Function Networks, IEE 2nd Conference on Artificial Neural Networks, p336-339.

Brown M. , Harris C.J. ( 1991) , On-Line Non­Linear Time Series Prediction, Panorama Techi­cal Report.

D I I )

Figure la. Width Order • l

Figure lb. Width Order • 2

Fig. 1 . Spline field roll-off for a lD input

• • • • • • •

• • • • • • •

• • • • • •

• • • • • • •

• • • • • • •

Fig. 2. Field center placement for a 2D input ( C = 3)

y(t-l)

-1 . 5 �-�-�-�-�--�-

-1 . 5 o . o y(t-2) 1 . 5

Fig. 3. Noiseless 4D time series (y1(t) vs. y1(t - 1)) .

92

y(t-1)

-1 . 5 L______J_�----'----'----'----

- 1 . 5 0 . 0 y(t-2) 1 . 5

Fig. 4. Noiseless 4D time series (Y2(t) vs. Y2(t - 1 )) .

1 . 2

0 / . I ) . . \ \ /

\ .-·-· \ _/

\ \ \ i

./

-1 .2 ...__ ____ ___ ....,.

·• ,, -.. l . - 0 1 . 2

Fig. 5 . RBF iterated phase (y1 (t-1) vs. y1 (t))

1 . 2

0 I

� I I I. \ . .

·-· I ··- ....... --. ... /

I

- 1 . 2 "----------!

- 1 .2 0 1 .2

Fig. 6. RBF iterated phase (y2 (t- 1 ) vs. y2(t))

93

y[t-1)

-1.5 �---'--� ·-�-�-�� -1.5 0.0 y(t-2) 1 . 5

Fig. 7. BSPL iterated phase (y1 (t) vs. y1 (t-1)) .

y(t-1)

-1.5 .____,___..__ _ _,__ _ _,__ _ _,___ -1.5 0 . 0 y(t-2) 1 .5

Fig. 8. BSPL iterated phase (y2( t) vs. y2( t-1) ) . 1 . 5 .---,.---,.---,.-----,,------,----,

y[t-1)

0 . 0

-1 .5 ��-�-�-�-�-� -1.5 0.0 y(t-2) 1 . 5

Fig. 9. CMAC iterated phase (Y1(t) vs. y1 (t-1)) .

94

1 . 5

� - --

/ v----y(t-1)

/ '\ '�

..•

.

0 .0 .... , · . . / \ / l-/"

-1.5 -1 . 5 0 . 0 y(t-2) 1 . 5

Fig. 10. CMAC iterated phase (y2(t) vs. Y2(t-l)) .

Yd(l+1) ���� ­bM��i�t Plant

;t: e(l+1)

Y(l+1)

Fig. 1 1 . A tracking error-based controller.

; -1 - - -· - - : - ..... ... - ! -

8•60 ! ·2 ··-· · c-10 - -j ·- ·-·- · -· + #•500d

-a �.�������������� 0 0.2 0.4 0.8 0.8

Input

Fig. 12. Desired output vs. CMAC output

95

Network

RBF

B SPL

CMAC

- 40

-eo�-�--�-��--�-� 0 0.2 0.4 o.e 0.8

Input

Fig. 13. Desired derivative vs. CMAC derivative

# weights Update Roll-off operator

50 RLS Thin-plate Euclidean

650 NLMS Linear Product

279 NLMS Linear Superellipse

Table 1 4D time series summary.

96

Center

OLS

Fixed

Fixed

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

INDUCTION OF CONTROL RULES FROM HUMAN SKILL

K.J. Hunt and Y.M. Han

Control Group, Department of Mechanical Engineering, University of Glasgow, Glasgow G 12 SQQ, UK

Abstract

Human beings are capable of learning to manually control com­plex nonlinear dynamical systems. It is well known, however, that lmmans have great difficulty in acticulating the rules un­derlying their skilled behaviour. This paper focusses on the au­tomatic machine induction of control rules from past records of skilled human behaviour. The aim of this endeavour is to install the induced rules as an automatic control program; it is antici­pated that this will lead to more consistent and reliable control performance.

The approach we study is based on the automatic induc­tion of production rules from examples. The algorithms used are a product of the machine learning sub-field of artificial intelli­gence research.

We present experimental results describing induction of executable models of skilled human control behaviour. Experi­ments were performed on physical laboratory apparatus.

1 Introduction

Human beings are capable of learning to manually control com­plex nonlinear dynamical systems. It is well known, however, that humans have great difficulty in acticulating the rules un­derlying their skilled behaviour. This paper focusses on the au­tomatic machine induction of control rules from past records of skilled human behaviour. Since human controllers can be viewed as nonlinear dynamical systems we seek to develop a modelling technique having the following important features:

• development of general black-box nonlinear models,

• models dealing with both numerical and symbolic (linguis­tic) data,

• models expressed in a high-level human orientated (under­standable) format,

• automatic induction of models from examples of past be­haviour.

This combination of features is unique amongst nonlinear mod­elling techniques. In the emulation of human skill the lmman is viewed as the nonlinear dynamical system which we wish to model.

The approach we study is based on the automatic induc­tion of production rules from examples. The algorithms used are a product of the machine learning sub-field of actificial intelli­gence research. The proposed method is verified in a real-time laboratory experiment.

Modelling

The black-box approach to modelling stands in contrast to 'physically'-based models. In special cases it may be possible to build a model from physical insight and fundamental system

knowledge. The parameters of such models usually correspond to physical quantities. In the case of linguistic model building

97

the process is complicated by the difficulty of eliciting knowledge from human experts. When little physical insight is available we may resort, as in this paper, to black-box models. Black-box models can be viewed as mappings from system input to output variables and can be fitted to observed data.

The process of fitting models to observed data is known as system identification. For linear systems with numerical data a large literature has evolved [1, 2, 3]; these techniques have been widely applied in the adaptive control field [4]. Generally, in linear systems, the identification procedure involves selecting numerator and denominator polynomials of a rational transfer function in order to optimise some goodness-of-fit criterion.

For nonlinear systems the development of black-box mod­elling techniques is less well developed. One possibility is to use a parameterised polynomial model such as a Volterra expansion [5]; this approach clearly lacks generality and moreover handles only numerical data.

The recent focus of interest on artificial neural networks provides strong potential for the development of a general frame­work for nonlinear black-box modelling. Such networks have been shown to have the universal approximation property (6, 7, 8, 9] and applications to dynamical systems and control have been reported [10, 11, 12, 13, 14, 15, 16]. Further, by appropriate en­gineering, networks are able to deal with both symbolic and nu­merical data. A drawback of networks, when considering the list of desirable features outlined above, is the lack of transparency in the knowledge representation framework; knowledge about the system being modelled is stored as the numerical values of the inter-neuron weights.

The fuzzy logic formalism overcomes the latter objection. Fuzzy logic systems deal with imprecisely known and nonlinear systems where variables are described in a fuzzy, linguistic form [17, 18]. Fuzzy logic control systems are now well established and have met with strong industrial success (19, 20, 21, 22]. However, the problem of elicitation of system knowledge in the form of fuzzy linguistic rules still does not have a general solution. An interesting possibility, based on the acquisition of fuzzy rules from examples, can be found in the recent paper by Wang and Mendel (23].

In this work we present an alternative approach to the linguistic representation and knowledge acquisition problems for nonlinear dynamical systems modelling. The approach is based upon concept learning from examples by machine induction. A full account of the work summarised in this paper is in Hunt [24j. All of the experimental details and figures which are omitted in this summary can be found that reference. Related recent work on this theme can be found in Han [25], Stromberg et al [26], and in Batur et al [27].

Machine Induction

Machine learning is one of the many sub-fields of artificial in­telligence research. The machine learning area itself consists of many diverse techniques. See the texts by Michalski et al [28, 29] for an overview of the field. Here, we focus on concept learning from examples. This type of learning is an example of inductive learning; induction seeks to formulate plausible general asser­tions that explain the given facts and are able to predict new facts. Thus, concept learning systems produce general descrip­tions of concepts (or classifications of objects) from specific in­stances. Moreover, these general descriptions are in a high-level, human orientated format.

At the beginning of this introduction we categorised a sought-after approach to nonlinear black-box modelling which had four desirable features. It is now clear that machine induc­tion systems of the type just described hold considerable promise; this promise is explored in the sequel.

We consider dynamical systems modelling and control tasks as problems of classification; one approach to the induc­tion of classifiers from pre-classified examples is pursued. This involves the acquisition of production rules. One such approach, known as the AQ algorithm, was developed by Michalski (30]. Clark and Niblett (31] modified AQ to cover problems signifi­cantly affected by noise. An implementation of their algorithm, known as CN2, is documented in Clark (32] and Boswell (33]. CN2 is used in the experiments reported here.

Techniques for the induction of decision trees provide an alternative to AQ-type production rule induction algorithms (see, for example, Hunt et al [34], Breiman et al (35], or Quinlan (36, 37]). The application of induced tree classifiers to control and modelling is reported in Hunt [24].

Application to Control

As mentioned above, the emulation of skilled human control be­haviour can be viewed as a problem in nonlinear dynamical sys­tems modelling. This is perhaps the most interesting application of the proposed approach. The task can be formulated as the acquisition, from examples, of machine executable and human understandable models of skilled human control behaviour. The ultimate aim of course is to install the derived model as an au­tomatic control program. Michie and colleagues have recently pursued this aim [38]. As pointed out by these authors, skilled humans have great difficulty in articulating the rules underlying their actions. However, past records of control behaviour can serve as a rich source of material for building models of that be­haviour. Induced models of human control of a dynamical system (a simulation of the inverted pendulum) were shown by Michie et al to capture the skilled human's behaviour and often to produce a more reliable and consistent performance.

This specific facet of our general inductive approach to modelling of nonlinear dynamical systems is pursued in the latter part of this paper; we present experimental results describing in­duction of executable models of skilled human control behaviour. Experiments were performed on physical laboratory apparatus.

2 Classification

A classifier is a systematic way of predicting to which of a finite number of classes a given object belongs. Objects, or cases, are defined by a set of measurements or attributes. Based on these measurements we wish to predict which class the object is in. As described below, a classifier may be viewed either as a mapping from a set of attribute values to a particular class or as a partition of the measurement space according to the class values.

2.1 Partition of the Measurement Space

Objects are defined by the values of their attributes z1, . . . , Zna. In general, the attributes may take on numerical or symbolic values; in any measurement vector z = (z1 , . . . , Zna)T some at­tributes can be numerical and some symbolic. We define the measurement space to be the space containing all possible mea­surement vectors and denote it as X· Thus, z E X·

Suppose that any object is a member of the class c, one of nc classes. Denoting the set of all classes as C we have c E C = { c1 , . . . , Cnc}. A classifier assigns a class c E C to every measurement vector z E X· The classifier can be thought of as a mapping f where

f : x -+ C. (1)

98

An alternative way oflooking at a classifier is as a partition of the measurement space x. We define Ac as the subset of x on which /(z) = c. Thus, the classifier partitions the measurement space into the subsets

Acee = {z; /(z) = c}. (2)

The subsets A.,1 , . . . , Ac,., are disjoint and the space x is the union of these subsets, x = Uc A.,. The subsets Ac therefore form a partition of x; the classifier partitions x into nc disjoint subsets Ac1 , . . . , Acn, (X = Uc Ac) such that for every measure­ment vector z E Ac the predicted class is c.

2.2 Construction (Induction) of Classifiers

Classifiers are constructed, or induced, using a past history of pre-classified examples. This training set consists of a series of measurement vectors z together with their actual classification c. A formal definition of the training set is given below. The ulti­mate aim in constructing classifiers is to use the finished product to predict the classes of future, as yet unclassified, examples. Many types of classifiers exist, including

1. decision trees and,

2. production rules.

In this paper we consider the latter.

2.3 Notation

In this section we summarise some of the notation used above and introduce some new definitions. In this paper we consider only discrete-valued attributes and classes which can take on one of a finite number of distinct values.

Each object is described by na attributes z.,

z; : i E {1, 2, . . . , na}, (3)

and belongs to the class c, one of nc distinct classes;

Each attribute z; may take on one of 11i distinct values i.e.

The feature vector

(6)

contains all attribute values describing a particular object. One feature vector together with the associated class defines a training sample z;

z = (z1 , z2, . . . , zna, c)T. (7)

If the pre-classified set of examples has N samples then the train­ing set Z may be denoted as

ZN = {z}iN. (8)

3 Induction of Production Rules

Here, we consider the induction of production rules in an if-then format. A family of algorithms having this output format is discussed here. This family is derived from Michalski's AQ algo­rithm (30]. AQ-type algorithms induce a set of decision rules from pre-classified training data; each set of induced decision rules is associated with one of the nc classes. New examples are classi­fied by finding which of the decision rules have their conditions matched by the example and then choosing one of those rules (either by ordering or majority precedence).

Each decision rule has the form 'if <condition> then pre­dict <class>'. Here, <condition> is a Boolean combination of attribute tests. The basic test on an attribute is called a selec­tor (examples of selectors are <temp = high>, <speed < 50>, <pressure = medium V low>). A conjunction (logical and) of selectors is called a complex. The <condition> part of the de­cision rule can generally be a simple selector, a complex, or a disjunction (logical or) of complexes1 .

3.1 The AQ Algorithm

The basic AQ algorithm (30] generates a decision rule far each class in turn. The <condition> part of a decision rule in AQ takes the form of a disjunction of complexes. For each class, the induction procedure proceeds in stages; each stage generates a single complex and then removes the examples it covers from the training set. This is repeated until the disjunction of the complexes found covers all examples of the class. This whole process is repeated for each class in turn.

When generating a complex the AQ algorithm follows a general-to-specific search for the best complex. This is done by repeatedly specialising the empty complex (which covers all ex­amples) using selectors from some seed positive example which exclude a given negative example of the class. The seed is chosen as a positive example not already covered. The specialisation pro­cedure ensures that the seed example remains covered and con­tinues until all negative examples are excluded. The algorithm proceeds in parallel since a number of 'best complexes found so far' are specialised together; this size-limited set of complexes is called a star.

Since the AQ algorithm depends on specific examples dur­ing search it effectively assumes no noise is present and searches for a description that classifies the training data perfectly. As with the basic decision tree approach described earlier, this ap­proach leads to overfitting of the classifier. Developments of basic AQ leave the core algorithm unmodified and deal with noise us­ing pre- and post-processing techniques (see Michalski et al (39]). Clark and Niblett [31 ], on the other hand, designed the CN2 algo­rithm specifically for problems with noisy data. The algorithm, described below, is conceptually similar to AQ but fundamental changes to the underlying algorithm have been made.

3.2 The CN2 Algorithm

CN2 (31, 32, 33] can be viewed as a generalisation of the AQ algorithm. The dependence on specific training examples during specialisation of complexes is removed. The specialisation pro­cess is broadened to include all specialisations of a complex; the aim is to find the best complex which covers large numbers of examples of a single class and a few of other classes. Thus, we no longer search far perfect classification and in this way problems with noisy data can be covered. Specialisation of complexes is halted when no further specialisations are possible. Complexes which are found not to be statistically significant are prevented from becoming the best-complex and thus from joining the in­duced rule list (this is analogous to decision tree pruning) . Like AQ, CN2 maintains a star of 'best-complexes-found-so-far' dur­ing search.

1 A disjunction of complexes is sometimes called a cover.

99

The decision rules induced by CN2 have the form 'if <complex> then predict <class>'. The algorithm produces an ordered set of if-then rules2; during classification of new exam­ples each rule is tried in order until one is found whose condition is matched by the example.

During each iteration the algorithm searches for a complex that covers a large number of examples from a single class c and a few of other classes. The complex must be of acceptable quality and must be significant. The heuristic functions used in CN2 to evaluate quality and significance are discussed below. Having found a good complex, the examples which it covers are removed and the rule 'if <complex> then predict class c' is added to the end of the rule list. All possible specialisations of the current star of complexes are examined. Each complex is specialised by either adding a new conjunctive term or removing a disjunctive term in one of its selectors.

3.2.1 Complex quality evaluation

The quality of complexes must be examined for two purposes. First, during search the algorithm maintains a best complex and each new complex generated must be evaluated to determine whether it should replace the current best complex. Second, the algorithm must determine which complexes to discard if the maximum star size is exceeded. Here, we follow the notation in­troduced in Section 2.3. The subset of examples which a given complex covers is denoted by Z'. The total number of examples covered by the complex is denoted by N', and the number of positive examples by N;. Three possibilities for complex quality evaluation are:

• Entropy: the entropy measure used in quality evaluation is similar to the information theoretic attribute evaluation measure used in the ID-type decision tree induction algo­rithms. We denote the probability that a sample in Z' has class c,, by P.,,. Thus, the probability distribution among classes in Z' is (P.i. . . . , P.nc) · The following measure is then used to evaluate complex quality:

entropy = - L ncP.,,log(P.,,). (9) p=l

Here, a lower entropy measure indicates a better complex. This evaluation function favours complexes covering a large number of examples of a single class and a few of other classes.

• Naive error estimate: the CN2 implementation also allows a very simple quality evaluation, the naive error estimate, given by

N' . p naive = N'

' (10)

This is the measure traditionally used in the AQ algorithm.

• Laplacian error estimate: this is defined by

N' + 1 laplace = _,, __ ,

N' + nc

where nc, as before, is the number of classes.

(11)

The first of these (entropy) is suggested in the published CN2 algorithm [31] but the other two are options in the latest im­plementation [33]. It has been suggested by Clark [32] that the Laplacian error estimate performs best.

2Note that the latest implementation of CN2 allows unordered rules to be

generated if desired. This involves a change in the evaluation function and

a change in the way in which examples are removed from the training set

during iteration.

3.2.2 Complex significance evaluation

The significance of each complex must also be evaluated. A com­plex is said to be significant if it reflects a genuine correlation be­tween attribute values and classes, rather than a regularity which occurred by chance. To evaluate complex significance CN2 uses the likelihood mtio statistic. The obseroed frequency distribution in Z' among classes is denoted as (/1 , . . . , Inc)· The expected dis­tribution of the N' examples in Z' assuming the complex selects examples randomly is ( e 1 , • • • , enc). This distribution is calcu­lated as the N' covered examples distributed among classes with the same frequency as that of examples in the whole training set Z. The likelihood ratio statistic is

2 2: ncfplog (�) . p=l p (12}

This statistic provides a measure of the distance between the ob­served and expected distributions; the nearer the distributions (the lower the score) the more likely it is that the apparent reg­ularity is due to chance. The user provides a threshold of signif­icance below which rules are rejected.

4 Modelling and Control as Classification Problems

In this section we reformulate the modelling of discrete-time dy­namical systems as a classification problem. The aim is to de­scribe dynamical systems modelling in terms consistent with the framework of the induction algorithms outlined above. Note that we consider the task of emulating an existing feedback controller (for example, a skilled human) as a modelling problem; the ex­isting controller is considered as a dynamical system which we wish to model. Thus, the dynamical system S referred to below can be an existing controller we wish to emulate or a plant we simply wish to model.

Consider a general nonlinear discrete time dynamical sys­tem S described by the input-output relation

y(t) = f(y(t - 1}, y(t - 2}, . . . , y(t - n}; u(t - k), u(t - k - 1), . . . , u(t - k - m)).

(13}

Here, u is the system input and y the output. The index t denotes discrete instants of time. The order of the system is n, while the delay-time is given by k. Thus, the present system output y(t) depends (in the sense defined by the nonlinear function f) on n past values of the output and m + 1 past values of the input. In general, the variables u and y are real valued, u E !Rnu, y E !Rny. For the moment we consider only single-input single-output systems where nu = ny = 1.

The relation (13} may be thought of as a classification mapping from the argument of f to the class variable y(t). Thus, in accordance with the notation and terminology introduced in Section 2.3, we may consider the feature vector of attribute values z (see Equation ( 6)) to be the argument to the nonlinear function in (13) i.e.

z.(t) = (y(t - 1), y(t - 2}, . . . , y(t - n}; u(t - k), u(t - k - 1}, . . . , u(t - k - m))T. (14}

Here, we use the subscript r to emphasise that the elements of this vector are real valued, Zr E !Rn + m + 1. The number of attributes na is given by na = n + m + 1.

These real valued variables may now be quantised into a finite number of distinct values by some discretisation operator which performs the mapping y -+ Yd. u -+ ud. The quantised feature vector becomes

z(t) = (Yd(t - 1}, yd(t - 2), . . . , yd(t - n); ud(t - k), ud(t - k - 1}, . . . , ud(t - k - m)}T.

(15}

100

Comparing this expression with the general feature vector ex­pression (6) the individual elements of z may be identified as

z;(t) = { Yd(t - i); i = 1,

: . . , n

. (l6) ud(t - k + n - i + l} ; i = n + 1, . . . , n + m + 1

Each element of z (i.e. z; : i = 1, . . . , na) may take on one of n; distinct values, { {Y<11 (t - i}, yd2(t - i), . . . • Ydn; (t - i)}, i = 1, . . . , n

z;(t) E �udl (t - k + n - i + l}, . . . , udn; (t - k + n - i + l)}, ( l i = n + 1 , . . . , n + m + 1

Thus, the individual values which each z; can take ( Ziq : q = 1, . . . , n;) may be compactly expressed as { Ydq(t - i}, q = 1, . . . , n;; i = 1, . . . , n

Ziq(t) = �dq(t - k + n - i + 1 } ,q = 1, . . . , n;; i = n + 1 , . . . , n + m + 1

( 18}

As mentioned above, the class variable is the current sys­tem output y(t). The class variable is quantised into nc distinct regions (c.f. Equation (4)),

c(t) = Yd(t) E {Y<11 (t) ,yd2(t), . . . , Ydnc(t)}, (19}

or,

ep(t) = Ydp(t},p = 1, . . . , nc. (20}

The above formulation is general enough to allow each attribute z; to take on a different number n; of discrete values. However, it is very likely in practice that all the past values

Yd(t - i} which constitute the attributes z; for i = 1, . . . , n will be quantised into an equal number of regions (since they are the same variable, just delayed}. The class variable c(t) = Yd(t) will also have this number of distinct possible values. Similarly, all the past values ud(t - k + n - i + 1} making up z; for i = n+ 1, . . . , na will likely be quantised into an equal number of regions. To summarise, the following will normally hold,

nc = ni = n1 ; i = 1, . . . , n n; = t1.n+1 ; i = n + 1, . . . , na, (21}

where n1 and t1.n+1 are integer constants.

5 Experimental Results - Ball & Beam Control

We now apply our approach to real time control of the physical ball & beam apparatus. In this case we first define a control objective in qualitative terms and then train a human to perform this control task. The ultimate aim is to induce a computer executable model of this skilled behaviour and install these rules as a control program.

5.1 Description of ball & beam apparatus

The apparatus consists of a light aluminium T section approxi­mately 1.lm long. Two insulated bridge pieces are mounted lm apart on the beam onto which two wires, 1.3cm apart, are tautly stretched. The hybrid beam is fixed on a cradle which in turn is mounted, via a bearing block, to a rigid back plate. The beam is pivoted about the axis of rotation and is driven via a universal joint coupling by means of a vertically mounted moving coil ac­tuator. The angle of the beam and the position of the steel ball on the beam are measured by a potentiometer and can be used for control.

5.2 Control objective

The ball & beam system is naturally open-loop unstable, be­ing well approximated as a double integrator (i.e. the transfer­function between beam angle and ball position is proportional to -!2, where s is the Laplace transform complex variable). The dynamics of the system are thus similar to the familiar pole-cart benchmark. From a control theory viewpoint this is not con­sidered to be a difficult control problem. If, for example, the actuator position is allowed to vary continuously and the ob­jective is to balance the ball at a given position on the beam then a standard analytical controller can be derived rather easily (even with roughly estimated model parameters). We verified this assertion by roughly estimating the constant of proportion­ality in the double integrator expression and calculating a simple LQ (linear quadratic) controller (see Hunt [40] for details). This controller gave very accurate position control at any demanded ball position.

For the purposes of this investigation we placed con­straints on the available control actions, and defined a qualitative control objective. This provided a suitable task for a human con­troller. In particular, the actuator was constrained to have one of two values, corresponding to

1. left end of the beam just below horizontal ( 453 of range ),

2. right end of beam just below horizontal(553 of range).

Note that the horizontal corresponded to the actuator position at 503 of total range. Clearly, under these constraints exact stabil­isation of the ball at a desired position was impossible. Accord­ingly, the control objective was stated as vary the constrained actuator position in such a way that the ball oscillates between two points respectively slightly left of the beam centre and slightly right of beam centre (where 'slightly' was roughly 3 centimetres) .

A human w as trained t o proficiency i n this control task. Typical results of human control are found in [24]. In the trial, the ball was repeatedly placed at arbitrary positions near either end of the beam and the human was required to return the ball to the specified range. The human is observed to achieve the required oscillatory behaviour.

Note that we have specified a highly nonlinear control problem (due to the nonlinear actuator constraints). Thus, an analytical design using standard theory would be difficult in this case. The specification of an oscillatory (roughly sinusoidal) ref­erence is a further complication. The human, on the other hand, acquires the necessary skill with ease. The objective now is to capture the decision rules underlying that skill.

5.3 Overview of the induction experiment

Two variables are available for feedback:

1. y(t): the position of the ball in the range 0.0 to 100.03,

2. ydot(t): the speed of the ball, derived from position as ydot(t) = y(t) - y(t - 1).

These attributes were used to calculate the control signal u( t) which physically corresponded to the actuator position and in this case served as the class attribute for induction. The con­trol problem therefore translated to a classifier mapping from y(t), ydot(t) to u(t).

For the purposes of induction the variables were quantised as follows:

• attribute: ydot: four discrete regions such that

1. Rp2 when ydot :;:: 1.0,

2. Rpl when 0.0 ::; ydot < 1.0,

101

3. Rnl when -1.0 ::; ydot < 0.0,

4. Rn2 when ydot < - 1.0.

• attribute: y: four discrete regions such that

1 . yr 2. ymr 3. yml

4. yl

when y > 50.0,

when 46.5 < y ::; 50.0,

when 43.0 ::; y ::; 46.5,

when y < 43.0.

• class attribute: u: two discrete regions such that

1. upos when u(t) = 55.0,

2. uneg when u(t) = 45.0.

5.4 Results

2056 examples of human control behaviour were used to induce decision rules for the controller. The program CN2 was used to generate production rules. This rule base was installed in the real-time feedback control loop as an automatic control program. A typical trial using this installed rule-base is shown in [24]. As shown there, the rule-based controller is initially faced with a ball position near the right hand end of the beam. According to the specification, the controller manages to return and maintain the ball in the desired range with the required behaviour. At around time t = 30s a disturbance was arbitrarily inflicted by manually moving the ball to a position near the left end of the beam. Again, the controller quickly recovers control and returns and maintains the ball in the desired range. Clearly, the deci­sion rules underlying the behaviour of the skilled human have been captured by the induction algorithm and this skill has been successfully installed in the automatic controller rule-base.

5.5 Discussion of Results

The ball and beam control results clearly demonstrate the princi­ple that skill-based dynamical control behaviour can be captured by inducing decision rules from past records of human behaviour. Moreover, the technique has been illustrated on a strongly non­linear system where the control task was qualitatively specified.

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[38] D. Michie, M. Bain, and J. Hayes-Michie, "Cognitive models from subcognitive skills," in Knowledge Based Systems for Industrial Control (J. McGhee, M.J. Grimble, and P. Mow­forth, eds.), vol. 44 of IEE Control Engineering Series, pp. 71-99, Peter Peregrinus Ltd, 1990.

[39] R.S. Michalski, I. Mozetic, J. Hong, and N. Lavrac, "The multi-purpose incremental learning system AQ15 and its testing application to three medical domains," in Proc. 5th National Conference on Artificial Intelligence, pp. 1041-1045, 1986.

[40] K.J. Hunt, Stochastic Optimal Control Theory with Appli­cation in Self-tuning Contro� vol. 117 of Lecture Notes in Control and Information Sciences. Berlin: Springer-Verlag, 1989.

Copyright @ IFAC Anificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

A KNOWLEDGE ACQUISITION AND PROCESSING STRATEGY BASED ON FORMAL CONCEPT ANALYSIS

G. Nowinski and V. Krebs

lnstilutfiir Regelungs- und Ste�rungssysteme, Universilat Karlsruhe, Kaiserstrasse 12, D-7500 Karlsruhe J, Germany

Abstract . A new method for knowledge acquisition and processing is developed by using the mathematical theory of formal concept analysis. First it is demonstrated how a decision table for a process control problem (distillation column) is obtained by a dialogue between the expert and the computer. Then the concept analysis approach is briefly outlined. This enables an optimization of conventional expert systems. However, more important for practical real time applications is the direct processing of the knowledge contained in a decision table by combining concept analysis with Shannon's entropy. Thus the resulting knowledge based system is optimal in an information theoretical view. It can be implemented in a procedural language and therefore simply be embedded into existing process control systems. Keywords. Artificial intelligence; knowledge acquisition; knowledge engineering; chemical industry; expert systems; concept analysis; process control;

INTRODUCTION

It is well known that knowledge acquisition turns out to be the bottle neck during the process of building a knowledge based system. Therefore, in this paper a new method will be presented that overcomes most of these difficulties and thus can help to widen the bottle neck.

The strategy developed is based on formal con­cept analysis, a mathematical approach for han­dling knowledge of all kind which is particularly useful for ordering and classification of objects. Our strategy can be applied both for diagnosis and process control. Due to the primary scope of the symposium in the sequel only the aspect of process control will be developed.

In the beginning of the knowledge acquisition pro­cedure a dialogue between an expert for a spe­cial problem and a computer takes place. The expert's knowledge is step by step transformed into a three-valued truth table. This table can be edited without loss of consistency.

Then, the truth table can be transformed into rules that can be used for expert systems. By means of the concept analysis, meta-rules are gen­erated which list dependencies between the rules' premises. By this an acceleration of the execution time of the rule based system will be possible.

Alternatively, the table itself can represent the

103

is coolinq system runninq? N� set cooling rote to 50%

set healing role to 75%

Fig. 1 Elementar decision tree

knowledge base. In this case, concept analysis and Shannon's entropy help to decide which condition has to be taken next to find the following action. This procedure further increases performance of the knowledge based system. Instead of an in­ference engine of an expert system, now a short procedural algorithm is used to process the knowl­edge. By this strategy it is comparatively simple to embed knowledge based components into ex­isting process control systems which are usually programmed in a procedural language.

KNOWLEDGE ACQUISITION AND REPRESENTATION

Usually, knowledge acquisition is performed en­volving at least two persons: the expert( s) and the knowledge engineer(s) . The latter has to under­stand the expert's strategy and then to transform his knowledge into a representation ( e. g. rules) in the computer.

Our strategy omits the knowledge engineer by means of a dialogue between the expert and the computer. The latter generates questions which have to be answered by the experts, and thus step by step a decision tree1 is acquired which models the expert's knowledge.

To be more specific, consider the decision tree in fig. 1 which contains some knowledge about how to reach the operating point in a process con­trol problem for starting up a distillation column. This example will be used throughout this paper.

Now the expert wants to add his knowledge about when to turn on the temperature controller: The computer uses his "knowledge" to pose the ques­tion at the root of the decision tree: Is cooling system running? The expert thinks about this question. He knows that the cooling system must run before the tem­perature controller may be activated and thus an­sweres "yes" .

Using his incomplete decision tree in fig. 1 , the computer finds a leaf of the tree and prompts Set heating rate to 70% The expert knows that this is not the action he was thinking about when he answered the computer's question and enters the desired action: "Turn on tempera­ture controller." Now a new question is needed in the knowledge base to distinguish between the action Set heating rate to 76% and Turn on temperature controller. The expert enters the criterion he uses when he has to decide which of the two actions he has to take in form of a ques­tion: " Is heater working?"

The extended decision tree developed so far is shown in fig. 2 .

is coolinq system rvnninq? N� set cooling rate to 50% is /Jeoler workinq?

~ set heating rate turn on temperature ta 75% controller

Fig. 2 Extended decision tree

This dialogue is repeated for every situation the expert knows, and so the tree becomes larger till it contains all the expert's knowledge about this particular process.

1 Generally it is more than a tree, as will become clear later

104

In our strategy, it is allowed to reuse a condi­tion already used earlier to distinguish some sit­uations. When this is done the condition appears on many places in the tree although it is only one condition. Therefore the representation as a tree is not quite correct. The appropriate method for representation of knowledge of this kind is a decision table. Every row describes a situation that requires an action, and every column repre­sents a condition. Table 1 shows the decision table that will emerge from Fig. 2 after adding further knowledge. It gives the dependencies between sit­uations described by conditions (attributes) and the necessary actions (objects) . It is obvious how the decision tree has been mapped to the table.

TABLE 1 Process Control Decision Table

Action Situation attributes) (object) cool heat s > 1 hreb sta- flr

on on > 10 ble > 10 1 cool50 n n y y n 2 heat75 y n y y n 3 press6 y y n y y 4 controlon y y y y y y 5 emerg.off n

I Abbrev. I a I b I c d I e I £ After the expert has entered all important situa­tions the computer asks him about those depen­dencies between conditions and actions that are not yet answered and that are marked in the ta­ble by a dot. The expert can fill up the table by replacing the dots using positive or negative answers or leave the dependencies open as they were. For example the computer may ask: Is flr>10 true for the action "set setpoint of pressure controller to 6 bar (press6 ) " ? Since the expert does not know any dependency between this condition and the corresponding ac­tion he gives no answer, and the dot is not re­placed. The expert can even expand the table by adding further conditions. Further actions must be added as described earlier.

Compared to manual generation of such a table, our strategy has several advantages:

Uniqueness

For every pair of actions there must be at least one condition that can be used to distinguish them. In other words, every action must be uniquely iden­tified by a set of conditions.

Even if many actions are contained in the knowl­edge base our strategy guarantees this. This stems from the fact that the dialogue between ex­pert and computer generates a decision tree. All operations allowed by the strategy on the table add further information without destructing the initial tree. It is a property of trees that there is

exactly one condition that distinguishes every two actions. Therefore the property of uniqueness is maintained.

If such a table is generated manually, it soon becomes too complex to be tested visually for uniqueness.

Consistency

Necessarily, only one action should be taken at a time to prevent the actions to interfere with each other.

This is guaranteed by use of the before men­tioned knowledge acquisition and representation strategy. If knowledge is written manually di­rectly in rule form one can hardly overview if the premises fulfill the consistency property because of the large number of rules.

The problems stem from the fact that part of the knowledge is not considered unvoluntarily. This will not happen if the knowledge is handled auto­matically.

Completeness

The knowledge acquired must cover all important situations. It is hard to keep all possible condi­tions in mind when a knowledge engineer (who is not an expert for the particular problem) builds a knowledge base manually because all the knowl­edge must be handled simultaneously.

In our program, a knowledge engineer is not nec­essary and the expert is asked directly by the com­puter. He is not obliged to have all the knowledge in mind simultaneously; instead, the computer asks precise questions using the expert's terms. Thus, the expert can consider all situations step by step and is reminded repeatedly even to prob­lems that seldom appear.

Usually, the development of a knowledge based system involves iterative modifications of the knowledge acquired so far after tests. It is very difficult to predict the effect of rule modifications to the system's behavior because of the high com­plexity of such systems.

Our strategy prevents the users from adding new mistakes when removing old ones because changes are made in the truth table and not in the rule base. The initial decision tree is always main­tained. After changes have been made new rules are generated automatically.

CONCEPT ANALYSIS

Formal Concept Analysis was developed in the early 80s by R. Wille (Wille, 1 982). This method

105

provides facilities to handle objects and their at­tributes in a mathematical way, regardless of their meaning to the real world. Main applications are in classification of objects , ordering of objects, re­duction of special objects to elementar objects, implications between attributes of objects, and knowledge exploration (Wille, 1 987).

Concept analysis has not yet been used for process control purposes in knowledge based systems. We consider actions that have influence on a process as objects and conditions under which the actions have to be taken as attributes. Therefore we can handle dependencies between situations and ac­tions and process them by means of concept anal­ysis. This will turn out to be useful to increase the effectiveness of knowledge based systems.

First we define a formal context K = (G, M, t) consisting of a set of objects G = {g,} , a set of attributes M = { m; } and a binary relation t � G x M between the objects and their attributes. g,tm; means "object g, has the attribute m/' .

The context K can be written in a manner as shown in table 2 for a simple example.

TABLE 2 Sample Context about Vehicles

bell engine wheels m1 m2 ma

bike 91 x x car 02 x x

Then we define a function ' which, if applied to a set of objects, gives all attributes common to all members of the set of objects and, if applied to a set of attributes, gives a set of objects which have these attributes in common: X � G, X' := {m E Mlgtm for all g E X} Y � M, Y' := {g E Glgtm for all m E Y} ' forms a Galois connection.

Now we can define a concept in a context K =

(G, M, t) as a pair (A, B) of a set A of objects and a set B of attributes with A' = B and B' = A, which is equal to A" = A and B" = B. A is called the extent, B the intent of the concept.

This gives us an algorithm for the computation of all concepts of a given context: For every set X � G and Y � M, (X", X') and (Y', Y") are concepts.

In Table 2, there are four concepts: ( { } , {bell, engine, wheels}) , ( {bike} , {bell, wheels}) , ( {car}, {engine , wheels}) , and ( {bike, car}, {wheels}) . One can call the last three concepts bike, car and vehicle and conclude that bike and car are subcon­cepts of vehicle since they have more attributes which means that they are more specific.

The concepts form the set of concepts 8( G, M, t) of a given context K = (G, M, t) . (Ai , Bi) is a subconcept of (A2 , B2) iff Ai � A2 (which also means B2 � Bi) . This order is called �· (B(G, M, t) , �) is an ordered set and is called the concept lattice of the context (G, M, t) . The concept lattice can be drawn as a Hasse di­agram (fig. 3) . Each circle represents a concept with all objects belonging to it written below it and below other concepts reachable on paths lead­ing down and all its attributes written above it and on paths leading up, respectively.

wheels

bell

car

Fig. 3 Hasse diagram of context vehicles

Although Hasse diagrams are very useful to make dependencies visible, no reliable algorithm has been found that can draw Hasse diagrams auto­matically till now.

KNOWLEDGE PROCESSING IN EXPERT SYSTEMS

Usually expert systems are used for knowledge processing. Therefore knowledge must be repre­sented in rule form. The decision table (Table 1 ) which results from the process of knowledge ac­quisition has to be transformed into a set of rules. It will now be demonstrated how concept analysis can be helpful in doing this.

The table (Table 1) can easily be transformed into rules row by row, e. g. the first rule reads IF IOT cool-on AND IOT heat-on AID hreb>10 AND stable AID NOT flr>10 THEN cool50.

At run-time an expert system has to investigate every condition in the rule's premise before it can decide if a rule is applyable. This is not optimal because usually there are dependencies between conditions which are not used so far and which are not known even to the expert but which can be helpful - if applied - in avoiding additional measure"nents or tests.

These dependencies can automatically be deter­mined by means of formal concept analysis. For applying concept analysis, the three-valued truth table which is a result of knowledge acquisition with "yes" , "no" and " ." must be transformed into a two-valued truth table, like e. g. Table 2. This can be done by replacing every condition c

106

by two new conditions c+ and c_ . c+ is given for an action if c is true for this action, c_ re­spectively if c is false, and neither is given if c is unknown for this action. By this transforma­tion we get a new table with twice the number of conditions but containing the same information. This transformation also works for many-valued conditions (e. g. traffic lights can be red, yellow, green, defective, or unknown) , but this is not yet implemented.

Now all concepts of this context can be computed as described earlier. Fig. 4 shows the Hasse dia­gram of the context given in Table 1 .

Fig. 4 Hasse diagram of process control decision table

If a concept (Ai , Bi) is a subconcept of (A2 , B2) this means that (Ai , Bi ) has more attributes than (A2 , B2) , Bi 2 B2 . If an attribute b E Bi , b � B2 , is given this implies that every attribute in B2 is given. Thus all dependencies can be determined from the concept lattice (B(G, M, t), �) .

To be more concrete, in fig. 3 ( {bike} , {bell, wheels}) is a subconcept of ( {bike, car}, {wheels}) . If it is known that some­thing has a bell we thus can conclude that it also has wheels without further investigation.

These implications can be written as meta-rules which prevent our expert system from testing more conditions than necessary. Here the meta­rules are IF bell TRUE THEN wheels TRUE and IF engine TRUE THEN wheels TRUE. The knowledge represented in Table 1 and Fig. 4 is part of a system that has been successfully im­plemented to bring a distillation column to its operation point, hold it there and bring it down again. Some meta-rules visible on the left hand side of Fig. 4 are:

IF IOT cool-on (a) THEN NOT heat-on (b) IF IOT cool-on (a) THEN NOT flr>10 (f) IF IOT heat-on (b) THEN hreb>10 (d) IF IOT flr>10 (f) THEN stable (e)

Therefore, if the attribute cool-on is tested and found to be false all the other attributes ex-

cept s> 1 are known immediately by means of the meta-rules, and the action set cooling rate to 50% ( 1 ) is performed since s> 1 is not part of this rule's premise (Respondek, 1989) .

But there are still problems that cannot be solved by this method :

Expert systems are usually based on · languages like LISP or PROLOG and thus have an inpre­dictable runtime behavior which yields severe re­strictions on their practical applicability. Fur­thermore, they are not designed to be integrated into an existing software environment or to run on a process control computer. Sometimes the requirements of disk space or even main memory are tremendous and cannot be fulfilled.

In expert systems the order the rules are pro­cessed depends (in a more or less complicated way) on the order they appear in the knowledge base. A knowledge engineer can increase the sys­tem's performance significantly by ordering rules in a suitable way, e. g. by their probability etc. In a system containing hundreds of rules it is un­likely that the knowledge engineer (who is not a domain expert) will find the best order.

A similar problem concerns the order of condi­tions within the rules' premises. Conditions con­taining much information should be tested early. Later in this paper it will be shown how this prob­lem can be covered by using Shannon's entropy.

The optimal order both of rules and conditions de­pends on the situation present at run-time, and thus the order ought to be dynamically modifi­able.

DIRECT KNOWLEDGE PROCESSING

As it was just pointed out, the unflexible order of rules and conditions leads to a system behavior which is not optimal.

Direct processing of the truth table generated during knowledge acquisition by means of concept analysis and using Shannon's entropy (Quinlan, 1983) leads to better performance. The fewest possible conditions are evaluated to find an appli­cable action.

The algorithm for finding the next rule to fire is:

1) Determine what condition to test next 2) Compute the superconcept that contains

all now known conditions 3) If this superconcept contains more than

one object, repeat from step 1 with a modified truth table

4) Apply the rule

107

In step 1 , the entropy of each attribute2 ai is com­puted. ai+ is the number of objects with ai given or ai open, this means having a "yes" or " ." in the corresponding place of the decision table; ai­is defined for " no" and " ." respectively, and n is the number of objects3 .

With Pi+ = ai+/n and Pi- = ai_/n seen as the probability for a positive or negative answer we have the entropy

H(ai) = -P+ log2 p+ - p_ log2 p- (1)

Choose that attribute ai with minimal H(ai) and determine its truth value.

In step 2, form a set B of all attributes ai known by now and compute ( B', B") which is a concept. B C B". We can conclude that all attributes in B"-are given. This gives us further information.

In step 3, if B' (which is a set of objects) con­tains more than one object, we need further in­formation and must repeat this process from step 1 whereat we only have to consider a new decision table consisting of all objects g; E B' and all at­tributes mi rf. B". Remember we are looking for a subconcept of ( B' , B") what means this subcon­cept has less objects (namely only one) and more attributes than ( B', B") .

In step 4, we have found the one object we were looking for. This object is, in terms of process control, an action that has to be taken in this particular situation.

When, as already supposed in the section on ex­pert systems, the attribute cool-on (a) has been tested and turned out to be false, we have to com­pute the superconcept that contains the attribute (a) using the function ':

{cool-on}" = {cool50}' =

{cool-on, heat-on, hreb > 10 , stable, fir> 10}

or abbreviated: {a}" = { 1 }' = {a, b, d, e, f}

The superconcept found here (on the left side of Fig . 4) contains only one action, namely coo/50. Thus we can take this action.

In every iteration of the algorithm the size of the truth table (that holds all the knowledge to be considered) is significantly decreased. This modi­fication depends on the answers given in the pre­ceding steps and thus is optimal.

There are two possible further modifications for this strategy.

2 Attributes describe the process' situation and objects are the actions that influence the process.

3 Note that a;+ + a;_ can be greater than n because of the open fields " ." .

If some attributes are difficult or expensive to test the entropy H(ai) can be weighted with a fac­tor c(ai) that is the greater t_he more difficult the value for ai can be determined (see Eq. 2).

The other possible modification concerns proba­bilistic knowledge. In step 1 we called Pi+ and Pi­the probabilities for a positive or negative answer when the attribute ai is tested, and we computed them from their relative frequency in the given context. This result does not match their proba­bility in the real world. If statistical information about real probabilities p:f. and p� of a positive or negative answer are available from former experi­ences with the process we can use the modified formula

2 c(ai) * (2)

[- (1 - p�(ai)) P+ (ai) log2 P+ (ai) - (1 - p:f.(ai)) p_ (ai) log2 p- (ai)]

Eq. 1 = Eq. 2 if Pi. = p� = � and c(ai) = 1 .

Furthermore, the algorithm described here is a procedural one and can be implemented in lan­guages like C and even in FORTRAN and thus can be used to expand existing control systems by knowledge based components.

REAL-TIME PROCESS CONTROL

In practical applications it is difficult to combine a process control system and an expert system shell for multiple reasons:

1 ) Data structures and interfaces are different 2) Source codes are not available and thus not modifiable 3) Timing problems arise from data interchanges between multiple processes 4) Reaction time of expert systems is hard to de­termine and defined reaction time cannot be guar­anteed

For those reasons expert systems are sometimes used only for knowledge acquisition and testing, but for their application the entire expert systems are reprogrammed on the process control com­puter in a procedural language (Soltysiak, 1988) .

The direct knowledge processing strategy de­scribed in our contribution solves the problems listed above. It is easy to implement in a pro­cedural language as a part of a process control program so that no problems result from differ­ent data structures, unavailable source codes or data interchanges.

The necessary computing operations are mainly counting of entries in the truth table. With n as

108

the number of attributes, in the average less than log2 n conditions must be tested to find the next action to apply (In the usual expert system ap­proach, n attributes have to be tested) . When Eq. 2 is used, extensive4 tests of attributes are avoided and replaced by more effective ones if pos­sible. As a result, the system time required by this strategy for control problems of usual size (say, 70 to 100 rules) is in the order of milliseconds.

CONCLUSIONS

This paper has demonstrated that a very effec­tive method of knowledge acquisition and pro­cessing can be developed by using the formal con­cept analysis approach. If, in addition, the con­ditions which have to be met for any action are arranged dynamically with respect to their infor­mation content, a minimum of execution time is obtained. Since the knowledge processing soft­ware is implementable in a procedural language, the integration of knowledge based components into the existing world of process control systems is feasible in a convincing manner.

REFERENCES

Quinlan, J . R. ( 1983). Learning efficient classi­fication procedures and their application to chess end games. In R. S. Michalski, J . G. Carbonell, and T. M. Mitchell (Ed.). Machine Learning: An Artificial Intelli­gence Approach. Tioga Publishing, Palo Alto. pp. 463 - 482.

Respondek, T., and Krebs, V. ( 1989). Hardware and software structure of a real-time ex­pert system for control of chemical plants. Proc. of the 2nd IFAC Workshop on AI in Real-Time Control. Shenyang, People's Republic of China. pp. 37 - 42.

Soltysiak, R. ( 1988). Praktische Anwendung von Expertensystemen in der ProzeBleit­technik. A utomatisierungstechnische Praxis, 30, pp. 247 - 251.

Wille, R. (1982). Restructuring lattice theory: an approach based on hierarchies of concepts. In I. Rival (Ed.) . Ordered sets. Reidel, Dordrecht, Boston. pp. 445 - 470.

Wille, R. (1987) . Bedeutungen von Begriffs­verbanden. In B. Ganter, R. Wille, and K. E. Wolff (Ed.). Beitriige zur Begriflsanalyse. BI Wissenschaftsverlag, Mannheim, Wien, Ziirich. pp. 161 - 211 .

4 e. g. difficult to execute, not cost-effective, or time consuming

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

IMPLEMENTATION OF A HUMAN-FRIENDLY SYSTEMS METHODOLOGY FOR INTELLIGENT

CONTROL SYSTEM MODELLING AND SIMULATION

Y. Nakamori* and Y. Sawaragi**

*Department of Applied Mathematics, Kanan University, 8-9-1 Okamoto, Higashinada-ku, Kobe 658, Japan

**The Japan institute of Systems Research, 6 Ushinomiya-cho, Yoshida, Sakyo-ku, Kyoto 606, Japan

Abstract. We have been developing an interactive computer software for the systematic support to

modeling and simulation of intelligent control systems, based on a human-friendy systems methodol­

ogy. The support system has a universal application in data analysis, system structuring, statistical

and fuzzy modeling, and simulation , with the aid of human-computer interfaces to acquire knowl­

edge or judgment of the domain experts. This paper presents our soft systems methodology and

its implementation into the computer to develop intelligent process control systems. New technical

proposals include a modeling method of fuzzy implication inference models and a design method of

model predictive cont.rollers.

Keywords. Human-friendly systems methodology, modeling and simulation, intelligent control

system, fuzzy implication inference, model predictive control, human-computer interaction.

INTRODUCTION

The progress of systemization is a result of the advance

of information processing using computers. That is, sys­

temization is not a goal but a means. A system is getting

more and more inflexible as systemization progresses. For

a symptomatic treatment for this, people expect the de­

velopment of artificial intelligence. This is a challenge to

develop a computer-based system which has ability close

to human beings.

One of the technical difficulties is, as well known, how to

describe knowledge or sense so that a computer utilizes

it in solving problems instead of human experts. To put

it in other words, the difficulty comes from nonlinearity

and complexity with which human experts are inexplica­

bly dealing. In order to utilize this ability of human beings

in solving problems, people expect the fuzzy sets theory

and the neural networks.

A motivation to develop neural networks is explained that

human thinking could be rebuilt by the level of a neuron

which is thought the smallest element of the bra.in. But

in spite of such a noble motivation , it is in a position of

black-box modeling for engineering or social phenomena,

not a model of the brain itself.

Such a model is not thankful for system modeling be­

cause the model becomes wise by learning but the modeler

cannot. Apa.rt from pattern recognition etc., the system

modeling is generally an a.ct to learn things by ourselves.

Modeling is an act which clears up our vague knowledge,

not an act which tries to express vagueness vaguely.

109

From this point of view, we want to expect the fuzzy sets

theory (Zadeh, 1 965). But the study on human-theory

interface has not been developed well. This causes inflexi­

bility in using the theory. After a.II, we want to understand

that modeling is art. We have to develop an environment

to utilize the ability of human beings. In other words,

we should develop not only the theory it.self but also the

interface between human beings and theory.

We have been developing an interactive computer software

for the systematic support to modeling and simula.t.ion of

intelligent control systems, based on a human-friendy sys­

tems methodology. The support system has a universal

application in data analysis, system structuring, statisti­

cal and fuzzy modeling, and simulation, with the aid of

human-computer interfaces to acquire knowledge or judg­

ment of the domain experts.

This paper presents our soft. systems methodology and its

implementation into the computer to develop intelligent

process control systems. New technical proposals include

a modeling method of fuzzy implication inference models

(Takagi and Sugeno, 1985) and a design method of model

predictive controHers (Oshima, 1 989) .

In designing model predictive control based on the iden­

tified fuzzy dynamic model, heuristics should be used to

adjust parameters in models and criteria by means of the

developed software. We briefly introduce an application

study on a rotary kiln control, expressing the motivation

of our research and difficulties in applying the theory to

an actual process.

HUMAN-FRIENDLY SYSTEMS METHODOLOGY

Nowadays, as a world wide trend of the age in advanced

information society, CIM (Computer Integrated Manufac­

turing) or SIS (Strategic Information System) is noticed as

a technology which will lead new industrial society of the

21st century. That is the reason for our country Japan, an

international joint project called IMS (Intelligent Manu­

facturing System) on the initiative of the Ministry of In­

ternational Trade and Industry has taken a step for its

realization.

As a new industrial technology in the advanced informa­

tion society, the word SI (System Integration) has been

much used lately. The Ministry of International Trade

and Industry already founded in 1988 a measure called

"System Integration Tax System" to encourage SI indus­

try. In thinking of the vast amount of investment for in­

formation technology in the future, it is considered to be

a proper measure showing that SI is expected to take a

great part in industrial development.

This technology is the very systems approach whose im­

portance we have been advocating for a long time. In this

sense, this is the turn of us, systems engineers. Of course,

the above mentioned technologies are not the problems

of only systems approach. We need very much develop­

ment of basic technologies relating to traditional individ­

ual fields. We earnestly hope for cooperation of systems

engineering with the traditional individual technologies.

Now, systems engineering has long been kept at a distance

by users and criticized as a kind of scholars' toy. As a

reflection to this, over ten years have already passed since

we started to make efforts to make systems engineering

more practical.

Systems engineering is thought as a methodology which

offers a clear answer integrating knowledge of existing sci­

entific techniques and human heuristics. But, to the end

for decision of pra.ctical problems, we have to recognize the

lack of efforts to understand the reality. '.!'here are many

cases that uncertain factors hard to model are neglected,

because we often think tha.t simple theoretical handling is

important.

It is a notable fact that the existence of human beings

is very important to all systems, though it gives systems

vagueness and ambiguity. Therefore, in modeling the re­

ality we have to think of a system with human beings as

its center. Systems engineers should play coordinators or

integrators to help people in solving their problems.

From this point of view, we would like to emphasize a soft

approach which harmonizes human judgment and ability

of the computer. The main feature of this approach lies in

intervention of human beings at every phase of the prob­

lem solving. We name this approach Shinayakana Sy8tem8

Approach.

1 10

The shinayakana systems approach never makes light of

mathematical methods and models, but limits them to

playing the role of problem solving support only. We

should always keep it in mind that any precise models

of the reality will never incorporate all human concerns.

Therefore, an essential part of problem solving are issues

of human-computer interaction.

Models should be built interactively, involving not only

analysts but also domain experts. Their perceptions of

the problem, relevant data and model validity should be

taken into account in model building so that the model

can express their goals and preferences definitely and cor­

rectly. Intera.ction is essential at the decision stage as well,

and it should be dynamical because users typically learn

when using a support system, and we cannot assume that

a user comes to the system with fixed preferences.

In order to make good use of interaction, the support sys­

tem must be intelligent. A problem solving support sys­

tem should have a working area in a knowledge-based sub­

system. Frameworks of dynamical knowledge utilization

should be designed so that we can not only retrieve data or

knowledge, but also acquire or modify them interactively.

At the modeling stage, a model is identified partly and

stepwise associated with mental models for the object

and the knowledge in the support system. The registered

knowledge for modeling support can be improved both

in quality and quantity by the results of data analysis

or by the users' perceptions. At the decision stage, the

knowledge-based system should suggest the objective of

optimization or the order of priority in constraints. New

knowledge can be obtained by considering the gaps be­

tween the target and the actual plan.

The third assertion of the shinayakana systems approach

is tha.t the problem solving should be carried out in an in­

terdi8ciplinary fashion. The new factor in contemporary

systems analysis is the realization that certain method­

ological principles and mathematical tools can be applied

to systems in an interdisciplinary fashion.

This methodology is a special one of a country in connec­

tion with its culture and social foundation because it in­

volves human beings. Here, the adjective "shinayakana"

has a nuance of Japanese characteristic and means be­

tween soft and hard in English and both; we cannot find

this word equivalent in an English adjective. Authors

would like to use the word "shinayakana" even in for­

eign countries as it is.

We are developing an integrated support system to de­

velop model bases as well as knowledge bases for intelli­

gent dynamic system control. In this paper we will present

an interactive modeling and simulation support system

based on the above mentioned methodology and an ap­

plication study on intelligent control system design for a

rotary kiln process treating excess sludge from a municipal

wastewater treatment plant.

MODELING AND SIMULATION SUPPORT

The fuzzy modeling (Sugeno and Kang, 1988) consists

of some difficult tasks in partitioning data, determining

membership functions, and selecting explanatory variables

in linear models. These tasks are strongly related to each

other to make the modeling quite difficult. We propose an

interactive fuzzy modeling technique which utilizes human

subjective knowledge on the process under study. The ba­

sic modeling steps are the following.

Step 1: Data Observation. The following data screening

should be carried out before going into the fuzzy modeling:

(1 ) adjustment of the sampling interval,

(2) examination of the periodicity,

(3) examination of collinearity,

(4) analysis of dominant frequency,

(5) examination of cross-correlation,

(6) elimination of noises, and

(7) estimation of the steady states.

Step 2: Linear Modeling. An ARX (auto-regressive ex­

ogenous) model is identified based on the all input-output

data. The identified model should be checked by com­

puter simulation using other data. sets or random inputs.

This step is carried out to examine the application sphere

of the model in the universe of discourse, and to compare

the performances bet.ween this model and a fuzzy model

which will be identified in the following steps.

Step 3: Data Division. The data set is divided into several

subsets by a clustering met.hod, for example, the Ward

method. Fuzzy variables used for partitioning are selected

among output variables by referring to the scatter plots.

Step �: Submode/ Building. Linear regression equations

are developed in each subspace. The important points

here are the careful selection of explanatory variables tak­

ing account of time lag, and the definition of the range of

validity of each regression equa.tion.

The following type of membership function is used here:

where q1 , q2 and q3 are the first, second and third quartiles

of the subset, respectively, and ti , t2 are parameters to

adjust the shape of the membership function.

Step 5: Parameter Tuning. The behavior of an identi­

fied fuzzy model is checked by computer simulation using

real data or random inputs. Adjustment of parameters

in membership functions is carried out by minimizing the

prediction error <lefine<l by

E = _!_ t I Yi - yf ' · N i=I Yi

where Yi is the given data, yf the predicted value, and N the number of data.

1 1 1

If the results of simulation are not desirable, we will return

to Step 3 or Step 1 and repeat Step 4 and Step 5 after

repartitioning the data space.

A Fuzzy ARX model consists of several rules such as

If Ya(t - la) is A! , and yp(t - 113) is A�, and · · · ,

then Y/ = ET=! elk . Yi-1 + ET=! Dt . Ut-1 + Vk'

where A! , A�, · · · a.re fuzzy subsets with respective mem­

bership functions, Cf, Df coefficient matrices, and

Yi = (Y1(t), y2(t) - · · , yo(tW

U1 = (u1(t) , u2(t) · · · , u1(t))T

output variables,

input variables,

Vk = (vt, v� · · - , v�)T · · · constants.

The estimate of Yi can be obtained by

Ep k y:k Y;* = k=� Wt ·,. 1 , w; = IT A:(y:(t - la)), Ek=1 w1

where p is the number of rules, and Yi,. the output from

the rule Ri.. The weight w: is given by the product of

membership grades of all conditional variables.

We have developed an interactive software to carry out the

above mentioned fuzzy modeling (Sawaragi and Nakamori,

1991) . The system integrates structural and statistical

modeling methods with advanced graphic techniques that

facilitate person-computer and interpersonal communica­

tion.

Figures 1 and 2 show the scenes of using the support sys­

tem implemeted on a workstation for parameter tuning

and model evaluation.

INTELLIGENT PROCESS CONTROL We have carried out an application study on a stable in­

cineration problem of a rotary-kiln process treating excess

sludge from a municipal wa.stewa.ter treatment plant. It

is a very complex process system with the following char­

acteristics:

( 1 ) The input to the system is cake-like substance con­

taining suspended solid, microorganisms, sands, etc., dis­

charged from the wastewater treatment process. Their

components and physical states are different day-by-day,

that is, water contents, calorific values, sizes of solids, vis­

cosity, etc. are changeable.

(2) There are a lot of strong interference between manip­

ulated variables and controlled variables; this fact forces

us to consider a multi-variable control.

(3) The incineration reaction in the rotary-kiln is very

complf'x hf'caus.. drying, comhustion, aging of 11;;;h , f'k. occur in the kiln. Since we have no index to represent

the incineration reaction directly, we have to estimate the

state of incineration in the kiln indirectly from measurable

temperatures at several restricted points. This fact forces

us to build statistical models instead of theoretical models.

LIFE & Konan Un t v . • • • • • • •

Fig. 1 . Interactive tuning of para.meters in membership functions.

LIFE & Konan Un i v . • • • • • • • •

Fig. 2. Evaluation of explanatory and predictive powers of the model.

The control of this process should maintain the finishing

point of incineration in the desired range to produce good

ash with a few percent of ignition loss and to prevent

creation of clinker. However, in the present case, almost

operations have been left to the skilled operators yet be­

cause of the difficulty in developing useful mathematical

models describing the process dynamics. The usual op­

eration is to control the fuel gas rate for maintaining the

exhaust gas treatment equipment.

1 12

The operators always have to regulate the manipulated

variables (set points of the fuel gas rate, the air flow rate,

the cake supplying rate, the rotating speed of the kiln,

etc.) for maintaning the finishing point. of incineration

stably within the desired zone by watching the state of

combustion with an industrial TV camera. These works

put a large load to opera.tors. Therefore, an effective au­

tomatic control satisfying the above objectives has been

required.

An attempt to design controllers using fuzzy models was

done in Sugeno and Kang (1988) , where the linear control

theory is used to design optimal regulators based on the

respective rule models, and then the optimal control in the

universe of discourse is obtained by taking account of the

degrees of confidence of rules. However, the weighted sum

of respective optimal regulators is not necessarily optimal

in the universe of discourse.

We propose here an algorithm for control design based on

the idea of model predictive control as follows:

Step 1: Model Transformation. First we transform the

ARX models to fuzzy impulse response models:

The number of impulse steps q is determined by observ­

ing impulse response curves. Hf is an impulse response

matrix, where Hf = 0 for I > q. Putting

<;'"'P k Hk Ht - L,,k=I Wt . I I - Et=! w� '

we can write the output of fuzzy dynamic model as

q q Y;m = L H{ · Ut-1 + L Gf · I=! I=!

We assume that the series of inputs Ut-1' Ut-2, · · · were

added to the process, and the series of inputs Ut, Ut+1 , · · .,

Ut+M-I will be added from the current time t, and assume

that

Ut+M+I = Ut+M-1 for I � 0.

We can further rewrite the out.put equation as follows:

where

H',+L+P-1 L+P-1 H',+L+P-1 L-M+P+I

Ef=-;_M+l H:+L l Ef ,:i.r.1+2 H:+L+l

"L�M+P Ht+L+P-1 L,,f=l I

113

Step 2 : Output Prediction. Predicted outputs may differ from the measured data because of identification errors or the existence of disturbances. The following equation is provided to reduce the difference:

where Yp is the vector of predicted outputs, Y the vector of mesured data:

Let us introduce a reference trajectory YR:

which is given by

where Y* is the target vector, and a a tuning para.meter.

The reason why we introduce the reference trajectory is that it is desirable to move the output along a smooth trajectory to the target than to move it drastically. When a first order delay curve is chosen as a reference trajectory, the time constant can be used as a parameter to adjust the response speed.

Step 3: Optimal Con trol. The control action at the cur­rent time should be determined in order to minimize the difference between the predicted and reference trajectories during some time steps from the current time. Therefore an optimal control can be obtained by minimizing the function:

The solution to this problem is that

Though U F includes M time steps of control actions, just one-step control will be put into the process.

Here a problem occurs: the future values of confidence of rules are required in evaluating HF and H0• One solution to this problem is that. we can a.clop membership gm.des obtained by the reference trajectory.

Step 4: Repetition. T�e measured outputs at the next time step t + 1 may be different from the predicted values at the current time t, because of inaccuracy of the model or the existence of disturbances. Then we repeat the same steps from Step 2 by resetting t + l as the current time.

Figures 3 and 4 show the interactive scenes of examining the above-mentioned model predictive control.

CONCLUSION We emphasize a soft systems approach which harmonizes human judgment and ability of computer. The main fea­ture of this approach is the intervention of human beings at every phase of the problem solving. As an example of this approach we present a methodology and software for decision support in modeling and control of process systems, in which a difficulty lies in developing effective models based on input-output data. Therefore the prob­lems are how to design cont.rollers using poor models as well as how to build process models.

Fig. 3. Targets and reference trajectories of the objective variables.

L I PE & Konen Un i v .

Fig. 4 . A result of the model predictive control of a rotary kiln process.

REFERENCES Oshima, M. (1989). Model Predictive Control. in Text of

Process Control Techniques 1989, The Society of Chem­

ical Engineers. Sawaragi, Y. and Y. Nakamori ( 1991). Computer Aided

Modeling and Simulation in Process Control Systems. Proc. of !FA G Sympo. on Comp11ter Aided Design in Control Systems, Swansea, 227-232.

1 14

Sugeno M. and G . T. Kang ( 1 988). Structure Identifica­tion of Fuzzy Model. Fuzzy Sets and Systems, 28, 15 -33.

Takagi, T. and M. Sugeno ( 1 985). Fuzzy Identification of Systems and Its Applications to Modeling and Control. IEEE Trans. on Syst. llfan and Cybern. , SMC- 15-1 , 1 16- 132.

Zadeh, L. A. ( 1965). Fuzzy Sets. Information and Con­trol, 8, 338-353.

Copyright @ IF AC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

MACHINE LEARNING USING VERSION SPACES FOR A POWER DISTRIBUTION NETWORK FAULT DIAGNOSTICIAN

J. Ypsllantls and H. Yee

Department of Electrical Engineering, University of Sydney, NSW 2006, Australia

Abstract : There has been much interest in the application of expert systems to a wide variety of power system problems. One important application is the diagnosis of electrical faults in power distribution systems. A common problem with expert systems is the 'knowledge acquisition bottleneck' which arises with the generation of rules for the expert system, and there is benefit in automating this procedure as much as possible. This paper presents a fault diagnostician which uses a version space to learn from data in a SCADA system. The end user specifies background knowledge for use by the version space algorithm, but other than this the procedure is automatic. A test system was implemented and evaluated with the aid of a distribution network simulator. The results of this evaluation are presented. Keywords: power distribution . learning systems, supervisory control .

INTRODUCTION

In recent years, there has been much int.�rest in the use of expert systems to provide assistance to operators in the supervision and control of elec­tric power systems. An area. of particular interest concerns the diagnosis of faults in distribution sys­tems.

When a fault occurs due to a line clash , lightning strike or a fallen conductor, it must be cleared by protection as quickly as possible. In distribution networks, the protection usually comprises simple overcurrent prevention devices, such as fuses or overcurrent relays coupled with circuit breakers. More elaborate protection schemes incorporating distance relays, intertripping and phase sensitive relays are not often found at the distribution level for reasons of economy.

Ideally, when a fault occurs, protection operates to isolate only the faulted line or bus. In practice, it often happens that unnecessary protection opera­tions cause inadvertent loss of supply to otherwise healthy sections of the network , giving rise to the need for rapid diagnosis and subsequent restora­tion.

The diagnosis of faults and the determination of protection misoperation are essentially heuristic procedures which may be carried out by an expert system, making use of data available from the su-

115

pervisory control and data acquisition (SCADA) systems used in modern distribution systems.

In the application of expert systems to electrical fault diagnosis, a common problem, as with expert systems in general , is the 'knowledge acquisition bottleneck' . A major part of the overall develop­ment and maintenance effort lies in the acquisition and coding of knowledge structures. This is espe­cially the case when knowledge acquisition is car­ried out using conventional methods, e.g. meet­ings and interviews with domain experts.

The knowledge acquisition task may be automated using machine learning techniques. Various ma­chine learning algorithms have been devised, many of which induce knowledge from a supplied set of examples. These are particularly useful in the au­tomation of knowledge acquisition for an expert system because a domain expert often finds it eas­ier to cite examples of a concept rather than rules.

Modern process control and SCADA systems pro­vide information about the plant being supervised. Plant operators are a further source of informa­tion, either directly or indirectly via the recording of operator actions in response to changes in the condition of the plant. All of this information may be used to create examples for use with a suitable machine learning algorithm.

This paper is concerned with the application of

version spaces to automate the learning process for a distribution system fault diagnostician. The no­tion of a version space was introduced by Mitchell ( 1982) .

Earlier work (Ypsilantis ( 1991)) describes a di­agnosis technique which handled a class of par­ticular cases using certain features of the post­fault network to discriminate between different faults. These features are either recorded by, or may be calculated from, data. available in a typi­cal SCADA. The features used, i.e.,

• The last circuit breaker(s) to operate in re­sponse to the fault, and

• The system islands resulting from protec­tion operation, and their respective states, i .e. live or dead,

were found to be effective and are used in the work described here.

A problem with using only features to discrimi­nate between faults is that an exhaustive training phase is required before the diagnostician can per­form well. This results in a requirement for a large number of examples. Another problem is that the features in the examples are specific to the fault conditions present at the time of recording. Al­though the examples facilitate good discrimina­tion between faults, they may fail in the presence of noise.

In the work described in this paper, the above fea­tures are used in the creation �f training examples for a version space algorithm. A restricted form of the version space algorithm is used to simplify the recorded features, the aim being twofold. Firstly, the number of examples stored is reduced because generalisations concerning them are induced. Sec­ondly, the process of generalisation makes the di­agnostician less sensitive to noisy input.

The diagnostician was trained and tested using a distribution system simulator. The ability of the diagnostician to locate faults was evaluated for faults generating high and low spurious pro­tection activity, and the degree of generalisation achieved using different sets of background knowl­edge was evaluated. The results obtained indicate that the version space algorithm can induce diag­nostic rules resulting in a reduction of the num­ber of examples necessary for good diagnosis, and make the diagnostician less sensitive to noise. The data. used is that normally available in a SCADA system, and the procedure is essentially unsuper­vised.

116

VERSION SPACES

The method of version spaces, as described in Mitchell ( 1982) and in Chapter 7 of Genesereth (1987), is a machine learning algorithm which maintains consistency of an evolving concept de­scription using (continually updated) sets of ex­amples and counter examples of the concept. A version space is the set of all relations over a given domain which describe previously revealed posi­tive examples of a concept while describing none of the previously revealed negative (or counter) examples of the concept.

Machine learning may be accomplished via use of version spaces to create progressively better de­scriptions (a smaller set of relations) as more ex­amples are revealed to the learning system. The version space is restricted or pruned with each ex­ample, until the subspace contains a set of rela­tions that can classify the examples with some ac­curacy. If the concept can be clearly defined, the version space will eventually be pruned to a single relation which defines the concept precisely.

For any real problem, a version space will contain many elements. The manipulation of the version space can be quite cumbersome. Mitchell (1982) develops a method requiring manipulation of only the most specific and most general elements of the version space, i .e. the boundaries of the version space. This reduces the number of elements to be manipulated to typically two or three.

The accuracy of the resulting boundaries is sen­sitive to ambiguities or noise in the input data. When such data is used, it is possible that the boundaries will not coincide. However, the rules contained in the boundaries will usually converge around a subspace of the version space that best describes the examples seen.

The Algorithm Implemented

The formulation of machine learning using version space boundaries adopted in this work is based closely on the description in Genesereth (1987). Extensions beyond this formulation are:

Constrained variables. In Mitchell's original for­mulation, the non variable attributes were con­strained to a fixed value, e.g. 'red , ' rather than a type, e.g. 'colour. ' Variable attributes were com­pletely unconstrained. Genesereth and· Nilsson's formulation allows the constraint of a variable to a type.

Rule generation. The version space boundaries can be used to classify test examples. In this im­plementation, classification rules are produced by

listing the specific boundary elements followed by the general boundary elements. This creates rules which are sorted in increasing generality. If a test example falls within the classification, it will sat­isfy these rules, otherwise it will not. In the case where the concept is not completely defined, i.e. the specific and general boundaries are not iden­tical, there exists a possibility of misclassification.

The initial general boundary element contains un­bound variables. As a result, it will classify any test example if it is used to produce a rule. It is necessary to suppress the use of the general boundary in the generation of rules until at least one negative example has been revealed, i.e. until at least one of the variables in each general bound­ary element has been constrained.

Binary relations. The algorithm (in particular the candidate generation section) was implemented in such a way as to allow the handling of binary rela­tions as well as unary constraints. This allows the algorithm to work with more complex constraints.

The use of binary, ternary1 and higher order back­ground knowledge allows the algorithm to discover relations between the attributes, rather than sim­ple type constraints on the attributes. An exam­ple of a useful binary relation, in the context of a distribution system, is the relationship between the direction of current flowing in a line, and the voltage drop in the line.

Multiple concepts . In general, a learning diagnos­tician must accomodate several concepts. In this application, each diagnosis is treated as a poten­tially separate concept requiring a separate ver­sion space, and the implementation allows the au­tomatic generation of extra version spaces as nec­essary. A new specific boundary is created when generalisation against at least one of the existing boundaries is not possible.

?ome of the version spaces will not be generalised , i .e . they will simply contain the training examples used to initialise the specific boundaries. This en­sures that any examples which cannot be incorpo­rated into a rule will not be lost after training, i.e. all of the information in the original training set is retained.

Characteristics of SCADA data

SCADA systems contain information which may be used to generate positive examples, but it is difficult to generate negative ones. This limits the

1 The implementation of the algorithm in this work was restricted to binary background relations. However, it is possible to cast a given problem, where ternary and higher order relations are to be learned, into one requiring only binary relations.

117

utility of the general boundary in a version space algorithm.

The general boundary may be used as a check to determine when a concept is fully described. SCADA data will rarely give rise to a clearly de­fined concept in which case the boundaries will not become equivalent.

When the general boundary is not used, it is not possible to estimate how well a concept is defined at a given point . However, only positive examples are needed for training. General boundaries were not used in this work, i.e. the version space was implemented in generalisation-only form.

TESTING PROCEDURE

Training Set Generation

The simulator described in Teo (1990) was imple­mented under a SCADA MMI interface developed for a Sun workstation, and was used in the gener­ation of training and test data. A fault diagnosti­cian, developed for the SCADA MMI, was used in the evaluation of the machine learning algorithm. Figure 1 shows the data and control flow for the test environment. Figure 2 is the single line dia­gram of the distribution network used in the eval­uation .

Fig. 1 : Test environment

Version space-based learning was applied to the induction of classification rules from the training examples. Generalisation results in rules which cover at least two examples. This in turn results in a reduction of the number of examples which need to be stored and searched during diagnosis, thus speeding up execution.

� train!ng set for the algorithm was formed by s1mulat1on of each fault location on the distri­bution network without relay noise and with all breakers closed prior to the introduction of the fault. One of three cases resulted from each sim-

11

u

Fig. 2: Distribution network

ulation:

l. The diagnostician could not offer a diagno­sis. The example was added to the training set.

2. The diagnostician successfully recognised the fault , using a previously learned train­ing example. This would occur, for exam­ple, for faults at either end of an electrically short line. In this event , the example was discarded.

3. The diagnostician presented an incorrect di­agnosis using a previously learned training example, i .e. another fault, electrically close to the one simulated, had the same features. The example was added to the training set .

Following formation of the training set, each fault was again simulated and it was verified that the diagnostician provided correct diagnoses, i.e . , it provided a list of hypotheses which included the correct fault location and in which the alterna­tive hypotheses were electrically close to the ac­tual fault simulated . 'Electrically close' was taken to be no further than two buses away from the actual fault.

The training set so formed comprised only positive examples of faults. These were presented to the version space boundary algorithm with the mod­ifications described above. A series of tests was performed in which the version space boundary al­gorithm was used to generalise the set of training examples. The set of training examples was input to the learning algorithm for several different sets of background knowledge.

Background Knowledge

A set of background rules was devised for this problem. This comprised five rules, a to e de­scribing:

1 18

• a . a dead bus adjacent to the last breaker to open,

• b. a line on which last breaker operated,

• c. a line which became fully isolated,

• d. a dead bus connected by a bus coupler to another bus, and

• e . an isolated line on the periphery of a dead island.

·

These background rules were used to create four sets of rules, referred to as Sets 1 through 4. Ta­ble 1 indicates the background rules present in each set. Set 1 is a subset of Set 2, which is a subset of Set 3 etc. This resulted in a range of generalities in the background knowledge.

In addition, in various parts of the testing, the original training examples were used as a 'control' case to allow comparison with Sets 1 to 4 .

TABLE l . Background Knowledge Sets

I I Set I Generality I Rules I I Present

1 Most Specific a, b 2 a, b, c 3 a, b, c, d 4 Most General a, b, c, d, e

RESULTS

The evaluation of the machine learning technique concentrated on three areas:

• The effectiveness of the learning algorithm.

• The ability to reject irrelevant background information.

• The performance of the induced knowledge when noise is introduced in the input.

Each fault was simulated, and the diagnostician was tested using the results of learning. The cri­terion for correctness of diagnosis described above was used here as well .

Rejection of Irrelevant Knowledge

Initial learning was made separately with each of the background knowledge sets to determine which types of background knowledge were not used in generalisation. Each resulting knowledge base was examined manually.

It was found that Set 1 and Set 2 produced dis­tinct knowledge bases, with a greater degree of generalisation in the case of Set 2. Generalisation using Set 1 background knowledge resulted in 23

training examples being left in their original form, with 2 rules describing the remainder. In the case of Set 2, 15 training examples were left in their original form, and 3 rules described the rest.

Set 3 and Set 4 resulted in the same knowledge base as for Set 2, indicating that the additional background knowledge added by these sets was not found to be relevant, i .e. a dead bus with a coupler, and a line on the edge of a dead island.

Further tests used the knowledge bases produced with Sets 1 and 2 .

Effectiveness of Learning

Ea.ch distinct knowledge base was used in a subse­quent simulation of the original faults, a.gain with­out relay noise. The resulting diagnosis was, m

each case, classified as one of the following:

• Successful diagnosis.

• A near miss.

• Failure or no diagnosis.

The classification was ma.de based on the list of hypothesised fa.ult locations that the diagnostician produced in response to a simulation of t.he fault. A diagnosis was considered successful if the list of hypotheses included the faulted element and any other hypotheses were for faults no further than two buses away from the actual fault. A near miss was taken to be the case where ea.ch hypothesis was no further than two buses away from the fault but the actual fa.ult was not included . A failed diagnosis was any case where the list of hypotheses included at least one fa.ult location more than two buses away from the actual fa.ult .

Table 2 summarises the results of this test .

In a.II cases, there was either a successful diagnosis, or a failure; there were no near misses. All of the failures occurred in the diagnosis of faults in the vicinity of the infeed buses.

It may be seen that the effectiveness of the knowl­edge base falls as the level of generalisation in­creases. This is expected, since the number of rules or training examples that fire increases with increasing generality, and thus the cha.nee of mis­diagnosis increases. This may clearly be seen from the average number of rules or training examples that fire.

Effects of Relay Noise

A series of tests to assess the performance of the diagnostician in the presence of noisy data., was conducted using the same knowledge bases.

119

TABLE 2 . Effectiveness of Learning

II Set I Result I Av. No. II S I NM I F Firing

None 51 0 0 approx 1 1 48 0 3 1.63 2 45 0 6 2 .33

'S': success, 'NM': nea.r mISs, 'F': failure or no dia.gno­SIS

Noise was simulated as a random error in the nom­inal trip time and pickup current settings of the relays, as described in Ypsila.ntis (1991) . The er­ror was set up to 2% either side of the nominal value. This simulated a realistic level of noise and timing error.

Fa.ult locations resulting in various fa.ult clearing mechanisms were chosen for the testing of the di­agnostician. Three line fa.ult and three bus fa.ult locations were chosen. For ea.ch group of three, one was typical, one ca.used much breaker activ­ity under no-noise conditions, and one resulted in isolation of an island around the fa.ult .

Ten simulations were ma.de at ea.ch fault location, for each distinct set of rules. The resulting diag­noses were classified as successful , near misses or failures as before. In addition, the original train­ing set was tested under the same conditions for a comparison.

Table 3 summarises the results of tests under noise.

It may be seen that the level of noise has an ad­verse effect on the performance of the system when the original training set is used, i .e. without gener­alisation. The noise level , although small, resulted in a relatively severe disruption of the diagnosti­cian's performance.

The knowledge bases from Sets 1 and 2 resulted in fair performance, however. In both cases, a signif­icant number of successful diagnoses were made, with a similar number of near misses.

There was a significant rise in the number of fail­ures in the case of Set 2 as compared to Set 1 , i .e . there is a greater chance of misdiagnosis with increasing generality.

DISCUSSION

It was found that several training examples ap­plied to other faults that were electrically close to the original one used in training. The original 51 fault locations resulted in 40 training examples.

In each of the cases where a rule was induced '

TABLE 3 . Effect of Noise

I I Set I Result I Av. No. II S I NM I F Firing

None 1 9 2 39 0.35 1 32 28 0 1 .02 2 28 22 1 0 1 .73

'S': success, 'NM': near rmss, 'F': failure or no diagno­sis

the relation found comprised exactly one back­ground knowledge element. In other words, the background knowledge needed for effective use contained sufficient detail that no further back­ground knowledge was required to characterise the examples. There were no rules that included a conjunction of two or more background elements. The implies, at. least for this application. that the knowledge engineer indirectly solves the problem in specifying the background knowledge. This may not be completely disadvantageous. While the background knowledge needs to bl:' detailed , knowledge engineers need not concern themselves with the problem of relevance of the background knowledge, since the algorithm will determine this automatically.

As is evident in these results, greater generalisa­tion may often be realised when more background knowledge is included. This results in greater 'compression' of the training examples, but at the same time increases the risk of misdiagnosis. In implementing such a learning algorithm, care must be taken to ensure that a good tradeoff be­tween these conflicting features is found .

Finally, because the version space algorithm em­bodies the majority of generalise/specialise ma­chine learning procedures, it would be reason­able to expect similar behaviour for any gener­alise/specialise algorithm. It is interesting to note that data intensive machine learning algorithms such as ID3 due to Quinlan ( 1986) , rather than knowledge intensive ones, seem to be successful for problems in the field. Version spaces would be expected to perform well in much more supervised and controlled learning environments.

CONCLUSION

This paper presents a fault diagnostician which produces rules using a version space algorithm. The user only needs to specify a set. of background rules for the version space to use. Learning is oth­erwise automatic.

The version space algorithm is useful in automati­cally determining relevant background knowledge. It is possible to implement a generic diagnostician

120

which contains all possible background rules for a SCADA task. The version space algorithm will only use background knowledge which is relevant to the task.

The version space algorithm produces knowledge which is less sensitive to noise, and it reduces the size of the knowledge base.

ACKNOWLEDGEMENTS

This work was supported by an Australian Post­graduate Research Award and an Australian Elec­trical Supply Industry Research Board grant. The authors wish to thank Associate Professor Teo Cheng-Yu, of the School of Electrical and Elec­tronic Engineering, Nanyang Technological Uni­versity, Singapore, for use of the distribution sys­tem data.

REFERENCES

M. R. Genesereth and N. J. Nilsson ( 1987) . Logical Foundations of Artificial Intelligence. Morgan Kaufman, 1987.

T. M. Mitchell ( 1982) . Generalization as search . Artificial Intelligence, 18, 203-226, 1982.

J. R. Quinlan ( 1 986) . Induction of decision trees. Machine Learning, l, 81-106, 1 986 .

C. Y. Teo and T. W . Chan ( 1990) . Develop­ment of computer-aided assessment for distri­bution protection. Power Engineering Journal, 1_, 21-28, January 1990.

J. Ypsilantis, H. Yee, and C-Y Teo (1991) . An adaptive, rule-based fault diagnostician for power distribution networks. March 199 1 . Submitted to IEE Proceedings Part C .

Copyright C IFAC Artificial Intelligence in Real-Time Conttol, Delft, The Netherlands, 1992

ST ABILITY OF FUZZY CONTROL SYSTEMS BY USING NONLINEAR SYSTEM THEORY

A. Garcia-Cerezo•, A. Ollero• and J. Aracn••

•E.T.S. de lngen�ros lndustriales de Malaga, Plaza "El Ejide", 29013, Malaga, Spain E.T .S. de lngen�ros lndustriales de Sevilla, Avda Reina Mercedes, 41012, Sevilla, Spain

Abstract. In this paper we consider fuzzy control system as nonlinear control systems. We present an unifying framework of methodologies and summarize three different methods. The first one is based on the geometrical interpretation of the system dynamic behaviour in the phase portrait. The second uses stability and robustness indices defined from the qualitative theory of dynamic systems. The third method adopts the input-output stability approach by using the conicity criterion. These methods provide the basis for the development of new me­thodologies for the design of stable and robust fuzzy control systems.

Keywords. Nonlinear control system, stability theory, fuzzy control.

INTRODUCTION

Fuzzy control systems are essentially knowledge­based control systems that use fuzzy set theory for knowledge representation and inference. The first ap­plications of fuzzy control emerged in the mid 70's. (Mamdani, 1974). Fuzzy control techniques were ap­pealing because it allowed the possibility of defining a control system based on heuristic rules, without the requirement of any previous knowledge of the mathematical model of the process to be controlled. These techniques have obtained good results in seve­ral applications (Sugeno, 1985; Takashima, 1991). In spite of some valuable efforts, the emphasis of most work on the subject is in the particular charac­teristics of each application rather than the develop­ment of general analysis and design methods that could assure basic control properties such as the sta­bility and robustness of the feedback control system.

The definition of the fuzzy control rules is apparently simple. However, the assumption that the heuristic rules are well experimented and robust, are not enti­rely correct in many applications. This fact has moti­vated the research on the analysis techniques since the seventies (Tong, 1977). Early works on fuzzy control analysis include the use of the well known "descriptive function method" by considering the fuzzy controller as a mulli-level relay in the control loop (Kickert, 1985).

This work has been partially supported by the Comi­si6n Interministerial de Ciencia y Tccnologfa, Project CICIT ROB89 0614.

121

As we will show in the second section of this paper, a fuzzy control system can be considered as a nonli­near control system. Thus, from a general perspecti­ve, two ways for stability studies can be followed:

1 . Nonlinear system theory, by considering the fuzzy control system as a particular class of non li­near control systems.

2. Within the frame of fuzzy dynamic systems.

The second line emerge from the Zadeh's Extension Principle, and is undoubtably of great theoretical in­terest. Works of this line are shown in DeGlass (1984). In Gupta and col ( 1987) the concept of "Energetistic functions" as a measure of the stability of fuzzy systems is introduced.

This paper is centered in the first line of study. One of the first work dealing with the relation between the dynamic behavior and the fuzzy control rules was introduced by Braee and Rutherford (1977) by using the concept of linguistic trajectory. In fact, this con­cept is an approximation to the clasical phase plane analysis. The geometric method for stability analysis (J.Aracil, Garcia-Cerezo and Ollero,1988) is based on the study of the contributions of vectorial fields of the system and the controller. The third section pre­sents some basic concepts related with this techni­que. Futhermore, these previous ideas were formali­zed with the definition of the stability and robustness indices (J.Aracil, Garcia-Cerezo and Ollero,1989) in the frame of the qualitative theory of dynamic systems. This approach is summarized in section 4.

Input-Output stability techniques have also been ap­plied for the stability analysis of fuzzy control

system. The theory of input-output stability, and classical Liapunov techniques can be envisaged wi­thin a unifiying frame (Safonov,). The separation principle can be considered as common reference point to derive stability in the sense of Liapunov, and through the conicity criteria which is a generali­zation of input-output stability criteria such as the circle criterion or the Popov criterion. In this line, J. Aracil and A. Barreiro (1990) and (J. Aracil, A. Gar­cfa-Cerezo, A. Barreiro and A. Ollero, 1991) present refonnulations of the conicity criteria and the appli­cation for the analysis in fuzzy control system. In the fifth section we will summarize the basic ideas of this input-output syability method.

Fig. 1 shows a unifying framework in which the above mentioned stability methodologies can be in­cluded.

Liapunov theory

Input-Output stability

Fig. 1 Stability analysis of fuzzy control system.

FUZZY CONTROL AS A NONLINEAR CONTROL SYSTEM .

A fuzzy control system can be represented by a set of conditional propositions or control rules in the form:

This set of control rules define a fuzzy relation, R, with membership function given by:

µR(x l , . . . ,xn,u) = Y µ R j(x l , . . . ,xn,u)

µR(x l , . . . ,xn,u) � µA l i x ... x Ani x Ci (x l , ... ,xn,u)

The fuzzy inference process allows determining a conclusion (C) from the previous definition of a set of fuzzy input terms ( A1 , . . . ,An) , and the fuzzy rela-

tion, R, through the compositional rule of inference:

where o represent the composition operator.

122

When using a fuzzy controller, an interface is required to connect the fuzzy process (the set of control rules and the inference mechanism) and the process to be controlled (see Fig. 2).

Process

Inference fuzz

Fuzzy set of rules

Fig. 2. Fuzzy controller.

The fuzzy antecedents are obtained from the input va­riables through fuzzifying operators. In a similar way, the control actuation, can be obtained from the consequent by means of defuzzifying operators. The most simple fuzzifying operator is given by (Manda­ni, 1974):

µA (x) = 1 if x = x(t), and µA (x) = 0 otherwise.

Thus,

The consequent can be reduced to an scalar by the de­fuzzifying operator, SC. Then, the control variable is given by:

u = 0(x) = scu�(u)) = SCU(�(x(t),u))

This result leads to the conclusion: "A fuzzy control system is a particular class of

a non-linear system, represented by the nonlinear fun­ction �(x)".

PRELIMINARY ANALYSIS OF A FUZZY CON­TROL SYSTEM.

Let P(x) be a partition of the input space, X. The element P/x)E P is associated with the rule j if it ve-

rifies that:

This condition lead us to easily detennine the parti­tion. Then, the interpretation of a fuzzy trajectory in

the sense of Braae (1977) is a simple operation. De­tection of design errors, non-operative rules, analysis of linguistic terms, modifications in the protocol rules and other operations can be easily implemented in this frame.

In Aracil, Garcia-Cerezo and Ollero (1988) a stability analysis technique is presented. This technique is based on the study of vectorial fields associated to the plant and the set of control rules. Let us consider a system represented by

dx/dt = f(x) + bu (1)

where f(x) is a non linear function, x, b are vectors of dimension n. u = 0(x) is a non linear function representing the fuzzy controller.

and it is assumed that f(O) = 0(0) = 0.

The closed loop behaviour will depend on the nature of f(x) and b0(x). For single input system, under certain monotonic conditions on f(x) and 0(x), stable conditions of a closed loop system can be predicted if:

i) The autonomous system, dx/dl = f(x) is stable.

ii) The vectorial field associated to b0(x) tends to 0(x)=O.

Even though the conclusions about stability are qua­litative, they may be enough Lo characterize the dyna­mic behaviour of feedback systems.

Fig. 3. Fuzzy partition of input space and linguistic trajectories.

123

STABILITY AND ROBUS1NESS INDICES.

The stability and robustness indices (Aracil, Ollero and Garcia-Cerezo, 1989) are based on the qualitative theory of nonlinear dynamical systems.

Let us consider the system given in (1) with

u = 0(x). (2)

Consider that f(x) is a nonlinear and monotonic fun­ction, with f(O) = 0, and 0(x) is a non linear function representing the fuzzy control.

The Jacobian at the origin of the feedback system, J, is given by:

J = A + b 0x (3)

where A is the Jacobian of f(x) and 0x is given by:

0 = (0 ... 0 ) with 0 = i10(x)/ik (4) x x1 Xn Xi 1

Under the assumption that the linearized system around the origen is stable, the stability loss occurs if any of the two following conditions are verified:

- Stability loss on the linearized system - Apparition of new atractors

Generically, the two simplest forms of stability loss in the origin are:

- A real eigenvalue crosses the imaginary axis to be­come positive (static bifurcation).

- A pair of complex poles cross the imaginary axis and take positive real part. This branching is the so­called Hopf bifurcation.

We have defined two indices to determine how far is the system from the stability loss; the index 11 is re-

lated �ith a static bifurcation and the index 12 with a

Hopf bifurcation. These indices can be defined

through the Hurwitz matrix, H. If P(s) = sn

+a1 sn

-1 + . . . +an- l s+an is the characteristic polinomial of

linearized system, the Hurwitz matrix is given by:

H =

0

0

0 . . . . . . a 2 � n- -n

(5)

Thus, the indices are given by :

(6)

where Hn _1 is the principal minor of order n-1 of H.

It can be shown that:

(8)

The stability loss at the origin is produced if any of both indices take negative values. Thus, the values of the indices can be considered as a robustness mea­sure of the closed loop system.

Index I3 is defined as a distance to the appearance of

other equilibrium points. Thus, this index measures how far is the system from an atraction-repulsion bi­furcation. This situation will ocurs when the vecto­rial fields associated with the fuzzy controller and the plant are compensated exactly. For the system (1) this will only occur when:

(9)

This expression represents an one-dimensional subs­pace, called the auxiliar subspace.

I f(x) + 0(x) I ____/

Fig. 4. Auxiliar subspace analysis. a) atractors­repulsors over the auxiliar subspace. b) defi­nition of the index 13 .

124

The index I3 is given by the minimun distance bet­

ween the plant and controller modules, calculated over the auxiliar subspace, excluding a region P around the origin (see fig. 4):

I3 = min I f(x) + b0(x) I x� P

INPUT-OUTPUT STABILITY.

(10)

The application of the circle stability criterion was proposed by Kickert and Mamdani (1978) and Kumar and Majumder (1984). In Ray, Gosh and Majumder (1984) the circle criterion is also used and a graphical interpretation is proposed by introducing the concept of Li-stability. In the following we deal with the ap-

plication of the conicity criterion, a generalization of the circle criterion to multivariable systems (Zames, 1966; Desoer and Vidyasagar, 1975).

Consider the fuzzy control system in Fig. 2 compo­sed of a linear part and a nonlinear feedback. If the process to be controlled is non linear we assume that a linearized model with transfer function G(s) can be determined, and the nonlinear components of the pro­cess are included with the nonlinear feedback 0(x).

Then, the conicity criterion can be applied for stabi­lity analysis.

A sufficient condition for stability is that for some scalar r (called center) and for some matrix C (called radius), the following conditions hold:

a) II 0(x) - Cx II < r II x II, for all x. (1 1)

b) The linear feedback system obtained from the substitution of 0(x) by C, with transfer function

F(s) = G(s)(I + CG(s)r1 •

must be stable.

c) (max00 II F(jro) ll)·r < 1 ;

where the 2-norm i s given by II F(jro) I I = A.max ( F

T(-jro) F(jro) ).

(12)

(13)

(14)

An interpretation of the Conicity Criterion is shown in Fig. 5. For some stable feedback C, the robus­tness r0(c) of G(s) with feedback C must be greater

than the conic deviation r0(C).

The problem is to find, in the space of all cones (C, r), a suitable one (C0, r0) for which the three above

conditions hold.The first ant third conditions yield:

def I I 0(x) - Cx I I r � r (C) = max ------·

0 x*° 1 1 x 1 1 def -1

r < r0(C) = (maxx II F(jw) I I ) where r0(C) is the conic deviation of the fuzzy con­

trol law y = 0(x) from the linear law y = Cx, and r0(C) is a measure of the robustness of the feedback

linear system formed with G(s) and C.

The second condition restricts the possible cones to the subset Sc, formed with centers C that give rise

to a stable linear feedback of G(s), are restricted. In the boundary of Sc, maxw II F(jw) 11 tends to infi-

nity, and r0 tends to zero (see fig. 6).

Fig. 5. Graphical interpretation of conicyty criteria.

Furthermore, we can define the concept of rule coni­city. Let xi be the controller input for the partition Pj corresponding to the rule j. The contribution of this rule is given by :

with c = (c1 , c2) and xi = (x 1 i,x2i) T. The global de­

viation of the set of fuzzy rules is:

r0 (c) = ma� { rg) (c) } (17) l

In the r-C space, this deviation is the polyhedrical surface of Fig. 7. where each face is labelled with (or associated to) one of the fuzzy rules. The surface will normally have a global minimun at some c*. To de­termine the critical fuzzy rules with more influence on stability, we compare the conic deviation surface r0 with the linear feedback surface r 0 obtained from

125

r (dim 1 ) ::::rt::: Stability r G < r 0

..... ��--�����--��- c (dim n)

Fig. 6. Conicity of fuzzy rules.

Fig. 7. Deviation of the set of fuzzy rules.

the plant G(s). This rules are normally associated to one of the adjacents faces at the minimun r0(c*).

The conicity criterion can also be asily applied to study the stability of control systems with fuzzy au­totuning of the gains of conventional controllers. For example, consider a motion controller with a li­near control law

(18)

where ep is the position error and ev is the velocity

error. In this case fuzzy rules can be applied to mo­dify the feedback gains in order to compensate nonli­nearities, change in working conditions, and external perturbations (Ollero and Garcia-Cerezo, 1988, Ba­rreiro and others, 1990).

For given values of the feedback gains (Kp=c 1 ,

Kv=c2) we can take the central values C = (c1 ,c2) .

Then, it is possible to compute the conic deviation rG(c1 ,c2) whith gives a measure of the robustness.

The stability condition imposes that the modified gains must be inside a circle of center (c1 ,c2) and ra-

dius ro- Thus, this condition can be used to cons­

traint the fuzzy modification of the gains in such a way that stability of the closed loop system is gua­rranted.

CONCLUSIONS

Fuzzy control systems are nonlinear control systems. Then, under some assumptions on the process dyna­mics, the theory of nonlinear dynamic system can be applied to study the stability of control systems with fuzzy logic components in the control loop.

The qualitative theory of nonlinear dynamic systems provides geometrical interpretations and lead us to de­fine indices which give a measure of the control system robustness. These indices can also be used to study the stability of control system with fuzzy logic for autotuning of parameters of conventional contro­llers.

Input-output stability analysis is also useful. Early work, on the application of the circle criterion can be extended to analyse multivariable systems by means of the conicity criterion. Moreover, this criterion is a valuable tool for the analisys of fuzzy autotuning control systems.

Futher extensions of the proposed methods include the analysis of other fuzzy modelling and control strategies based on the linear combination of inferred variables, and fuzzy predictive approaches.

Moreover, most results presented in the paper can also be applied to other intelligent control methods including learning and neural-networks based techn iques.

REFERENCES

Aracil J., A.Ollero, A.Garcia-Cerezo. (1989) Stability Indices for the Global Analysis of Expert Control Systems. IEEE Trans. on S.M.C., Vol. 19, No. 5, , PP• 998-1007 I

Aracil, J., Garcfa-Cerezo, A. Ollero, A. (1988). Stabi­lity analysis of fuzzy control systems: a geomerical approach Artificial Intelligence.Expert Systems and Languages jn Modemng and Sjmulatjon. Else­vier S. Ps. North-Holland. pp 323-330.

Barreiro A., Ollero, A., A. Garcia-Cerezo. (1991) Des­ign of expert controllers using conicity criteria. IEEE Congress of ECS. pp. 225-228. Dayton USA.

Braae M. and Rutherford A.O. (1977). "Selection of

126

parametres for a fuzzy logic controller". � Sets and Systems.

Desoer C .A. and M.Vidyasagar. ( 1975) Feesback Systems. Input-Output Properties, Academic Press.

DeGlass M. ( 1984) "Invariance and Stability of Fuzzy Systems". J. Math.Analysis Aru>l. Vol. 199, pp. 299-3 19 .

Jerzy, B. , Kizka, Madan M. Gupta, and Peter N. Ni­kifomk (1985). "Energetistic Stability of fuzzy Dynamic Systems". IEEE trans. on S.M.C. Vol. 15, N 6.

Kickert M. K. and Mamdani H.E. (1985). "Analysis of fuzzy logic controller" Fuzzy Sets and Systems. Vol. 1 . pp. 29-44.

Kuman, S. Ray, Amanda, M. Ghash, and D. Dutta Majun­der (1984). "Stability and the Related Design Con­cept for SISO Linear System Associated with Fuzzy Logic Controller". IEEE Trans. on S.M.C. Vol 14, N. 6.

Kuman S. Ray and D. Dutta Majunder (1984). "Applica­tion of Circle Criteria for stability Analysis of Li­near SISO and MIMO Systems Associated with Fuzzy Logic Controller". IEEE Trans on S.M.C. Vol. 14, N. 2.

Mandani E.H. (1974) Aplication of fuzzy algorithms for control of simple synamic plant, Proc. IEE-E 121 il.21. pp-1585-1588.

Ollero A., A. Garcia-Cerezo, (1989). Direct Digital Con­trol, Autotuning and Supervision ussing Fuzzy Logic. Fuzzy Sets and Systems. Vol. 30 pp. 135-153 .

Safonov, M.G.(1980) Stability and Robustness of Mul­tivariable Feedback Systems, M.l.T. Press.

Sugeno M., and M. Nishida, (1985) Fuzzy Control of Model Car. Fuzzy Sets and Systems 16, pp.103-113

Sugeno M. and G.T. Kang, (1988). Structure Identifica­tion of Fuzzy Model. Fuzzy Sets and Systems, Yol.28, ppl5-23.

Takashima S., ( 1989) 100 Examples of Fuzzy Theory

Applications mostly in JAPAN, Trigger.

Tong M.R., ( 1977) Some Problems With the Design and Implementation of Fuzzy Controllers, British Steel Copr., Res. Associate. Control and Management System Group. Univ. of Cambrigde, England,

Zames G., On the 1-0 stability of time yarying Non­Linear Feedback Systems. IEEE Trans. on Autom. Control. vol AC-1 1, pp. 228-238. 1966.

ACKNOWIEDGMENI' We would like to thank Prof. Barreiro, coauthor of other papers on the application of the Conicity Criteria

Copyright © IF AC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

STABILITY OF FEEDBACK S YSTEMS WITH UNCERTAIN DYNAMICS

A. Barreiro• and J. Aracil**

*E.T.S.lng. lndustriales, Universidad de Vigo, C/Lagoas-Marcosende No. 9, Vigo, Spain **E.T.S.lng. lndustriales, Universidad de Sevilla, Avda Reina Mercedes sin, Sevilla, Spain

�- The application of functional analytic methods to the stability of feedback control systems with nonlinear, imprecise or unknown models is discussed. A method is proposed to find the appropiate center and radius parameters of the Conicity Stability Criterion. A technique is also presented to deal with unmodelled plants and to obtain its functional gain in an empirical way from energy measures.

Keywords. Stability criteria; Nonlinear control systems; Input-Output methods; Uncertain dynamics.

!. INTRODUCTION

The Stability theory of nonlinear systems follows two main di­rections: Liapunov stability and Input-Output stability. The first one is concerned with internal stability (the approaching to zero of the state vector), while the second is concerned with external stability (ensures small output-no!"!�' when the input has small norm). The Input-Output stabiE\y is re! ·ltcd tu the small-gain cri­terion and the notion of conicity (Zames, 1966), and a complete theoretical formulation can be found in Desoer and Vidyasagar (1975), where special attention is paid to passivity and positivity as particular cases of conicity with relevant physical meaning.

The approach to robustness in Safonov ( 1980) is a more general formulation that contains as particular cases the Liapunov crite­rion and the conicity and circle theorems. All these criteria give sufficient (not necessary) conditions for stability. It has been shown that for a wide class of systems (Shamma, 199 1 ) the small gain criterion is necessary as well as sufficient. In Aracil, Ollero and Garcia-Cerezo ( 1989) the global robustness of nonli­near expert control systems is studied by means of geometric bi­furcation-indices.

In this paper we choose the Conicity Criterion as a starting point (Barreiro and Aracil, 1990). In section 2 we state the main pre­vious definitions and results on conicity. In section 3 it is shown how the application of conicity is facilitated by means of certain functions called the conic deviation and the conic robustness; and a new robust synthesis method is proposed. In section 4 it is shown how the method can be applied to unknown plants where only input-output energy measures are available.

2. INPUT-OUTPUT STABILITY

2.1. Signals

In the Input-Output methods, it is assumed that all the signals x(t) are functions of time x(t):IR+-�IR n, taken from a normed

vectorial space 3 . The more common spaces are 3 =L2, the

127

space of square integrable functions, and 3=L00 , the space of essentially bounded functions:

L2 = { x(t) :

L""' -= [ x(t) :

l l x(t) ll22

= r xT(t) x(t) dt < oo ) , 0

II x(t) 1100 = e.•s sup I ! -.:(!' II < °" 1 . t .

The space 3=L2 has more physical relevance, because it con­tains all the finite-energy signals. To cope with typical control signals (step, ramp, sinusoidals) that may not belong to 3 , we define the truncation of a function after time T as (Fig.1):

PT(x(t)) = xT(t), where

xT(t)= x(t) if tST, and xT(t)=O if t>T.

T T

Fig.l . Truncation of signals

The extended space Xe is the set of all the signals x(t) such that

all the truncations x'f(t) belong to %:

%e = { x(t) : ¥TEIR+ I I xT(t) II < oo }

The extended spaces contain all physically conceivable signals.

A signal has finite norm when x(t) £ % and infinite norm when x(t) £ % e\% .

2.2. Systems

A dynamical system is interpreted as a device that takes input signals x(t) and produces output signals y(t) from extended spa-ces %e, '.Ye, respectively. In a first level one may associate to

the input x(t) a set of one, many or none output signals, depen­ding on initial conditions or disturbance signals. In this way a system G is represented by a relation G C %eX '.Ye, formed by

all the pairs (x(t),y(t)) such that y(t)=Gx(t) is a possible input related to x(t).

In a second level, the system G may be regarded as an operator G : %e--�'.Ye, i.e. for every input x the system gives rise to

one and only one output y=Gx. Although the approach of systems as operators is more frequent, most of the stability re­sults here are valid for systems as relations; the last approach being somewhat preferable in the sense that it avoids existence and uniqueness problems.

2.3. Stability

The intuitive notion of Input-Output Stability of a dynamical system is related to the idea that the system produces small out­put signals provided the input signal is small enough. Keeping this in mind, a system G is said (finite-gain)-stable when:

g(G) = sup { I I (Gx)T I I I I I xT I I } < 00•

x,T,llxTl l;tO

The quantity g(G) is called the: gain C;f G (if G is an operator, then g(G) is the induced norm) :ne sy,tem is stable when it has

finite gain and in this case llyTll::; g(G) llxTl l for every T and

every pair (x,y) of input and output signals. If a system is sta­ble, then it is bounded input- bounded output (BIBO) stable,i.e., it transforms bounded sets of inputs into bounded sets of out­puts. Other related definitions of stability are made in Safonov ( 1980), putting llyTll$ 0(11xTll), with 0 a more general function.

In the Input-Output stability, the asymptotic approach to equili­brium is strongly related to the extended space %e chosen. For

example (Fig.2) consider an input pulse x(t) of unit height and lenght. As llx l l2=1 1xl l00=l, the output y(t) when x(t) passes

through an Li-stable or L00-stable systems verifies llylk00 for

both norms, but this does not prevent a limit cycle oscillation in the L00-stability. Even the Lz-stable system may produce un-bounded output provided the square integral is finite. Further­more, nothing is said about how fast the signal tends to zero.

Although to deal with these questions more theoretical tools must be considered, in practical simple nonlinear systems those anomalous behaviour does not occur and a Li stability guarante-es an adequate performance.

A concept highly related to stability is the notion of continuity. An operator G is continuous when, if y=Gx, then small chan­ges of the input x produce only small changes in the output y. If a system is going to work in the presence of noise, it is prefe­rable to ensure continuity rather than stability, but as the treat­ment is completely analogous (using the incremental gain instead

128

x(t) _J_i'. � L2 stable

system l l y 1 1 2 «"'

x(t) _J_ •I L;Y,::'!'e I �t) "

...__ ___ _. l l y I I < =

Fig.2 . The L 2 and L � Input-Output Stability for a unit norm input Uxd=l

of the gain, see Zames ( 1966) ) only the objective of stability will be addressed here.

2.4. Stability Criteria

The above definition of stability is referred to an open loop system. In control systems, feedback configurations must be considered. Most of the block diagrams of control systems can be reduced to the closed loop in Fig.3 with two dynamic sy3!�ms G 'llld H, that may reflect the natural separation P"iwe­en plant and wn:roller or an artificial separation or dynHmic>, m11d:: furstabiiity pu.-po�es.

Assume that all the signals is Fig.3 belong to the extension .r;e of a normed space X:. The closed loop operator (relation) F has (u 1 ,u2)£ X: eX X: e as input signals and (x1 ,x2) £ X:eX X: e as

output signals. The closed loop system is said to be stable when F has finite gain, g(F)<oo. The main result on Input-Output sta­bility is (Zames, 1966) the Small Gain Theorem:

G

H

Fig.3 . The general feedback system

Criterion 1: The above feedback system is closed-loop stable if

g(G) g(H) < ! .

The condition i s sufficient but not necessary, and if i t does not

hold, nothing can be said about instability. A way to increase ap­plicability is to add and substract the same block C, manipula­tion that gives rise to the transformed closed loop T(F,C) of Fig.4. Under mild conditions, the stability of F (Fig.3) and of T(F,C} (Fig.4) are equivalent, as stated in the loop transforma­tion theorem (Desoer, 1975):

Ge

y1 G

c

c

I -H

X2 U2

H-C

Fig.4 . The transformed system T(f,C)

Criterion 2: Assume that G, H, Feedb (G,CJ= r.o+CG)-1 and H-C are well defined :C-� :C operator�. ;;n:l that C is lineal.

Then F is stable if and only if T(F,C} is stable.

Putting together these two results, we get the Conicity Criterion:

Criterion 3: In the above conditions, the feedback system F is stable if there is a linear operator C::C--� :C . and a positive r£1R+ such that:

g(H-C) < r,

g( Feedb (G,C) ) = g( G(I+CG)- 1 ) � l/r.

The auxiliary elements C and r are called center and radius, res­pectively, and a graphical interpretation is given in Zames ( 1966) and Safonov ( 1980) in the sense that H must lie inside (and the inverse of -G must lie outside) certain geometric cone of para­meters (C,r).

The Conicity Criterion is stated in an abstract frame and contains as particular cases (Safonov, 1980) the well-known Circle Crite­rion and results on passive-positive systems, such as the Popov Criterion.

3. APPLICATION OF THE CONICITY CRITERION

3. 1 Conic deviation and robustness radius

Many practical questions arise when trying to apply the abstract results above to particular nonlinear control systems. Perhaps

129

the main problem is to obtain the functional gain of a general nonlinear system. For two classes of systems it is straightfor­ward to obtain the gain. For a nonlinear static (memoryless) system given by a nonlinear function H: JR m_� JR n :

g(H) = supllxll*O II H(x) I I I II x II.

The simplification is due to the fact that the time-dependence dis­sappears of the general expression of g(H). For a second class of systems, the linear time-invariant operators, the simplification comes from Parseval identity in Fourier theory. If 9(jco) is the Fourier transform of the mXn impulse response (convolution kernel) of G, then:

g(G) = sup co

[ A.max< 9*(jco) 9(jro) ) J 112

This fact relates g(G) to the frequency response 9(jco), obtained analytically from the Laplace transform G(s}, or experimentally, from frequency measures.

To apply these two expressions, the particular control system must be rearranged as Fig.3 so that one block, say G , retains the linear dynamics, and the other, say H, retains the static me­moryless characteristic. A separation like this can always be done, and need not to coincide with the natural association G=plant, H=eontroller, but can be built from a different arran­gement.

To introduce now the Conicity Criterion, the linear center C must be appropriately chosen. If C is a linear dynamic system, then H-C is nonlinear dynamic, and the gain g(H-C) is not easy to deduce. !nis foc:t suggest that C must be a linear static (memoryles�: 0pc1atc•• , i .� . a center nXm matrix CE JR (n,m)

At this point the question is how to select the center matrix C so that the conicity conditions hold, if possible. As no a priori in­formation is in general available, an idea is to explore all possi­ble centers that may verify the conicity inequalities. This leads to the following definitions and criterion. The conic deviation d8(C) of the system H from the center matrix C; and the conic

robustness rG(C) of G with the feedback C are given respecti­vely by:

du(C) = g(H-C) and rG(C) = 1/ g( G(I+CG)- 1 ).

Criterion 4. The feedback system of Fig.3 is stable if, for some linear law y=Cx, the conic robustness rG(C) of G with the fe-edback C is greater than the conic deviation du(C) of H from the center C:

The criterion is a corollary of the Conicity Criterion, but adds implicitly the idea of exploring among all possible centers. As it may happen that the stability condition does not hold for some centers, but holds for anothers, we must look for an appropriate center.

3.2 Prooenies

To simplify the determination of an adequate center, if it exists, some propenies of the conic deviation d8(C) and conic robus-tness rG(C) can be given (Barreiro and Aracil, 1991).

y

H G

L-------x�2----(Joill;r-� r2 L-------�X�l-----C1'- r 1 (a)

(b)

C1 -I

rG

(f) cl (c2=0)

Fig.S (a) System G(z) and controller y= H(x 1 ,x2) (b,d,f) d H(c l,c2), surface, level curves and cross-sections (c,e,g) r G(c 1 ,c2), surface, level curves and cross-sections

(el

(g)

First, if the center C is an nXm matrix, assume that some of its nXm coefficients take fixed values and that only NY!Xm are va­riable entries. Furthermore, without loss of generality consider that N=2, so that the deviation can be identified with a function du(C): JR 2-� IR+, i.e. a surface in JR 3 (Fig.Sb). In the same way the robustness can be identified (Fig.Sc) with the surface rG(C): �CIR 2-�IR+, where � is the subset of stable centers

in JR2 that gives rise to a finite value for rG(C).

Prooerties of the conic deviation du©

(DI) The deviation du(C)=g(H-C) is a convex function of C.

cl (c2=0)

Hence, du(C) reaches its minimum value d* on some

convex subset �8*CIR 2. ( Usually, at a point �H* =

{ cH* }).

(D2) The gradient of du(C) (where defined) has unit mo­dulus.

Assume that H:IR2-�IR. Put x=pu9, with O*P EIR, and

u9=(cos0, sin0). Define hM(0) = sup { H (pu9) /p } , p

and hm(0)=in/ { H(pu9) /p ) .The functions hM(0) and p

hm(0) represent the maximum and minimum conicity of

H along the 0-direction. The surface and level curves of du(C) can be easily built from these functions (Barreiro and Aracil, 1991).Suitable generalizations can be made for N>2.

Properties of the conic robustness r!i©

(RI) The gradient of rG(C) (where defined) has modulus less or equal than I .

When G is a time-invariant linear system (continuous or discrete) of frequency response 9(w), the robustness is:

rG(C) = I/sup { 1 1 9(w) (I+C 9(w))-1 l l J . (I)

And this expression can be related to the usual distance to -I of the Nyquist plot of tht �ysttm CG.

The maximum value r* of rG(C) may be not unique, in

general. Even the stable domain � for the centers may be not convex or even not connected, in general.

If there is a multiplicative gain uncertainty on the plant, one can substitute G by KG . This results in a surface rKG(C), homothetic to the rG(C) surface. Considering

all probable values of K around K= 1, Ke % = [Kmin•Kmax], putting rcx: G(C) = min

Ke % rKG(C),

the conicity condition for gain uncertainty results in rcx: G (C) > du(C), where now rcx: G (C) encloses a more restrictive volume than rG(C).

In a similar way can be treated a phase uncertainty 'If, changing

K by K=ei'V. Thus, using certain smaller volume, instead of that enclosed by the surface rG(C) (Fig.Sc), one can address the question of robustness. plant uncenaintY and �ain and phase �·

3.3. Synthesis procedure and example

Consider the feedback system of Fig.Sa. The system H is given by the nonlinear static law y=H(x). The conic deviation, depends only on the maximum and minimun conicities hM(0),

hm(0), along the discretized directions (01 ,. . .,Sg, in the figure). The surface du(C) is bounded by planes (Fig.S.b) whose po-

130

sitions depend on hM(0k),hm(0k). Level curves and cross­section of dH(C) are shown in Fig.5b,d,e.

The process G is assumed to be the double time-delay ( z-1 ,

z-2). Every second order discrete-time SISO system (e.g. a sampled servomotor) can be put, changing variables, as in Fig.5. The stability region 'G for the feedback coefficients C= (c1 ,c2). is the triangle limited by c2=l and by c2=-l±c 1 . The surface rG(C) and its level curves and cross-section are given in Fig.5.c,e,f.

If the conicity stability condition do not hold, i.e., if:

for all Ce'G

C.G* OJ QI•

Fig.6 . Robust Synthesis by Conicity Method

(see Fig.6) then we must modify H. Many modifications of H will produce the desired results. In particular, making H linear, H(x)=C 1 x with C 1 e 'G , we get du(C 1 )=g(H-C 1 )=g(O)= 0 <

rG(C1). and the stability-robustness is achieved.

The question here is that the modification Ho of H must be llS small as oossible. The relevance of this fact is that, if H is a non linear controller (obtained from an adaptive, neural-network, or fuzzy control method), it would be desira- y=H(x 1 ,x 2) ble to minimize the change of the adaptive, neural or fuzzy scheme from which H is built.

Now we must establish a cost fun­ction J(H,Ho) that gives a measure of the size of the change of H by Ho. For conicity purposes, the rele-vant functions are not H,Ho. but its maximum and minimum radial restrictions hM(0), hm(0), hoM(0) (a)

c

mum hm to h0m. The cost function can be defined as:

J(H,Ho)=max( max0( I hM(0)-hoM(0) I ),

max0

( I hom(0)-hm(0) I ) } .

The following property says, essentially, that the conicity stabi­lity conditions must be searched with respect to the center Co of minimum distance between dH(C) and rG(C) (Fig.6).

Property (Robust synthesis method): If the feedback system of Fig.3 formed by G and H do not verify the conicity stability condition, then the following modification Ho of H ensures the conicity stability, and minimizes the change-cost J(H,Ho):

1 . Find c0 such that Co= arg min ( dH(C) - rG(C) )

2. Put ro = rG(Co). do = dH(Co). ue=(cos0,sin0),

and x=pu9, as in Section 3.2.

3. Define hoM(0)=

min ( c0u0+ r0, max ( hM(0), Coue- ro l ) ,

and h0m(0)=

max { Cou0- ro, min ( hm(0), Coue+ rol ) . 4. Then Ho is given by :

Ho(x) = H(x), if p hom(0) s H(x) s p hoM(0)

Ho(x) = p hom<0),

Ho(x) = p hoM(0),

if H(x) s p hom(0)

if p hoM(0) s H(x).

The cost of the compensation is J(H,Ho)= do-ro . A com­mon situation is that of Fig.6, with dH(C) presenting a unique minimum at center c8•, and rG(C) a unique maximum at cen­ter CG* . The gradient behaviour of dH(C) (gradient equal to unity) and rG(C) (gradient less or equal than unity) suggest that more frequently Co=CH*· However, examples can be found (Barreiro and Aracil, 1991 ) where, due to discontinuities in the gradient, the synthesis center Co does not coincide necessarily

0 1 03 05 07 0 1 (b)

and hom(0) (as defined in section 3.2). The only way to achieve stabi­lity (decrease the deviation dH(C))

Fig.7 .(a) Conic admissible volume for the controller Y= H(x l ,x 2) .

is to decrease the maximum hM to hoM and/or to increase the mini-

( b) Conic-Band {h m(0), h M(0)}, before (white+gray) and after (gray) application of the robust synthesis method.

131

with the minimum deviation center Cu*·

The final aspect of the conic admissible volume for the con­troller y=H (x 1 ,x2), is sketched in Fig. 7 ., as well as the

conic functions hm(0), hM(0) along the discretized direc­

tions ek, after a particular application of the above synthe­sis method.

4. UNCERTAIN DYNAMICS

4.1 Functional gain and energy measures

The stability techniques based on the Conicity Criterion can be applied to situations where the process is bad modelled or even completely unmodelled. A robust control is achie­ved when the deviation of the nonlinear controller H is smaller than the robustness of the plant. The key idea here is that if no model is available, one can experimentally ob­tain the plant robustness by energy measures.

Denote by E(x,n=llxTll2 the total energy of the signal x(t) taken from t=O to t=T. From the definition, the functional gain of an unknown operator (system) G:x-+y is given by

x(t)

Uncertain System G

A Smax

Oscilloscope

y (t)

g(G) = sup { E(y ,T) I E(x,T) } x, T ,llxTll;C()

Fig.8 . Experimental measurements of robustness r G(C), for an uncertain system.

To design a robust controller H by conicity methods it suf­fices to know the value of the robustness rG(C) of G with a stable feedback center C. To obtain empirically rG(C) for an un­certain plant G, consider the Fig.8, where an adequate stable fe­edback C is first selected empirically.

Then a set of input test signals x(t) is applied to the system, and for every input-output pair (x(t),y(t)) and every time T, the energy quotient s(T)=E(y,T)/E(x,n is determined. In the figure, W de­notes the instrument that makes the energy measures. The quotient s(n is equal to the maximum slope smax of the oscilloscope trace

when E(x,t) passes through the X-channel and E(y,t) through the Y-channel.

Then, the robustness is equal to:

After that, one can freely design the nonlinear controller H provi­ded that du(C)<rG(C)= 1 I sqrt ( smax ). The robust synthesis method in Section 3.3 is applicable to adjust H.

5. CONCLUSIONS

In this paper we propose a method for the stability analysis of fe­edback systems with nonlinear uncertain dynamics. The approach is based on the Conicity Criterion of Zames and offers simple tests for stability, based on certain deviation and robustness functions, represented by surfaces and cross-sections. A robust synthesis procedure is also presented.

The results are applicable to nonlinear control methods such as adaptive, fuzzy or neural-network based, as well as to uncertain or unknown systems where the robustness function can be obtained empirically from simple energy measures.

132

ACKNOWLEDGEMENT

The a:;ihors would like to aknowledge CIC'l'T for !°•mding the work unctP.r grant # ROB89-0614.

REFERENCES

Aracil, J., A. Ollero and A. Garcia-Cerezo. ( 1989). Stability Indi­ces for the Global Analysis of Expert Control Systems. IEEE Trans. Syst. Man Cyber. Vol. SMC-19 no. 5 pp. 998- 1007.

Barreiro, A. and J. Aracil. ( 1990). Applications of the Conicity Stability Criteria to Multivariable Expert Control Systems. Proceedings of the IEEE International Con­ference on Systems Engineering, pp. 148- 15 1 . Pitts­burg, PA.

Barreiro, A. and J. Aracil. ( 1991) . Aplicaci6n de/ Criteria de Co­nicidad a estabilidad de sistemas no lineales de con­trol. Internal Report. ETSII Vigo-Sevilla.

Desoer, C.A. and M. Vidyasagar ( 1975). Feedback Systems. Input-Output Properties. Academic Press.

Safonov, M.G. ( 1980). Stability and Robustness of Multivariable Feedback Systems. MIT Press, Cambridge, MA.

Shamma, J.S. ( 199 1) The Necessity of the Small-Gain Theorem for Time-Varying and Nonlinear Systems. IEEE Trans. on Autom. Control, Vol. AC-36, No. 1 0, pp. 1 1 38- 1 147.

Zames, M.G. ( 1966) On the Input-Output Stability of Time­Varying Nonlinear Feedback Systems. /£££ Trans. on Autom. Control, Vol. AC- 1 1 , No. 2, pp. 224-234.

Copyright © IF AC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

A COMPUTATIONAL CAUSAL MODEL FOR PROCESS SUPERVISION

K. Bousson and L. Trave-Massuyes

LAAS-CNRS, 7 avenue du Colonel Roche, 31077 Toulouse Cedex, France

Abstract: This paper proposes a causal modeling framework for the purpose of process supervision. It is based on a qualitative automata (or q-automata) concept that we have devised. A q-automaton captures both the dynamics of a process variable and the expert knowledge necessary for supervising the variable's behavior. We use a two-level representation scheme for the description of the relationships between the q-automata underlying a process: a local constraint level and a global constraint one. The local constraint level describes the qualitative causal relationships between the q-automata, and the global constraint level states the quantitative constraints among them. The formalism is shown to allow the modeling of deep knowledge as well as compiled knowledge. Furthermore, it is suitable for the modeling of partially-known, hybrid (numeric and symbolic), continuous and discrete processes. A causal engine (CA-EN) using the formalism is under intensive development. It is at the core of the process supervision system.

Keywords: Process Supervision; Qualitative Reasoning; Causal Modeling; Qualitative Automata; Compiled Knowledge; Deep Knowledge; Influence Combination.

1 Introduction

The main tasks of a process supervision system are to assess the process behavior and to act, or to advise a human op­erator about what occurs and what to do when the process behaves unwantedly. Therefore a supervision system must meet the following requirements:

• Real-time: The system must be reliable in response time. For that purpose it must be endowed with fast processing strategies and deal with time.

• It must track the behavior of the process over time from state to state. That ensures the detection of early deviations from the nominal behavior.

• In a process, all the variables are not necessarily mea­sured or observed, that is, some of them may be inac­cessible. A process supervision system must be pro­vided with means to predict the behavior of those inaccessible variables as well as the behavior of acces­sible (measured or observed) ones.

• It must be supplied with trustworthy structural and behavioral models of the process to enable it to meet the above mentioned requirements. This is all the more achieved as the model captures more relevant available knowledge. Consequently, it must deal with both numeric data (e.g. numerical equa­tions) and symbolic ones (e.g. experential knowledge, physical qualitative constraints). Indeed, supervision appears as the last and skilled level of automation that control theories do not master and that Artificial Intelligence techniques are welcome (Aguilar-Martin ( 1991)). Meanwhile, knowledge from lower levels (e.g.

. regulation-oriented numeric models) should be used if need be.

133

Expert systems are decision support systems; however today, it is widely recognized that their knowledge is too 'shallow' to cope with engineering problems in the sense that they are based on pre-specified relationships between conditions and actions, or causes and effects, (e.g. between system behavior abnormalities and corresponding causes) rather than on a model of the domain of interest (eg. struc­tural description, including physical laws).

The weakness of shallow reasoning systems and the lack of mathematical models of incompletely-known engineer­ing systems (e.g. biotechnological processes) have recently led Artificial Intelligence communities and control engineers to investigate qualitative reasoning about physical systems (or qualitative physics) (Bobrow ( 1984), Weld and DeK­leer ( 1990)) . As a component of qualitative reasoning, the aim of causal reasoning is to derive system behaviors from structural descriptions for the purpose of, among other tasks, prediction, causal explanation and situation assess­ment. Hence causal reasoning is well suited for process supervision.

Causal modeling is the cornerstone of influence repre­sentation within devices, more often than not at the basis of causal reasoning. Consider we were asked to supervise a sprinkler (fig. 1) so that the level of the liquid in the tank remains in the interval [y2, y3[ and that the color of the liquid stays green during the sprinkling process. To do that, we first have to use a set of conventions to represent the dependences between the tap flow rates and the liq­uid level, the pipe flow rate and the liquid level, etc . . . In other words, we need first to model causally the interrela­tionships among the system's variables. Here, 'Causality', as we understand it in engineering, stands for something that links the structure (set of numeric or symbolic equa­tions, topological description) of a system to its functions and behavior.

Tap B

[P): prodllCI concenniion me Fa: flow raie froni tap A F'o: flow rae from tap B

y� y3

Ille color of the liquid ch•ngos occordin& IO lhe conccnntion rue or produci P

Fp: flow raie in the pipe y : level oi !he liquid in the unk y' : liquid height powlh in Ille rw

yl y l 0

pipe

col 'c6Y� ��g.�� in the Wik ymu: the hei&ht o( the wll<

Spnnklin& is ensw.d by muns of device D which rotates proponionally to y. Suuable �pnnkllng is obwned when y 1s in the interval (y2. y3( >nd col is ¥t0""· s0: ro111ing speed or devi« o

ice D

· /r:v/ , /J? 1 Figun: I: Sprinlder

Causal modeling has received considerable attention in qualitative physics. Work has been done in process model­ing for supervision tasks (Leyva! and Gentil (1991 )) using the notion of qualitative transfer function which is the qual­itative counterpart of transfer function in control theory, or propagation function like in (Vescovi ( 1990)). Meanwhile, the existing approaches suffer from some weakness in that they are generally supported by directed-graph representa­tions:

• Multi-variable relationships induce the problem of in­fluence combination so that those systems generally assume linear relationships, which may be a very rough approximation in many cases.

• Constraints involving more than two variables (e.g. mass balance relations) are not representable, which makes difficult to model processes whose supervision requires an interminglement of first principles and ex­perential knowledge.

• Although they may allow reasoning in time, they do not allow reasoning on time so that intermittent in­fluences or influences with limited duration are not

representable. Time representation is of event type which makes difficult tracking the process behavior.

• The formalism used for representing process dynam­ics is too inflexible so that hybrid processes (i.e. pro­cesses involving both numeric and symbolic variables, such as the above mentioned sprinkling system) can­not be handled. A consequence of this is that they do not cope with processes involving both continuous variables and discrete ones.

On the other hand, qualitative differential equation based (Kuipers (1986)) or component-based (DeKleer and Brown ( 1984)) approaches can easily cope with multi-variable rela­tionships and constraints involving more than two variables. However, they also suffer from event-type time representa­tion and from the fact that they do not allow reasoning on time. The last mentioned issue is a problem as well.

In addition, causality paths are not explicitely repre­sented. First, that makes it difficult to represent exper­ential knowledge understanding oriented influences which rises the problem of involving "informative" variables, for instance how can you represent in the QSIM formalism that the color of the water in the tank depends on the concen­tration rate of product but not the converse ? Second, it complexifies several tasks like diagnosis and causal expla­nation.

This paper proposes a causal modeling framework which captures most of what is needed to reason about partially­known, hybrid, continuous and discrete process for the pur-

134

lntluenccs

from mhcr

q·automata

Figure 2: Dynamics of• q1,ulliuuivc automaton

Influence

IO olhcr Q·iUU>malll

pose of supervision. We use a two-level representation scheme for the description of the relationships between the process variables: a local constraint level and a global con­straint one. The local constraint level represents the qual­itative causal relationships between the process variables, and the global constraint level states the quantitative con­straints among the variables .

2 Representing process knowledge

Dealing with the supervision of physical processes requires having a relevant representation of the quantities at hand which are time and the process variables.

2.1 Time representation

The algebra of temporal intervals (Allen ( 1983)) is a tem­poral reasoning framework which suits most of Artificial In­

telligence systems for it has a higher expressive power and is easy to implement. However it is shortcome by the fact that it may accept an inconsistent set of temporal relations as being consistent (incompleteness problem) and it runs in O(n3), which is a too high computational complexity for coping with real-time applications such as supervision tasks. Vilain and Kautz ( 1986) have shown that the com­pleteness problem can be solved by representing time in the restricted interval algebra which allows the same expressive power as Allen's temporal algebra. Recently, Ghallab and Ala.oui ( 1989) solved the complexity problem by proposing the IxTeT temporal management system which guarantees linear time complexity for data retrieval and updating, and which has been proven sound and complete ensuring the same expressive power as the restricted interval algebra.

Therefore, the temporal representation and management strategies we have chosen for dealing with processes are that of IxTeT system. A time-interval is represented as a pair T = (t1, t2) where t1 and t2 are time-instants with t1 < t1. However we regard the temporal axis as regularly sampled with temporal landmarks at which the physical process must be checked up. Hence, the temporal unit for the supervision system is the (constant) distance between adjacent landmarks. The temporal unit must be chosen so that the behavior of the process at hand can be assumed to be linear within it.

2.2 Qualitative Automata

When a human operator supervises a process he concerns himself with checking whether the value of each variable equals some (discrete) value, when the variable is discrete, or falls into some interval, when the variable is real·valued.

When a variable behaves unwantedly, the operator uses knowledge about its dynamics and about the causal rela­tionships between that variable and others to correct the variable's behavior. In other words, on one hand the op­erator checks the qualitative behaviors of the variables in somewhat regarding each process variable as a kind of au­tomaton moving from an interval or a value to another, and on the other hand he uses a set of knowledge to act on the variable. Therefore, this motivates that we assign a qualitative automaton (or q-automaton for short) to each process variable and to the knowledge-base which is needed to reason about the behavior of that variable.

Our perception of a physical process is a world of in­teracting q-automata influencing one another. The set of q-automata underlying a process is called the q-automata universe. In order to cope with any type of process vari­ables, a q-automaton may be of numeric or symbolic type according to whether the underlying process variable is real­valued or takes discrete (or symbolic) values (e.g. red, green, blue).

2.2.1 Quality spaces, states and values

The significant discrete values and intervals according to which the values of a process variable must be evaluated over time by the human operators are pre-specified by pro­cess experts. We assume that for real-valued variables, these intervals describe a finite and totally ordered parti­tion of their respective ranges. We call quality space (Hayes (1985)) of a numeric q-automaton such a partition. The quality space of a symbolic q-automaton is its value set (which is, in fact, a discrete set), and is assumed to be fi­nite and totally ordered according to the context of use. The state of a q-automaton is an element of the quality space; it corresponds to relevant information for a human operator in the decision-making tasks. Contrarily to con­ventional automata theory, a q-automaton's state does not necessary summarize the whole history of the q-automaton.

The value of a q-automaton X at time-instant t is the value of the associated variable at t. It will be denoted by value-of(X, t) ; if t=now (i.e. the current time-instant) , that is simply written value-of(X). The same shorthand applies to state-of for the description of states. If X is a symbolic q-automaton, the state of X at t equals its value at t; but if X is numeric, value-of(X, t) is element of state-of(X, t).

2.2.2 Dynamics

The dynamics of a process is due, on one hand, to the in­teractions among the q-automata and, on the other hand, to actions coming from the process outside world. An ac­tion is an operation made by a human operator or a de­vice in the way to increase or decrease the state of a q­automaton. Actions are made by means of process con­trol q-automata ( q-automata underlying the process control variables) . The interactions among the variables of a pro­cess can be represented by influences from one q-automaton to another. The influence that a q-automaton exerts on an­other q-automaton is due to the variation (change) in the

former. A q-automaton X is said to influence (directly) a q-automaton Y if, assuming no action to be done on Y and all the q-automata to be quiescent except X and Y, a change in X is necessarily followed by a change in Y. A q-automaton X influences indirectly a q-automaton Y if there exists a chain of q-automata X, X1 , •.. , Xn, Y which successively influence directly one another. Unless other­wise specified, the word influence, from now on, will refer to direct influence implicitly. We assume influences to have durations, that is, they hold throughout time-intervals (and

135

not only at time-instants) when they occur.

Definition 2.1: The causal history of a q-automaton is the chronological sequence of its states and the actions that it suffers (if it is a control q-automaton} or that the control q-automata which influence it directly or indirectly suffer.

Causal histories are main sources of relevant information to achieve the goals of prediction and explanation in process supervision. From the definition, the causal history of each q-automaton grows as the process runs. However, some of its elements can be discarded when they are no longer necessary for behavior prediction or explanation.

Definition 2.2: The variation space of a q-automaton is the set of possible amounts of change it bears within a temporal unit. The variation (amount of change) of a q­automaton X is denoted by l:l.X.

The dynamics of a q-automaton is defined by a set of influence values (its inputs) , a quality space, a variation space, and mappings on those sets.

Definition 2.3: The dynamics of a q-automaton is rep-resented as a 5-tuple D = (I, S, V, f, g) where:

I is the input set. It is a set of influence values. S is the q-automaton's quality space, V is the q-automaton's variation space, f is a mapping from I into V, g is a mapping from V x S into S .

Dynamically, a q-automaton processes as follows (fig. 2) Mapping f enables to sum up the inputs the q-automaton

receives over time. Mapping g is used to combine the result of that computation with the q-automaton's most recent state and its current variation to update the q-automaton's state.

2.2.3 Dealing with influences

When several q-automata influence the same q-automaton, some of them may influence with a higher degree of sen­sitivity than others. On the other hand the subset of q­automata influencing a given q-automaton may be time­dependent. Therefore, the set of q-automata influencing a given q-automaton is a time-dependent fuzzy subset of the set of all the q-automata.

To reason about influences we make the:

Influence Sameness Assumption: The degree of sen­sitivity of an influence between two q-automata is constant whenever the influence holds.

The assumption states that:

• The degree of influence (i.e. the degree of sensibility of the influence ) that a q-automaton X exerts on a given q-automaton Y, denoted by µy(X), remains steady throughout the time-intervals on which the influence holds (it equals zero elsewhere),

• If X influences Y on two distinct time-intervals T1 and T2, the degree of influence throughout T1 equals the degree of influence throughout T2.

Instead of reasoning by means of the explicit numeric values of influence degrees, we will rather consider relative orders of magnitude at the level of the influences exerted upon the same q-automaton. This is dictated by the way process experts reason about influences. The O(M) formal­ism (Mavrovouniotis and Stephanopoulos (1988)) has been chosen for it has shown to be the closest formalism to the one process experts use. Table 1 presents the primitive relations of the formalism and the explanations of these re­lations. For instance, assume Xi, X2 to be two q-automata influencing a q-automaton Y throu.qhout a time interval T.

O(M) rdatiun

A << B

A -< B

A -< B

A == B

A >- B

A >- B

A >> B

Ve1bal explanation

A is much smaller than B

A is moderately smaller than l A is slightly smaller than B

A is exactly equal to B

A is slightly larger than B

A is moderately larger than B

A is much larger than B

Table I : Primitive relations of the O(M) formalism

If µy (Xi ) = = µy(X2), that is, the degree of influence of X1 on Y is exactly equal to that of X2 on Y, then, Y is influ­enced by X1 and X2 in the same proportion throughout the time-interval T. Now suppose that µy (X1) > - µy (X2), then Y will be influenced by X1 moderately larger than by X2, therefore the net influence on Y is nearer to the influ­ence exerted by X1 on Y than the one exerted by X2 on Y, and so on . . .

2.3 Local and global constraints

A local constraint in the q-automata universe is a causal relation involving two q-automata. A causal relation de­scribes the interactions between a pair of q-automata. Then are two kinds of causal relations: one is concerned with cause-effect relations (e.g. if the amount of liquid in the tank increases then we can say that the pressure at the bot­tom of the tank increases as well) and the other is concerned with information about q-automata (e.g. the color of the liquid informs us about the concentration rate of a certain chemical product in it, but the influence rather goes from the concentration rate to the color). We refer to infiuence­based relations as the former relations and information­based relations as the latter ones. Influence-based relations are used to predict behaviors, whereas information-based relations allow fast interpretations.

The q-automata akin to a physical process can be net­worked by means of the causal relations linking them. This leads to a directed graph whose nodes are q-automata and edges are labeled with causal relations.

A global constraint in a q-automata universe is a nu­merical or qualitative equation involving possibly several q-automata.

3 Modeling with q-autornata

Modeling with q-automata starts with the collection of all the relevant process variables and the compiled knowledge as well as the deep knowledge that process experts have about them. Then a q-automaton is assigned to each vari­able in the way to build the q-automata universe underlying the process. The information needed for a process supervi­sion system consists in :

• The behavioral and structural relationships between the q-automata. These relationships are phrased by local and global constraints as presented previously.

• The dynamics of each q-automaton, as stated in def­inition 2.3.

• A knowledge-base needed for a reliable monitoring and control of each q-automaton's behavior.

136

In this section, we propose a specification of q-automata and then define the local and global constraint representa­tion levels.

3 . 1 Q-automata specification

The q-automata specification provides a clear statement of relevant knowledge needed to reason efficiently about q­automata. It includes three parts: monitoring attribute:> , dynamics and control knowledge-base. The monitor­ing attributes describe the knowledge about the monitoring tasks (e.g. when can we say that a q-automaton is behaving unwantedly ?, or is the q-automaton measured or observed ?) . The dynamics consists in a set of information under­lying influence combination and state updating. The con­trol knowledge-base contains the compiled knowledge about what action to do to make the q-automaton behave suitably according to situations.

Monitoring attributes are:

Type: numeric or symbolic

Accessibility: measured, observed or inaccessible

Quality-space: {subrange;, i = l , . . . , n }

Each subrange; is an interval if the q-automaton is numeric, or a single value if the q-automaton is sym­bolic.

Nominal-range: default nominal range

Set of nominal (desired) values of the underlying pro­cess variable for the supervision purpose. The nomi­nal range should be one of the above mentioned decision­making subranges or a contiguous union of some of them. Since the nominal values may change according to situations, the reasoning system using the model must enable the change to the nominal range in op­eration when necessary.

The dynamics part copes with influence computation tables and methods to calculate net influences and update the q-automaton's states. That requires knowing the varia­tion space, the influence combination function (function f) and the state updating function (function g). The dynamics computation is postponed until section 4.

The control knowledge-base contains expert knowl­edge described by means of the following primitive func­tions:

do-action(preconditions, actions): states the actions which should be done when the preconditions are true,

set-nominal(preconditions, new-nominal-values) : allows us to change nominal value sets to new-nominal-values when preconditions are true,

red uce-history(precondi tions, elements-to-be-withdrawn­from-causal-history): allows us to abstract from some parts of the causal history while predicting behavior in stating the information which is no longer useful for prediction.

Example 3.1

Q-automaton Y (level of the liquid in the tank, see figure 1 ) could be specified as follows:

Monitoring attributes : Type: numeric Accessibility: observed Quality space: { [O, Y1 [; [y1 , Y2[; [y2, y3[; (y3, Y4[i [y4, Ymax] } Nominal-range: [y2 , y3[.

Dynamics : Ta.hies 2 and 3 contain pairwise combined influence val­

ues for q-a.utoma.ta. F,., Fb and Fp which influence Y; they enable to compute the net influence on Y. In these ta.hies, NL, NM, NS, PS, PM and PL mean respectively negative large, negative medium, negative small, positive small, pos­itive medium and positive large.

Control knowledge-base (an example of rules) :

do-action(value-oj{Y) < y3 and value-oj{rol) = green, "turn tap B off")

do-action(value-oj{rol) = red and value-oj{Y) < y1,

"turn tap B off and increase flow rate from tap B"}, . . .

� NL NS 0 PS PL FD

- PS PS PS PM PL

0 PS PS PL PL PL

+ PS PM PL PL PL

Table 2: Effects of A Fa and AFb on A Y

� I

NL NS 0 PS PL p

- PS PS PM PM PL

0 PS PS PS PS PM

+ PS PS PS PS I PM

Table 3: Effects of 6 Fa and A Fp on 6 Y

3.2 Constraint specification

In this section we present the representation levels germane to the local and global constraints stated in section 2.3.

3.2.1 Global constraint level

As mentioned earlier, global constraints a.re numeric or qual­itative equations involving possibly several q-a.utoma.ta. in representing deep knowledge a.bout the process. Therefore global constraints a.re concerned with numeric q-a.utomata.. There a.re two kinds of global constraints which a.re p+ (resp. p-) and equations:

• P+(X, X1 , . . . , Xn) (resp. p-(X,Xi , ... , Xn)) holds if, a.nd only if:

- When X behaves normally, so do X1, ... , Xn.

- When the state of X is below or a.hove the nomi-nal range, so a.re the states of Xi, ... , Xn (resp. when the state of X is below (above) the nomi­nal range, those of Xi, ... , Xn a.re above {below)

137

the respective nominal ranges).

• The equations a.re given in the usual interval alge­bra. using the usual equality (i.e. =) or the quali­tative equality (i.e. :::::) (Tra.ve-Massuyes and Piera. ( 1989)). They link the states or the states and vari­ations of q-a.utoma.ta. by means of the opera.tors $ a.nd 0 which a.re respectively the qualitative sum and product (Missier ( 1989)) defined as the qualitative function associated with the classical sum and prod­uct operators on reals. The constraints linking exclu­sively variations a.re all considered a.t the local level either in causal relations or in the influence combina.� ti on function f.

Example 3.2.1

In the sprinkler example, the mass-balance equation link­ing the tank input a.nd output a.mounts to the volume vari­ation in the tank during a. temporal unit r is represented as follows:

( 1 )

where S i s the section of the tank given as a. real number or interval.

3.2.2 Local constraint level

The local constraint level includes the causal relations among the q-a.utoma.ta.. They a.re influence-based relations which causally link the a.mounts of change (variations) of two q­a.utoma.ta. and information-based relations which constrain two q-a.utoma.ta. states.

An influence-based relation is of the form:

R(X, Y, c, µ, d, p), where:

R is the name of the causal relation.

X the influencing q-a.utoma.ton.

Y the influenced q-a.utoma.ton.

c the activation condition of the causal relation. The influ­ence occurs if, and only if c holds.

µ is the relative order of magnitude in O(M) formalism (see section 2.2.3) of the influence degrees when X influences Y.

d is the delay of the influence. It is a real number.

p is the influence duration (response time). It is a real number, or equals oo if the influence holds perma­nently.

To model influence-based relations we use predicates I! and /;; defined as follows:

I!(X, Y, c, µ, d, p) (resp. I;;(X, Y, c, µ, d, p)) holds if, and only if X influences positively (resp. negatively) Y, where a is a.n integer which describes the rate of change.

Let us consider the predicate I!. If a = 0, Y increases (or decreases) in the same proportion as X does. If a = 1, Y increases (or decreases) slightly more than X does. If a = -1, Y increases (or decreases) slightly less than X does, and so on... The same example could be dealt with I;; dually.

An influence-based relation ma.y be the disjunction of n other relations:

n

R(X, Y, c, µ , d, p) = V R;(X, Y, e;, µ, d; , p;) (2) i=l

where two different conditions e; and c; do not hold throughout the same time-interval. In equation (2), for any pair of different elements i ,j, R; = R; implies that d; and d; , or p; and p;, are different from one another. Such a re­lation describes influences whose nature changes over time or according to circumstances, and so, it is termed as com­posite.

An information-based relation is not associated with de­lay', persistence duration, conditions and influence degree because it does not describe influences but informs about what is occurring in some q-automaton. Hereafter is an ax­iom about the quality spaces of q-automata linked by an information-based relation.

Quality space axiom: The quality spaces of any pair of q-automata linked by an information-based relation have the same cardinality.

An information-based relation is represented by a pair I(X, Y) where X is the informing q-automaton and Y the q-automaton that X informs about. Therefore, X must be an accessible (measured or observed) q-automaton. The information underlying such a causal relation is described by a one-to-one mapping from the quality space of X into that of Y. The idea of mapping quality spaces has origi­nated from the study led by Guerrin (1991) about influence propagation in hydroecological processes.

4 Qualitative automata dynamics

4.1 Global influence calculus

Let Y be a q-automaton influenced by N other q-automata Xi , X2, . . . , XN and assume C1, C2, ... , CN to be the respec­tive variation spaces. Then the input set of Y is defined as the cartesian product I = C1 x C2 x . . . x CN.

The mapping f is an operator that combines the in­fluence values composing I to yield an element in C (the variation space of Y). Actually, if e = (ci , c2, ... , cN) E I, the global effect of the input e is:

(3)

where each f;( e;) is the marginal effect of the influence value e; (i.e. the effect of e; assuming that it is the sole acting) on the q-automaton Y, and © an influence combining operator defined on C.

Compiled knowledge about influence combination is de­scribed in tables (e.g. tables 2 and 3) for known pair­wise combined influences, or given by correspondences. Al­though in general experiential knowledge is available for the combination of several influences at once, we give hereafter an algorithm to compute the global effect when only a few marginal influences and influence tables are available:

1 . Combine the terms in equation (3) relatively to the avail­able tables. (That process yields a number of partial net influences in addition to marginal influences).

2. Calculate the order of magnitude associated with the influence degree of each partial net influence.

3. Compute the net influence using relative orders of mag­nitude calculus. That may gives rise to several possi­ble net influences some of which may be spurious.

4. Filter out for consistency using global constraints.

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4.2 State updating and output

The state of a q-automaton over time is computed by means of mapping g (definition 2.3) using the global effect of the influences it undergoes and its near-past state. But comput­ing the new state that way may bear ambiguities. However, these ambiguities can be filtered out by means of global con­straints and the causal history of the q-automaton.

The output of a q-automaton at any instant equals the current global effect of the influences that it suffers.

5 Prediction algorithm and sprin­

kler example

The behavior prediction in the q-automata universe con­sists in applying in parallel the behavior updating algorithm (global influence and new state calculi stated in the last section) to each q-automaton. The full causal propagation algorithm which accounts for influence delays and durations will not be presented here because of space.

Applying the algorithm to the causal model of the sprin­kler as depicted in fig. 3 will allow us to now, for instance, if the level of the liquid will behave abnormally in mean-term, and to correct the q-automata's behavior if necessary.

6 Conclusion and perspectives

In this paper, we have presented a causal modeling method­ology in the framework of process supervision. The pro­posed formalism relies on a qualitative automata concept that we have devised for the purpose.

The proposed approach is based on a two-level mod­eling: a global modeling of the structure (numerical and qualitative constraints involving several q-automata) and a local modeling (the behavioral model of each q-automaton and the interactions with its surroundings). The modeling of a process starts with the representation of every relevant process variable as a qualitative automaton. Then the be­havioral influence of qualitative automata variations is rep­resented, at the lower level, by causal relationships among the underlying qualitative automata and a cognitive model of each qualitative automaton. The higher level accounts for global constraints involving sets of qualitative automata. It is used by the reasoning mechanism as a multi-automata coupling level. The main avantages of this formalism are the followings:

• It deals explicitly with time by using a temporal logic which puts instants and time-intervals on the same footing.

• It allows the representation of both deep knowledge and compiled knowledge.

• It copes with hybrid (numeric and symbolic), contin­uous and discrete processes.

A causal engine (CA-EN) using the formalism is under intensive development for the supervision of biotechnologi­cal processes. It is meant to be validated as a generic sys­tem for the supervision of fed-batch fermentation processes which require tedious tasks. However, our ultimate goal is to make the formalism as robust as possible for most of dynamical processes. Herein, the present limitations are that it assumes relative order of magnitude influence de­grees and tables to be given by experts. Some work has al­ready been started to deepen the formalization of influence combination techniques, notably, the investigation of meth­ods to generate automatically influence combination tables

Globol Constroint Leuel Constraints on

states

Constraints on

variations

locol Cons troint Leuel

Figure 3: The causal model of the sprinkler example

given minimum expert information about the interactions among the process variables (Bousson and Trave·Massuyes (1992) ).

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Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

DESIGN OF AN INTELLIGENT SUPERVISOR OF A SHIP ENGINE ROOM

J.M. Marchal* and E.F. Camacho**

*Escue/a Superior de la Marina Civil, University of Cadiz, Spain **Escue/a Superior de Ing. lndustriales, University of Sevilla, Spain

Abstract This paper presents the prototype of a knowledge based supervisor for a turbo -charger system of the main engine of a ship. The knowledge representation is based on quali­tative models and uses Propagation of perturbations and Qualitative Simulation as reasoning techniques. Qualitative models of the main parts and some illustrative examples showing different time-scale processes are given.

Keywords: Qualitative modelling, causal propagation, supervision, engine monitoring.

INTRODUCTION

The application of knowledge based techniques in ship engine control rooms is a field of increasing interest because of the following factors: a) the complexity of the installations, b) the singular on board working situation, c) The economic benefits of any improve­ments of the performance of the installations and e) the ever decreasing number of maintenance and super­vision personnel. During the last few years a number of comercial systems and rule based prototypes such as IAES (Katsoulakos et al. 1989) dedicated to super­vision and diagnosis have been developed.

Any knowledge based system needs to solve two cru­cial aspects: the representation of the knowledge and the manipulation of the knowledge, (reasoning) in or­der to fulfill determined objectives. There are different techniques to represent and manipulate the knowledge involved in the domain of a specific application. From the representation point of view, rules, predicates, ob­jects or frames and other more complex entities, such as models, can be mentioned. From the knowledge ma­nipulation point of view, forward and backward rea­soning, propagation and simulation can be mentioned as the most used techniques.

One of the most useful fields of application of expert systems is intelligent monitoring of complex processes. Intelligent monitors are supposed to assist control cen­ter operators by performing, among other things, the following functions: Presenting relevant information about the present state of the process to the opera­tor. Diagnosing faults, if any, that lead the process to its present state. Predicting possible future states or faults if certain actions are (are not) taken. Giving advice about possible actions to be taken.

All these functions need analysis and interpretation of sensor data to determine their meaning in order to explain what is (or may be) taking place in the process. It is clear that this type of interpretation must be based on a profound knowledge of the process. This must comprise not only knowledge of the separate

141

parts, but also of how they are connected and about how they work together.

Object-oriented programming languages are good tools for representing this type of knowledge. Con­cepts of parts, components and their relationships are easily coded in these types of languages. On the other hand, Qualitative Simulation (Kuipers,1986) seems to be the appropiate technique to perform the causal reasoning needed in some of the functions mentioned above.

This paper presents the prototype of a knowledge based supervisor for a turbo - charger system of the main engine of a ship. The knowledge representation is based on qualitative models and uses the propagation of perturbations and Qualitative Simulation as rea­soning techniques. Artificial Intelligence Techniques have been applied to ship engine monitoring in the past (Katsoulakos et al., 1989), although the approach used was rule based and did not consider qualitative behaviour. The main objective of this work is to de­velop qualitative behaviour models of the main engine a ship that could be used for monitoring, failure de­tection, diagnosis, prediction and instruction.

Here we consider a system as a collection of inter­connected components. So the behaviour of the sys­tem is obtained from the behaviour ef each component and the connections between them. This is compo­nent based ontology, but each component is modelled following Kuipers' ( 1984) interpretation. The models are based on variables which are linked between them­selves by several types of constraints.

The reasonin� is done by using the Qualitative Simu­lation (QSIMJ algorithm proposed by Kuipers (1986). The result of Qualitative Simulation is a description of the possibles qualitative states the system can reach in its evolution from an initial state.

In the quasic-static processes we apply qualitative propagation of disturbances through the constraints. The possible ambiguities in the tendency of any vari-

Figure 1 : Ship main engine turbocharger system

able are reduced by the use of heuristic rules, causal constraints, (De Kleer 1984, Oyeleye and Kramer, 1990).

The system developed has been implemented in SMALLTALK (Goldberg and Robson,1984) , which is a general purpose object-oriented language and thus allows Qualitative Simulation and time causal reason­ing to be integrated into a more general reasoning sys­tem.

The paper is organized as follows. Section 2 describes the process concerned and the model developed while section 3 is dedicated to presenting the supervisor structure. Some simulation runs showing malfunction detection are presented in section 4. Section 5 is ded­icated to presenting some concluding remarks.

MODEL DESCRIPTION

The engine room of a ship considered is composed of the following subsystems: The main engine, the main engine turbocharger, the auxiliary engine, the lubri­cating subsystem, the sea water system, the combus­tion feeding system, the compressed air system etc . . The engine room of a ship is a fundamental part of the same and has, therefore, to be continuously su­pervised.

The process considered , see figure 1, corresponds to a ship main engine turbocharger system. Naturally aspirated engines draw air of the same density as the ambient atmosphere and this density determines the maximum weight of fuel that can be burned in the cy­clinders and therefore the maximum power obtained. If the air density is increased, by a compressor, the amount of air is increased and more weight of fuel can be effectively burned and the power developed also in­creases. This procedure is implemented in most mod­ern diesel engines by using exhaust gas turbocharging

142

where exhaust gases are used to power the compres­sor. A substancial amount of the total heat energy is wasted to the exhaust gases, and although it is rel­atively inexpensive to drive the compressor directly from the engine by gear, an increase in power is ob­tained by using the exhaust gases to drive the com­pressor.

The inlet air is filtered and goes through the compres­sor. As the temperature of the inlet air after being compressed is too high to go into the cylinders, it has to be cooled down. This is accomplished by an air cooler using sea water as a coolant. Some of the sur­plus energy of the exhaust gases is used to power the turbine coupled with the compressor as indicated be­fore.

Temperatures of gases in ship diesel engines are very valuable sources information for monitoring their con­ditions. A model of the behaviour of the gases was considered to be a good tool for the supervision of ship engine rooms. In this sense, a qualitative model of the turbocharger subsystem was developed. A modular and hierarchical decomposition of the system was es­tablished. This way of representing the system adapts to physical reality, topology, the operator's mental models and allows for easy generalization when rep­resenting the global complexity of a ship engine room.

The main variables taken into account by the model are: cylinder inlet air pressure and temperature, air­cooler inlet air temperature and pressure drop, sea­water inlet temperature, turbine and compressor tem­peratures and exhaust pressure and temperatures.

All these components have been modelled according to Kuipers (1984) although the idea used for their ag­gregation in order to form the the system is nearer to the component ontology used by De Kleer (1984) as mentioned before. The same applies to the concepts of connections, causality and heuristics used.

__(--:r--- PoE PiE �- DtPE 8 1-1= ::;:

DtTaw ll E P•E 8- TJE

Tswi

Fig 2. Cooler Model

TiCyl 8-Tg I DtTcb

fb 1 � r Gcb �'0-Pot M Ga1r �yl � Ef �--�Rm

Fig. 3 Cylinder Model

The models have been obtained using physical laws and heuristic rules, given by the experts. The heuris­tic rules are used to resolve the ambiguities originated in the Qualitative Simulation. Two type of models, corresponding to two different time frames, were con­sidered. The first type of models corresponds to quasi stationary conditions models, whilst the second type corresponds to faster processes.

Figure 2 shows the model of the air cooler. The dif­ference (DtTaw) of inlet air temperature ( TiE) and sea water temperature ( Tswi) multiplied by the heat transfer coefficient determines the heat flow ( QE). The heat flow is also related to the air flow ( GairE) and the difference (DtTE) between inlet air temperature ( TiE) and outlet air temperature ( ToE). The air flow is also related to the difference ( DtP E) between the inlet air pressure ( PiE) and outlet air pressure ( PoE) as indicated.

The qualitative model of the cylinders can be seen in Fig. 3 The air flow ( Gair) multiplied by the fuel to air ratio (Rm) will determine the oil consumption ( Gcb),

143

EfM-1� Gcb �� PotM

r( + I RpmSet

Fig. 4 Speed Regulator Model

which in turn if multiplied by the cylinder efficiency (Ef) will generate the output power (Pot). The ex­haust gas flow ( Gg) is related to the air flow and the difference ( DtTcb) of the gases ( TgCyl) and air inlet temperature ( TiCyl) as shown.

Figure 4 shows a model of the engine speed regula­tor. The mechanical power given by the engine is the product of the oil compsumption ( Gcb) by the effi­ciency (EJM). This power is related to the engine speed (RpmM) by a monotonic relationship. The speed gov­ernor has an integral type of control and the speed error (DtRpm) will increase the oil consumption as in­dicated. Notice that this model runs in a faster time frame that the models described before.

We consider a system to be a collection of intercon­nected components and the interaction between them to be a form of directional causality. Thus the be­haviour of the system is obtained from the behaviour of each component and the connections between them (Williams,1990). The Qualitative Simulation (Kuipers 1984;Kuipers 1986) begins with the propagation of the known infor­mation, or known disturbances, to the system through the constraints, in order to complete the description of the direction of change for each variable, at a given time-point.

SUPERVISOR STRUCTURE

The supervisor has being designed with two main ob­jectives in mind: failure diagnosis and condition vigi­lance. The rn,ain characteristics of the supervisor are:

• Model based knowledge. • Object-oriented implementation. • Modular approach. Models are modules that

can be interconnected into more complex mod­els forming a natural hierarchical structure.

• Numeric information about the process is used.

In diagnosis process three tasks can be considered (Davis and Hamscher 1988): generating hypotheses by reasoning about symptoms, testing each hypothe­sis, and discriminating among those that survive test­ing. The supervisor perfoms the three tasks in a very similar way to the hypothesize and match cycle pro­posed in (Dvorak and Kuipers, 1988) as is indicated in the following.

Table 1 : Normal Conditions

air receiver pressure, PCol 1589 bar turbine speed. RpmT 7175 rpm exhaust gas temperature inlet turbine, TiT 457.8 °C alarm exhaust gas temperature outlet turbine, ToT 343.3°C air temp.inlet compressor, TiC 37.7 °C air temp. inlet cooler, TiE 144.3 °C air temp. outlet cooler, ToE 35.9 °C air receiver temp., TCol 43.6 °C air flow, Gair 12.27 ton/h air filter diff. pressure, DtPF 89 mmW cooler di ff. pressure, DtP E 98 mmW

Hipotheses generation. When any abnormal sit­uation is encountered, the supervisor generates a set of hipotheses about the possible faults that led to that alarm. Hypotheses are generated by rea­soning about symptoms with the help of influence graphs. These graphs describe how models and ob­servations (alarms or incidences) are interconnected from a cause-reaction point of view. By transversing these graphs a list of possible defective modules or fault hypotheses can be made.

Hipotheses test. Each of the hipothesis is tested with the help of qualitative propagation of perturba­tions, qualitative simulation and heuristic rules. The models associated to each hypothesis are first initial­ized and then simulated.

The hypothesis test is done by comparing the simu­lation results to the observations. Those hypotheses producing results which do not match the observations are rejected.

Hipothesis discrimination. A diagnosis is pro­duced by discriminating among those hipotheses that survived the test.

APPLICATION EXAMPLE

Two situations have been considered as illustrative ex­amples, the first one corresponds to a diagnosis in a quasi state regime, whilst the second illustrates the Qualitative Simulation on a faster time scale case.

In the first case, the procedure starts when any devia­tions of the system aria bl es from their normal values is produced. The problem of diagnosis is to match these deviations with a hypothesis of fault or malfunction that justifies the observations. Initially there is not a direct relationship (rule - made) between the observations and the hypothesis of fault. The reasoning about models must establish this asso­ciation.

A full ahead quasi-static regime is considered. The normal values of the main variables for this state, which have been obtained with a numerical situation in the DPS 100 simulator of NORTHCONTROL, is given in table 1 .

A malfunctioning of one of the elements is introduced

144

Table 2: Abnormal Conditions

air receiver pressure, PCol 1769 bar turbine speed. Rpm T 6882 rpm exhaust gas temperature inlet turbine, TiT 389.2 °C exhaust gas temperature outlet turbine, ToT 282.8°C comp. inlet air temp., TiC 35.4 °C cooler inlet air temp., TiE 137.4 °C cooler outlet air temp., ToE 38.1 °C air receiver temp., TCol 45.0 °C air flow, Gair 14.76 ton/h air filter diff. pressure, DtPF 95 mmW cooler diff. pressure, DtP E 143 mmW

in the simulator, originating an alarm in the exhaust gas temperature and other deviations from the normal situation values in other variables (table 2).

The transition between the normal and abnormal sit­uations has been considered as a continuous transition in a specified time. For the qualitative analisis we must express the state of these variables by means of its qualitative values and tendencies. The value of each variable is set by a landmark (written between brackets), which defines a qualitative value for the time points or by a pair of landmarks for the time intervals. The air flow Gair is between a landmark value ( Gairt) corresponding to to the full ahead normal engine regime and another landmark ( Gairst) which represents the minimal air flow to ensure a complete combustion . All air flow landmarks are placed in the following or­dered space:

[ 0 . . . . Gairst . . . . . Gairt . . . . +oo ]

The tendency can take one of the three qualitative values inc dee std. The abnormal situation can be expressed qualitatively as shown in table 3:

The hypothesis of a dirty air filter is made for trying to explain the abnormal state of the engine. This process is modelled by setting the tendency of the effective section of the filter SuF to be dee. By applying a heuristic rule, we get that the air flow through the filter GairF decreases.

With this information the tendency of the air filter differential pressure could be dee as given by the ob­servations. Next by the connection between the filter model and the compressor model we can see what happens in the latter when the air flow decreases and the power su­plies (an external variable) remain constant.

comp. speed Rpm C (O,RpmCt) me comp. outlet pressure PoC (atm,PoCt) inc

In the cooler model we have an ambiguity (this is an essential feature of qualitative reasoning) with the ten­dency of the outlet air pressure PoE, because the inlet

Table 3: Qualitative Abnormal Conditions

Variable Q. Value Tend. air rec. press.,PCol (atm,PoEt) me turbine speed,RpmT (O,RpmTt) inc exhaust gas temp. inlet turbine, TiT ( Tgt,+oo) inc exhaust gas temp. outlet turbine, ToT ( ToTt,+oo) inc comp. inlet air temp., TiC ( Tsm) std cooler in air temp., TiE ( ToCt) std cooler out air temp., ToE ( ToEt) std air receiver temp., TCol ( ToEt) std air flow, Gair ( Gairst,Gairt) inc air filter diff. pressure,DtPF (DtPEt) std cooler diff. press.,DtPE (O,DtPFt) inc

air pressure decreases PiE, but the difference pressure between input and output DtPE decreases too, so we cannot say anything about the tendency of PoE. To resolve this ambiguity we apply a KVL type heuristic rule proposed by De Kleer (De Kleer 1984):

i/ the input cooler pressure PiE changes, then the out­put cooler pressure will change in the same direction.

And we obtain

Cooler outlet press. I PoE I ( atm,PoEt) I dee

from the cooler-receiver conection we get:

Air rec. pressure PCol ( atm,PoEt) dee

which matches the observations and corresponds to the malfunctioning that caused the abnormal devia­tions of the variables from the normal values. That is, by propagation of a disturbance ( a hypothesis of mal­function) through all the models of the components we can infere the qualitative state of the variables. If they match the observations we can consider this hypothe­sis as a possible cause of the situation being analised.

For modelling complex systems we must make a hi­erarchical decomposition of them. This hierarchical decomposition includes time-scales (Kuipers, 1987). Models with similar time responses are grouped and the corresponding relationships between them are es­tablished. Thus a rapid model may have variables shared with a slower model.

To illustrate the second kind of model, running in a faster time frame, an example affecting the speed gov­ernor is given. The engine is considered to be in a stable state (all variables with std tendency) and a drop in the motor efficiency from its initial landmark (E/MO) to another landmark (E/Ml), as shown in Fig. 5, is experimented.

145

Efl10

Rpl'i1J. CcbMu Ccb1

Cc b l

... ........ i . . . . . . . . . . . . . . . . . . �-.� ��·.· t�.· ·.� - ��--.� i � � � � ' "·· -6· · · · · · · · · · · · · · · · · . . . . . . . . , , . . . . . . . . · · · · · · · · · · · · · · .·& · · • • • • • 1 .. . . . . .. . . I _ ,. · • i • • • • • • • •

. .. . . • . . • • • . • • . . . . . . . . • . . •. ! 111 .• 9 - - · . . . . . . . - . . . . �- 't' ·� :·��:·� �·; ::.:.·��-� ... ; � �-� ;.· i ...... ...... '6·. .. . . . . . . . r

<II II> <11 u < 1 1> ( 1 2) < 2 2)

Fig. 5.a Qualitative Simulation, speed recovery

Ef110 tf H1

· · · · · · · i · - · · · · · · 1 . . . . . . .. . J, . ""'"' I • • • • • • · · · · · · · · · · · · · · · · · · · · · · · · · . . . . . . . . . . . · · · · · · · · · · · €)- ·

Rpl"'l'1t ·· - · - · · · · i

.. . . . . .. . i - · · · · · · · . . . . . . . . . . . . . . . ' . t .· �-� �-1!' .•. �--a -

Ccbt . .

. . . . . . . . . . . . . . . . . . "· _C\.. · · · · · · ·0 · · · · · · · 0 . . . - � t, . ,. , . ,, - - · - ·

<11 •> <II 1> (1 1 > Ci 2 ) ( 2 2 )

Fig. 5.b Qualitative Simulation, speed loss

If this tendency is propagated in the model all the rest of the variables will have a dee tendency except the oil consumption that will have an inc tendency. Various situations can be obtained from here, depending of which variables reach their landmarks first, as illus­trated by Fig. 5.

The numeric response of the simulator for a deter­mined efficiency is shown in Fig. 6. which corresponds to the qualitative simulation of Fig 5.a.

Figure 7 shows the diagram of the possible qualitative states that can be reached. The diagram tell us that there is a drop in the engine speed and that from there two basically different things may occur: the engine stabilizes its speed at the set point with an increase in oil consumption, or a lower speed regime is obtained with maximum oil consumption.

448 428 488 388 368 72

8 58 188

Fig. 6 Numerical Simulation

S PEED NORMA l.

! SP£E:O OCC . / �

SPEEDf/ FUtl �X.

S PEED I NC . S PEEO OCC • I � ! SPEED NORMA L S PEED S PEED l.OSS f"UEl. MA X. NORMA l.

Fig. 7 Qualitative state diagram

Notice that the results of this rapid process ( for exam­ple the value of the conbustible flow Gcb or the motor speed RpmM) can be incorporated into the slower pro­cesses for reasoning on a greater time scale.

CONCLUSIONS

It has been shown how qualitative models can be used for intelligent monitoring and supervision of the diesel engine turbocharger system of a ship. The qualita­tive models permit the kind of reasoning about physi­cal systems, related to commonsense, that people can make. The object oriented approach has proved to be quite adequate for representing complex systems. A structure of classes for Qualitative Simulation has been proposed.

ACKNOWLEDGEMENT

The authors would like to acknowledge CICYT for funding this work.

146

REFERENCES

De Kleer J. (1984). How circuit work, in D.G. Bobrow (Ed.) Qualitative Reasoning About Physical Sys­tems. North-Holland, Amsterdam, pp 205-280.

De Kleer J. and J.S Brown (1984). A Qualitative physics based on confluences, in D.G. Bobrow (Ed.) Qualitative Reasoning about Physical Sys­tems. North-Holland, Amsterdam, pp 7-84.

Dvorak D and B. Kuipers 1988). Model-Based Mon­itoring of Dynamic Systems, 11th International Joint Conference on Artificial Intelligence, De­troit, USA.

Goldberg A.] and D. Robson ( 1989). Smalltalk-BO: The language . Reading, MA. Addison-Wesley.

Katsoulakos P.S., J.Newland, J.T. Stansfield and T. Ruxton (1989). Monitoraggio, Raccolta Dati e Sistemi Esperti per la Diagnostica delle Avarie di Machina, Tecnologie per il Mare, L'Automazione Navale april 1989, pp 38-42.

Kuipers B. (1984). Commonsense reasoning about causality: deriving behaviour from structure, in D.G. Bobrow (Ed.) Qualitative Reasoning About Physical Systems. North-Holland, Amsterdam. pp 169-204.

Kuipers B. (1986). Qualitative Simulation, Artificial Intelligence 29, pp 289-338.

Kuipers B.J.(1987). Abstraction by Time-Scale in Qualitative Simulation.Proceedings of National Conference on Artificial Intelligence (AAAl-87).Morgan Kauffman,Los Altos, CA.

Oyeleye 0. 0., M.Kramer (1990). The Role of Causal and NonCausal Constraints in Steady­State Qualaitative Modeling.Artificial Intelligence Simulation and Modeling, chap. 13 . John Wiley.

Williams B.C. (1990). Temporal Qualitative analy­sis: explaining how physical systems work, in D.S. Weld and J. de Kleer (Ed.) . Readings in Qualita­tive Reasoning About Physical Systems, Chap.2. Morgan Kaufmann, San Mateo, California. pp 133-177.

Copyright @ IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

QUALITATIVE MODELLING AND SIMULATION BY PIECEWISE LINEAR ANALYSIS

M. Toro, JJ. Arrabal and L. Romero

Facultad de lnformtitica y Estadfstica, Universidad de Sevilla, 41012 Sevilla, Spain

Abstract Since applications of expert systems were typical in domains with no well defined models, qualitative methods for modelling and reasoning were soon developed. Most current qualitative reasoning programs derive the qualitative behaviour of a system by simulating a hand-crafted qualitative version of the differential equation that caracterizes the model of a system. This paper describes a method to construct a family of piecewise linear dynamical systems from the qualitative information contained in a model. We apply the dynamical system theory to deduce results about the behaviour of the family of dynamical .systems constructed as a consequence of the qualitative model.

Keywords Artificial intelligence; qualitative modelling; nonlinear systems.

1 Introduction

A lot of work is being published at present with the name of Qualitative Modelling, Qualitative Simulation and Qualitative Reasoning (Kuipers 1986 and Sacks 1987c). They all have one thing in common, which is to obtain conclusions from models of systems, where the information is either qualitative or incomplete. The systematic gathe­ring of all qualitative information about a system makes a qualitative model. That qualitative in­formation can be structured as a set of constraints that join together show the evolution of the diffe­rent system sections. These constraints can have a derived form, an arithmetic form, a functional form, etc. Once a qualitative model has been COf!Structed, the question is to get obtain the maximum infor­mation from it. A set of theoretic tools and some practical implements have been developed. Qua­litative Simulation is one of them. With some differences, the qualitative information contained in the qualitative model that we take into con­sideration in this paper, is similar to Qualitative Simulation, but the method to obtain conclusions will be very different. At this point we construct a family of piecewise linear dynamical systems con­taining the qualitative information and later we will apply the dynamical system theory to obtain conclusions from the model. The research of constant piecewise linear dyna-

147

mical systems has received enough attention in different fields at the last decade (Chua 1983 and Sacks 1987c) , but the same hasn't happened to the family of piecewise linear dynamical systems. To contribute to the study of the latter, it is pos­sible to apply the theory of bifurcation to obtain interesting qualitative results.

2 Qualitative

Analysis

Model and

Let's assume in this paper that a qualitative m<r del has a set of variables, constants and a set of constraints among them. The variables and the constants take their values in a quantity space. Each quantity space is defined by an ordered set of landmark values. We are going to consider the landmarks that determine the quantity space as variables, with a partial order extracted from the specifications. The value of the variables, as well as the constants, is described qualitatively in terms of their quantity space. Every variable or constant may take a value in a landmark of its quantity space, or between two landmarks. The constraints among variables can be: Arit­hmetic, where +, - , * • / , represent the arithmetic operators respectively. Functional, where M +, M-, Nm, they are representable by continuous functions, f : R -+ R and so that M + is a mon<r tonic increasing, M - monotonic decreasing and

Nm no monotonic. And Derivative with refe­rence to time. This is represented by D. The associated information to the functional constraints can be extended with a list of pairs of points. In the event Nm joined with the va­lues of the points that the function takes, we de­signate with the signs +, - , 0 if in this point the function is increasing, decreasing or it takes an extreme respectively. The list of Nm would contain the points where the function takes the extremes. A qualitative model about the evolution of preys, predators and their interactions it is given in the following equations:

y

x(J(x) - g(y)) y h(x)

( 1)

where the number of preys are representable by x, the number of predators are representable by y, the rate of births of the preys is representable by f, the rate of mortality of the preys by predators is representable by g and the rate of births of the predators is representable by h. We assume that:

The consumption of prey by predator is proportional to the number of preys, and it depends on the number of pre­dators by an increasing monotonic fun­ction. In the absence of predator this consumption is null ( g(O) = 0).

Birth of predators depends on the prey number, by an increasing monotonic function. In the absence of preys (x = 0) predators die out (h(O) < 0 , or equiva­lent h(h1 ) = 0 with hi > 0).

In the absence of predation,preys grow without limit,for small x and when x is medium the birth rate decreases beco­ming negative (J takes a maximum in ho and /(h2) = 0 with 0 < ho < h2

The information contained in the qualitative mo­del above is given in a more formal way in the Figure 1. As we can observe, the relevant information has been defined for every variable in the quantity space and for every constraint of the form M +, M- and Nm. So we can see that g takes through (0, 0) , the maximun of f is in (ho, ki) , and takes through zero in (h2, 0) , h takes through zero in (h1 , 0) with ho < h2, etc. The problem now is what information we can ex­tract regarding trasitory behaviour, and for long­term, from the system whose qualitative informa­tion we have specified. One way to study the problem is to consider the qualitative information as a set of constraints

148

(quantity-spaces (x (0 hO h2 int) (0 h1 h2) ) (y (0 int ) ) (f (mint 0 kO k1 int ) ) (h (mint 0 int) ) (g (mint 0 int ) ) (tnx (mint 0 int ) ) (tx (mint 0 int) ) (ty (mint 0 int) ) )

(constraints ( (Ha x t ) (0 kO +)

(hO k1 0) (h2 0 -) ) ( (H+ y g) (0 0 ) ) ( (H+ x h) (h1 0) ( (- t g tnx) ) ( ( • x tnx tx) ) ( (• y h ty) ) ( (D x tx) ) ( (D y ty) ) )

Figure 1 : Equations of the Model

that bind the variables in a symmetric way. This is Kuiper's Qualitative Simulation approach (Kuipers 1986) . However, we will consider an asymmetric causal order and the constraints as some bonds between a cause and its effect. This allows us to approach the concepts and the met­hods of the dynamical systems in the sense it is understood in Mathematics. In this paper, we apply tecniques from the theory of dynamical system to obtain information from a qualitative model. The use of these techni­ques consists of two stages: first, in the constru­ction and regularization of a family of piecewise linear dynamical systems and then in their analy­sis. The first stage consists of a sequence of events that holds up the qualitative information of the model. The second one is the application of the methods of qualitative analysis to the dynamical system that has been constructed.

3 Piecewise

tions

A continuous function

Linear Fune-

is piecewise linear if Rn can be divided into a fi­nite number of polyhedral regions by a finite num­ber of hyperplanes and in each region i, f is an afin f untion Ji :

where A} is a constant n x n matrix and b} is a constant n-vector. At the following the set of regions associated to the piecewise linear function J are representable by 0 J . O} is a region of 0 I and Ji the afin function associated to J at region 0} . The set 0 J and the set of afin functions Ji have to be given to specify the piecewise linear function J. If J is continuous the equation:

(2)

must be held for each x in the boundary between the regions O} ' �. We show now the way to associate a piecewise li­near function or an operator on piecewise linear functions to each constraint in our qualitative mo­dels. In the constraints of monotony M +, M -and N m,the polihedral regions are being defined by:

o�+ = (hi , hi+1 ) where ho , h1 , . . . . , hn are the landmarks of the co­rresponding function. In each region i,the corres­ponding afin function has the form ax + b where a > 0 if the constraint is M +, a < 0 if it is M­and the sign of a depends on the region if the constraint is Nm. To the arithmetic constraints + or -, we associate an operator of piecewise linear function defined in this way. Given the continuous and piecewise linear functions:

and h = J $ g with EB = + or $ = - where h : Rn x Rm - R, then the function h is also a piecewise linear function. If Oj and o; are the canonical partitions of � x Rm induced by 0 J and 09 respectively. Each region of Oh is formed with the no empty inter­section of a region of Oj with another one of o; :

where

Oji = O} x Rm , o;i = Rn x O� In the case J, g have identical domain

J, g : Rn - R

(3)

each non null region of oh is formed simply by intersection

o� = o} n o� The piecewise linear function that results in each region is:

(4)

This introduces ambiguity about the constraints that may support the element of the correspon­ding A, b. If a1 > 0 and a2 > 0 the sign of a 1 - a2

149

is unknown. The opposite happens if a 1 > 0 and a2 < 0 We can observe the composition of function, now. If

J : Rn - Rm , g : Rm - R

are piecewise linear functions, the composition :

g o J : Rn - R

is a piecewise linear function too. The partition 0901 of Rn that will be associated to g o J is formed with the no empty intersections of regions of 0 l with the inverse image by J of a region of 09 :

o1: - oi n (/i)- 1 (oi ) go/ - I u

and the associated afin function is

(g 0 /)1: = gi 0 !'

If prod = J * g is defined with J, g piecewise li­near functions. We want to find a piecewise linear function that is a piecewise linear approach of the prod. We can define the piecewise linear function

s = J + g (5) D J - g

then

g if S 2'.: 0 and D 2'.: 0

prodL = J if S 2'.: 0 and D < 0 -J if S < 0 and D 2'.: 0 (6)

-g if S < 0 and D < 0

The selected method assures that the zeros of prod are the same as the prodL . The regions of prodL are obtained following the rule in (6). So to obtain OprodL , each region of Os = OD is divi­ded into subregions where the sign of S = J + g and the sign of D = J - g are preserved. The operator division / will be considered in a forthcoming paper.

4 The construction of the

family of piecewise linear

dynamical systems

The construction process consists of rules for buil­ding a methodical way. As we have establis­hed, the constraints are asymmetric, this means that if the system is well specified, the set of cons­traints defines implicity a directed acyclic graph that has as the initial node the state variables and the ending nodes in the variables that specify the field. This graph, without loops, specifies a par­tial order which is the one we follow to construct the result.

Figure 2: Directed acyclic graph associated to the example

Each node has no more than two inmediate pre­decessors. Every node of the graph specifies an allowed constraint. The directed acyclic graph as­sociated to the example above is shown in Figure 2. Therefore, the constructive method consists of:

First, for each node to obtain the piecewise linear function or operator on piecewise linear function that is associa­ted to constraint as the rules of the pre­vious paragraph.

Second, to reduce this graph by suc­cesive application of one step that con­sists to replace a function node and their inmediates predecessors nodes by anot­her one whose associated function is the composition of associated functions to them.

After we have applied the succesive constraints in the determined order we will obtain a family of the piecewise linear functions and a set of cons­traints for their parameters. This family, after to regularize it in the boundary of each regions is the field of the dynamical system that we wanted to construct. The application of the qualitative analysis of the dynamical system and the bifurcations theory to the resultant family of dynamical systems provide us the relevant information from the qualitative point of view.

5 Qualitative Analysis

Dynamical Systems

Given the family of dynamical systems:

x = /(x,p)

of

(7)

The qualitative analysis of (7) is the long term study of its solutions for a fixed value of its pa­rameters p = po . The long term behaviour is

150

related to the class of attractor that the system (7) has for p = Po· The stable equilibrium is the most known of these attractors. It is related to a long term where z = 0. Another attractor is the Limit Cycle. This is related to the periodic oscillations. The bifurcation theory is the study about the change in number and kind of attractors when the parameters change. If the system (7) is a family of piecewise linear dynamical system its qualitative analysis is sim­plified. So the equilibria (i) must verify:

(8)

and its stability is given by the A} matrix. When the parameters change the number and kind of attractors changes too. The bifurcation theory can help us to find new kind of atractors. For example, the Hopf bifurcation (a couple of ei­genvalues of Jacobian matrix cross the imaginary axis) can be used to find limit cycles. If ;c E R2 the characteristic polynomial of the Ja­cobian Matrix evaluated in the equilibrium i(p) is

A2 + ai (P)A + a2(P) = 0 A Hopf bifurcation appears if ai(p) crosses the zero and a2(P) > 0 when parameters change (Gu­ckenheiner 1982).

6 Applications to t he exam­

ple

The application of the above method to example give the following conclusions (see the appendix for intermediate steps) . The differentiable field f x, fy is null in three points:

• El: (0, 0) in the region O}z n O}, • E2: (h2 , 0) in the region 01z n o,, • E3:

- (hi , (a}hi + b] )Ja;) in the region 01z n OJy • if ho < hi - (hi , (a}hi + b} )/a;) in the region O}z n OJy • if hi < ho.

El: In the region O}z n O}, the field is

x = ;c y = -y

(9) (10)

eigenvalues: Ai = 1 > 0, A2 = -1 > 0. So (0, 0) is an unstable equilibrium. E2: In the region 01z n O'y the field is:

x a]x - a!y + b] y = y

(11) (12)

and the eigenvalues : Ai = af. < 0, A2 = 1 > 0. So (h2 , 0) is an unstable equilibrium. E3: In the region O}z n 0}9, if ho < h1 , the field is:

z = a}z - a!y + bJ ( 13)

Y = alz + bl ( 14)

If ho < h1 the system has an equilibrium (h1 1 (aJh1 + bJ)fa!) ,with characteristic polyno­mial:

A2 - aJA + ala! = 0 ( 15)

Both eigenvalues have a negative real part. So this point is an attractor. If 0 < hi < ho, the field, in region O}z n 0}9, is:

z = a}z - a!y + b} ( 16)

y = alz + bl (17)

The equilibrium E3 changes. It is the point (h1 , (a}h1 + b})/a!) ,with characteristic polyno­mial:

A2 - a}A + ala! = 0 (18)

Now it is a repulsor . When parameter hi changes from ho < hi to hi < ho the characteristic polynomial of equi­librium E3 changes from (15) to (18). Since ala! > 0, -a} > 0, -a} < 0 then a Hopf bifurca­tion appears. If hi < ho a Limit Cycle exists. We can conclude from the qualitative model in Figure 1 that the system will evolve only to the attractor. This attractor is a stable equilibrium if ho < hi and a Limit Cycle if hi < ho.

7 Conclusions

This paper has described a technique for deriving the properties of nonlinear dynamic systems from their qualitative description. These dynamic sy­stems are interesting because they pose unsolved problems in the representation of knowledge, and because they appear fundamental to common­sense knowledge of causality. The example presented above demonstrate a re­presentation for qualitative reasoning about cau­sality in ecological mechanisms, and it is possible to be applicationed to others problems. The technique developped can be used to deduce results from the qualitative information about a system. It uses the theory of dynamical systems to avoid the ambiguity that appears in other me­thodologies.

8 References

Javier Aracil and Miguel Toro ( 1991) . Qualita­tive methods for system dynamic models. In Revue Internacional of Systemique.

151

Leon Chua and Robin Ying ( 1983) . Canonical Piecewise-Linear Analysis. IEEE Transac­tions on circuits and Systems, Vol.Cas-30, NO 3. pp, 125-140.

J. Guckenheimer and P. Holmes ( 1982). Nonli­near Oscillations, dynamical systems and bi­furcations of vector fields. Springer Verlag.

Benjamin Kuipers. Qualitative Simulation. In Artificial Intelligence 29, pages 289-338.

Elisha P. Sacks ( 1985) . Qualitative mathemati­cal reasoning. In Proceedings of the Ninth International Conference on Artificial Intelli­gence, pages 137-139.

Elisha P. Sacks ( 1987a). Hierarchical reasoning about inequalities. In Proceedings of the Na­tional Conference on Artificial Intelligence, American Association for Artificial Intelli­gence.

Elisha P. Sacks ( 1987b ) . Qualitative sketching of parameterized functions. In Proceedings of the Second International Conference on Applications of Artificial Intelligence in En­gineering, August 1987.

Elisha P. Sacks (1987c). Piecewise Linear Reaso­ning. In Proceedings AAAI-87, 655-659.

Miguel Toro and Javier Aracil (1988a) . Qualita­tive Analysis of System Dynamic Ecological Models. In System Dynamics Review, Vol. 4, Num. 1-2, 56-60.

Miguel Toro and Javier Aracil (1988b). Oscilla­tions and Chaos in Ecological Populations. In Proceedings of the Internacional Confe­rence of the System Dynamics Society, 391-403.

9 Appendix

General Constrainsts 0 < ho < hi < h2 < oo 0 < ko < ki < oo Regions O� = {z lz � O, z � ho} n, = {zlz � ho} Afin Functions

f = Ji = a}z + b} , J2 = a}z + b} Parameter Constrainsts al > 0, a}ho + b} = kt b1 = ko a} < 0 a}ho + b} = ki a}h2 + b} = 0

g =

h

tnx

Regions O} = {yjy � O} Afin Functions g l = a}y Parameter Constrainsts a1 > 0 g

Regions Ol = {xix � O} Afin Functions h1 = alx + bl Parameter Constrainsts al > 0 alh1 + bl = 0 Regions Ofnz = O� x Of Oinz = o1 x 09 Afin Functions tnx1 :: a 1 x - a1y + b1 tnx2 = a}x - a!y + b}

The constraints of the fx and the coefficient of tnx and h involve the next definition of fx and fy, and the product rule (6):

Regions O}z = {(x, y) E Olnz lx + tnx1 � 0,

x - tnx1 � O} fx OJz = {(x , y) E Olnz • X + tnx1 � 0,

x - tnx1 < O} 01z = {(x, y) E Olnz • X + tnx1 < 0,

x - tnx1 � O}

f y =

152

O}z = {(x, y) E Olnz • x + tnx2 � 0, x - tnx2 � O}

Ojz = {(x, y) E Olnz, x + tnx2 � 0, x - tnx2 < O}

01z = {(x, y) E Oinz, x + tnx2 < 0, x - tnx2 � 0}

Afin Functions f x1 = tnx1 fx2 = x fx3 = -x fx4 = tnx2 fxs = x fx6 = -x

Regions O}v = {(x, y) E Ol, y + h1 < 0,

y - h1 � O} OJv = {(x, y) E Ol , y + h1 � 0 ,

y - h1 � O } 01v = { (x, y) E Ol , y + h1 � 0,

y - h1 < O} Ojy = {(x, y) E Ol , y + h1 � 0,

y - h1 < O} Afin Functions fyl = -y fy2 = hl fy3 = y fy4 = -hl

Copyright @ IF AC Al1ificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

IMPLEMENTATION OF A KNOWLEDGE-BASED PID AUTO-TUNER

C.C. Hang, T.H. Lee and W.K. Ho

National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511

Abstract

This paper presents a particular implementation of a knowledge-based control system. It attempts to show how heuristics developed in recent re­search on intelligent PID control can be imple­mented to attain some of the visionary goals of knowledge-based control. The other characteris­tics of the implementation are the blackboard ar­chitecture of the knowledge base, and the clear separation of heuristic logic from the numerical algorithms.

1 Introduction

Despite the advancement of control theory over the last 30 years, there is still a large class of problems in control that are solved by heuristics developed by practising engineers over the years. For example, the choice of controllers for a given situation is often based on past experiences. Con­trollers are also often designed and tuned using trial and error and heuristic rules-of-thumb. In adaptive control, heuristics in the form of safety jackets often have codes that are much larger than that of the control law. These are ill-structured problems and do not lend themselves well to al­gorithmic solutions using conventional program­ming languages because there are just too many p088ibilities. There are, however, motivations for an expert system solution (Astrom et al., 1986; Arzen, 1989).

This paper presents a particular implementation of a knowledge-based controller (Astrom et al., 1986; Arzen, 1989). It attempts to show how heuristics developed in recent research on intel­ligent PID control can be implemented.

The paper is organized as follows. The hardware and software architecture are described in Sec­tions 2 and 3 respectively. The knowledge base design is given in Section 4. Section 5 describes

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the knowledge sources. A sample session with the system is given in Section 6 and conclusions are given in Section 7.

2 Hardware

The hardware and software configuration for the present implementation was first described in Yue et al. ( 1991) . It is shown in Figure 1 . The hard­ware consist of a HP9000 workstation connected through an IEEE 488 bus to an IBM AT personal computer (PC). The PC serves as a development system for real-time simulation of different con­troller algorithms and processes for testing. The expert system shell resides in the HP9000 work­station while the PID controller is implemented in the PC. The process is also simulated in the PC. This configuration makes it possible for the PID to do real-time control while inferencing continues in the HP9000. Another advantage of the present architecture is that additional PID controllers can be naturally accommodated.

3 Software

The software for the HP9000 workstation consists of three concurrent processes: (1 ) the expert sys­tem, (2) the numerical routine, and (3) the user­interface. They run on top of a multi-tasking op­erating system, HP-UX, which has some real-time extensions.

The approach taken in the software design is to separate the heuristics from the numerical func­tions. The heuristics are coded in the expert sys­tem while the numerical routine and the user­interface are written in the C language. This separation of numerical functions from heuristics structures the software and makes large programs easy to understand and develop.

In expert control, the coupling of expert system and numerical functions must meet certain real­time demands. Rule execution in a knowledge­based system is essentially a large search problem which is inherently slow and non-deterministic. On the other hand, the numerical control func­tions must be able to compute an output within a fixed sampling interval. It should not be halted or delayed by a knowledge-based system searching among different rules. As a result, the usual prac­tice of coupling an expert system and numerical algorithms, that is, by making an expert system call external numerical functions or by embedding an expert system in conventional procedural lan­guages, is not suitable for this application. The solution is to implement the two differing parts as communicating concurrent processes with dif­ferent priorities. The numerical algorithms should be given a higher priority. In this implementation, the numerical routine is given a time priority of l ; the expert system, 2 ; and the user-interface, 3 .

4 Knowledge Based Design

The knowledge base is implemented using a com­mercial expert system shell, NEXPERT Object, which uses a combination of rules and objects for its knowledge representation. The blackboard model (Nii, 1986a, 1986b) is employed in this im­plementation to provide a structured approach to problem solving. In this model, problem solving state data are kept in a global database (the black­board) and knowledge is partitioned into knowl­edge sources.

In this implementation, the knowledge base is decomposed into six knowledge sources: sched­uler, manuaL.control, relay_tune, RZN..tune (Re­fined Ziegler-Nichols tune), integral.. control and monitor. Each knowledge source specializes in one function and they communicate to each other through the blackboard.

5 Knowledge Sources

A general description of each of the knowledge sources are given below.

5.1 Manual Control Knowledge Source

In manual control, the loop is opened and the user can manipulate the control signal directly. The manual..control knowledge source can call a C function to estimate measurement noise. While

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the control signal is held constant, the output of the process is monitored and the maximum devia­tion is taken to be the maximum amplitude of the measurement noise. This information is placed on the blackboard. It will be used by the relay knowledge source to set the relay amplitude and hysteresis. It will also be used by the RZN_tune and integral..control knowledge sources to choose between a PID and PI controller.

5 .2 Relay Tuning Knowledge Source

The theory of relay feedback auto-tuning is pre­sented elsewhere (Astrom and Hagglund, 1984a; Astrom and Hagglund, 1984b) and will not be re­peated here . The main function of this knowl­edge source is to supervise the relay operation. The ultimate gain and ultimate period are de­termined from the relay experiment to install a Ziegler-Nichols (1942) tuned PID or PI controller.

Load disturbances are common in process con­trol. It was shown in Hang et al . (1988) that static load disturbance during the relay experi­ment could cause asymmetrical limit cycling and introduce significant error to the ultimate gain and ultimate period estimates. It was also shown in the same paper that symmetry in the limit cycling and accuracy in the estimates can be re­stored by adding a bias to the output of the relay. A rule in this knowledge source monitors the limit cycle and biases the relay when asymmetrical limit cycling is detected.

5 .3 Refined Ziegler-Nichols and In-tegral Control Knowledge Sources

These two knowledge sources supervise the fine tuning of the Ziegler-Nichols (1942) tuned con­troller. For stable processes , the Refined Ziegler­Nichols tuning formulas developed in Hang et al. ( 1991) are used in the RZN..tune knowledge source to fine the controller. For processes with integra­tion, the gain and phase margin tuning formu­las developed in Ho ( 1990) are used in the inte­gral_control knowledge source to fine tune the con­troller . In this implementation, the gain margin and phase margin are fixed at 4 and 60° respec­tively. The PID controller implemented is of the form (Astrom and Hagglund, 1988):

Uc = kc[(byr - y) + � j edt - Td � ](1)

e Yr - Y (2)

N -(y - yJ) Ta

(3)

where Yr , Ue and y are the set-point, control sig­nal and process output respectively, and ke , � . Ta and b are the proportional gain, integral time, derivative time and set-point weight respectively.

The user can choose a PID or a PI controller ; oth­erwise, there are rules in the knowledge source to make the choice. The factors considered are control signal fluctuation, normalized process gain and whether tight control is required or not . The factors are discussed below.

A simple estimate of the control signal fluctua­tion at steady-state due to measurement noise can be made (Fertik, 1975) . For the PID control law given by (1) to (3),

Aue(t) � ke(l + N)Ae(t) (4)

at high frequencies. Therefore the control signal fluctuation can be estimated using ( 4) when Ae(t) is replaced by the estimated measurement noise. In this implementation, PID control is selected only when the control signal fluctuation at steady­state is less than a user specified amount (default is 10% of measurement span), otherwise, a PI con­troller is selected.

The PID controller is not effective for processes with large normalized dead-time (dead-time to time constant ratio) because the prediction made by the derivative action is no longer valid (Astrom et al., 1991) . Therefore a PID controller will not be used for a process with large normalized dead­time, or equivalently, small normalized process gain (product of the ultimate gain and the pro­cess static gain) as Hang et al (1991) and Astrom et al. ( 1991) showed that the normalized process gain and the normalized dead-time are correlated. In this case, a PI controller is selected. Finally, a PI controller is deemed sufficient if tight control is not required. A PID controller will be considered only if tight control is demanded by the user.

5.4 Monitor Knowledge Source

This knowledge source contains heuristics to pre­dict the achievable performance of the system. It can decide whether the controller is properly tuned by comparing the actual performance with that predicted. If they differ by a given bound, then it may be suspected that the controller is not properly tuned. Future enhancement of the system could include the comparison of the pre­dicted with the desired performance. Suggestion of a more complex controller structure can then be made if the predicted PID controller performance is unable to meet the desired performance.

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In this implementation, for stable processes with Refined Ziegler-Nichols tuning, the normalized rise-time is predicted according to (5) and (6)

and

T = 5 + 46kekp

5(5 + 4kckp) (5)

(6)

for 10% and 20% set-point response overshoot re­spectively (Ho, 1991 ; Astrom et al. , 1992). The expert system assesses the load rejection capabil­ity of the PID controller by injecting a step load disturbance with amplitude set to the amplitude of the relay. The peak load error is then measured and compared to that predicted by (7) (Ho, 1991 ; Astrom et al. , 1992) .

Im = 2.5 + 3.4kekp lo

5 + 4kekp ke (7)

This knowledge source also contains heuristics to monitor stability and to recover from instabil­ity. In most industrial implementation, the un­stable system is stabilized by successively reduc­ing the proportional gain by half (and possibly doubling the integral time at the same time) un­til the magnitude of oscillations is damped. This type of recovery may involve several cycles of un­controlled oscillations and is therefore slow. A new technique is introduced in this implementa­tion: once instability is detected , relay feedback auto-tuning will be activated which will not only auto-tune the PID controller but also double up as the mechanism for recovery from instability by damping the oscillations. This technique allows a rapid recovery from instability due to a change in process time-constant or dead-time because re­initialization and re-tuning of the controller occur within the recovery cycle. If the instability is due to change in process static gain, then the relay os­cillation may be quenched. In this case, the pro­cess will be put under manual ci:mtrol. A small step input is then given and the loop closed with a PID controller designed from the step response.

6 A Sample Session

A sample session with the knowledge-based con­trol system is shown in Figure 2 to 7 where the user-interface on the HP9000 workstation is being shown. The interface includes two trend displays. The set-point and the process output are shown on the upper display, while the control signal is shown on the lower display. A message box is pro­vided for the display of messages. The face-plate of a typical commercial controller is also drawn.

Various buttons are provided for the'operation of the system.

A process of transfer function:

G ( ) 1 -88

P 8 = ( 1 + 15s)2 e

was simulated on the IBM AT (PC). Figure 2 shows the relay experiment where the ultimate gain, ku , and ultimate period, tu , were estimated. Before the commencement of the relay experi­ment, we put the controller to manual and es­

timated the measurement noise. The value ob­tained was displayed on the message box. The PID parameters tuned using the Ziegler-Nichols ( 1942) tuning formula and the set-point weight, b, were also shown in the message box.

We made the first set-point change as shown in Figure 3. With this set-point change, the expert system extracted more information about the pro­cess. The dead-time, the rise-time, and the pro­cess static gain, kp , were estimated. This informa­tion would be used later to fine tune the controller as well as to predict its performance.

At this stage we let the expert system choose be­tween a PID and a PI controller. The PID con­troller was chosen based on the criteria discussed in Section 5.3. With the additional information of the process static gain, kp, the expert system fine tuned the PID controller using the Refined Ziegler-Nichols formula. The improved second set-point response was due to the Refined Ziegler­Nichols tuning. The new controller parameters as well as the measured and predicted rise-time were displayed in the message box as shown in Figure 3.

We made another set-point change as shown in Figure 4. The rise-time was monitored and the inference was displayed on the message box. It indicated that the controller may not be properly tuned. The dead-time of the simulated process was in fact changed from 8 seconds to 4 seconds. An advice was also given to the user to confirm whether the controller was properly tuned by in­jecting a small step load disturbance. The advice was accepted and the expert system then used heuristics described in Section 5.4 to analyse the load disturbance response as shown in Figure 5. The inference which was displayed in the message box confirmed that the controller was not prop­erly tuned. The amplitude of the load disturbance response is smaller than expected because the pro­cess is now "faster" .

Since the controller was deemed not properly tuned, a relay experiment was carried out as shown in Figure 6. However, this time a static load disturbance resulted in an asymmetrical os-

156

cillation. The expert system applied a bias to the relay and restored symmetry and accuracy. The PID controller parameters due to Ziegler-Nichols ( 1942) tuning were shown in the message box.

Finally, the dead-time was changed from 4 sec­onds to 9 seconds and Figure 7 shows that the system became unstable when a set-point change was made. When instability was detected, the relay was switched in to stabilize the system. Si­multaneously, the controller re-tuned itself using the ultimated gain and ultimate period estimated from the relay oscillation.

7 Conclusions

A particular implementation of a knowledge-based PID controller has been presented. The black­board model for knowledge-base design and the clear separation of heuristics from numerical al­gorithms kee.Ps software development structured. This leads to a control system with software that is easy to modify, extend and understand. In terms of functions, the knowledge-based controller has the following capabilities: ( 1) relay-feedback tuning, (2) automatic fine tuning, (3) automatic relay biasing to overcome static load disturbance during the relay experiment, ( 4) selecting between a PID or a PI controller, ( 5) performance monitor­ing, and ( 6) rapid recovery from instability. This paper has shown how heuristics developed in re­cent research on intelligent PID control can be implemented to attain some of the visionary goals of knowledge-base control.

8 References

Akhrif, 0., G.L. Blankenship and L.S. Su ( 1987) : "Computer algebra systems for analysis and design of nonlinear systems,'' Proceedings of the American Control Conference, Min­ne!'-polis, MN, pp. 547-554.

Arzen, K.E. ( 1989) : "An Architecture for expert system based feedback control," Automatica, 25, pp. 813-827.

Astrom, K.J ., J .J . Anton and K.E. Arzen ( 1986): "Expert control," Automatica, 22, 3, pp. 227-286.

Astrom, K.J . and T. Hagglund (1984a): "Auto­matic tuning of simple regulators,'' Proc

IFAC 9'th World Congress, Budapest, Hun­gary, pp. 1867-1872.

Astrom, K.J . And T. Hagglund (1984b) : "Auto­matic tuning of simple regulators with spec­ifications on phase and amplitude margins," Automatica, 20, pp. 645-651 .

Astrom, K.J . And T. Hagglund ( 1988): Auto­matic Tuning of PID Controllers, ISA, Re­search Triangle Park, NC, USA.

Astrom, K.J . , C.C. Hang, P. Persson and W.K. Ho (1992): ''Towards intelligent PID con­trol," Automatica, 28, pp. 1-9.

Fertik, H .A. ( 1975): '"Tuning Controllers for noisy processes," ISA Transactions, 14, 4.

Hang, C.C. And K.J . Astrom (1988) : "Practi­cal aspects of PID auto-tuners based on re­lay feedback," Proc. of IFAC Int Symposium on Adaptive Control of Chemical Processes, Copenhaen, Denmark, pp. 153- 158.

Hang, C.C., K .J . Astrom and W.K. Ho ( 1991): "Refinements of the Ziegler-Nichols tuning formula," IEE Proc. D, Control

° Theory and

Appl. , 138, 1 , pp. 25-32.

Higham, E.H. ( 1985) : "A self-tuning controller based on expert systems and ar�ificial intelli­gence," Proc. Control 85, UK, pp. 1 10-115 .

Ho, W.K., ( 1990): "Tuning of PI controllers for processes with integration based on gain and phase margin specifications," Report CO­DEN: LUTFD2/TFRT-7472, Department of Automatic Control, Lund Institute of Tech­nology, Lund, Sweden.

Ho, W.K., (1991) : "Towards intelligent PID con­trol," Ph.D. Thesis, National University of Singapore.

James, J .R., D.K. Frederick and J .H. Taylor ( 1987): "On the application of expert sys­tem of lead-lag precompensators," IEE Pro­ceeding D: Control Theory and Applications, 134, 137-144.

Kraus, T.W. And T.J . Myron (1984): "Self­tuning PID controller 4ses pattern recogni­tion approach," Control Engineering, June, pp. 108- 1 1 1 .

Moore, L .R., L.B. Hawkinson, M.Levin, A.G . Hoffman, B.L. Matthews and M.H. David ( 1987): "Expert system methodology for real-time process control," Preprints, IFAC Workshop on AI in Real-Time Control, Swansea, UK, Pergamon Press, Oxford, UK.

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Moore, R., H. Rosenof and G. Stanley ( 1990) : "Process control using a real-time expert sys­tem," Preprints 1 1th IFAC World Congress, Tallinn, Estonia, USSR.

Nii, H .P. ( 1986a): "Blackboard systems: the blackboard model of problem solving and the evolution of blackboard architectures," AI Mag., 7, 2, pp. 38-53.

Nii, H.P. ( 1986b) : "Blackboard systems: Black­boa.rd systems from a knowledge engineering perspective," AI Mag., 7, 3, pp. 82-106.

Pang, G.K.H. and A.G.J . McFarlane (1987) : An expert system approach to computer-aided de­sign of multivariable systems, Springer Ver­lag, Berlin.

Shinskey, F.G. ( 1986): "An expert system for the design of distillation controls," in M. Morari and T.J . McAvoy {Eds.) : Chemical Process Control - CPCIII, CACHE, Elsevier, Amster­dam.

Yue, P.K . , T.H. Lee, C.C. Hang and W.K. Ho ( 1991) : "Intelligent self-tuning PID con­troller," IFAC Intl. Symp. on Intelligent Tuning and Adaptive Control, Singapore.

Ziegler, J .G . and N.B. Nichols (1942) : "Op­timum settings for automatic controllers," Transactions of the ASME, 64, pp. 759-768.

............. I =· ,�, -. -..:.-.. � HP llOOO -

--

I I

marMMChiM i __ ,

D I \

Sha,., ,,._.,. wi" ,_.,._.�Cftiu,-

- ... ..

.... ,

Figure l . Hardware and software architectures.

Figure 2. Relay tuning

Figure 3. Set-point responses of the Ziegler-Nichol'

and Refined Ziegler-Nichols tuning.

Figure 4. Monitoring of rise-time .

158

Figure 5. Monitoring of static load disturbance re

Figure 6 . Static load disturbance during the

relay experiment .

Figure 7. Recovery from instability.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

DIMENSIONS OF LEARNING IN A REAL-TIME KNOWLEDGE-BASED CONTROL SYSTEM

N.V. Findler

Department of Computer Science and Engineering, and Artificial Intelligence Laboratory, Arizona State University, Tempe, AZ 85287-5406, USA

Abstract. We first describe and justify the domain in which cooperating and learning real-time distributed expert systems perform control operations of urban street traffic signals. We then present the general design of the ultimate system as well as the simplifying assumptions used in a running prototype. The latter, proving the technical feasibility of the approach, has attained a 42% improvement in the traffic flow under non-saturated conditions. Finally, we draw some conclusions concerning the methodology of distributed planning and problem solving systems.

Keywords. Street traffic signal control; learning, collaborating and real-time expert systems; predictive control; optimization of rule bases.

INTRODUCTION

Research in Artificial Intelligence has identified a variety of learning modes in which computing systems can adapt themselves to improve their level of performance on the basis of experience. The range of machine learning covers different levels of abstraction, from rote learning (e.g., d ata gathering and utilizing pre-arranged classification schemes) to procedural learning (e.g., automatic program writing systems).

Traffic engineers have been using different tools of mathematics, statistics and computer science to devise systems that can improve the traffic conditions of congested cities. Some techniques of Artificial Intelligence have also been employed to generate, for example, better constant control of street traffic lights and real-time expe rt systems controlling street traffic lights centrally in a dynamic fashion. Distributed and dynamic control, however, has not been used although it can offer a number of advantages as follows:

• Spatially and chronologically local conditions are usually more relevant to the decisions to be made. Traffic accidents, the ending of a major sport event, road repair or an "unscheduled" holiday are examples of local changes that cannot be considered by a centrally controlled regime. • The rate of change in local conditions is usually very high. Even with high-performance sensors for data input, communication and computational bottlenecks would not allow the existence of a timely and responsive control environment. • A centrally organized, real-time planning technique of high quality is not feasible because of the overwhelming amount of data to be processed and the large number of decisions to be made and communicated to the traffic lights. • Changes to a distributed control system are

159

easy and inexpensive to make, when the "permanent" traffic environment changes.

THE APPROACH

The fol lowing working c onditions and assumptions have been established for our long­term efforts:

• There is one processor at each intersection, which c ommunicates directly with the four processors at the adjacent intersections. • The communicated information is three-fold:

• raw data (essentially, the number and the speed of cars going in each of the four directions at an intersection), • processed information (the type and rate of change of certain traffic flow features), • expert advice (e.g., "lengthen the period of green light in the East-West direction").

It should be noted that the latter two types of information can propagate over an indefinite number of intersections but with gradually changing contents. Such information coming from many intersections in a given direction is the weighted average of the contributing information - the farther away the source, the less important its contribution is.

• The operation of the whole system is based on • a set of cooperating real-time expert systems which work in conjunction with a simulation-based planning system, • a small amount of noisefree communication which triggers both gradual and sudden changes in the traffic light control regime.

• There are several possible criteria of operation or measures of effectiveness which represent the objective function to be minimized. These can be the average travel time, the maximum waiting time at intersections, or the average number of stops during travel, etc. • The system would attain local and global

optima within moving "time windows" through learning programs. The learning programs work in two phases and along different dimensions, as discussed later.

We hope to show that the system will produce several benefits, such as faster traffic flow, more e fficient usage of available roads, fewer accidents, lower driver frustration, reduced air pollution and fuel consumption.

ON THE CONTROL STRATEGIES

There are different control strategies possible -each with its own set of rules. In describing these, we will use the average travelling velocity of cars going though an intersection! as the objective function to be minimized. The control variables for the traffic light are:

• the length of the cycle; • the length of "active time" (sum of the periods of amber2 and green lights in one or the other direction); a related way is to use the concept of "cycle split" - the ratio of the green periods in the two directions; • the point of time when the cycle starts.

There are three basic strategies, depending on the prevailing local traffic pattern. The third strategy can be further divided into three substrategies, with reference to the type of control variable used. We present the strategies in the order of usage priority.

Strategy I: The Semiactuated Regime

This strategy is to be used when the traffic flow in one of the intersecting streets is extremely small. The light stays green in the busier direction until one or more cars approach the intersection in the less busy street. Then the light turns green in the latter direction as needed, up to a predetermined maximum time.

Strategy II: The Platooning Regime

In moderate traffic, cars are to be encouraged to travel in "platoons" - in small groups separated by gaps. Ideally, the light should be green when the cars are coming to cross the intersection, and red when the gaps appear. (Note that the staggering of the traffic lights to attain this effect can be easily controlled also by a static and global control system.) Since it is more effective to stagger the traffic lights to handle platoons than to follow one of the lower priority schemes to be described below, the platooning scheme should be followed when possible.

Strategy III: The Regime To Control Individual Characteristics Separately

This mode of operation can be based on three

1 The terms "intersection' and 'traffic light' will be used i n t e r c h a n g e a b l y .

2 Traffic experts d o not vary the time period for the amber phase, ta . Its duration (3 to 5 seconds) depends on several f�ctors, such as the usual car speed and average decelera11on rate m that direction, the width of the �ntersection, and so on. A good rule of thumb is to keep It at

where vm ax ta[scc] = O. l *vmax [m/h]

is the speed limit.

160

sets of rules. Each controls a different variable. We rank them in the order of usage priority.

Substrategy Illa: Modify Cycle Length

As a general heuristic, it has been found that when the traffic flow is heavy (say, above 1 300 c ars/lane/hour), longer cycle lengths speed traffic . In turn, when traffic is lighter, shorter cycle lengths are advisable. However, cycles of longer than 1 80 seconds or shorter than 40 seconds are inefficient and should not be used.

Substrategy Illb: Change Cycle Splits

The cycle should, in general, be split so that the direction with heavier traffic flow receives the longer green light.

Substrategy Ille: Change Cycle Start Time

If it is found that too high a proportion of cars arrive on the red light or they have to wait longer than seems appropriate with the given the flow and cycle split, the cycle start time should be adjusted to reduce waiting time.

Depending on the prevailing traffic pattern, such a measure may be of long-term help or may improve the situation only temporarily.

THE INFO R MATION COMMUNICATED BETWEEN CONTROLLERS

The fol lowing symbolic and numeri cal information is the result of calculation on locally sensed data, which must then be transmitted to the appropriate adjacent processor:

• a car crossed the intersection in the direction in question when the light turned green; • the number of cars that have crossed the intersection in the direction in question; • data on cycle length, cycle start time, and cycle split time; • a congestion is being experienced at the controlled intersection, which is moving toward the adjacent one; • a congestion i s moving from the adjacent intersection toward the controlled one; • a severe congestion is being experienced at the controlled intersection, which is moving toward the adjacent one; • a severe congestion i s moving from the adjacent intersection toward the controlled one.

In the above, the term fl o w references the number of cars clearing the intersection per minute and per lane, congestion occurs when a car must wait a whole cycle before clearing the intersection, and severe congestion occurs when a car must wait at least two cycles before clearing the intersection.

THE RULES AND META-RULES TO CONTROL THE TRAFFIC LIGHTS

There is a possible natural segmentation of the rules. Each of the strategies and substrategies listed above corresponds to a particular mode of operation whose controlling rules belong to a distinct rule segment. (Different rule segments may have a small but necessary overlap of membership). We have also identified a set of m eta-rules that, in response to the current traffic

pattern and the characteristic period, point to the appropriate rule segment to be applied until the environment perceivably changes.

ON SCENARIO GENERATION

A large number of experiments needs to be performed in trying to optimize the rule base of the distributed, cooperative expert systems. Each series of experiments has to be provided with an overall traffic pattern that applies to a characteristic period of the day (e.g., early morning rus h hour, mid-day traffic, late afternoon rush hour, evening traffic and night

traffic), of the day of the week (e.g., workday, Saturday, Sunday, other holiday) and, possibly, of the season of the year (e.g., vacation time). In our explanation, we will refer to the Manhattan grid (see Fig. 1 ) as the generic basis of city maps. (This was also used in our first simplified prototype program.)

L---___.I � � L j cn en ! l cn

Jcn l 00 :Dien enf0;.

Dlen cn j (ii" (ii" l[cn

en en en en en en en ,--, en en ,- -,en en ,- -,en � � � I

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cn l j cn en f f en en ! l cn -riil cn j 10 0 1 1 c; 01 Fig. 1 . The Manhattan grid used as the street pattern in the prototype program. There is a processor, P , at every intersection, which receives input data from its own sensors, S, and from the processors at the adjacent four intersections. The number of lanes in one direction is two and no left turn is permitted.

The following idea enables us to study only a relatively small segment of the whole network, without losing information and ri sking unreali stic traffic situations. Let us call a rectangle cut out from an indefinitely large Manhattan grid the area of concern. If the number of intersections in the E-W direction is w (width) and in the N-S direction is d (depth), we can name each intersection within the area of concern by a number as shown in Fig. 2. Further, let the area of concern be surrounded by four peripheries, each of which contains a sequence of street intersections. Therefore, the names of the intersections along the four peripheries are as follows:

Top, E-W: 1 2 w

Left, N-S: 1 w+l (d- l )w + l

Bottom, E-W: (d- l )w+ l (d- l )w+2 d . w

Right, N-S: w 2 w d . w

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Fig. 2. The area of concern cut out o f an indefinitely large Manhattan grid; the four p eripheries bordering it are marked by heavy lines and the intersections are numbered.

We can represent the traffic pattern of a scenario to be generated for one characteristic period, as defined before, by two wxd matrices. The matrix elements stand for the " source" and " sink" specifications, respectively, for each intersection - that is, the number of cars originating from a given intersection and coming to it as a destination. The actual values of the elements, produced by pseudo-random number generators, have two types of constraints:

• The sum of the source numbers equals the sum of the sink numbers, and they both equal a constant representing the characteristic period. • The source and the sink numbers associated with the intersections on the peripheries equal a user-specified constant times the random numbers obtained. We can thus take care of the fact that a lot of traffic goes to and comes from the area of concern across the peripheries.

THE OPTIMIZATION OF THE RULE BASE

We have designed two fairly distinct phases of l e a r n i n g . The first can be characterized as laboratory-based and the second field-based (although some computing activity o f the two phases takes place both in the laboratory and in the field). Let us discuss these concepts next.

The phase one or laboratory-based learning prepares the optimum rule bases of the expert system for each defined scenari o . It means that the system will be operating in an optimum manner if the traffic flow is steady and equal to the one associated with the scenario at hand. To arrive at the optimum rule base requires a two­stage development which concerns the selection of appropriate set of rules a n d the best parametric values of each rule, respectively. For either, the researcher selects one of several possible measures of effectiveness (the objective function to be optimized) as noted before. Note that experimentation is needed to find out which is the most relevant from the viewpoint of traffic patterns, air pollution, fuel economy and driver's psychology. An important criterion is also computational appropriateness; that is, the time and memory requirement of computing the measure of effectiveness being considered.

The optimum parametric v alues is to be

determined by an efficient hill-climbing method (e.g., the steepest ascent approach) which is usually invoked with numerical optimization problems when the objective function to be optimized is not available in analytical form.

The following approach is taken for selecting the most appropriate set of rules. First, one identifies a core set of, say, 6-8 rules that are considered indispensable. Their parametric values are then optimized and kept constant during the later development. Next, one rule at a time is added to the core set from the total set of possible rules; its parametric values are optimized and the additional benefit due to the new rule i s evaluated in quantitative terms. The rule with the best such effect is added to the core set which now becomes the basic set of rules. This basic set keeps on growing until the system finds that the addition of the next best rule is no longer cost-effective - the improvement no longer justifies the cost of computing it.

At this point, we have a rule base with optimum parametric values and with an optimum set of members with reference to the a v e r a g e operation within a scenario. That is, it is the best control mechanism statistically speaking. One major advantage of the dynamic, distributed approach is that the control system can respond to local spatial and chronological perturbations; i.e., it can react optimally to a sudden change in the environment (e.g., an accident, the ending of a sport event, a snow storm) or to a temporary but longer lasting change (e.g., road repairs). This is the task of phase two learning.

The response of the control regime to local perturbations consists of temporary changes in both the set of active rules and their parametric values. The former references the invocation of certain rules that were not active in the "equilibrium operation". Recall that there are different control strategies for street signals and corresponding sets of rules (e.g., semi-actuated, platooning, changing individual characteristics) that become active when the appropriate traffic pattern prevail s . Similarly, we envisage some special rules that come into action in response to particular sudden changes in the environment. The " statistically optimum" parametric values are subject to temporary modifications to respond to local perturbations. The system is prepared for it - in fact, it operates in a predictive mode - because the processor at each traffic signal gets the information from the four adjacent processors (some of it even percolates down to it from indefinitely distant processors). Another aspect of learning concerns changing rule prionttes , when warranted, for the resolution of conflict between rules whose condition part match the current situation.

The above powerful but complex methods must be tried out and fine-tuned first in the laboratory but the routine, field operations are also likely to affect them.

THE IMPLEMENTATION OF A PROTOTYPE SYSTEM

We have implemented a prototype system to prove the feasibility and usefulnes s of the

1 62

approach described above. It consists of five program components: a traffic simulator, a traffic scenario generator, a graphics display module, a rule-base coupled with a rule-driver to control the traffic signal parameters, and a hill-climber optimization module for the rule parameters . There were a number of simplification s introduced, as compared to the ideas presented before, which can be summarized as follows:

• We first used the Manhattan grid as the street pattern. It means that left turns are prohibited, all streets are two-way, have two lanes in each direction, cross at right angles, and run either in the North-South or East-West direction3. • Since left turns are not permitted in the Manhattan grid, a significant skew developed initially by the overwhelming number of clock­wise routing patterns. This was then rectified by some ad hoc techniques involving nodes at the peripheries of the area of concern as well as suboptimal routings that compensated for the skew. Also, each intersection had a traffic signal. • There was only one quality measure for the rule set, the average travelling velocity, i.e., the ratio between the total travel distance and total travel time during a simulation run (with reference to a certain scenario). • To speed up the simulation runs to an acceptable level, it was necessary to reduce the number of routine calculations and the number of items the system had to keep track of. This meant, for example, a uniform formula for the acceleration and deceleration of cars. (However, the initial and final speeds, of course, depended on the local conditions.) • Cars would switch lanes when it is safe to do (a simplification . . . ) and they are in the left lane and wish to make a right turn soon or the occupancy levels of the two lanes are very uneven. Also, start-up delays after the signal turns green were made uniform for all first cars and, to a different degree, for all subsequent cars. • We have decided to speed up execution and use only compiled (and not interpreted) LISP programs. Thus new rules could not be generated automatically by the program - missing out on a very high-level learning feature. • A rather s ignificant (and i l l -advised) simplification was to ignore the possibility of several rules satisfying the current conditions and the need to resolve the conflict among them. The system simply fired the first applicable rule and never tried to re-arrange the order of the rules on the basis of their level of expected success or frequency of usage. (We have done some re-ordering manually to respond to certain apparent problems in the results but this can be only an ad hoc remedy in a prototype system.) • The amount of processed information passed from adjacent processors was very limited and, therefore, did not yield the predictive value needed for effective control . Further, no expert a d v i c e/re q u e s t propagated from other processors at all . The net result of this preliminary choice was that, although the the traffic signal at a given intersection did respond

3 The new system has been designed so that other realistic features (e.g., one-way streets, changeable lane directions, left-turn lanes) can later be added, and an appropriate computer network can be custom-made for most existing road configurations.

to a suboptimum local traffic flow, the overall traffic pattern did not get much help. • Only a simplified, quick-and-dirty version of the hill-climbing method was implemented that could make simultaneous use of some 30 Apollo workstations connected in a network(!) It is less than certain that a set of o verall , rather than local, optimum rule parameter values have been reached (although the improvement in the traffic flow was over 42%).

• Limitations in computing resources have enabled us to complete scenario runs that generate only either relatively light or a l r e a d y saturated traffic flows - neither o f which can really show the strength and flexibility of the proposed system.

SUMMARY

We have discussed an economically important domain - improving urban traffic flow by using cooperative, distributed, learning expert systems that control street traffic signals. This domain has specific reliability concerns, quality measures, timing aspects, computational and communication requirements, geographically di stributed input and output operations, inter­node cooperation, and a need for reliable and gracefully degrading performance when some operational and/or computational units become disabled . These characteri stics point to a distributed approach, using a network of identical processors.

Some of the knowledge is needed by every node (e.g., the rules of the control operation), some is node-specific (e.g., geometrical information about its close environment). The system works in real-time and requires satisfactory solutions b y certain time. The control task has a medium-

163

level time-criticality.

Our current efforts aim at generalizing the area of applicability of the work on the prototype system, eliminating the simplifying assumptions and inefficiencies in it to produce a system that can be custom-made for all realistic road configurations. The expected benefits are faster traffic flow, more efficient usage of available roads, lesser cost of building future roads, reduced air pollution, reduced fuel consumption, fewer accidents, and lower driver frustration.

REFERENC�

Findler, N. V. (1 990). Contributions to a Computer-Based Theory of Strategies. Chapter 6: Distributed Planning and Problem Solving

Systems. Springer-Verlag, New York, Berlin, Heidelberg. pp. 1 1 1 - 1 85.

Findler, N. V. and J. Stapp ( 1 992) A distributed approach to optimized control of street traffic signals. Journal of Transportation Engineering, ill. No. l, 99-1 1 0.

Foraste, B. , and G. Scemama (1986). Surveillance and congested traffic control in Paris by expert system. Institution of Electrical Engineers International Conference on Road Traffic Control. 9 1 -94.

McShane, W., and R. Roess (1 990). Traffi c Engineering. Prentice Hall, Englewood Cliffs, NJ.

Steffi, Y., and W. B . Powell (1983). Optimal signal settings over transportation networks. Journal of Transportation Engineering, 1 09, 824-839.

Zozaya-Gorostiza, C., and C. Hendrickson (1 987). Expert system for traffic signal setting a s s i s tance. Journal of Transportation Engineering, 1 1 3, 1 08-1 26.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

EDUCATIONAL ASPECT OF EXPERT CONTROL OF TECHNOLOGICAL PROCESSES

J. Michal, D. Burian and P. Kminek

Institute of Chemical Technology in Prague, Technickfl 5, 166 28 Praha 6, Czechoslovakia

INTRODUCTION

As the complexity of technological processes increases, the problem of their control is becoming more important. We focused our attention on a technological process whose behaviour is very difficult to define due to the number of nonlinearities and parameters that are impossible or difficult to estimate. In this case, classical feedback control cannot be used. One of the reasons for this is the difficulty of expressing the desired behaviour of the process in terms of classical control theory. Control by means of an expert system is a promising way to solve such a problem.

EXPERT CONTROL

Expert control of technological processes acts according to rules that are based on: - deep knowledge about the construction and

instrumentation of the controlled system - intuitive knowledge based on the operator's experience

(rules of thumb). Both deep and intuitive knowledge have the form of

semantic rules as well as mathematical formulas which allow us to express almost any desired fact about the properties of the controlled system and its behaviour. This information is concentrated in a knowledge-base by the knowledge engineer. One part of the knowledge-base is a semantic net; it consists of the statements and rules. A priori probability values are assigned to all statements. Its meaning is a belief that the fact is true. Every rule links two statements together, an evidence to a hypothesis. The strength of the liajs is given by two conditional probabilities p(H/E) and p(H/E). These two values determine the power of the rule. All probability values are determined by the expert during the knowledge-base construction and reflect the uncertainty of the system. The deterministic data are related by mathematical formulas or other algorithms, creating a parallel plane of the expert system (Fig. I ). Some facts in the rule plane can trigger computation of relevant algorithms and update the numerical values in the data plane. Some data on the other hand influence the semantic net.

1 65

Creating the knowledge-base structure for expert control can be divided into three stages. In the first stage, the input data are examined from different points of view: - test the validity, - fi 1 ter noise, - detect periodicity, - detect some correlation with previous samples or with

another signal etc. The starting evidences are the input data of actual

values of several - but not necessarily all - process variables. This knowledge is obtained by means of direct or indirect measuring or - especially in the food industry - by means of subjective human observation such as vision, smell or tast�. The intermediate hypotheses that are to be proven at this stage concern properties of the input variables. Their form may be any of the following: - the actual value of the variable x in time t lies in the

interval <x1, Xi> the variable x is periodic and the period is T

- there is a linear correlation between variables x and Y the mean value of the variable x is x,,, and its dispersion variance is a.

According to the input data, the a priori probabilities of these hypotheses are modified during the expert system run to reflect the actual stage of the system. Computation routines may be activated at some nodes of the semantic net to evaluate formulas expressing deterministic relation among data.

The expert control strategy is derived from the fact that the control rule can be expressed for some surrounding of its present state however complicated the system behaviour may be. The whole state space of the controlled process can be divided into smaller parts or domains. The selection of the domains and their borders is done so the control rule can be expressed by a simple formula. The domains can overlap and the borders between the domains can be fuzzy.

The second stage of the control starts with the proven hypotheses from the first one. Its task is to find out the domain of the present state of the controlled system. All final hypotheses of the second stage have the same form: The present state of the system is in domain D; . The differences in the probabilities encountered in several

RULE PLANE

PLANE

Fig. 1. Expert controller structure.

succeeding runs will show the tendency of the controlled system behaviour.

The last stage of the expert control must find out how to influence the system in order to follow the desired trajectory in the state space taking into consideration all criteria and limitations. It has been assumed it was possible to determine the control rule in every domain D; of the state space. Thus the control rule is known for each final hypothesis.

Now a decision is made, which control rule will be applied. This task would be simple if one final hypothesis is proved with probability P; = 1 and all the others are rejected. This is unfortunately very rare case. Usually the probabilities of final hypotheses don't reach their margins and due to uncertain input data and overlapping domains their sum LP; * 1 .

There are two possible strategies to determine the value of the manipulated variable of the controlled process. Let us assume there are n domains D; and the control rule says the manipulated value should be U; in domain D; . The expert system finds out the a posterior probability P; for each final hypothesis. Every u; is assigned the probability P; which is a measure that the value 11; should be used for control of the process. The simplest possible strategy is to apply the value U; which is associated with the highest probability Pi :

(1)

This strategy however neglects the influence of the other final hypotheses with smaller but still comparable Pi· It can lead to the bang-bang control as a small change in input data can cause other final hypotheses to win and hence quite different output to apply.

The second strategy is based on a weighted average. The value of the manipulated variable is calculated according

166

to the formula:

n E p. u. i:l I I

u = ----n E P· i:} I

(2)

The control is smoother in this case. Both strategies can be used either to determine absolute value of manipulated variable - position control - or a change of the manipulated variable in one control step - speed control. The creation of the knowledge-base structure in the second stage is influenced by the chosen strategy. The weighted average control may in some cases reduce the number of final hypothesis.

TUTORIAL ENVIRONMENT FOR EXPERT CONTROL

The ESPIN program has been developed to study and to teach the properties and behaviour of an expert system control. It consists of an empty expert system - FEL­EXPERT - which is a rule-based expert system originally dedicated for diagnostic purposes which works with uncertainties. It is used in the semantic rule plane to derive the best control strategy and to control the data flow on the data plane. The algorithms on the data plane are programmed according to control needs, in C language. Identification and simulation program packages are intended to be used at the data plane in the near future. The second part of the program system is a model of the controlled technological process created by means of PSI/e simulation program. Both parts are executed periodically and a simulation control in closed loop is performed on a simple PC ( Fig. 2 ).

Expert controller

Expert system

l r Data and Controlled

> deterministic > process =

procedures model

Fig. 2. Program structure for simulated expert control.

The process we want to control by means of an expert system must be sufficiently complicated, otherwise the expert control cannot prove its advantages. On the other hand, its behaviour must be transparent in order to be useful for didactic purposes. The students must understand the behaviour of the process to be able to study and to evaluate the expert control. It is impossible to demonstrate and to understand the expert control without understanding the controlled process. The transparency of the controlled process is necessary to show how "clever" the expert control is. We have chosen a three vessel system (Fig. 3.) which has complicated behaviour due to two different types of nonlinearities. It is transparent enough because only simple physical processes - flow of liquid - are present. The input flows into vessel A. There are two outlets, one to vessel C in the bottom, and the other to vessel B located on the side. This causes a nonlinearity: dead space with respect to flow into B, and saturation with respect to the level in A. Vessel B empties as soon as the liquid reaches a certain level. When it is empty, the output valve is automatically closed again. A hysteresis is introduced in this way. It is like a simple batch process in chemical technology. The liquid is pumped out from the vessel C.

Expert control

�--� 1hc I I I I L

I

c

I I aIJ

Fig. 3. Simple technological process for expert control demonstration.

167

A mass flow control can be studied on such a model in different situations. There are several interesting problems that can be used for students to practice. One category of tasks is an estimation of non-measured process variables: - the levels in vessel A and B can be estimated using value

of level in vessel C, valve position and knowledge of the disturbances character in input flow.

- the frequency of the limit cycle depends on the valve position and on the input flow , the knowledge-base can be created to discover such relation.

Another category for tutorial exercises is a control task which can be formulated in several mutations: - the simple control of a two-vessel system - overflow outlet

from A to B is closed - can demonstrate the problem of interfacing two technological processes by means of a buffer vessel. The aim of the control is to reduce the propagation of disturbances from one process (input flow) to another (level in vessel C) with minimum volume of the buffer vessel (vessel A).

- the control of the level in the vessel C as an example of the parallel operation of continuous (vessel A) and batch (vessel B) processes (see example in the next paragraph).

- the control of the limit-cycle frequency, the aim is to keep the frequency within certain prescribed limits.

All these task are simplified problems which exist in real technological processes. They were chosen and simplified to posses two common properties: - the controlled process itself is simplified to be transparent - the aim of the task would be very difficult to fulfill by

means of classical linear control.

In all tasks the solution is not unique. The students can try different methods to: - program the procedures and data structu res in the data

plane, - create the knowledge semantic net - find the way how to tune it to reach the desired behaviour.

The simulation of the expert control is a handy and inexpensive tool. This is why ESPIN is very useful for didactic purposes in expert control of technological processes.

EXAMPLE

In the following example a simple control for the three-vessel technology model is demonstrated. A knowledge-base for an expert control ought to be designed. The task is to keep the level in vessel C as steady as possible. Due to the limit cycle caused by the hysteresis in vessel B it is not possible to maintain the level in C constant all the time. Without any control, the level in C has a saw shape time function. The control strategy is based on closing valve x when vessel B is nearly full. It causes a faster decrease of the level in C but on the other hand the increase of the flow to vessel B which empties fast into vessel C. The result is a steady level in vessel C for a substantial part of the limit cycle. The knowledge-base structure for such control is on Fig. 4. The input data - levels in vessels A, B, C - are converted into statements which express the relation to a significant value, for example "vessel B is nearly full". The conversion is specified by a nonlinear function r, (x) which defines the relation between the value of the deterministic variable and the validity of the statement. For example for vessel B the probability of the statement "vessel B is nearly full" is defined by f3 (B), as in Fig. 5. These functions are designed by the knowledge engineer and they are one of the tuning parameters of the expert control.

A - level in vessel A B - level in vessel B C - level in vessel C V - valve position 1 - C is nearly empty 2 - B is nearly full 3 - A overflows to B

v

4 - C is nearly full 5 - increase flow to C 7 - decrease flow to C 10 - increase flow to B 1 1 - decrease flow to B 1 6 - decrease flow from A 17 - increase flow from A

Fig. 4. Knowledge-base structure for three vessels expert control.

1 68

Fig. 5. Functions for the conversion of the input data to the statement validity.

They decide when and how the statement influences the behaviour of the whole semantic net. The rules start with statements 1 till 4 as initial evidences and lead to final hypotheses 16 and 17. See Fig. 4. Those hypotheses state the wanted change in output flow from vessel A. All rules are derived only from the causality of the process operation. For instance:

IF not (2: "B is nearly full") and (5: "increase flow to C") THEN (17: "increase flow from A").

All rules have two tuning parameters: - probability that the hypothesis is true when the evidence

is sure - probability that the hypothesis is true when the evidence

is surely not true. These parameters "weigh" the rules. It is used to express one rule considered to be more important than the other one.

During the consultation the expert system checks the rules and evaluates the actual probability of all final hypotheses. The final hypothesis probability p16, p17 is a measure of the state of the process. It identifies the domain where the process is taking place. Therefore the final hypotheses can be applied:

16: "decrease flow from A", 17: "increase flow from A",

taking the final probabilities into consideration. The valve position is then calculated in the data plane by the Eq. (2). The simulation of the expert control by means of the knowledge-base structure is in Fig. 6. For more than 60% of limit-cycle, the level in vessel C is kept steady. For simplicity sake only the immediate values of levels were used for the domain diagnosis. Taking past values into account considerably increases the quality of control.

CONCLUSION

Application of AI in control of technological processes is moving from the theoretical studies into practice. The most important part of a successful application is the representation of the available knowledge and its acquisition. A new profession - knowledge engineer - has appeared recently. Education in process control must reflect this fact. This paper contributes to the practical teaching of the expert control.

NAM: LC MAX· f i-i r

THREE VESSELS llOOEL VALVE TIME

10

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ri �-=-���-Le�

ue-

l�

fn�

ve-sse�

l-

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r I i­i L i ! i- Value position i "'='"--'"----l---L-----·-' ___ L__,__, __ _ MIN; 0 ACT: 2.450251 0.904

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Fig. 6. Results of the expert control of three vessels model.

REFERENCES

Astrom,K.J ., J J .Anton and K.E.Arzen (1986). Expert Control. Automatica, vol.22, no 3, 277-286.

Bosch van den, P .P J ., H.Butler and A.R.M.Soeterboek (1990). Modeling and simulation with PS/le. BOZA Automatisering BV, Pijnacker, The Netherlands.

Durkin,J. (1990). Introducing students to expert systems. Expert Systems, May 1990, vol.7, no. 2, 70-80.

Maffk,V. and T.Vleek (1991). Expert System FEL-EXPERT. Czech Technical University, Faculty of Electrical Engineering, Department of Control Engineering, AI Group, Prague, Czechoslovakia.

Verbruggen,H.B., A.J.Krijgsman and P.M.Bruijn (1991). Towards Intelligent Control. Journal A, vol.32, no. l, 35-45.

Verbruggen H.B. and K.J.Astrom (1989). Artificial Intelligence and Feedback Control. In 2nd IFAC Workshop on Artificial Intelligence in real-time control, China, September 1989,pp. 1 15-125

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Copyright @ IFAC Anificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

A PREDICTABLE REAL-TIME EXPERT SYSTEM FOR MULTI-SENSOR FUSION

G. Wang••••, 0. Dubant•• and J. Magnier••

*China Yichang Research lnstiluJe of Testing Techniques, P.O.B. 549, Hubli, Yichang 443003, PRC ••Ecole des Mines d'A/es, 6 avenue de Clavieres, 30319 Ales Cedex, France

Abstract . Predictability o f response t imes i s c ruci a l f o r real-time expert systems . I n this pape r , we discuss the importance o f the determinism o f response t imes and analyse the condit ions under which each maximum response t ime will be predictable . We present a ls o the appl icat ion o f t he concepts described to multi-sensor fusion .

Keywo rds . rea l - t ime expe rt s y s t em; predi c t ab i l i t y o f response t imes ; fusion o f multi-sensory data .

INTRODUCTION

S ince the middle o f the eighties , many papers have been published on rea l-t ime expert systems , and s ome she l l s f o r bui lding such systems a r e c omme r c i a l l y a v a i l a b l e . Howeve r , the re e x i s t s very few ope r a t i o n a l re a l - t ime e xpe rt systems . Why ? We be l ieve that there are two reasons . Firstly, the concept of real-t ime expert system is not we ll def ined . Consequent ly, some systems or shells reported are not rea lly concerned with the s o cal led re al-t ime expe rt systems . Secondly, t he wo rk done on this t opic is not sufficient , at least not enough .

S ome people cons ider rea l-t ime as fast comput ing . As a consequence of thi s , a lot of work has been done on high performance . However, speed alone i s not real-t ime . In fact , the most important characteristics of a r e a l - t ime s y s t em a re r e l a t i v i t y o f s p e e d a n d predictability o f response t imes .

In this paper , we t ry t o give , for the first time t o our knowledge , a rigorous de finition for real-t ime expert systems . We then reveal the importance of the predictability of response t ime s and analyse the

171

conditions under which each maximum response t ime ( see t he next section f o r t he de f in i t i o n ) w i l l be predictable . F i n a l l y , we p re sent the application o f the concept s described t o multi-sensor fusion .

TERMINOLOGY

Before giving a rigorous definit ion for rea l-t ime expert systems , we spec ify first o f a l l s ome terms we will use during our discussion .

A n e w fa c t i s a f a c t wh ich corresponds t o the t ranslation of s e n s o ry dat a rep r e s e n t i ng o ne s ituation o f the external world .

Sol ve a problem cons ists in adding a fact to the factbase or executing an action of a rule .

A fin a l fa ct i s a fact yielded by the res o lut ion o f a problem, but the p re sence o f wh ich no l onger drives the resolut ion of any other problems .

Sol ve a fi n a l probl em means t o so lve all the succes s ive problems , from a new fact to a final fact .

For a given knowledge bas e , it is a lways po s s ible to ext ract a sub­set which contains only the rules

intervening in the res o lut ion of one final problem . Such a sub-set is called a task .

Time of probl em ( TP ) is the limited t ime o f response imposed by the consid�red application for s olving a final problem .

Minimum t ime of problem (MTP ) is t he minimal va lue o f TPs in all situations .

Time of a c qu i si t i on ( TA) i s the t ime for the acquisit ion of sensory data .

Time of t ran s l a t i on ( T T ) i s the t ime f o r t he t ran s l a t i on f rom numerical data to symbolic facts .

Time of resol u t i on of probl em ( TRP ) is the time for solving a problem .

Time of genera t i on ( TG) is the t ime for the gene rat i on of an act ion linked with a final fact .

Rel a t i ve t ime of wa i t ( RTW) is the t ime du r ing which the s y s t em processes informat ion which is not concerned with the ongoing task .

Absol u t e t ime of wai t ( ATW) is the t ime between the end of TT of one fact and the beginning of TA o f anothe r fact due t o the nature of the external world .

R e sp o n s e t ime ( RT ) is the t ime between the detection o f senso ry data and the end of the resolution of a final problem .

Maximum response t ime (MRT ) is the maximal value of RTs for one fina l problem .

It should be noted that it is the MTP that makes t he di f ference between a real-t ime applicati on and a non rea l-t ime appl icat ion : for t he former one , the MTP is ve ry short ( one second o r les s ) , and st rictly limited, whereas for the latter one , the MTP is long even without limit theoret ically .

DEF INITION

There are , in the l iterature, many de finit ions of real-t ime systems . We adopt t he one de f ined by

172

( O ' Re i l ly and C roma r t y , 1 9 8 5 ) , which expre s s e s that t he re i s a strict t ime l imit by which t ime the s y s t em mus t h a ve p roduced a response t o environmental stimuli .

Definition A real-time expert

system is an e xpert system which can gua rentee that each of its maximum re sponse t ime s for each task i s always inferior or equal t o e a c h o f t he re l at ed t imes o f p r o b l e m o f a c o n s i d e r e d application .

This definition is not useless . In f a ct , it appea r s s u f f i c ient ly complete and representat ive of what we demand of a real-t ime expert system, and seems t o summarize very wel l the problematic l inked with the subject .

A BAS IC THEOREM

S upp o s i n g t h a t t h e c o n s ide red appl i c a t i o n h a s N s it uat i o n s . Therefore , there will be N t imes of problem . By definit ion, MTP = { TPi }

with i = 1 . . . N .

Theorem 1 : An expert system will be cal led real-t ime expert system i f f it can ensure t he f o l l owing inequalities : MRTi � TPi ( 1 ) with i 1 . . . N .

Proof T rivial according t o the above definition .

Corollary 1 A real-t ime expert

system should have at least as many t a s k s a s t he s ituat ions o f t he considered application .

Proof : I f a system possesses less tasks than the s ituat i ons o f the applicat i on , t he re wi l l be s ome cases in which the system has no s o lut ions . For t he se s it uat i on s , the system w i l l certainly not be able t o ensure the formula ( 1 ) . Corollary 2 : Every MRT of a real­t ime e xpert s y s t em s hould be determinable .

Proof : I f one of the MRTs is not determinable , we will not be able to c ompa re t h i s MRT w i t h t he re levant T P . C o n s equen t l y , t he formula ( 1 ) can not be ensured .

PRED ICTABI LITY OF MAXIMUM RESPONSE T IMES

According to Corolla ry 2 , each o f the MRTs should b e dete rminable . For this , a l l of the RTs should be det e rmin i s t i c . Howeve r , the two ma j o r drawbacks o f expert systems compa red with a classical program are the s l ownes s of execut ion due to pattern-matching, and the non­de t e rmin i sm a s ment i o n e d by ( Ghal l ab and Philippe , 1 9 8 8 ) . S o , i n order that a n expert system be a pp l i c a b l e t o a r e a l - t i me applicat ion , it should unde rgo a double re s t r ict ion t he t iming constra int s ( MRT i � TPi ) and the

int erna l constraints unde r wh ich the MRTs will be determinable .

For the first aspect , a lot of work has been done aiming to improve the performances of the system . We can cite, for instance , the compilation of knowledge base ( F o rgy, 1 9 8 2 ; Mi ranke r , 1 9 8 7 ) . As f a r as the second aspect is concerned, l ittle work has been reported, and we will present our work on this topic .

Hypotheses

We propose the following hypotheses unde r which ou r discus s ion w i l l take place .

Hypothe s i s 1 There a re no non-recognizable new facts .

Hypothe s i s 2 The expe rt system has no lea rning abi lity so as to modify the rule-base .

Hypothe s i s 3 : The re lat ive time s of wait are deterministic .

Determinism of the RTs

I n o rde r t o understand the non­determinism o f an expert system, let us t ake an example . Figure 1 shows a very s imple rule-base and its representat ion on a rborescent nets . In this example , the re are two t a s k s c o r re sponding t o two f ina l problems L and M, each represented by a net .

I f we conside r each net as a black box, the one for problem L can be s a id mu l t i -AND -OR- input s mo n o ­output , while the one f o r problem M

173

w i l l be s a id mon o - i nput mon o ­output . Gene r a l ly speaking, there may exist other net s l ike multi­AND -output s , multi -OR-output s , o r mu l t i -AND -OR-output s . The mono­output net is the most popular one . S o , we will only study this kind of nets .

In the above example, it is easy to deduce the following formulas :

RTL1 = TAc+TTc+ATWco+RTWx+TAo+TTo

+TRPco+TRPB+TGL ( 2 )

It is c le a r that there a re two response t imes f o r problem L . S o , the response t ime f o r L is not determinist ic . On t he other hand, if RTLl and RTL2 a re determinable ,

acc o rding t o hypothes is 2 , there exists a MRTL , with MRTL = { RTL1 1

R T L 2 } . For problem M, i f RTM is determinable, we obta in MRTM by MRTM = RTM .

Seeing that the TA, T T , TRP and TG a r e conce rned w i t h i n f o rma t ion proce s s ing, they a re dete rminable . T h e r e f o r e , RT L 2 and RTM a re

det e rminab le . As f a r as RTL 1 is

conce rned, according t o hypothe s is 3 , RTWx i s de t e rmin ab l e , but ,

gene ral ly, ATWco may t ake any value

up to infinity . In other words , RTL1 will be determinable i f and only if ATWco is so, and only in this case

that MRTL is predictable .

I n conclusion, the det e rminism of RT s depends on t he st ructure o f a r b o r e s c e n t n e t s . T a b l e 1 summarizes the dete rminism o f RTs and the predictability of MRT .

It should be noted that i f e ach task of a rule-base is t rans fomable into a deterministic net , t hen a r e a l - t ime expert s y s t em may be built by u s ing t h i s rule-base . Otherwise, we can not build a real­time expert system .

APPLICATION TO MULT I-SENSOR FUS ION

The princ ipa l concept s des c r ibed above have been used in the design o f a real-time expe rt system for

the fusion o f multi-sensory data p r o v i d e d b y a n u l t r a s o n i c t ransducer and a CCD camera . I n this sect ion, we demons t rate how the sensor-data fusion problem is embedded in the rea l-t ime expe rt s ys t em environment , and pre sent some s imulated results .

Problematic of multi-sensor fusion

I n recent years , there has been an i n c re a s i n g i nt e r e s t i n t h e development o f mult i-senso r fus ion for aut onomous mobi le robot s . We can dist inguish two categories o f sensor-data fusion process :

• the fusion of homogeneous sensory da t a i n o r de r t o r e d u c e uncertainty .

• the f u s i on o f hete rogeneous senso ry data in o rder to ut il ize the advantageous cha racteristics of s o me i n o v e r c o m i n g t h e disadvantages o f others .

In our mult i-sensor system, for the s ake o f low price , we u s e an ultrasonic sensor and a CCD camera . Thus , our study is concerned with the fus ion o f heterogenous sensory data .

The ult rasonic sensor can measure the distances t o an obj ect through a range of 5 0 cent imetres up to 1 0 metres . The ultra sonic beamwidth is about 1 0 ° . Consequent ly, it has a p o o r angu l a r re s o lu t i on the d i s t a n c e me a s u r e d i s n o t nece s s a rily the dist ance in the direction that the sensor points .

F igure 2 shows a r o om t o be recogni zed . F igure 3 present s a rough representat ion o f the room in the l ight o f expe r iment a l data provided by the ultrasonic sensor o n ly . It is c le a r t h a t t he environment is much deformed .

The CCD Camera is able t o f ind edges of an ob j ect along with (by c a l c u l a t i n g ) t h e i r r e l e va n t o r ien t a t i o n s , w h i c h w o u l d be blurred by the ultrasonic senso r , but can not provide any information about the re levant distances . That is that it can only provide two­dimensional informat ion .

174

Figure 4 shows the vision area in a g i ve n p o s i t i o n . F i gu r e 5 illustrates the orientat ions of the edge s , 0 1 , 02 and 0 3 . F igure 6 presents a two-dimensional image .

It is easy to see t hat neithe r o f these senso r s i s suitable for the percept ion o f environment . We can hope to get better informat ion for repre s ent ing t he s cene by us ing both senso rs t han i f either sensor is used a l one . Howeve r , how to integrate these s e n s o ry dat a ? S ince it is dif ficult t o model t he me a s u reme n t s o f t he u l t ra so n ic s e n s o r , t he r e w i l l be n o a l g o r i t hmic s o l ut i o n s f o r t he fus ion process .

Production rules for the fusion

The non existence of an algorithmic s olut ion has led us t o use an AI approach, and e specially an expert system .

According t o figure 2 , there a re t h ree type s o f ob j e c t s t o be recognized wa l l , doo r way and corner . In our approach, we use an unrolled polar coordinate , shown in f igure 7 , t o represent s e n s o ry dat a . After an e xpert s tudy o f figure 3 and f igure 7 , and a t the close of our heurist ic research for t h i s pa r t i c u l a r c a s e , we have ext racted a set o f fuzzy production rules a l l owing us t o reconst ruct the scene from multi-sensory data . He re a r e s ome o f t he r u l e s (Wang, 1 9 9 1 )

• I f the re i s a val ley and the distances change smoothly between two edge s , then t he re is a wall between these two edges .

• I f the re is a wal l between · two edges , then the minimum value o f the val ley i s qu i t e a c cu rat e , corresponding t o the distance from the robot to the wall .

• If there are infinite distances or t he di s t ance s change rapidly between two edges , then there is a doorway between these two edges .

• I f. there is an edge near a crest , then this edge c o r re sponds t o a corner .

S ince the expe rt system will be implanted on the mobi le robo t , it should have a l l the nec e s s a r y funct ionnalit ies a real-time expert system should have .

Simulated results

In our study, we haven ' t been able to make a complete study o f our s y s t em . Neve rthe l e s s , we have proved that all o f the tasks in our system a re determinable . Table 2 shows some simulated results .

Note that the MRTs is the maximum

response t ime for taking an urgent decision when the robot reaches the distance of safety ( in our system, ds a fety = 0 , 3 m) . For a robot who

moves at 0 , 1 m/ s , our system can work in real-time , s ince TPs = 0 , 3 + O , 1 = 3 s , and the inequal ity MRTs � TPs is ensured . Now supposing

that the robot moves at 0 , 6 m/ s , if we use the same distance of safety, then TPs ' = 0 , 3 + 0 , 6 = 0 , 5 s . In

this case the inequal ity MRTs � TPs '

can not be established, and our system will not be a rea l -t ime expert system .

CONCLUSION

We have rigorous ly defined " real­t ime expert systems " , and analysed the condit ions under which a such sys tem can be bu i l t . We have demo n s t rated t hat a r e a l - t ime expert sys tem is not an expert system with some s imple extension of new funct ionnalities , but one w h i c h s u f f e r s f r o m d o u b l e constraints .

We have a l s o p r e s e n t e d t h e problematic of the fus ion o f mult i­s e n s o ry dat a p r o v ided by an ultrasonic sensor and a CCD camera, and explained why and how t o use a real-t ime expe rt system for solving this problem .

The e xamp l e demon s t r a t e d t wo impo rtant point s . Firstly, fast is not real-t ime , but it may play a determinative role . I f the MRTs = 1 hour, for instance, the system will p ro b a b l y neve r be re a l -t ime . Secondly, the same system may be a real-t ime one in some cases, and be a non real-time one in other case s .

175

S o , predic t ab i l it y o f ma ximum response t imes i s vit a l for real­t ime expert systems .

For the purpose o f this paper, we haven ' t talked about interrupts . In a general fashion, they influence re sponse t imes of a system, and thus should be taken into account .

REFERENCES

F orgy, C . ( 1 9 8 2 ) . RETE : a fa s t a l go r i t h m f o r t h e m a n y p a t t e rn /many obj e c t ma t ch p r o b l e m , A r t i f i c i a l

Intelligence. l.i, 17-37 . Gha l l a b , M . , and H . P h i l ippe

( 1 9 8 8 ) . A compi l e r for rea l ­t ime kno wl edge -based sys tems, in Proc . of I n t e r n a t i o n a 1 Wo rkshop on A r t i f i c i a l

Intelligence f o r I ndus t ri a l

Application s , Hitachi C ity,

pp . 3 8 7 -3 9 3 . Miranker , D . P . ( 1 9 8 7 ) . TREAT : a

bet ter ma t ch algori thm for AI

produ c t i on sys t ems , in P roc .

of AMI ' 87 , Seat t le , pp . 4 2 -47 .

O ' Re i l ly, C . A, and A . S . C roma rty ( 1 9 8 5) . "Fa s t " is not "rea l ­

t ime " i n design in g effe c t i ve

r e a l - t ime A I sys t em s , in

Applications of Ar t i f i c i a l

Int e l l igence I I , P roc . o f

S P I E , Vol . 5 4 8 , pp . 2 4 9-257 . Wang , G . ( 1 9 9 1 ) . I n t e g r a t i n g

acoustical and opt i cal sensory

da t a for mobi l e robo t s , in

Applications of Art i f i c i a l

Intelligence IX, P roc . of SPIE

Vol . 1 4 6 8 , pp . 47 9 - 4 8 2 .

Rule-base If A Then L; If B Then L; If C and D Then B; If E Then M;

Figure 1 . Representation of rule-base by a rborescent nets

T- -· 7 m

1 1 .. 8,2 m

Figure 2 . Room be observed

y

-t-------cd ,,' , ,. bb' ,,; .,,.,, ,,.,,. 93 --- ••

81

I door A

•I to

Figure 5 . Orientations of edges

Structure of net

mono-input, mono-output

multi-AND-inputs, mono-output

multi-OR-inputs, mono-output

• ultrasonic sensor

Figure 3 . Observat ion of ultrasonic sensor

Figure 6 . Vision image

Determinism of RT

yes

may be

no

multi-AND-OR-inputs, mono-output no

() CCD C1111era

Figure 4 . Vis ion a rea of CCD camera

p (diltmce) distance obtained by sonar

valley

0 ..._ _______ e!--tl� e (angle

Figure 7 . Unrolled polar coordinate

Predictability of MRT

yes

perhaps

yes

perhaps

Table 1 . Determinism of RT and predictability of MRT

Time

Value (second)

MRT1

MRT2 MRT3

1 ,3 0,85 0,9

Table 2 . S imulated results

176

MRT 4 MRT 5

0,95 0,6

Copyright © IFAC Anificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

ADAPTIVE AND SUPPLEMENTARY INTELLIGENT CONTROL OF POWER SYSTEM STABILIZERS

J. Heydeman and G. Honderd

Delft University of Technology, DeparttMnt of Electrical Engineering, P.O. Box 5031, 2600 GA Delft, The Netherlands

Summary The presentation is devoted to the me­thodology of design of an adaptive con-

. trol algorithm combined with knowled­ge-based rules to improve the robustness of power-voltage control under variable load conditions and with a variable num­ber of turbogenerators, which are con­nected to the tie line system. This presentation is centered around a control-research project in the Nether­lands. The power-generator system is modeled and field tests are carried out for verification. The purpose of the research project is to design and to im­plement an adaptive algorithm, based upon the PSS-approach, combined with observer filters. Because of the fact that already a power system consisting of a cluster of genera­tors with variable load conditions, ope­rating in an isolated area, has several well-known boundary conditions, related to different operating points, the MRAC adaptive control algorithm has to be supervised by a set of rules, governed by a knowledge base. This expert-oriented knowledge is based upon the normal "intelligent" control actions as they are carried out by the unit operators. These rules are non-analytic and can be descri­bed by fuzzy membership functions. In the presentation this fuzzy-set ap­proach, in this project used to improve

177

the adaptive-controlled behaviour, will be explained. Experimental results of the total system will be presented .

1 . INTRODUCTION A power turbogenerator tied to an infini­te bus or to a cluster of generators gene­rally has a weak damping of regional mode oscillations (1 ,4] . To improve the system damping, artificial means of producing torques in anti-phase with the speed are introduced. These are called " supplementary stabilizing signals" . The networks used to generate these signals have come to be known as "power sy­stem stabilizer" (PSS) networks [2,3,9] . Stabilizing signals are introduced in excitation systems at the summing junc­tion where the reference voltage and the signal produced from the terminal volta­ge are added to obtain the error signal fed to the regulator-exciter system. In

• this presentation a control-research pro-ject will be regarded in which the input signal of the PSS is a signal representing the acceleration power. This signal is derived from the mechanical power and the electrical power. The electrical po­wer is derived from the terminal volta­ges and the stator phase currents. The mechanical power is not directly availa­ble. It is obtained by a simple observer. Figure 1 depicts the observer scheme.

+

Fig. 1 The observer

IOILU

l,ligh pass til ter

p m

tuUii.'ls uc1na

u

V�IN �i-..������ r F . s+l

l

Fig. 2 The model of the excitation system

COD

Fig. 3 The schematic diagram of one generator tied to an infintite bus

The input signals of the observer are the steam valve position and the electrical power Pe [3, 7] . Since the power system is non-linear, some parameters of the PSS have to be adapted to the state of the system for a stronger damping. The calculation of the optimal values of these parameters is time consuming. Moreover this calcula­tion needs data which are not always available. This means that after a large disturbance like switching off of a line or the tripping of a generator, the PSS should be adapted after a long time, or should not be adapted at all. This research project shows that with an expert system approach for the adaptati­on of the PSS, suitable values of the parameters of the PSS are derived within an acceptable time. In this expert system fuzzy logic has been implemented. The usefulness of such an approach is repor­ted earlier [7, 8] . The expert system was tested on an analogue power simulator shown in

178

figure 3. The generatormodel is accor­ding to Park's equations. The model of the excitation system is shown in figure 2. In this figure the input for the stabili­zing signal is marked "Upss" . 2. THE POWER SYSTEM STA­BILIZER The transfer function of the PSS is

P0(s) Kpss· (a· 'T 1 ·s+ l) · 'T 2·s Upss(s) (.,. 1 ·s+ l) · (.,. 2·s+ 1)

For this system experiments show that suitable reponses can be obtained by adapting the gain Kpss of the PSS only. Figure 4 shows suitable values of Kpgs for 4 operating points of the generator. These values were determined by experi­ments. For these experiments the high voltage terminals of the machine trans­former were short-circuited during a short time. The responses of the accelerating power

-o.s

2

3

Q IPUI

Fig. 4 points

1<1'SS•2 x QC 1 PL

QLI

KPSS•t x

2 3 p Pli IPUI

KPSS•2 x

were considered. The criteria were the damping Pa2/Pa1 and the settling time T.

Second level

Third level

PERFORMANCE MONITORING

BASIC CONTROL

Fig. S Hierarchial structure of expert control system

The supervision level does all the decisi­on making and the appropriate control algorithm selection. It is like the human brain. The second level - performance monitoring (or on-line information ac­quisition) - is basically a perception problem in general. In this case of one generator tied to an infinite bus the input signals of the ex­pert system are the real and the reactive power of the generator. The output sig­nal represents a suitable value of Kpss.

To obtain suitable values of Kpgs eigen value analyses were performed at four operating points. Also the high-voltage terminals of the machine transformer were short-circuited during 10 to 20 ms and the responses of the system at diffe­rent values of Kpgs were considered.

�_._._.,.....,_,......,...._"T-l,.....��-.--,._.. ..... _._,_,_._.-.1-..._1-• ..-.

Kt•ss·0 l'a2/1'11 I • •

2 , 7'4 1 1 1 .

) . ) I I '"'·

'•

. J l 4 I Y J . i;.,1 1 1 . 1 1 1.i •

Fig. 6 Responses of Pa at p= 1 .0 pu and Q=-0. 7 pu

K1•ss·2 ) '• 6

l'112/l'11 I • • n> . 714

179

Fig. 7 Responses of Pa at P= 1 .0 pu and Q = 4.4 pu

At this operating point K =2 the most suitable value is of KPSS is 2. Figure 7 depicts a series of responses at the ope­rating point P= l pu and Q = 4.4pu.

Here the minimal value of Pa-ii Pa1 is at Kpss =4, but the minimum settling time is at Kpss =5. For this operating point Kpss =4 was chosen intuitively. In the same way suitable values of Kpgs at the other two operating points were determi­ned. Based on this knowledge PL and PH have been defined as: Pi is true if P< 1 pu P8 is true if P> 3 pu. Qc, Qu and QH1 have been defined as:

Qc is true if Q < -0. 7 pu Qu is true if Q = 2.6 pu QH1 is true if Q > 4.4 pu

The fuzzy membership functions of P and Q used in the fuzzifier are depicted in figure 8 .

Fig. 8 The membership functions of P and Q

Experiments and eigenvalue analysis show that the region in which Kpss = 1 is a desired gain, should be small . This was achieved by choosing the slope of the fuzzy membership function of PH steeper. The other fuzzy membership functions were determined experimental­ly in the same way. The rule base needs also membership functions of Kpss· Experiments show that linear members­hip functions of Kpss give satisfying results. The used functions which are used are depicted in figure 9 .

. " ..

Fig. 9 The membership function of KPSS

Now the knowledge base is complete for determining suitable values of Kpss of the PSS of a generator tied to an infinite bus. For adapting the gain of the PSS the expert system needs the real and the reactive power of the generator. The process in the expert system is depicted in figure 10. With the data of P and Q the fuzzifier determines the grades of memberships of

Pv PH• Q0 Qu and QHI· The fuzzifier

180

,. ---------- - -- - - - - --, I • I I I Ot· ' : luuif..,. I I I I

Lunu�"�---- - - - - - -----�

. .......... -----t SIAlllllf• -------"'

'·

Fig. 10 Expert control system using fuzzy reasoning

uses the fuzzy membership functions of these variables. Next the grade of mem­bership of the combinations PL n Q0 PL n QHI> PH n Qc and PH n Qu are de­termined. Experiments show that the average of the grades of membership of P; and of Q; gives the best results, or

The rule base establishes the combinati­on P; n Q; with the highest grade of membership (µ-;) and the combination � n Qj with the next highest grade of membership (µ.). As can be seen the supervisor consists of three distinguishable parts: the fuzzifier, the fuzzy rules and the defuzzifier . For each fuzzy region fuzzy rules and conditional statements have to be formu­lated. The expression of Kpss is:

(Kpssj - Kpssi ) Also the configuration of the network between the machine and the infinite bus related to the PSS was examined. The line was replaced by a network as indicated in figur:! 1 1 .

1 .. l a

Fig. 11 The extended network

Eigenvalue analysis and experiments show that this network hardly changes the suitable values of Kpss· Hence the membership functions of the figures 8 and 9 can also be used for this system.

4.APPLICATION OF CASE STUDY Suppose the machine of the system of figure 3 is loaded with P = 1 . 7 pu and Q = 0.9 pu. The system determines a suitable value of KPSs in the following steps:

1 . The fuzzifier determines the grades of memberships of Pv PH, Qc, Qu, QH1 from the fuzzy membership func­tions depicted in figure 8, or µ, p = 0.73 L

µ, = 0 PH µ, Q = 0.57 c

µ, Q = 0.53 u µ, = 0 QHI

2. The fuzzy rules determine the grades of memberships of the sets PL n Qo PL n QHb PH n Qc and PH n Qu from the grades of memberships of P; and Q; according to the formula µ,P. n Qi = 1/2 (µ,pl + µ,Qi ) .

I

Set P; n Q;

1 8 1

PL (\ QC

P1 (\ QHI

PH ('\ QL

PH n Qu

0.65

0.365

0.285

0.265

2

4

1

2

The values of the gain Kpss are accor­ding to figure 4.

3 . The defuzzifier determines the value of KPSs from

Kpgs = Kpss. + (µ,; - µ,) • (KPSs . -Kpss ). ' J i

The set PL n Qc has the highest grade of membership, so that Kpss. = 2 with µ,i = 0.65 . I

The set PL n QH1 has the next highest grade of membership, so that KPSsi = 4 with µ,i = 0.365. Then Kpss = 2 + (0.65 - 0.365) (4 - 2) = 2.57.

Finally figure 12 shows the response of p on the opening of line 1 1 . T�e tests were performed at constant Kpss and at adaptation of �Pss by t�e expert system. The system with adaptati­on has the best reponse. •-··· .. I �-. · ··· ·- · ·· ::

· ··--. . .... --.. ·• · · . . . . .... ..... . . .. ...... -.. . . . - . .

. .. .. . -� L1:���¥� Y.xp. ::y:i t .

Fig. 12 The response of Pa without and with adaptation

s. CONCLUSION A fast adaptation of a PSS is possible by means of artificial intelligence.

The acquisition of the knowledge for the

adaptation of a PSS of a generator tied to an infinite bus is very simple. The acquisition of the knowledge for the adaptation of a PSS of a generator which is one of a cluster of generators tied or not tied to an infinite bus is far from simple. Comprehensive analysis may be needed for the knowledge base.

The rules are rather straightforward. This means that a lot of flexibility in control of a complex multi machine system exists by the application of en­hanced expert oriented adaptation of the power system stabilizers.

References [l] Larsen , E. V. and Swann, D.A.

Applying power system stabilizers, IEEE Trans. , 198 1 , PAS-100, pp. 3017-3046

[2] Bayne, J.P. , D.C. Lee and W. Watson , A power system stabilizer for thermal units based on deriva­tion of accelerating power, IEEE Trans. on PAS, vol. PAS-96, No­v./Dec. 1977

[3] Amerongen, J. van , P.J. Buys, H.W.M. Barends and G. Honderd, Modelling and control of a 1 80-MW power system, In: Proceedings of 23rd Conference on Decision and Control, Las Vegas, USA, pp. 494-499, December 1984

[4] Anderson, P.M. and A.A. Fouad, Power system control and stability, The Iowa State University Press, Armes, Iowa, USA, 1977

[5] Negoita, C. V. Expert systems and fuzzy sets, The Benjamin/Cum­mings Publ. Co. , 1985 , ISBN 0-8053-6840-X

[6] Nauta Lemke, H.R. van, Trends in control engineering, Journal A, vol. 3 1 , no. 1 , 1990, pp. 45-5 1

[7] Honderd, G . , M.R. Chetty and J. Heyde man, An expert system ap­proach for adaptation of power system stabilizer, In: Proceedings

182

Second Symposium on Expert Sys­tems Application to Power Sys­tems, July 17-20, 1989, Seattle, USA

[8] Hsu, Y. -Y. and C.-H. Cheng, Design of fuzzy power system stabilizers for multimachine power systems, IEE Proceedings, vol. 137, Pt, C , no. 3 , May 1990, pp. 233-238

[9] Fleming, R.J. , M.M. Gupta and Jun Sun, Improved power system stabilizers, IEEE Trans. Energy Conversion, vol. 5, no. 1 , March 1990, pp. 23-27

Copyright @ IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

FUZZY INFERENCE IN RULE-BASED REAL-TIME CONTROL

R. Jager, H.B. Verbruggen and P.M. Bruljn Delft University of Technology, Department of Electrical Engineering, Control laboratory, P.O. Box 5031,

2600 GA Delft, The Nttherlands

Abstract In this pa.per research into the a.pplica.tion of 'expert system'-like inference

mechanisms in the field of fuzzy control is a.dressed. Using techniques from

the a.rea. of rule-ba.sed expert systems, a. more flexible wa.y of design a.nd modifi­

cation is presented of new and existing fuzzy systems for modelling a.nd control.

In comparison with 'normal' applications of fuzzy inference, the 'compositional

rule of inference' is replaced by a fuzzy inference engine. General applicability

of the fuzzy inference engine is ma.de possible by its general character as a

fuzzy expert system shell. Succesful implementations in simulation and real­

time control environments show the flexibility and usefullness of the described

fuzzy inference engine.

Keywords Fuzzy, Real-Time, AI, Rule-Based, Inference, Control

1 Introduction

Application of fuzzy set theory in control is gain­ing more and more attention from industries. Besides a growing number of applications in con­sumer goods (washing machines, cameras) , in­dustrial applications are described in literature: waste water denitrification process [ 13], temper­ature control of glass melting furnace [ 1] and ce­ment kilns [4]. Application of fuzzy control in a cement kiln was probably the first industrial application of fuzzy control.

All those applications have in common that they are designed for a specific application, although there exist software packages for designing fuzzy controllers. Some software packages provide ad­ditional hardware for speeding up the inference of fuzzy rules. Those tools are build for the de­sign of fuzzy controllers and can not be used like a 'conventional' expert system shell, because they operate within the field of fuzzy logic and not in the field of boolean logic or first-order predicate logic.

183

On the other hand expert systems has been introduced in the field of control and during the last decade the emergence for Al-techniques in control has become evident [8]. Most 'con­ventional' expert systems contain an inference mechanism that only deals with boolean logic. Because of the fact that the knowledge and in­formation used by the expert system are some­times not completely known, it seems plausible that the inference mechanism of the expert sys­tem should be able to deal with fuzzy and/or uncertain information and knowledge [11]. In this way information 'from outside' (measure­ments) as well as knowledge 'within the expert system' (rules based on operational experience) can be represented in a more 'human' way.

To increase the flexibility of the systems and to allow the use of boolean as well as a fuzzy logic in a correct way, a fuzzy inference engine has been build. This inference engine is able to deal with boolean as well as fuzzy logic and is capable of applying reasoning and search methods as used in 'conventional' expert systems.

The next section (2) describes the ideas on which the fuzzy inference engine is based. Sec­tion 3 outlines the capabilities and restrictions of the fuzzy inference engine. In section 4 an example and some experiments are shown. Con­clusions and a discussion are presented in section 5 .

2 Fuzzy rules and inference

The theoretical approach of fuzzy inferencing is based on the idea of relations rather than on the idea of implications. A fuzzy controller is a function of more than one variable, which is a combination (union) of the functions represent­ing the individual fuzzy rules. The 'direction' of inference is dictated by the fuzzy rules. A typical rule i can be stated as:

IF x1 is X{ AND . . . AND XN is X}v THEN y is Yi

The complete fuzzy controller, however, is a multi-dimensional relation, combining all indi­vidual fuzzy rules

R = Vll; (1)

where the membership of every relation describ­ing a fuzzy rule is given by

µR; (xi , · · · , XN , y) =

N { /\ µx; (xi)} t\ µy; (y) J i=l

(2)

As can be seen from (1) and (2) the resulting fuzzy system has no longer a 'direction' like in rules (if . . . then . . . ) : it is a relation. This is why, for example, fuzzy models can be used for predictions as well as 'inverse' control [2].

By applying the 'compositional rule of inference'

Y = X o R (3)

and using a fuzzification of the inputs, which results in fact also in a relation, a fuzzy output is obtained. The most commonly used inference rule is the ma3"rmin-rule. One could also denote (3) as an OR-AND operation, which is a more general interpretation.

184

In practical applications however, usually a more efficient method is used [5] . This method is based on the assumption that the fuzzification of a input is represented by a singleton. Apply­ing the 'compositional rule of inference' on the relation, using the fuzzified input, results in a fuzzy output. The fuzzified input is represented by the union of all the singletons describing the individual (numerical) inputs. The same fuzzy output can be obtained by determining for every fuzzy rule i the individual fuzzy output

N µ� (y) = { /\ µx; (xi(t) ) } t\ µy; (y) (4)

J i=l

Combination of those individual fuzzy outputs by applying a union results in the complete fuzzy output of the system

µy (y) = v µ� (y) (5)

Note that the inputs in (4) are represented in a numerical way and the output is represented in a fuzzy way. Several defuzzification methods are available to translate the fuzzy output into a crisp, numerical output value [7].

Based on this practical way of applying fuzzy rules and inference, a generalization of the in­ference mechanism can be made allowing to ap­ply fuzzy rules and inference in a way rules and inference mechanisms are used in 'conventional' expert systems. The next section will describe the way how both methods are combined into one inference engine.

3 Fuzzy inference engine

First of all the inference engine should con­tain all 'conventional' reasoning methods: back­ward reasoning (top-down or goal-driven in­ference) and forward reasoning (bottom-up or data-driven inference) . For real-time applica­tions the fuzzy inference engine should be able to perform temporal and progressive reasoning [9, !OJ. For the application of progressive rea­soning all knowledge in the knowledge base can hierarchically be divided in knowledge layers, which are inferenced in a specific sequence. A knowledge layer can be seen as a knowledge base which is an extension of 'lower' knowl­edge layers: every 'higher' knowledge layer con­tains 'higher/deeper' knowledge and 'includes'

the knowledge (static as well as dynamic) of the lower ones.

To make the fuzzy inference engine capable of dealing with fuzzy as well as boolean logic, the following two ways of implementing knowledge are offered:

• rules

• relations

Rules are primarily based on the rules from first­order predicate logic. They have an antecedent, consisting of conditions, and a consequent, con­sisting of actions. The conditions can be com­bined by an intersection (AND) or a union (OR) . The actions are only fired in case the antecedent of the rule is 'not more false than true'. The level 'not more false than true' can be adjusted for each action within a rule. So a fuzzy rule can be implemented by choosing this level equal to false ( 0). The actions in the consequent of the rule can be of the THEN- or the ELSE-type.

Relations on the contrary, are based on fuzzy rules, which are based on a relational idea of im­plication (see section 2). Those relations does not have an antecedent and a consequent but only consist of 'dimensions'. The use of the word 'dimensions' has its origin in the multi­dimensional functions representing fuzzy rules theoretically. This results in a kind of reversible fuzzy rules (see section 2), which can be used by the inference engine to infer one dimension from the rest of the dimensions by applying a intersection on those. For example, a bi­implication as used in first-order predicate logic can be achieved by defining a relation with just two dimensions.

Both approaches influence the 'truthness' (cor­responding with grade of membership in case of in- and outputs) of symbolic statements, for ex­ample 'error is negative big' or 'weather is nice'. Because the system should have a connection to the outside world, a symbolic statement inside the knowledge base can be 'linked' with source code, written in the C programming language. Argument passing by symbolic statements in the knowledge base to the C-code is possible. This offers the ability to reuse symbolic statements like routines and thus limit the number of sym­bolic statements and C-code.

The source code can be used to perform, for ex­ample, classifications of measurements and de­fuzzification of fuzzy outputs of the system. The symbolics in the knowledge base are used to represent the 'dynamic' knowledge, the impli-

1 85

cations and relations are used to represent the 'static' knowledge. The terms 'dynamic' and 'static' are not to be taken literally, because within the knowledge base it is, for example, possible to alter the 'truthness' of actions of im­plications and/or dimensions of relations.

In the application of implications as well as re­lations it is possible to have different interpreta­tions of the intersection and union in the fuzzy inference engine. Several T- and S-norms, like the ones according to Zadeh, Lukasiewicz or probability theory are already implemented, as well as functions for using several 'families' of T­and S-norms [12j are offered. Those 'families' or other, user supplied, types of T- and S-norms can be used in the inference engine to represent the AND- and OR-operation.

Most fuzzy controllers consist of a rule base which has a rule for every symbolic input com­bination possible. The fuzzy rules have classi­fications of the inputs as conditions, and have a classification of the output as action. The rule bases of those fuzzy controllers are normally implemented in the form of a 'matrix'. When quantizations of the inputs are used it is even possible to reduce the complete fuzzy controller to a simple look-up table.

In case of using the fuzzy inference engine it is possible that the conditions of rules are actions of other rules. The first question that arises is: 'what happens with the intermediate results?'. The relevance of this question depends on the way the rule base is composed. Rules with actions which are used as conditions in other rules can be regarded as a kind of short hand notation for implementing more complex rules. In another perspective one can conclude that such a rule actually has defined a new imagi­nary membership function for a specific input. The correctness of this interpretation depends on the conditions and actions defined in the rule. Wether or not the result of the fuzzy inference engine is in agreement with the 'compositional rule of inference', depends on the correctness of the fuzzy rules implemented and the coherence between them.

Another possibility is the fact that a rule does not have a condition for every input avaible, which is however not relevant when assuming the following:

• the antecedent of every rule should imagi­nary contain a classification of every input

• the membership grade of a 'missing' input classification in the antecedent of the rule is assumed 1 (true)

From this point of view, rules are defined for every possible symbolic combination of the in­puts, although not every rule is really individu­ally provided in the rule base. Because 'missing' input classification are assumed to have a mem­bership grade of 1, in fact the union according to Lukasiewicz is applied on all classifications of the input in question, assuming consistent choices of membership functions for those classifications. So in fact a large imaginary rule base is defined which has a fuzzy rule for every situation, but only the relevant parts are actually provided. In this way it is possible to design fuzzy controllers which use different inputs in different situations: the inputs which are not relevant are simply ig­nored by the system.

4 An example

In this section an example is given in which the fuzzy inference engine is used in a control system for the level control of a water column, as shown in figure 1.

i n ter face

pressure sensor

Figure 1: Standpipe used in level control prob­lem.

Although it is a simple control problem, it is sufficient for showing how the fuzzy inference engine can be easily embedded in a simulation and/ or real-time control environment. First we set up the knowledge base as shown in figure 2. The REM-keyword is used for comment (re­marks) . Input as in figure 2 is an easy way of setting up a knowledge base. To do so, two macro's were

1 86

REM the knowledge base as a matrix REM horizontal : error (e) REM vertical : error change (ce) REM e REM ce REM .. P l-row PB P l-row PM P l-row PS P l-row AZ Pl-row NS Pl-row NM Pl-row NB

: NB : NM : NS : AZ : PS : PM : PB

: AZ : PS : PM : PB : PB : PB : PB : NS : AZ : PS : PM : PB : PB : PB : NM : NS : A Z : PS : PM : PB : PB : NB : NM : NS : AZ : PS : PM : PB : NB : NB : NM : NS : AZ : P S : PM : NB : NB : NB : NM : NS : AZ : PS : NB : NB : NB : NB : NM : NS : AZ

Figure 2: FUZZYPI.KB: knowledge base file containing the knowledge base .

defined to transform this to the maximum num­ber of 49 rules, expected by the compiler of the fuzzy inference engine. In the file included by the knowledge base, the two necessary macro's are defined (see figure 3) .

REM a macro for a fuzzy rule REM - Zadeh-type of AND-operation REM - weight/truth value of l (true) REM - logical threshold of 0 (false) DEFINE Pl-rule ZANDRUN error is #1 ZANDRUN error change is #2 PTHENRUN change contol #3 : 1 : 0

REM a macro for a 'row' of the fuzzy rule base

DEFINE P l-row PI-rule NB : #1 : #2 Pl-rule NM : #1 : #3 Pl-rule NS : #1 : #4 Pl-rule AZ : #1 : #5 Pl-rule PS : #1 : #6 PI-rule PM : #1 : #7 PI-rule PB : #1 : #8

Figure 3: FUZZYPI.KI: knowledge include file containing the macro definitions.

The addition RUN to the AND- and THEN­keywords makes the link between symbolic statements and code in the C programming lan­guage. Examples of such links is

LINK(" error is NM" , GRADE = trap(e , -4, -3, -2.5, 1} ; ) ;

LINK(" change control PS" , du_grade [4] = GRADE; ) ;

where the LINK and GRADE are keywords. The LINK-keyword links a symbolic statement with C-code. The GRADE-keyword represents the grade of membership or truthness, which can be assigned a value (in a condition) or which its value can be used (in an action) . The

time(•)

time(•)

Figure 4: Simulation of water level control.

first LINK-statement determines the member­ship value of the error in case of a trapezio­dal (trap(. . . J) membership function, the second stores the grade of truthness, determined by the fuzzy inference engine, in an array ( du._grade[J). This array can be used to determine the crisp value for the control signal change by means of defuzzification. All symbolic statements in the knowledge base can be linked this way, if neces­sary. In this example a total 21 (3 x 7) linkages between symbolic statements and C-code were defined. This could be limited to 3 when us­ing the possibilty to work with argument pass­ing from symbolic statements in the knowledge base to the C-code.

For simulation experiments the fuzzy inference engine was used in a simulation package devel­oped at our laboratory on an IBM-compatible machine (40486DX/33Mhz) . The result of the simulated level control of the water column is shown in figure 4.

In order to perform the real-time experiments, the fuzzy inference engine was used in a simu­lation and real-time control environment, called MUSIC1 [3], running on VAX2-stations. In fact the fuzzy inference engine can be used on any platform where a ANSI-C compiler is available. In figure 5 the results of the real-time experi­ment of the level control are shown.

The example and experiments, as discussed in this section, give an idea of the relation of the developed fuzzy inference engine and the appli­cation of fuzzy control. Fuzzy controllers are easily implemented within a fuzzy inference ex­pert system shell, because they use only a small part of the capacity of such a tool. The advan­tage of a fuzzy expert system shell is the ability to 'add' knowledge, exceptions, demons, etc.

1MU1ti-pupose Simulation and Control. :ivAX is a trademark of Digital Equipment.

1 87

time (•)

time (•)

Figure 5: Real-time water level control.

5 Conclusions

In the perspective of theoretical fuzzy inference, this fuzzy inference engine replaces the 'com­positional rule of inference'. The application of 'standard' fuzzy control can be considered a spe­cial case when using the fuzzy inference engine: it is 'included' . Application of real-time fuzzy control is one of the capabilities of the infer­ence engine, because all necessary features are available like, for example, progressive reason­ing. The use of a fuzzy expert system shell in the application of fuzzy set theory in control, com­bines the advantages of conventional (boolean) expert system shells and the advantages of fuzzy control [6].

The fuzzy inference engine is written in the C programming language according to the ANSI standard. All possible communication between the inference engine and the user can be redi­rected by the user. It allows the inclusion of 'fuzzy expertise' in programs for all kinds of purposes as long as the capability of compiling and linking C-code is available. Implementa­tions have been done in the real-time control environment DICE3 [9] and in the interactive block-oriented simulation and real-time package MUSIC. Applications of the fuzzy inference en­gine in combination with DICE can be found in [6J.

Currently work is carried out on an object­oriented implementation of the fuzzy inference engine in the c++ programming language, which allows knowledge base development in an object-oriented and portable programming lan­guage, resulting directly in fast machine code after compilation. Also work is performed on using the fuzzy inference engine in combination

3Delft Intelligent Control Environment

with the G24 real-time expert system to allow fast and fuzzy inference of the 'lower' parts of the knowledge base.

References [1] S. Aoki, S. Kawachi and M. Sugeno. Appli­

cation of fuzzy control logic for dead-time processes in a glass melting furnace. F\J.zzy Sets and Systems, vol. 38, pp. 251-265, 1990.

[2] M. Brown, R. Fraser, C.J. Harris and C.G. Moore. Intelligent self-organising con­trollers for autonomous guided vehicles. Proceedings of IEE Control 91, pp. 134-139, Edinburgh, U.K., March 1991.

[3] J. Cser, P.M. Bruijn and H.B. Verbruggen. MUSIC: a tool for simulation and real-time control. Proceedings of the 4th IFAC/IFIP Symposium on Software for Computer Con­trol, Graz, Austria, May 1986.

[4] T.J.M. Flintham. Expert systems in con­trol, why so few? Proceedings IEE Control 91, Edinburgh, U.K., March 1991.

[5] C.J. Harris and C.G. Moore. Intelligent identification and control for autonomous guided vehicles using adaptive fuzzy-based algorithms. Engineering Applications of Ar­tificial Intelligence, vol. 2, pp. 267-285, De­cember 1989.

[6] R. Jager, H.B. Verbruggen, P.M. Bruijn and A.J. Krijgsman. Real-time fuzzy expert control. Proceedings of IEE Control 91, Ed­inburgh, U.K., March 1991.

[7] R. Jager, H.B. Verbruggen and P.M. Bruijn. The role of defuzzification methods in the application of fuzzy control. Proceed­ings IFAC SICICA '92, Malaga, Spain, May 1992.

[8] A.J. Krijgsman, P.M. Bruijn and H.B. Ver­bruggen. Knowledge-Based Control. Pro­ceedings 27th IEEE Conference on Decision and Control, Austin, USA, December 1988.

[9] A.J. Krijgsman, R. Jager, H.B. Verbrug­gen and P.M. Bruijn. DICE: a framework for intelligent real-time control. Proceed­ings 3th IFAC Workshop AIRTC '91, Napa (Ca) , U.S.A., September 1991.

[ 10] M. Lattimer Wright, M.W. Green, G. Fiegl and P.F. Cross. An expert system for real­time control. IEEE Software, pp. 16-24, March 1986.

4G2 is trademark of the Gensym Corporation.

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[11] K. Ng and B. Abramson. Uncertainty man­agement in expert systems. IEEE Expert, pp. 29-48, April 1990.

[12] I.B. Turksen. Interval valued fuzzy sets based on normal forms. Fuzzy Sets and Sys­tems, vol. 20, pp. 191-210, 1986.

[ 13] C. Yu, Z. Cao and A. Kandel. Application of fuzzy reasoning to the control of an acti­vated sludge plant. Fuzzy Sets and Systems, no. 38, pp. 1-14, 1990.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

LABORATORY EVALUATION OF FUZZY CONTROLLERSl

R. Babu�ka and P. Hora�ek

Departmenl of Control Engineering, Faculty of Electrical Engineering, Czech Technical University of Prague, Karlovo nam. 13, CS-121 35 Prague 2, Czechoslovakia

Abstract. The paper discuss various possibilities of applying fuzzy set theory in Real-Time control. Three types of controllers are used for comparing their behaviour in control experiments on scale laboratory model of a real dynamic system. The objective of the first experiment is to compare the performance of a fuzzy logic, a PID and an LQ controller in terms of stability, response time and steady-state error in various control tasks. The second experiment evaluates fuzzy logic adaptation of a PID controller, utilizing some heuristic knowledge.

Keywords. Adaptive systems, Fuzzy control, Linear optimal regulator, PID control, Position control.

INTRODUCTION

Fuzzy logic enables us to incorporate human intelligence into automatic control. By means of fuzzy algorithms based on intuition and experience we can easily control highly nonlinear systems or systems which mathematical model of a dynamics is unknown or too complex to be treated analytically. In such cases a fuzzy controller may save a lot of engineering effort and can give better results than classical approaches. Even in systems which are easy to be controlled by means of a classical control theory, one can introduce fuzzy logic to improve the controller performance and, in some cases, to simplify the control algorithm. Thus we have used our Ball & Plate scale laboratory model as a pilot plant. This is a 2 by 2, naturally unstable system. Good results in controlling a ball position freely rolling on an inclined plate by a PID controller could be achieved. But still it is interesting to compare the performance of such a PID controller with a Fuzzy controller, where the control law is expressed by a set of decision rules. Because the rules are simple, transparent and easy to be modified, we are able to experiment with tuning the control rules to tackle the situations where classical controllers do not work properly. This happens

1 This work was supported by the EC TEMPUS programme under contract JEP-0886-91/2.

189

when the plate or the ball are not smooth enough and this stops the object movement. In addition to these two controllers we introduce an LQ controller, where the design is based on algebraic control theory. The "Ball & Plate" apparatus is also well suited for demonstrating the tracking (path­following) tasks. In this case a fuzzy controller can incorporate heuristic knowledge for adjusting the tracking speed according to the path curvature.

FUZZY CONTROL

The basic idea of a fuzzy controller is very simple. All system output signals are fuzzified, that is converted to linguistic variables, characterized by their membership functions. Using these linguistic variables, such as large positive , zero , etc. , a user defines a set of decision rules. These rules have, for example, the following form : If error is large positive and error change is zero then control input is medium positive. Rules are combined to form a decision lookup table. Output mapping of linguistic variables into real numbers corresponds to taking the mean or the median of the membership function. The whole procedure described above can be accomplished off-line. In real-time control only the

lookup table, which maps quantized state space into the control variable values, is involved. Therefore a fuzzy controller may be regarded as a nonlinear PD controller. Sometimes we want to introduce also integral control action. Then the lookup table defines the changes in the control variable. Such a controller is similar to a PI controller. In our case we combine both of these approaches. Two sets of rules and therefore two lookup tables are involved. A block diagram of this fuzzy controller is shown in Fig. 1 . The individual parts of the fuzzy controller implemented for testing will be described in detail.

y.j P L A N T II

Fig. 1 . Block diagram of a fuzzy controller.

Fuzzy sets

Eight linguistic variables (fuzzy sets) are defined: Large Positive (LP), Medium Positive (MP), Small Positive (SP), Zero (ZE), Small Negative (SN), Medium Negative (MN), Large Negative (LN), ANY (ANY). The belongness of an element to a fuzzy set is defined by its membership function. By the default, we use triangular membership functions. User can change the shape of the membership function and its range. Membership functions should cover the whole range of quantization levels. An example is shown in Fig. 2.

.. -6 � -3 -2 ·1 0 1 2 S 4 I e Qulnllzatlan ......

Fig. 2. Fuzzy sets and their membership functions.

Membership function of fuzzy set any equals to 1 for the whole universe of discourse.

190

Input and output guantization

Input values, i.e. error and error change, are quantized into a given number of discrete levels. The number of levels is typically small. In our case we use 13 quantization levels, ranging from -6 to 6, for both the error and error change variables. Limits for individual levels can be defined by the user. This allows testing of different quantization schemes, linear, logarithmic, etc.

Inference algorithm

The inference algorithm involved is simple. The two conditions in the first part of each rule are connected with logical AND, which means intersection of corresponding fuzzy sets. All rules are applied simultaneously, i.e. we can connect them with logical OR, union of fuzzy sets. Instead of taking the maximum we take the mean of the resulting membership functions. In this way we compute values of the control variable for all error -error change pairs to form a lookup table. All computations are carried out beforehand, off-line, and in real time control only quantization is performed and the corresponding lookup table value is applied to the system.

PID CONTROLLER

We use PID controller as the first reference. A modification of a textbook version of a digital PID controller has been implemented as follows

T T t u(k)=K,[e(k)-....!!(y(k)-y(k-1))+-E e(�)] (1) T 7j�-o All symbols in this equation have usual meaning. The backward difference is computed from the current and last value of the actual system output to prevent generation of extremely large control actions, when the setpoint is changed. The tuning procedure is based on classical root locus method, where linearized model of a plant dynamics is used. The problems with setting up the parameters will be described later.

LQ CONTROLLER

To have a wider range of reference controllers, an optimal design method based on Input-Output model has been implemented for design of an LQ controller (Astrom and Wittenmark, 1990). The optimization procedure for the problem given by the process dynamics

the criterion

y(k) = B(q) u(k) A(q)

and admissible controls

u(k) =- S(q) y(k) R(q)

(2)

(3)

(4)

gives the result in the form of the desired position of the closed loop poles. A, B, S and R are the polynomials in the forward shift operator, p is the weighting design parameter. The problem is called spectral factorization. The task is to find a stable, monic polynomial P(z), solving the Eq. (5).

pA(z)A(z -1) +B(z)B(z -1) =P(z)P(z -1) (5)

Ones this bas been solved, the LQ-problem becomes the pole-placement problem. The closed loop characteristic polynomial is chosen as C(z)P(z), where C is considered as the observer polynomial. Thus the Diophantine Eq. (6)

A(z)R(z)+B(z)S(z)=P(z)C(z) (6)

has to be solved. The Eq. (6) has many solutions. The control law that minimizes the criterion is, however, unique.

The LQ controller bas several good properties. It is easy to compromise between the magnitude of the control signal and the speed of the recovery by changing the weighting parameter p in the criterion. The LQ controller will always give a stable closed loop system.

FUZZY TUNED PID CONTROLLER

This controller is based on the idea of on-line adapting PID controller constants according to error and error change values. In this way we can introduce nonlinearities into the controller in order to compensate system nonlinearities such as friction, or to eliminate sensor noise and improve closed­loop system dynamics. Actually we obtain a controller of a higher hierarchical level then the classical PID controller, because it has the ability of using human operator experience. In this case, fuzzy inference engine involves three sets of rules and three lookup tables. Each table adapts one of

191

the PIO controller constant. Input quantization is the same as in the case of a fuzzy controller, output constant represent weights for individual constants. A simplified block of this fuzzy-tuned PIO controller is shown in Fig. 3.

- -

�>-----

• + P I D

�-y_.r----i p L A N T ___ u ______ �

Fig. 3. PIO controller tuned by fuzzy logic.

BALL & PLATE LABORATORY MODEL

The electromechanical model consists of a ball freely rolling on a plate. The sketch description is in Fig. 4.

Fig. 4. Ball & Plate sketch description.

The problem is to control the position of a ball by inclining the plate. System inputs are plate angles,

system outputs are coordinates of the ball. The Ball&Plate system is two by two, naturally unstable system. The simplified block diagram of the system dynamics is in Fig. 5.

P late angle control

Ba l l on P late

x max

[rad]

Fig. 5. Ball & Plate dynamics in x-coordinate.

It follows from the diagram, that the system is nonlinear due to the plate angle servo system, where the stepping motors are used. The most significant nonlinearity, however, has not been included into the formal model at all. This is the imperfect ball shape and plate surface which causes unpredictable "locking" of the ball. Both coordinates of the center of the ball can be controlled independently, because the coupling is negligible. The mechanical core of the system has continuous-time dynamics, the position sensor, CCD camera and frame-grabber, is a sampler and the stepping motors control system is a zero order hold element. From the control computer point of view the system is considered to be discrete in time. Detail description of the Ball&Plate apparatus can be found in the laboratory manual (Babuska and Horacek, 199 1). Because of the natural second order astatism, the use of a PD controller is the simplest solution. The integral action has to be added as well due to nonlinearities described above.

SOFTWARE SUPPORT

Four types of digital controllers described above in general terms, were integrated into an interactive software package. All significant parameters of the controllers can be changed from interactive menus, so the user can easily compare the close-loop performance for various parameter settings. System

192

response can be recorded and stored in a file, for graphical and numerical analysis by means of other package, such is MATLAB. Another software packages of a wider use have been prepared. These are Real-Time Toolbox (Houska, 1992) and Fuzzy Tools (Babuska, 1992), both for MATLAB. The first product enables the user to communicate with the laboratory model directly from the MATLAB environment, the second is a friendly environment for experimenting with fuzzy controllers on a model or in real-time. The software support is used in the instruction process for demonstrations and in practical laboratory sessions.

EXPERIMENTS

Serie of experiments was carried out on the Ball&Plate laboratory model. The aim was to compare the performance of various controllers and their settings, in terms of the response time, stability, steady state error and the overshoot. To assure similar testing conditions for all controllers considered, sudden change in the ball position was generated by the operator.Only the most significant results are presented here and typical features of each controller are briefly discussed. Tuning of a PID and LQ controllers is based on linearized model where stepping motor control is considered as the first order system.

PID Controller

A classical, root-locus method for tuning of a PID controller was used. Supposing the system has the second order astatism, there is no need for assuring high gain in low frequencies. In reality, however, imperfect ball and a plate surfaces as well as friction cause stopping the ball movement even if the plate is not in a horizontal position. The event is unpredictable and hardly to be included into the model. Thus integral term was introduced. Three dominant poles of a closed loop system are driven by the P and D-term and were placed on the same orbit far left from the s-plane origin to meet minimum overshoot and recovery time. The resulting response is shown in Fig. 6.

LO Controller

It is easy to use the LQ-controller design procedure. The polynomial C(z) was set in order the observer to be at least two times faster than the closed loop system characterized by the polynomial P(z). As the magnitude of the controller output had to be decreased, tuning procedure of the weighting parameter p was used. The effect of p ranging from the value of 0. 1 to 1 is documented in Fig. 1 1 . and

Fig. 9. Two versions of LQ design were applied. First it was assumed that the high gain in low frequencies was inherently given by the system

properties. The shape of the resulting response is very good (see Fig. 1 1), but unpredictable steady state error occurs (compare with Fig. 10). To improve the behaviour an integrator was introduced into the controller model during the design stage. The resulting step response is documented in Fig. 12. Large overshoot and longer settling time are significant.

Fuzzy Controller

It should be noted that in the case of our unstable system it is extremely difficult to tune the rules and quantization scales for the fuzzy controller to work properly. On the other hand good performance was achieved with this controller. As nonlinear feedback can be easily introduced, the fuzzy controller can tackle the nonlinear behaviour of the plant, i .e. varying time constant in plate inclination servo system, limits of a ball position, stopping the ball due to the faults in the ball or plate surfaces. Our set of rules, selection of quantization levels and membership functions lead to the response without an overshoot and almost the same recovery time as with a PID and LQ controllers. This is true for various initial conditions. The behaviour near the set point is not very good. The closed loop system oscillates around it. This can be improved by further division of quantization levels. The properties of a fuzzy controller with two different sets of rules are compared with a PID in Fig. 6 and Fig. 7. The comparison with an LQ Controller shows Fig. 9.

Fuzzy Tuned PID Controller

Good performance with this controller was achieved. Using heuristics transformed into fuzzy rules for on-line adapting the parameters, performance of a PID controller has been improved. The adaptation rules are (1) while far from the set point increase the proportional term, (2) approaching the set point, increase derivative term to reduce the overshoot, (3) decrease the integral term during the rise period, etc. The control actions are of course smoother than with pure fuzzy control of a system.

In all graphs the time axis is calibrated in seconds and y-axis in steps (input to the stepping motor control logic), resp. pixels (actual ball position).

193

51

-51

- \ , v .... .,.

... _

--

-181 .....__..___..____, _ __, _ __. _ __. _ __. _ __. _ __. I z 3 .. 5 7 8

Fig. 6. PID versus Fuzzy controller behaviour.

151..---..---..----.,..----.,..----.,--..,--..,---.---,

58

-SI

.. -.

---':/ �..// ·v ....

_ _ _ - � '

-188 '---�-�------------------------__J I Z 3 5 r. 7 8 9

Fig. 7. PID versus Fuzzy with different rules.

1&8 ,...--..---..---...--...--..---..-------

-188 .___..___..____...____...____. _ __. _ __. _ __. _ __, I z 3 .. 5 7 8

Fig. 8. PID versus fuzzy tuned PID.

CONCLUSION

No final conclusions concerning the recommendations for implementing fuzzy logic in control systems will be made as this is very much dependent on the application. In any case detail knowledge and experience with a process to be controlled is necessary. The experiments with fuzzy

control have been introduced into our control engineering courses quite recently, and very good

15•

Fig. 9. LQ (p= 1) versus Fuzzy controller.

2a8.------.,,------.,---.---.----.----.----.-----.-----.

158

-188 ._____.._____..______. _ ___. _ __. _ __._�-�---' I 2 3 4 5 ' 7 9

Fig. 10. LQ (p= I) versus fuzzy tuned PID controller.

15•

Fig. 1 1 . LQ (p=0. 1) versus Fuzzy controller.

194

251

I I 211 I I I 158 \

I 1e9 W1i--cl---�...-:::;....��-=-�-�-=-�-�-=-=-;,.....�:::::,,-==--�

.. _

51

• __ ...... , -

---51

-188 ._____.._____.._____. _ ___. _ __. _ __. _ __. _ __. _ __, I 2 3 1 5 " 7 8 9

Fig. 12 Fuzzy versus LQ controller with integral action (p= 1).

reaction has been received from students. To design a fuzzy controller, students are forced to understand how the controller should behave in different situations and what the situations are. This requires the mapping of a state space and realizing what information of a state of a system is necessary for the derivation of control actions.

REFERENCES

Astrom,K.J . , and B.Wittenmark (1990). Computer­controlled systems, 2nd edition. Prentice Hall, Englewood Cliffs. pp. 366-407.

Babuska,R. and P.Horacek (1991). Ball & plate laboratory model. Report No.3/91 , TEMPUS JEP-0886, Czech Technical University, Prague.

Babuska,R. (1992). Fuzzy tools for MA1LAB. Report No. 1 192, TEMPUS JEP-0886, Czech Technical University, Prague.

Houska,J. (1992). Real-time toolbox for MA1LAB. Report No.2/92, TEMPUS JEP-0886, Czech Technical University, Prague.

Huang,L.J. and M.Tomizuka (1990). A self-paced fuzzy tracking controller for two-dimensional motion control. IEEE Transactions on System, Man and Cybernetics, Vol.20 No 5.

King,P.J. and E.H.Mamdani ( 1977). The application of fuzzy control systems to industrial processes. Automatica, 13.

Li,Y.F. and C.C.Lau (1989). Development of fuzzy algorithms for servo systems. IEEE Control Systems Magazine,April 89.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

SUPERVISORY CONTROL OF MODE-SWITCH PROCESSES: APPLICATION TO A FLEXIBLE BEAM

R.A. Hilhorst*, J. van Amerongen*, P. LOhnberg* and HJ.A.F. Tulleken**

*Control, Systems and Computer Engineering Group, Department of Electrical Engineering, University ofTwente, and Mechatronics Research Centre Twente, P.O. Boz 217, 75()() AE Enschede, The Netherlands

**Department of Mathematics and Systems Engineering, Operational Analysis and Optimization Group, Koninldijkel Shell-l.Aboratorium (Shell Research B .V.), P .0. Boz ]()()], 1003 AA Amsterdam, The Netherlands

Abstract. Many processes operate only around a limited number of operation points. In order to have adequate control around each operation point, an adaptive controller could be used. Then, if the operation point changes often, a large number of parameters would have to be adapted over and over again. This prohibits application of conventional adaptive control, which is more suited for processes with slowly changing parameters. Furthermore, continuous adaptation is not always needed or desired. An extension of adaptive control is presented, in which for each operation point the process behaviour can be stored in a memory, retrieved from it and evaluated. These functions are coordinated by a "supervisor". This concept is referred to as supervisory conlrol. It leads to an adaptive control structure which, after a learning phase, quickly adjusts the controller parameters based on retrieval of old information, without the need to fully relearn each time. This approach has been tested on an experimental set-up of a flexible beam, but it is directly applicable to processes in e.g. the (petro )chemical industry as well.

Keywords. Adaptive control; Automatic tuning; Learning systems; Mode-switch processes; Time­varying systems; Supervisory control.

1. INTRODUCTION

Many processes cannot be controlled adequately by a fixed controller. Then for appropriate control, an adap­tive controller or even a variable controller structure is needed. When the process operates in a limited number of operating points, a limited number of controllers suffices. In practical situations a controller will not only yield satisfactory control performance in the oper­ation point, but also in the neighbourhood of this operating point. The set of operating conditions where one controller performs well, is called a mode. Pro­cesses which frequently return to an earlier seen mode will be referred to as mode-switch processes (Hilhorst et al., 199la). In practice there are several processes which exhibit this behaviour and operate in a limited numberof modes only. Such processes are common in e.g. the process industry and in robotics. For instance, this mode-switch behaviour is encountered in a chemi­cal reactor in which the yield and quality of the product has to be optimized to meet market demands, or in a robot which has to transport a limited number of pay­loads with different masses.

In order to meet the control demands in each oper­ating point, the use of a conventional adaptive control­ler (Astr6m and Wittenmark, 1989) could be considered. However, for mode-switch processes the

195

time needed for adaptation may be too long, i.e. larger than the average residence time in a process mode. For instance, because the closed-loop process signals are not sufficiently exciting. Although the addition of test signals can increase the adaptation speed, it obviously disturbs the process and hence induces performance loss. On the other hand, it seems not to be necessary to repeat the whole adaptation cycle each time the process returns to a certain process mode. The problem is that conventional adaptive controllers forget the useful in­formation which was available before.

A new solution to the problems described above is to exploit the mode-switch behaviour of processes. For this purpose it is attractive to store information related to each previously encountered operation condition in a memory and to retrieve it when necessary. When the process enters a new mode, model identification and subsequent controller design are carried out. The model and the controller together should be stored in the memory. These functions are coordinated by a supervisor. This approach has the advantage that only recognition of the new mode, and no identification of the process is needed when the process returns to an earlier visited recognized mode of operation or when the control criterion has changed. A performance monitor can take care of restarting the adaptation whenever necessary.

In this paper the supervisory control of mode­switch processes will be examplified with an ex­perimental flexible beam (Kruise, 1990) which has to transport different payloads with different masses. The main emphasis is on the detection of new and old modes. The paper is organized as follows. In Section 2 the modeling of the flexible beam is presented. In Section 3 a supervisory structure for detection of new and old modes is discussed. In Section 4 a detailed discussion about mode recognition is presented. In Section 5 the results of applying supervisory control to the flexible beam is shown. These results are compared with robust control. Finally in Section 6 conclusions are drawn.

2. FLEXIBLE BEAM

A good example of a mode-switch process is the ex­perimental set-up of a flexible beam. In this ex­perimental set-up the flexible beam has to transport a number of payloads. This process clearly shows the mode-switch behaviour, as the dynamics change with the mass. This implies that changes in dynamics occur only at the instants of a mass change.

2.1. Description of the process

In Fig. 1 the experimental set-up of the flexible beam is shown.

1.9 m

Fig.1 The flexible beam a) side view b) top view

The link rotates in the horizontal plane and is free at one end. The other end is clamped to the vertical shaft of a DC-motor. A payload can be attached at the free end of the link. The mass of this payload can be varied between 0 and 0.5 kg. The weight of the beam itself is about 1 .2 kg, so the ratio between payload mass and link mass is relatively high compared to other more common robots. Strain gauges are used to measure the bending in the link, and a resolver is used to measure the angle q>b of the motor axis. By use of these meas­urements, the tip angle q>o can be determined.

In a flexible beam with one end mounted to a motor shaft, torsional, longitudinal and transverse vibrations occur. Due to the geometry of the beam (length lb = 1 .9m, width Wb = 4.0 mm and height hb = 60 mm), the torsional and vertical vibrations are small and do not affect the horizontal vibrations

196

(Kruise, 1990). Therefore, only the transverse vibra­tions have to be modelled. Kruise ( 1990) indicated that only the first two transverse vibration modes have to be taken into account to obtain a good model of the process. Kruise showed also that the Coulomb friction can be disregarded for the controller design. In that case, for each payload mass a suitable linear model M; can be obtained. This linear model of the flexible beam is given by

q = (/ + F)-1 ( a,,tpb - Rq - W q)(vibrat. modes) (2. la)

<i>b = KaU - �bq (motor) (2. lb)

'Po = q>b + (q1 - qz)llb (tip angle) (2. lc)

where O.b is the coupling vector from base angle to bendings, �b is the coupling vector from bendings to base angle, q>b is the base angle, q>o is the tip angle, F is the coupling matrix between vibration modes, I is the unity matrix, Ka is the motor constant, lb is the length beam, q is the vector of vibration modes [q1 qz ]T. R is the diagonal damping matrix, u is the control signal, u � 151V, and W is the diagonal matrix of resonance frequencies. For the description of the various matrices, the reader is referred to Kruise (1990, page 49-50). The matrix F and vectors O.b and �b are dependent on the payload mass mp. For instance, when no payload is attached to the tip, the matrix F=O. In that case there is no direct coupling between the vibration modes, because R and W are diagonal.

: -' ' ' ' o.----JUiLPL.· :+ ' ' ' ' ' ' ' � - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ---· Fig. 2 Block diagram of beam for the new choice of

states The states are given by x = [ q>b q q] T. In order have a correct simulation of the system (2. 1), the dynamics of the beam were integrated once. This results in the state-vector x = [ q>b q itl T, where

ii = r q('t)d't (2.2) 0

In Fig. 2 a block diagram of the flexible beam for this choice of the state vector is shown.

3. SUPERVISORY CONTROL

The control objective is to realize a fast settling time and no overshoot of the tip for a limited number of different payloads of different masses. If the payload

mass can be measured or if it is known in advance, by use of a look-up table it can be searched whether this payload has been transported earlier or not. If the pay load has not been transported earlier, a model ident­ification cycle can be started and subsequently a con­troller can be designed. The controller can be stored in a memory together with the payload mass. Sub­sequently, the controller is installed in the closed loop. If the payload has been transported earlier, the related controller can be retrieved from memory.

When the payload is not known and cannot be measured this gain scheduling approach is inapplic­able. Another approach is to detect whether the process behaviour has changed, based on the available signals. If the present behaviour corresponds with the beha­viour of one of the models in the memory, the control­ler related to that model can be retrieved and installed in the closed loop. If the performance of this controller is still insufficient, then probably the mass transported by the beam is new. Hence then learning has to take place. This implies that a model of the beam with this payload mass is constructed and added to the memory. Subsequently a new controller is designed and in­stalled in the closed loop. The monitoring of the closed-loop performance is carried out by a perfor­mance monitor. Based on the performance criterion stated by the user and on the measured performance, a supervisor can detect whether the closed-loop control performance is adequate or not In the latter case, the supervisor will propose to start a new identification cycle. The introduction of a performance monitor and supervisor results in a third feedback loop, as is shown in Fig. 3. The performance monitor, supervisor, mode detector and memory together form the supervisory structure.

y

Fig. 3 Control system with supervisory structure

Figure 3 shows that the lower loop is the normal process feedback loop, which consists of a feedback controller and the process. The second loop is the adaptation loop, which consists of mode detector, memory and controlled system. Based on the-mode i detected, controller C; is selected from the memory and installed in the closed loop. The third feedback loop is the learning loop, which consists of perfor­mance monitor, supervisor and memory. Based on the measured performance and on the performance de-

197

mands, the supervisor adds models to the memory or changes existing models.

4. MODE DETECTOR

4.1. Definitions and goals

Mode recognition is the task of identifying the current mode of operation. Mode-switch detection is a sub­sequent task, which establishes whether or not the current process mode differs from the previous process mode. These two tasks are performed by the mode detector shown in the supervisory structure of Fig. 3. On the basis of the information provided by the mode detector, the supervisor decides whether the controller parameters should be adapted. If the method is quick in detecting mode switches, then noise may often give rise to wrong detections. On the other hand, if the method is insensitive to noise, mode switches may not be detected fast enough. As both situations are unde­sirable, a good balance between noise sensitivity and mode tracking is called for.

Finally, when the mode detector establishes a mode switch, the controller parameters should be adjusted. In order to prevent bumps in the control signal, bump­less transfer was applied.

In order to apply this idea to the mode recognition problem, a distinction has to be made between finite mode-switch processes, i.e. processes which can be described by a finite number of linear models such as the flexible beam, and generalized mode-switch pro­cesses which can be approximated by a finite number of linear models. In this paper we restrict ourselves to finite mode-switch processes. For a description of generalized mode-switch processes is referred to Hil­horst (1992).

4.2. Mode recognition

For a good balance between noise-insensitivity and mode-tracking, effective use can be made of the ideas developed by Fortescue et al. (1981) in the field ofleast squares estimation. Furthermore, in order to make a good distinction between the models, the models were run in a series-parallel structure with the process. The approach taken has similarities to the approaches taken by W illsky ( 1976), Isermann ( 1984 ), and Tz.afestas and Watanabe ( 1990) in the field of process fault detection. However, those approaches have severe drawbacks as described by Lund et al. (1991) like mode-track stop­ping and lack of distinction between the different mod­els. These disadvantages have been eliminated in the method proposed here.

If a finite mode-switch process P is in mode i, and if a Gaussian measurement disturbance 'I' is present

with variance � , then the process output y at time instant k can be written as

/\· Yk = Yk + \jfk (4. 1)

/\. where Yk is the output of model M;. For each model

i /\· M;, the error ek between model output Yk and process output Yk can be determined, i.e.

• A· ei= Yk- yi (4.2)

When the process is in mode i, the error ei is equal to the measurement disturbance, i.e.

ei = 'Ilk The expected norm of the error ei is given by

E llei 112 = E {<ei l<ei >}

(4.3)

= 1�· if process is in mode i (4.4) cif + �. otherwise

where cif is the additional variance due to the model error between the process and model M; • Equation (4.4) shows that the expected norm of the error is minimal for the modelM; related to the current process mode i. Hence, one straightforward method for mode recognition is by weighting the sum of errors and to select that model Mi for which the sum is minimal. This can be done by defining a distance d(P ,Mi ):

d(P .Mi ) = I:i (4.5)

where the weighted sum of squared errors

tl = Ak(I:i-1 + (ei lei ) (4.6)

with 0 < Ak � I the forgetting factor, and � = 0. The effective number of samples taken into account at an instant k is referred to as the memory length x,t. which is given by

Xk = A.I: (Xk-1 + 1) (4. 7)

with Xo = 0. The expectation of the distance between process P and model Mi at time instant k is given by

E {d(P .Mi )} = E { i:i} = !Xk �. if process is in mode i (4.8)

Xk <cif + �). otherwise Equation (4.8) shows that the smallest distance d(P ,Mi ) will converge to Xi �. Hence, the heuristic idea of Fortescue (1981) can be applied to the mode­recognition problem by keeping the sum i:i constant for the model with minimal sum tl. In the case of weighting both old and new information, the sum i:i can be kept constant at target Lo by selecting the forgetting factor

Ak = i:i-1 + (ei l<ei )

(4.9)

Astrl5m and Wittenmark (1989) motivate that it is required that

0 < 1..k � I (4. 10)

Because (ei lei �. it follows from (4.9) that this condition is fulfilled by I:i-1 2:: Lo (l��). In order tohaveI:i-1 2:: Lo ( l��n), r.b = O (l��). and l..t is taken equal to I till i:i-1 > Lo ( l�i�n).

198

By the use of the forgetting factor (4.9), the sum tl is kept constant In contrast, the sum I:{ of all other models is variable and may become smaller or larger than the sum i:i. If a switch from mode i to mode j occurs, then the error ei will increase, and simulta­neously the error d will decrease. Equation (4.9) shows that an increase in error ei results in a small forgetting factor and hence in a small memory length. Due to the drop in memory length and the fact that d is smaller than ei , the sum r4 will rapidly decrease and become lower than the sum i:i . A mode switch is detected at the time instant k at which I:{< U. At that time instant k, model Mj should be selected as the best model, and accordingly the sum i:{ of squared errors should be kept constant This is performed by taking the new forgetting factor Ak equal to

Ak = i:i-1+(d led ) (4. 1 1)

This mechanism guarantees an effective balance be­tween mode-tracking and noise-insensitivity.

4.3. Series-parallel structure

A· Until here the computation of yi was not discussed. One method to compute these predictions is to make use of the series-parallel structure. In MRAS literature (Landau, 1979) this structure is called the series-paral­lel structure, because the reference model (in this case the process model) is placed partly in series with the process and partly in parallel with the process. The advantage of this structure is that drift in the model states can be avoided by regular resetting of the model states to the process state. This is performed by select­ing an appropriate observation period To . The choice of the observation period To will be process-dependent and will therefore be discussed in more detail in section 5. 4.4. Mode-switch and bumpless transfer

Once the mode detector has detected a mode switch, a switch between controllers has to be made. At the instant the parameters of the controller are adapted, a bump in the control signal may be introduced. Bumps in the control signal are unwanted and therefore should be removed. This can be done by applying a bumpless transfer algorithm. In this paper bumpless transfer is established by the use of an integrating action with a leakage (Hilhorst et al., 1991b). By taking the leakage time constant (bumpless transfer time constant) 'tb

equal to an appropriate value, for instance related to the bandwidth of the control loop, the control signal remains smooth.

5. EXPERIMENTS AND RESULTS

5.1 Experiment design

In order to show the applicability of supervisory con­trol, three experiments with the flexible beam were

carried out. In the first experiment, a step from -90° to 90° was applied as the reference signal q>r for a payload mass mp = 0.0 kg. This experiment was repeated for payload masses mp = 0.25 kg and mp = 0.5 kg. The control objective is to realize a fast settling time and no overshoot of the tip for each payload mass.

In order to meet this goal for each of the payload masses, the mode centres were selected equal to the payload masses, i.e. ro1 = {o}. 002 = {0.25}, and 003 = {o.5}. For each of these mode centers a linear model M; was obtained by taking the parameter mp equal to (l)j •

In order to meet the control criterion, Kruise shows that a PIO-like controller for the motor axis only is insufficient, and that a slate-feedback controller is appropriate. The state-feedback controller is described by U = -K(X - Xr) (5.1)

where K is a row vector of control gains, x the process state, and Xr is the desired state. The control gains can, for instance, be found with the pole-placement method.

5.2. Real-time requirements

In order to apply the mode-switch concept to the prac­tical set-up, real-time requirements have to be met. strm and Wittenmark (1989) give a rule of thumb for the selection of the sampling interval Ts . Based on the natural frequency of the dominant closed-loop pole (i.e. 34 rad/s), the sampling interval should be selected between 0.003g's�0.015.

The implementation of supervisory control must be such that these real-time requirements are met. This is performed by exploiting the natural parallellism (Bak­kers and Van Amerongen, 1990) in the mode-detection scheme. A PC (286) and a transputernetwork with four T4's have been used. On each transputer one of the three models was run, and on the fourth transputer the mode-recognition algorithm. By the use of the trans­puter network a sampling interval Ts = 0.006s could be reached.

5.3. Experimental results

Sufficient distinction between the models could be realized with an observation period To of 0.06s (= lOxTs). The asymptotic memory length Xoo was se­lected as 40 samples (that is four times the observation period length T0). The variance � of the noise was 10-4. As a result the target Lo was taken equal to 0.004. At the end of an observation period, the controller related to the model with the smallest distance to the process was installed in the closed loop. Deactivation of the old controller and substitution of the new con­troller occurred by using the bumpless transfer algo­rithm described in Section 4. The bumpless transfer parameter tb has been selected 0.065 s. This is about twice the inverse of the natural frequency of the fastest closed-loop pole. The results obtained with the modc­switch controller were compared to those of a fixed

199

controller designed for a payload mass of0.5 kg, which shows no overshoot for all different payload masses between 0 and 0.5 kg. This controller is referred to as the robust controller.

The results obtained from the experiments with payload mass mp = 0, 0.25 and 0.5 kg are shown in Fig. 4 and 5 and 6 respectively. Figure 4 shows that the application of supervisory control results in a shorter rise time and a shorter settling time of the tip angle response compared to the robust controller. This is caused by the fact that the robust controller yields a smaller control signal than the controller Ct which is optimized for the beam with no payload. Figure 4 also shows that in the beginning (i.e. �0.25s) and at the end (i.e. t0!:3.0s) wrong models are selected. Further­more, after time instant 4s model MJ is continuously selected.

The wrong detection at the beginning can be ex­plained by the non-minimum phase behaviour of the different models and the process. Singh (1991) showed that this non-minimum phase behaviour is present in the model related to no payload. He also showed that the non-minimum phase behaviour decreases with in­creasing mass. However, the real tip response of the beam with no payload shows almost no non-minimum phase behaviour. Therefore, the models related to pay­load masses 0.25 and 0.5 kg are selected in the begin­ning.

The wrong model selection at the end can be ex­plained by the Coulomb friction. Figure 4 shows that after time instant 4s due to a small steady-state error, the control signal u is slightly larger than zero. Because of the presence of the Coulomb friction, a small control signal cannot accelerate the beam, and hence the tip position remains constant. Simultaneously, due to a non-zero control signal, the linear models predict that the link would accelerate. As the predicted amount of acceleration decreases with increasing mass, the tip position of model MJ related to the largest mass will be closest to the measured tip position. Hence, model MJ is selected at the end. From this experiment it can be concluded that a good model selection can be made only when the link moves.

Figure 5 shows that compared to the robust control­ler, the application of the mode-switch controller for the beam with payload mass mp = 0.25 kg results in a shorter rise time and shorter settling time of the tip angle response. Hence, the control performance is improved by supervisory control.

Figure 6 shows that both the control signal and the tip response obtained with supervisory control are equal to the ones obtained with the robust controller. 6. CONCLUSIONS

In this paper the concept of supervisory control was the basis for a novel method which can be seen as an attractive alternative for both robust control and con­ventional adaptive control for mode-switch processes. By the use of the mode concept, a controller is obtained which behaves less conservative than a robust control­ler, and which has the ability to adjust the control

l [VJ

4

2 l [VJ 2 l

[VJ 2

11 ;·�'"'"··�· .. : ... ... , . . . . . u u 0 0 0

-1 '------------' 100 ....-----------,

-1 '-----------� 100 ...-------------,

-1 '-----------�

100 ..-----------, .. .

l 0 l 0 [tleg] [deg] [tleg] • -50 0 • -50 0 • -50 0

-100 -100 -100 4 4 4 3 3 3 l l l 2 2 2

Mi 1 Mi 1 Mi 1 0 0 0 0 5 0 5 0 5

t [•] -- t (•] -- t [•] -

Fig.4 Responses with mass 0 kg Fig. 5 Responses with mass 0.25 kg Fig. 6 Responses with mass 0.5 kg u = control signal of supervisory controller (solid) and robust controller (dotted) Cj)o = tip angle using supervisory controller (solid) and robust controller (dotted) M; = model selected (associated with mode)

parameters fast using process knowledge more effec­tievely than a conventional adaptive controller does. The main problem in this approach is how to detect a mode switch. Various alternatives were considered and tested. The newly developed method of exponen­tial forgetting dedicated for the use on (finite) mode­switch processes has been demonstrated by real experiments.

In this application, supervisory control of the flex­ible beam results in a better overall performance than what is achieved with a fixed linear controller. That is without overshoot the settling time was smaller and even near minimum time. Problems of measurement noise and Coulomb friction could be solved by adequ­ate tuning of the detection method. The results show that fast adaptation of control parameters can be ob­tained without deliberately disturbing the process. Therefore, supervisory control should be used as a standard procedure for such processes. Because of the motivation given in Section l , this conclusion is ex­pected to hold more generally and might extend to the petrochemical processes as well.

REFERENCES

Astrom, KJ. and B. Wittenmark, (1989). Adaptive control, Addison Wesley, New York.

Bakkers, A.W.P., and J. van Amerongen, (1990), Transputer Based Control of Mechatronic Systems, 1 1 th IFAC World Congress, Talinn, Estonia, USSR, Vol. 7, 128-133, Pergamon Oxford UK.

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Hilhorst, R.A., J. van Amerongen, P. LOhnberg and HJ.A.F. Tul­leken, (1991 b ), Neural Network Based Control of Mode-switch Processes, Proceedings of the IFAC Conference ADCHEM'91, Pergamon, Oxford UK.

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Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

KNOWLEDGE SPECIFICATION AND REPRESENTATION FOR AN " INTELLIGENT"

INTERFACE DEVOTED TO PROCESS MONITORING AND SUPERVISION

E. Le Strugeon, M. Tendjaoui and C. Kolski

Laboratoire d'Automatique lndustrielle et Humaine, URA CNRS 1118, Universite de Valenciennes et du Hainaut Cambresis, B.P. 311, Le Mont Houy, 59304 Valenciennes Cedex, France

Abstract. This paper presents our approach of cooperation between a human operator and a decision aid tool by means of an "intelligent" interface manager : the Decisional Module of Imagery (D.M.I.). �e "heart" of the D.M.I. is an expert system which manipulates three mam objects (the WHAT, WHEN and HOW objects) described next. Knowledge specification and representation for the expert system, and the way we chose to implement it, are then explained.

Key words. Process control, man-machine systems, expert systems, knowledge engineering, inference processes.

INTRODUCTION

The increasing complexity of industrial processes necessitates the design of control, supervision and decision support tools that are able to evolve along with the control system. In such conditions, the man­machine interface plays a vital role where the information being manipulated becomes more and more complex i.e. safety systems, production control systems and environment protection systems (Rasmussen, 1986 ; Sheridan, 1988 ; Millot, 1988, 1990).

In a way to improve the co-operation between the human operators and the decision aid tools in the control rooms of industrial processes, our work concerns us with the study of an "intelligent" interface, and is aimed at realizing such an interface supervised by an "intelligent" manager called the D.M.I. (Decisional Module of Imagery). Our approach consists of using an expert system to ensu�e this co-operation (Tendjaoui and others, 1990). It is currently validated in the laboratory and is integrated into an experimental platform. The objective is to compare the operator's behavior with his performance wether an ordinary or "intelligent" interface is being used. This comparison is done by using a set of failure scenarios.

This paper describes first the D.M.I. and the objects manipulated by this approach of "intelligent" interface. Then we explain how the "heart" of the D.M.I. is implemented using artificial intelligence techniques.

201

THE DECISIONAL MODULE OF IMAGERY

Our approach is tailored to the area of supervisory process control. It's goal is to design an intelligent imagery manager called "Decisional Module of Imagery" (D.M.I.). This approach can be integrated into the global model of the Man-Machine system in automated process control rooms to obtain an overall assistance tool (figure 1). The supervisory calculator centralizes the whole process scored data. These data are accessible by both the decision support expert system and the D.M.I. Using this data, the decision support expert system infers information such as predictive, diagnosis or recovery procedures. This set of information is transmitted to the D.M. I., which selects those that can be presented to the operator. This selection is based on a task model to be performed by the operator, and on "operator" model containing information about the operator.

The task model is currently restricted to problem solving tasks and results from a previous analysis of fixed tasks which have to be performed by the opera­tor. This model is based on the qualitative general model of Rasmussen ( 1980). Whereby a task is built through four information processing steps : event detection, situation assessment, decision making and action. This task model contains a set of process significant variables used by the operator while performing his different tasks.

The operator model integrates a set of ergonomic data which is presently limited to : (i) three possible levels of expertise for the human operator (unskilled, experienced, expert), (ii) the type of displays associated to each of the operator's cognitive beha­vior, corresponding to Rasmussen's model, (iii) the

PROCESS

Acquisition Module

DECISION SUPPORT SYSTEM ---

Process model

I Tusk model

ommand Module

HUMAN OPERATOR

Ergonomic Graphical Dase

"What" "When" "How" Knowledge Knowledge Knowledge Base Base Base

Assistance system L �M.:.�: -Operator model

- - - - _, - - - - - - - - - - - - - - - - - - - -

Fig I . Global Man-Machine system integrating the Decisional Module of Imagery (Kolski and others, 1 99 1 )

representation mode associated to each type of display.

The aims of the D.M.I are : (i) to select the data that can be displayed on the screen taking into account both the operational context of the process and the informational needs of the operator, in order to enable the operator to supervise the process and to define possible corrective actions when a failure appears; (ii) to define the ergonomic parameters associated with presentation of this information in order to make the human operator's understanding easier; (iii) to add to this supervisory imagery the corrective advice given by the decision support expert system in order to justify its reasoning and thus to prevent possible conflicts between the system and the human operator.

THE OBJECTS MANIPULATED BY THE "INTELLIGENT" INTERFACE

Information " intelligent" selection is based on a model of the tasks to be performed. Alternatively the selection may be based on an operator model containing knowledge of the three ergonomic considerations shown in figure 2 (Tendjaoui and others, l 99la, 1991 b) : (i) What to present to the operator (we consider here that "what" contains the "why" by justifying the information displayed); (ii) When shall we display it, (iii) How shall we display it.

An ergonomic data base centralizes all the presentation modes that can be selected and displayed by the graphics module. This graphics module is controlled by the inference mechanism through a shared memory whose access is controlled by a supervisor. The D.M.I. is developed using the "C" language on a V AXNMS. The software hierarchy is

202

described in more details in a paper by Tendjaoui and others ( 1 99 1 b ).

The "What", "When" and "How" problems are described below.

The "WHAT" problem

The problem concerning what is to be displayed to the operator depends essentially on three criterion :

Operator reguests. If the operator, when performing his supervisory tasks, requests information on for example, the state of a variable or to justify an action, then the D.M.I . has to supply this information.

Operator classification. If the decision support tools perceive an error in the system and propose advice or action, the operator can (i) be in agreement with this advice and act accordingly or, (ii) disagree and request some justification for the advice. The level of detail in this justification will depend on the operators skill level, e.g., a novice operator will tend to require more detailed justification than an experienced operator.

The operators task in relation to different process operations. The operators tasks and therefore his informational needs will change according to the state of the process. For example, in a transition situation, the operator may need some advice on starting the process, whereas to assess the effects of a corrective action, the operator needs information about the progression of the correction. During an abnormal process state, alarms are automatically selected and displayed, but where an "uncommon" abnormal situation develops, the D.M.l. can focus on variables that can affect the production and/or the security of the system, by suppressing all

information or alarms that do not affect either production or safety.

OPERATOR'S

REQUESTS

OPERATOR'S

TASK

OPERATOR

SKILL UlVEL

SITUA"l10N SEVERJTY I

- - - _ I

ERGONOMIC GRAl'IUCAL DATAllASE

Fig. 2. The "What - When - How" concept

The "WHEN" problem

The problem concerning "when" re levant information has to be presented to the operator depends on the nature of the information that he requested and also on the seriousness of any impending situation. Severity evaluation is bound by production targets and security constraints. To know when the D.M.I. has to display information, we first have to know what this information actually represents (the "WHAT"). For example, alarms are displayed to the operator as soon as they occur, whereas information on action or advice proposed by the decision support tools is only displaye? to �he operator when requested or when a process s1tuat10n becomes hazardous.

The D.M.I. has, however, to evaluate the mental workload of the operator in order to determine whether any additional information could be adequately assimilated by him. Mental workload depends on many factors, e.g. , the number �f potential hazardous situations encountered, their severity, the operators skill level, and so on.

The "HOW" problem

To know how to present a piece of information �o the operator, we first have to know what this information represents and the severity of the process fault at that moment. Info�mation is th�n displayed in accordance with predefmed ergonomic modes (figure 2). If several different presentation modes are available to the operator which can be used with the same efficiency, then he can configure the interface according to personal preferences. Some examples of "HOW" are : (i) to indicate the progression of a variable duri�g the p�ocess, graphical curves might be. appropn�te (they. mform the operator about trends m the vanables h1.sto�y) ; (ii) color, red for example, can be used to md1cate process status.

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KNOWLEDGE SPECIFICATION AND REPRESENTATION FOR THE "INTELLIGENT" INTERFACE

The "heart" of the D.M.I. is an expert system which is in charge of giving to the supervisor means for controlling screen displays. Its function is, more precisely, to give answers to the three questions WHAT, HOW and WHEN (described earlier). Several methodological and technological choices were necess ary to be made before any implementation of the expert system .

Knowledge specification and representation

A first choice, the most important of all, is the choice of the knowledge specification. The expert system needs some knowledges defining the current state of the paramete rs .Those parameters characterize, on one hand, the supervised unit and, on the other hand, the operator that supervises this unit. The problem is to decide what is the knowledge required by the expert system to give interesting results. That means, in a more technical way : to choose the facts that will be manipulated by the expert system.

Nine facts are currently used to represent parameters characterizing both supervised process and human operator : the facts "Functioning_situation" , " S i t u a t i o n_ s e v e r i ty " , " Op e ra t o r ' s _ ta s k " , "Operator's_class" , "Operator's_request", "What" (must be displayed), "Previous_ what" (was displayed at the last step), "When" (the screen modifications will occur) and "How" (which type of display). These facts are interdependent. They are multi­valued : they may have several values simultaneously because they are used in the management of the screen displays on which more than one change can occur at the same time. In example, in an abnormal situation of the process, the supervision being made by a novice operator, the system may have to display, in the same time, a view showing the evolution of the variables and a view with acts advices. In that case, two answers are given to the question (WHAT) : "What must be presented to the operator ?". Three of the nine facts group together the results given by the expert system after inferences : the facts WHAT, WHEN and HOW. The rules base is split up into three "sub-bases" corresponding to those three results facts.

To allow associations between a fact and a value in a coherent way, an annex data base, called "Possible Facts Base", was created. It is used to check the validity of such associations. It contains all of the possible values for each fact. Its structure is identical to the established facts base's one. In example, the further information can be found in it : the fact "Factl " can take the values A , B and C. The association between Factl and value D would be recognized as disabled.

The data structures for the facts bases and for the rules base are illustrated in figures 3 and 4. Both of

FACT1

RULE1

value1 value2

value1 value2

value1 value2 value3

Fig. 3. The facts data base

conclusion1

value value H - condition1

value value

Fig. 4. The rules data base

- Task analysis Set of descriptors - Process and decision census characterizing the

tool analysis 11--------1.+ man-machine - Ergonomic of each

considerations concepts values system

Leaming examples database

D.M.I.'s database • "WHAT" • "WHEN" • "HOW"

Compiling Optimized decision

tree

Fig. 5. Method for constructing the knowledge data base (Tendjaoui and others, 1 991 a)

these structures are based on the "chained lists" technic. So, the facts base is represented by a variable of the type "facts list pointer". Each cell "fact" of the list contains another list with its current values.

solved is the kind of inference to implement to run the inference engine : data or goal-driven inference ? In the D.M.I. context, the data-driven inference seemed to be the most adapted. There are two reasons for that : (i) the searched goal is to establish a maximum of facts and to deduce all of the values that it is possible to deduce for one fact, (ii) a lot of rules have an identic conclusion, that is why the time needed by a goal-driven research would be too important.

In the same way, the rules base is represented by a pointer on a chained list of rules. Each rule is composed of a conditions (or premisses) list and a conclusions list. Conditions, like conclusions, are of the type "fact" (described in the appendices), excepted that a single value is associated to each of them. Examples of rules are given in appendices 2.

The kind of inference

A second development choice purpose is the inference mechanism. The problem that must be

204

Methodoloe;y for building the rules

A third choice concerns the way to build and handle the rules data base. "One of the attraction of the expert system approach lays in the possibility of "teaching" progressively the initial system in revising or completing the knowledge base put at its

disposal." (Farreny and Ghallab, 1 987). For all that, it is essential for the rules base to be easily modifiable, aiming at a progressive refining. Some rules are added, deleted or modified to improve, step by step, the rules data base. In that goal, the software FirstClass is used as described in the figure 5.

With a set of descriptors (characterizing the simulated process) and a set of examples, the software FirstClass generates a decision tree, by the use of the Quinlan's induction algorithm "ID3" (1979). That tree describes an hierarchy among descriptors. Although such a tree is "readable" by humans, it is not yet exploitable in that shape by the expert system. Actually, the E. S . uses production rules formed on the model : IF conditions THEN conclusions. The decision tree must be modified to become understandable for the expert system. This modification (or "compilation") of the tree is described now.

The technique used to translate decision trees into production rules is based on syntactic analysis. The program that "reads" the decision tree and produces the corresponding rules is a kind of "transducer" or "compilator" : it translates the tree written in a particular format (a language we called LI ), into rules written in another format (a language we called L2) . The compilator makes the operation of translation T such that : T(LI )=L2. The grammar used to specify the language LI is described in appendices 3.

The compilation module is composed of four important functions (the functions P, S, T and C) that correspond to the left members of the derivation rules. With a stack system and with pointers, the tree from FirstClass is "deciphered" and the production rules are built in an useful format for the expert system . This operation is repeated three times in order to build the three modules of the rules base (the modules "WHAT", "WHEN" and "HOW"). All the rules owning to the module "WHAT" have, in the conclusion part, a descriptor as followed : WHAT = a value . Both others modules are built the same way. In the actual advancement state of the D.M.I., the rules base is composed of 335 rules for the three modules.

That methodology has several advantages :

1 . Data (descriptors and examples) are easily modifiable.

2. To create or modify the rules base, the reflection medium is not production rules, but examples which are far closer to the natural way of reasoning than rules.

3 . The obligation to input the values of all descriptors for every examples is more an aid than a constraint. It imposes to define very precisely each of the particular cases that are the examples, because all of the parameters must be specified, even those that are not taken into consideration. So, if the descriptor A does not take place in any way in a given situation, that must be specified.

205

4. If in a particular situation, no solution has been proposed (the required example does not exist in the input data) the software FirstClass reports "no-data". It allows to reveal lacks that can exist among rules. One has to notice, however, that all possible situations do not have to be described as examples in an exhaustive way.

5 . With FirstC!ass, input examples can "run". It is like a guided route in the decision tree. It allows to check quickly if a specific situation is specified in the examples set and if the end result (which is a leaf of the tree) is the previewed one.

With this methodology, it is possible and easy to add, retry and modify elements of the rules base, to adapt and adjust the system to our needs. A simple methodology was also used in order to facilitate changes that may occur among the set of facts and values that are associated to them. Facts names are written in a file which is modifiable with a classical text editor. In the initialization step, the system just reads that file to update the Possible Facts Base.

Justifying the expert system's reasoning

Finally, the subject of the last choice is the justifications of the expert system reasoning. During the adjusting stage of the D.M.I. , the rules base is being modified (refereeing to last paragraph) because solutions given by the expert system are not always the best that could be expected. It is important to know in detail the inference course that leads to the imperfect result.

The expert system thought process must either be justified to the operator to allow him to understand why such answers are given by the system and, on that foundation, be able to decide if his own argument is correct.

So as to justify the expert system logical line of reasoning, some data are memorized : the initial context (like a photography of the facts base before any inference), the numbers of the activated rules and the final context (the current state of the facts base after the inferences). These informations are stored into memory. With this trace, the operator can understand which knowledge was brought into operation to deduce new facts and get out his conclusions about it. Actually, some explanations are very useful if operator and machine do not agree on what have to be done to solve one particular problem. They allow to solve potential clashes.

CONCLUSION

This paper submitted our works contributing at the "intelligent" interface notion, in the field of complex process control. We focused here on the way by which the "heart" of the interface is implemented with the help of artificial intelligence techniques. The management of the interface displays is condensed in the three questions WHAT, WHEN and HOW, to which the expert system gives the adequate answers. Now and in order to validate this approach, we are implementing a testbed. The results of that

experimental step will be the subjects of other articles.

REFERENCES

Farreny, H. and M. Ghallab ( 1 987). E lements d'intelligence artificielle. (Ed.) Hermes, Paris.

Kolski, C., M. Tendjaoui and P. Millot ( 1990). An "intelligent" interface approach. The second International Conference on "Human aspects of advanced manufacturing and h yb r i d automation", Honolulu, Hawaii, USA, August 12- 16.

Millot, P. ( 1 988). Supe rvision des procedes automatises et ergonomie. Editions Hermes, Paris, Decembre 1 988.

Millot, P. ( 1 990). Cooperation homme-machine : exemple de la teleoperation. Journees du GR Automatig,ue, 1 7- 19 Octobre 1 990, Strasbourg, France.

Quinlan, J.R. ( 1979). Discovering rules by induction from large collections of examples. In D. Michie (Ed), Expert systems in microelectronic Age, Edinburgh University Press.

Rasmussen, J. ( 1 980). The Human as a System Component. In "Human Interaction with computer" , H. T . Smith and T.R.G. Green (Editors), London Academic Press, 1 980.

Rasmussen, J. ( 1986). Information processing and human-machine interaction. An approach to cognitive engineering. North-Holland series in system science and engineering, (Ed) A.P. Sage.

Sheridan, T .B . ( 1 988) . Task allocation and supervisory control. In "Handbook of Human­Computer Interaction", M. Helander (ed.) , Elsevier Science Publishers B .V. , North­Holland, 1 988.

Tendjaoui, M., C. Kolski and P. Mi llot ( 1 990). Interaction between real-time aid expert system, intelligent interface and human operator. International Symposium Compu tational Intelligence 90 "Heterogeneous knowledge representation systems", September 24-28 , Milano, Italy.

Tendjaoui, M., C. Kol ski and P. Millot ( 1 99 1 a). Knowledge based interface approach for real­time aid expert system. IFAC/IMACS "SAFEPROCESS'91 " Symposium, September 10- 1 3, Baden-Baden, Germany.

Tendjaoui, M., C. Kolski and P. Millot ( 1991 b). An " intelligent" approach for ergonomic design of Man-Machine interfaces in process control. International Journal of Industrial Ergonomics, 8, 345-361 .

APPENDICES

1 . Implementation

The type "fact", written in C, is implemented as followed :

typedef struct fact { word name ;

*I

pt_value Iist_of_values ; struct fact * next ;

} fact, * pt_fact ;

/* name of the fact */ /* values list of the fact */

/* pointer on the next fact

206

2. Examples of rules

IF AND AND AND THEN AND IF AND THEN

IF AND AND THEN

Operator_Class = 3 Severity = 2 Request = No_Request Situation = Abnormal What := Actions_Plan What :=Deep_And_Justified_Fluence_Graph

Request = Help_To_Stop What = Help_To_Stop When := Now

Operator_ Class = 2 Previous_ What = Variables What = Deep_And_Justified_Fluence_Graph How := Detailed_Fluence_Graph

3. Grammar

The language L1 is specified by the following Chomsky grammar :

- the finite terminal vocabulary = { line_number, fact_name, fact_ value, ??, : , &, - )

- the finite auxiliary vocabulary = { S, T, C } - the axiome (or "sentence") = { A ) - the set of "context-free" derivation rules :

A::= line_number fact_name ?? S S::= {line_number fact_ value : T} T::= A I C C::= { - ) value_Conclusion_fact [line_number & CJ

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

INTEGRATION OF CONTROL AND ERROR MANAGEMENT FOR A FLEXIBLE ASSEMBLY CELL, USING A

COST FUNCTION

B.R. Meijer* and J. Stigler**

•control Laboratory, Department of Electrical Engineering, Delft University of Technology, P .0. Box 5031, NL 2600 GA, Delft, The Netherlands

••Knowledge Based System Group, Department of Technical Mathematics and Informatics, Delft University of Technology, Julianalaan 132, NL 2628 BC, Delft, The Netherlands

Abstract A flexible assembly cell is considered to be an essential building brick for flexible automation of small to medium sized order-based industries. In order to be able to respond adequately to market changes a production facility that can be reprogrammed or even reconfigured in a very short time is vital. Such a system will have to exhibit some form of intelligent behavior. By intelligent behavior we mean that this system should be able to learn from experience. The experience gained in making subsequent batches of products will be used to increase the efficiency of future batches. Unreliable strategies will be replaced by more reliable ones, actual time data will make it possible to choose a better plan. In this paper a reference model for planning, control and error management for a flexible assembly cell is presented and scheduling and a cost function for the selection of strategies for primitive operations are discussed.

Keywords error management, flexible assembly, hierarchical intelligent control, industrial robots, system failure and recovery.

I Introduction

The DIAC (Delft Intelligent Assembly Cell) project is a multi-disciplinary research project at Delft University of Technology aimed at the development, implementation and integration of the technology that makes up an assembly cell. Thus the DIAC project is intended to cover a wide range of research topics in the field of robotics and flexible assembly. It ranges from assembly process planning to the design and implementation of robot control strategies. In this paper an integrated approach for error management and control of a flexible assembly cell is discussed. First in section II the approach to planning, control and error management for the DIAC will be explained. This approach will be reflected in the reference model discussed briefly in section III. Furthermore it will be shown that this reference model reflects the capability of learning from experience at all planning levels. Finally in section IV scheduling and a cost function for the selection of strategies for primitive operations are discussed. This cost function forms the basis for an integrated approach to production control and error management.

II Planning and C ontrol for flexib le assembly.

2.1 Introduction

As Kerr indicates [ 1 ] , any planning and control system for manufacturing and assembly involves notions of second and third order feedback. This means that such a system is capable of initiating

207

alternative actions for a given set of external conditions to achieve a certain goal (second order) or that this system may even be capable of changing its goals by reflecting on past experiences (third order). The latter is a learning ability that implies the capability to redesign the type of feedback. Given the complexity of such systems two approaches can be taken : a controller either possesses a set of explicitly stored control responses for each system state or it has the capability to generate a response for each state. This distinction is also known as off-line (a­priori) planning systems vs. on-line (reactive) planning systems. The classical AI (a-priori) planners take a snap-shot of the world and produce a fixed sequence of actions to achieve a goal in that world. Lyons argues that this approach is too inflexible to work in an uncertain and dynamic environment. On the other hand a purely reactive system does not behave very well for situations that are outside the range of states for which reactions were programmed. Lyons among others proposes a hybrid approach called reactive planning [2]. In this approach planning is used to adapt a reactive system. This reactive system is a real-time system that continuously interacts with its environment. The planner is a concurrent system that tunes the behavior of this reactive system to ensure that goals are achieved. Changing the goals in this case means changing the structure of the reactive system in such a way that the new goal will be achieved. The DIAC approach to planning can also be classified as hybrid although the nature of the DIAC approach is much more a-priori than reactive. In DIAC a clear distinction is made between data that are unknown or

uncertain (and therefore necessitate measurements in real time) and data or knowledge that may be uncertain but for which models and estimates that are sufficiently accurate exist. An example will illustrate this distinction. A tray with objects is to be processed in such a way that when put together these objects form a product. A plan establishing the order in which the parts should be taken to form the product can be calculated a-priori. This plan is not subject to a changing environment, provided the design of the product is not changed. However the positions where the parts can be taken from the tray are not known sufficiently accurate to guarantee a successful grasp with a robot arm. It is even possible that the parts arriving at the cell are not the correct parts for the desired product. Before the handling of the parts a verification of the identity of the parts will be done and the position is measured accurately with some sensor device. The DIAC planning approach designs reactive systems that perform a (fixed) planned sequence of actions in order to achieve a certain goal. The expected uncertainties and possible changes in environment are modelled and sensor actions are planned to overcome these changes and uncertainties. A-priori knowledge and models are used to increase the efficiency of the assembly plan as much as possible without introducing the risk for using outdated data. This approach is valid as long as the time horizon of this planning system does not exceed the expiration time of the goal that is to be achieved. This planning system will be discussed in more detail in section 2.2. The nature of error management systems however is inherently reactive. Exceptions and failures cannot be foreseen or modelled in such a way that they can be treated as part of normal process behavior. Error recovery, if at all possible, has to be based on facts that can only be established after the occurrence of such an error (detection and assessment). The error recovery problem itself consists of two parts. First establishing a new goal, which may be trivial if the goal before occurrence of the exception state can still be achieved. In most cases this is not possible. Then a new goal has to be established that can be achieved. The second part is a planning problem that is very much the same as creating a plan to achieve a regular goal (produce a batch of products). The error management system for DIAC is described in more detail in section 2.3 [3,4].

2.2 The DIAC Planning system.

To avoid any misunderstanding the following definition of assembly process planning is used in this paper: "Assembly Process Planning is defined as the process of task decomposition, reasoning and program generation that has to be done before assembly on a given assembly cell can take place". Using this definition we assume that production means and layout are known input for assembly process planning.

208

The assembly process planning system for DIAC is based on the work of Heemskerk [5]. This approach can be classified as a product oriented approach. It distinguishes four levels of abstraction: batch level, product level, part level and primitive level. At each level alternative plans are generated in two phases. First the assembly process is analyzed in a product oriented way. In the second phase the applicability of alternatives for a given assembly system is evaluated (to avoid unlimited growth of the tree of assembly plans). The branches in the figure represent alternative ways to achieve the goal. The nodes represent (intermediate) assembly states (figure 1).

Batch Level

Parts for 30 x

Product Level

Parts for 1 x

Part Level

Parts B loo•

Primitive Level

Part B available

30 x aseembled 1 x assembled Part B aSMmble Part B graaped Figure 1 . Levels of abstraction in task oriented analysis.

At batch level the problem of producing n products is analyzed. These products belong to one product family but don't have to be identical. Decisions made at this level mainly concern the number of products assembled at the same time (splitting up into smaller batches or grouping into batches of identical products). This may be necessary due to limited capacity of the cell, but also it may be advantageous to group the order into batches of identical products when special tools are involved for each variant within the product family. The same argument is valid for splitting up a batch into subbatches of subassemblies in order to minimize tool exchanges. At this level of planning the order size is assumed to be known or a production forecast is given. There is a strong interaction with the layout of the cell, the availability of tools, and the the way parts are supplied to the cell [6]. The product level concentrates on the decisions for a single product. The main goal here is to establish feasible assembly sequences. In a first phase the product is analyzed to see in which order the parts can be treated. Access constraints (collisions between parts) play an important role here. In a second phase stability analysis is used to recognize subassemblies and cluster analysis to recognize opportunities for concurrent handling of parts and to remove branches that represent irrelevant alternate sequences (e.g. there are 6 "different" ways to mount 3 identical bolts). As a representation of assembly sequences "Assembly State Transition Diagrams (ASTD's)" are used [5,7 ,8]. ASTD's offer a compact representation of all possible assembly sequences. As a disadvantage ASTD's offer no support for concurrent handling of subassemblies as AND/OR graphs do [9].

At the part level only one part at a time is considered. From the 'parts' point of view the assembly task at this level is a fixed sequence of actions (FEED, GRASP, MOVE, MOUNT, CHECK), bringing it from the "loose" to the "joined" and "approved" state (figure 2):

Part level state I Transition I Primitive level state

Loose I I FEED I I Best guess position, ID I GRASP I I I Object under control I MOVE I I I Ready for mounting I MOUNT I

Joined I I I CHECK I

Approved I I Figure 2 Sequence of actions at the part level.

The sequence looks like a robot program, but it really is not. The difference between the abstract concept of parts going from one state to the next and the direct generation of robot commands is the key to the Task Oriented approach. The challenges at the part level are not so much in finding the right sequence of actions for each part, but in picking the best strategy for each step and in keeping track of the relations between parts that are undergoing transitions. Which strategies are feasible and which of them is best, depends on the results of a lower level of analysis. At the primitive level the scope is limited to one primitive at a time. The goal is to find an optimal combination of actuators, sensors and control algorithms to acquire the desired information or to establish the desired amount of control over a part. Software and (mechanical) hardware can serve the same purposes, and to some extent even be exchangeable: e.g. compliance may be acquired by purely mechanical devices (passive compliance) or through an active combination of a force/torque sensor, a drive mechanism and control software.

2.3 The DIAC approach to error management

For a general error management system a total of eight basic functions may be distinguished.

exception monitoring/detection. damage confinement, errors will be prevented to cause more damage through error propagation. damage assessment. recovery planning. fault/error diagnosis, to establish the cause of an exception. fault/error treatment, to prevent an exception from happening again. fault! error documentation. maintenance.

In error recovery planning there are two basic approaches: repair (forward error recovery) or abandoning some or all of the results of recent

209

activity in the system (backward error recovery). Fault/error documentation and maintenance are two meta functions. These functions are called meta functions because they are operating above the level of the detected error. The fault/error documentation function serves to find fault/error patterns in order to improve the system performance through either prevention or faster diagnosis of these kinds of faults. Maintenance serves to keep up system reliability and fault tolerance for continued service [10]. Error management and detection and damage confinement are decentralized reflex like functions. An example will illustrate this. A robot that is trying to move outside its workspace boundary is switched off automatically. A robot link passes a limit switch (detection) and as a result the power is switched off automatically (damage confinement) . Finally some message is sent to a higher level of control, indicating that the robot has stopped because of a workspace boundary problem. This message is not to be misunderstood as diagnosis; this message only serves as damage assessment from which recovery may or may not be possible. Diagnosis means finding the fault in the robot program or robot model that caused the robot to move outside its workspace boundary. Modelling exception detection and damage confinement as a reflex like decentralized function does not only apply for actuator systems. It applies to all systems (virtual as well as physical) present in a production system. The reason for this is that exception detection involves specialized knowledge that is (only) available with the people that design or build these systems. This knowledge may vary from sensor values that may not be exceeded to statistical models used for detection of system degradation. In the case of a complex system composed of sub­systems, error detection and damage confinement can only be done if sufficient knowledge is available about the interaction of sub-systems. Based on damage assessment (defining the system state after an exception has occurred) recovery planning can be done. Both forward and backward recovery planning rely heavily on the assumption that a goal is still available. This stresses the importance of a task oriented process plan from which achievable goals can be derived. The choice between forward and backward recovery strategies depends on the outcome of damage assessment and the costs associated with both strategies to get back in business. Although diagnosis may not be possible it is still possible to treat the system to prevent the occurrence of these exceptions in future occasions. A mechanism that can be used for this purpose influences the cost­estimates of the strategies that were chosen to carry out a certain operation. Unreliable strategies can be ruled out in future plans this way. The same accounts for fault/error documentation and maintenance. The occurrence of error patterns or a change of frequency of certain faults can be an indication that maintenance becomes necessary. This mechanism will be explained in more detail in section IV of this paper.

III A reference model for planning and control of flexible assembly systems.

3.1 Introduction

The reference model for planning and control of DIAC has been introduced in [ 1 1 ] (figure 3). As indicated in the previous sections the DIAC planning system generates a plan that is only valid if the information it is based on does not change before this plan is executed. Therefore such a plan is formulated in terms of operations on parts instead of actions carried out by certain systems. Such a plan usually remains valid even when errors have occurred. This plan may therefore serve as a guide-line to formulate new goals in the case of error recovery. The DIAC reference model for planning and control differs from other models in the sense that it is not a model representing the factory floor hierarchy like the well known NIS model or the reference model for manufacturing planning and control systems (MPCS) as proposed by Biemans does [ 12]. The DIAC reference model is a control model that reflects the information transformations that occur when transforming a goal supplied by the master controller into a detailed plan, which when executed will actually achieve this goal. Thus it represents a hierarchy of system classes involved in this transformation process. It cannot be interpreted as an information flow model. The arrows indicate "makes use of systems in class X" relations.

II

III

----·- IV

Figure 3. The DIAC reference model for planning and control of flexible assembly systems.

The key feature of this model is the introduction of a layer with virtual actuators and sensors that decouples task oriented assembly planning from the dynamics and uncertainties of the dynamic world in which the sub-systems at level IV are operating. Assembly processes can be described in terms of two classes of systems (sensors and actuators) and three types of information (location, identity and quality). Therefore six 'virtual' sensors and actuators can be distinguished at this level. Virtual in this context means that these systems are described by their function not by their way of operation. This means that a location sensor can be a vision system but also

210

a database with a priori knowledge or a robot with a contact probe. These sensor and actuator systems are related to the primitive actions at part level planning described in section 2.2 However this is not a one to one correspondence. A FEED is executed by the identity sensor, the location sensor and the location actuator (in this order). A GRASP can be performed by the location actuator. A MOVE is also carried out by the location actuator. The MOUNT primitive is executed by the identity actuator. The CHECK primitive is carried out by the quality sensor. For the design of a control system we will have to focus on the systems present at level II. Like the planner/reactor interaction of Lyons and the relation between MPCS management and MPCS execution as described by Biemans, we propose a similar integrated planning and control module that can be applied at all levels of abstraction as described in the planning section. Based on (a-priori) system data plans are generated by the planner to achieve a certain goal. These plans are called know-how. If a particular goal has to be achieved at a certain time, then a plan is selected and executed and the a-priori system data is updated with facts learned from the execution of this plan. This is shown in figure 4.

11.ich level

Product level

Part level

Primitive I level

Orders and due d81 ..

• ( S.�r and Actu81or ayetema ) - - - - - - r

Figure 4. Four level planning and control system for assembly.

In this figure the broken lines indicate the scope of some of the systems present in the model of figure 3. Area 1 is production planning, area 3 represents production scheduling and area 5 is the production dispatching system. Area 4 represents the part of the system where the virtual actuator and sensor systems play an important role. The database that was not present in figure 3 is represented in area 2. The monitoring functions are only implicitly present in the feedback arrows from execution to system data. The same accounts for the way exception handling will influence the normal process behavior. This will be discussed in section IV of this paper.

IV Scheduling and a cost function for the selection of strategies for primitive operations. 4. 1 Scheduling.

Scheduling involves determining the sequence of loading jobs on individual machines of workstations with due regard for capacity, such that precedence constraints on the ?rdering of operations are satisfied, and due dates of JObs are as far as possible met. A cost function that minimizes tardiness (and earliness to avoid storage problems) is commonly used to find the 'optimal' sequencing and distribution of jobs over stations. This problem is often referred to as job-shop scheduling and this class of problems has been 'termed' NP-hard since no known algorithm can be guaranteed to converge to an optimal solution. The practical complexity of scheduling for a flexible assembly cell is expected not to be NP-hard because there are more constraints involved. Part transport capacity and buffer capacity in a cell is limited and the stations to which jobs can be assigned are not always equivalent. This means that batches have to be split up into smaller batches that can be handled by the cell and that certain jobs have fixed assignments to stations because there are no alternative tools available. The combination of these constraints (some fixed assignments and limited transport and buffer capacity) will reduce the number of schedules to be evaluated considerably. However dealing with these constraints will introduce new problems (e.g. how to split up a batch into smaller batches). Like the planning approach, DIAC will use a hierarchical scheduler. Although suboptimal, the hierarchy allows the handling of these constraints in a structured way. The hierarchy also improves the understanding of complex schedules which is vital for error management. At each level in the hierarchy it is possible to build a network in which the nodes represent assembly states and the arcs represent the transitions with the associated time to proceed from one state to the next. So called Max-Plus algebra's can be used to find the critical path of such a network (the path with the longest time) and to analyze the robustness of such a network against disturbances [ 13,14]. A transition represents a set of networks at the level below it. The scheduler selects the network with the shortest time critical path also taking into account the setup time necessary to perform the operations in this network. The sum of this setup time and the critical path time is the transition time at a higher level. Note that setup times are made known explicitly at a higher level to allow minimization of setup times through the sequencing of jobs. At part and primitive level scheduling is defined as choosing a strategy to perform a primitive operation and thereby assigning a combination of tools to a station. Since tools are scarce resources, operation time alone is not enough to compare the costs of different strategies. Furthermore the time associated with a primitive operation may be uncertain because of the failure risk associated with a certain strategy.

21 1

4.� � .cost funct.ion for the selection of strategies for prumtive operations.

In this section a set of parameters for a cost function is . P!oposed that will serve more goals than just mm1mum assembly time. It will be shown that the value o_f these parameters can be controJied by mechanisms that allow the planning and scheduling system to learn from experience. The output of this cost function is a vector with two elements : the operation costs and the utilization index. The operation costs and the utilization index are used to select the best strategy. The operation cost of a strategy is defined as the operation time divided by (1 - failure rate). Operation time, utilization index and failure rate are discussed briefly below.

Operation time: unit operation time times the average number of retries. For both operation time and the number of retries statistics are to be maintained (mean and variance). The operation time is also used as an estimate of the transition time at a higher level.

Utilization index: this parameter is used to guide the search towards preferred solutions. It is based on a-priori knowledge. In case of equal operation costs, the utilization index is used to give priority to strategies that make good use of the capacities of the resources associated with them.

Failure rate: parameter controlled by the error manager to rule out failure prone strategies. In finding an optimal plan the scheduler may have to choose between a very reliable but slow strategy and a less reliable but fast strategy. Provided the costs of error recovery after failure are not very high, the unreliable solution may still be preferred. Therefore this rate should be weighted with a factor in order to rule out unreliable strategies from which autonomous recovery is not possible.

Setup time is not taken into account as a part of the operation time of a primitive, because setup is a primitive operation itself. Processes for updating performance data must be used with care to use only statistically relevant data and to rule out interference between costs and failure rate. In order to guide the system correctly the assembly time estimate refers to the non-failure case whereas the failure rate parameter weights this time to rule out fast disasters. Estimating the assembly time on all data (including failure data) may cause unwanted interference. For certain strategies a retry may be considered normal process behavior. In this case a retry will not have effect on the failure rate, but it will change the operation time and its variance. However the number of retries will have an upper bound. Exceeding this upper bound will be considered a failure and error management will have to deal with this failure. Since the average assembly time and its variance are related to the number of retries, these values can be used to detect the need for maintenance.

V Conclusions and future work. In this paper a reference model for planning, control and error management for the Delft Intelligent Assembly Cell is discussed. It is shown that this model has the necessary ingredients for a system with a learning capacity. Future work will be directed towards finding a formalism to model this learning capacity. Special attention will be paid to designing filters for estimating the actual cost parameters. A frequency analysis and a classification of exceptions for a flexible assembly cell has already been carried out ( 15] and can be used as a reference for tuning the parameters of the operation cost function.

Acknowledgements The research reported in this paper is sponsored by a grant from the national SPIN/FLAIR program. The DIAC project is a multi disciplinary project in which four departments (mechanical engineering, applied physics, electrical engineering and technical mathematics and informatics) participate. The authors wish to express their thanks to the PhD students involved in this project and the project leader Pieter Jonker for their valuable contribution to the discussions about planning, control and error management of DIAC. Especially we wish to thank Nico Boneschanscher for his valuable remarks on scheduling.

Literature [1]

[2]

[3]

[4]

[5]

[6]

Kerr R., "Knowledge-based Manufacturing Management", Addison-Wesley Publishing Co., 199 1 , pp. 50-5 1 . Lyons D.M., Hendriks A.J . , Mehta S.,"Achieving robustness by casting planning as Adaptation of a reactive system.", Proceedings of the 199 1 IEEE International conference on Robotics and Automation, Sacramento California, April 199 1 , Vol.1 pp. 198-203. Stigter J., "Integration of error management in the Delft Intelligent Assembly Cell: a de (n)ovo methodology", Proceedings of the 1990 European Simulation Symposium, Ghent, Belgium 1990. Klein L.J., "A specification method for the control of a flexible assembly cell", Masters thesis (in dutch), Department of Technical Mathematics and Informatics, Delft University of Technology, May 1991 . Heemskerk C.J.M., "A concept for computer aided process planning for flexible assembly", PhD thesis, April 1990, Delft University of Technology. Boneschanscher N. "On task assignment in a multi r

.obot flexible assembly cell",

Proceedings of the 1 1th International conference on assembly automation, Dearborn (MI), November 1 1-14 1990.

[7]

[8]

[9]

[10]

[ 1 1 ]

[ 12]

[ 13]

[14]

[ 15]

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Boneschanscher N., Van der Drift J.H.M., Buckley S.J. and Taylor R.H., "Subassembly Stability" IBM Research internal report No. RC 1 3569. Published in the Proceedings of the 1988 AAAI Conference, August 1988, St. Paul, Minnesota, USA. Boneschanscher N. and Heemskerk C.J.M., "Grouping Parts to Reduce the Complexity of Assembly Sequence Planning", presented at INCOM'89 6th Symposium on Information Control Problems in Manufacturing Technology, IFAC/IFIP, September 1989, Madrid, Spain. Homem de Mello L.S. and Sanderson A.C., "Representations of Mechanical Assembly Sequences", IEEE Trans. on Robotics and Automation, Vol.7 No. 2, 199 1 , pp. 21 1-227. Stigter J., "Theoretical considerations on error management", report 90-75 of the department of Technical Mathematics and Informatics Delft University of Technology.

'

Meijer B .R., Jonker P.P., "The architecture and philosophy of the DIAC (Delft Intelligent assembly Cell)", Proceedings of the 199 1 IEEE International conference on Robotics and Automation, Sacramento California, April 1991 , Vol.3 pp. 2218-2223. Biemans F.P.M, "A reference model for manufacturing planning and control" PhD thesis, October 1989, University of Twe�te. Cunningham Green R.A., "Minimax algebra", Lecture notes in economics and mathematical systems, no 166, Springer Verlag, 1979. Olsder

, G.J., "About difference equations,

algebra s and discrete events", Report 9 1-87, Department of Technical Mathematics and Informatics, Delft University of Technology. Evers M.GJ.,"Classification of exceptions for a flexible assembly cell" (in dutch), FPA report no. FPA9 1 .034, Department of Mechanical Engineering, Delft University of Technology.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

PRINCIPLES OF MODEL-BASED FAULT DETECTION

P.M. Frank

Fachgebiet Mess- und Regelungstechnik, Universitiit-GH-Duisburg, Bismarckstr. 81, 4100 Duisburg, Germany

Abstract. The paper outlines the principles of fault detection and isolation (FDI) in dynamic systems using a mathematical model of the system. Implemented on a digital computer, these model-based algorithms can efficiently be applied to signal validation, on-line detection of abrupt faults and early fault diagnosis in a long-term system supervision. 'l'he basic concept of the model-based approach to fault detection and isolation is described, and the different methods of residual generation developed in the past two decades are reviewed. Among the methods considered are the parameter identification approach, the different observer-based concepts, the parity space approach and the knowledge-based strategy. It is also shown how structured residuals for the localization of the faults can be generated with the aid of observer schemes. As an issue of great practical relevance the robustness with respect to modeling errors is taken into consideration. Here emphasis is placed upon the unknown input observer approach and its application to instrument, actuator and component fault detection.

Keywords. Fault detection, diagnosis, model-based fault detection, analytical redundancy, observer­

based fault detection, robustness

Introduction

The need for an effective fail-safe management in modern automation systems calls for powerful fault detection and isolation (FDI) techniques. Evoked by these needs and sup­ported by the advances of modern control theory and com­puter technology, a number of sophisticated FDI strategies have been developed in recent years.

Among these strategies the model-based is by nature the most capable one. Actually, if one could acutely under­stand the dynamic processes arising in any physical plant, and precisely and reliably measure every process variable of interest, one could detect, locate and identify any fault in the plant, almost immediately, by comparing the data collected with those of a functional mathematical model of the plant. This is the fundamental idea of the model­based FDI strategy, which is also known as the functional or analytical redundancy approach. In contrast the physical redundancy approach that performs the comparison on the basis of physical replica.

Unfortunately, the prerequisites for the model-based ap­proach formulated above do generally not hold in real tech­nical processes. Neither are the models perfectly known nor are all the necessary measurements reliable enough or available at all.

Inspite of this deficiency, the model-based methodology re­mains basically practicable even under such restricted con­ditions. However, it requires skillful treatment and proper arrangements, and can only provide more or less reduced efficiency depending upon the special type of plant and the given restrictions. This gives evidences why a comprehen­sive theory of model-based FDI for real plants does not exist but, instead, a number of different methods have been proposed.

In this paper we outline the principles of the model-based FDI methods known so far. They can roughly be dev-

213

ided into two major categories, the analytical redundancy approach using analytical mathematical models and the knowledge-based approach using qualitative (deep or shal­low) models associated with heuristic reasoning. All these methods are implemented on digital computers.

The analytical approach is tailored for information rich sys­tems that, by definition, provide enough sensor information and can satisfactorily be described by analytical models.

Note that even in this case model uncertainty and incom­pleteness of measurements to a certain degree can still be tolerated. Depending upon the degree of uncertainty, ro­bust or adaptive strategies have to be used.

In the case of information poor systems where unsatisfac­tory information and only poor models are available, only the knowledge-based approach comes into question. Log­ically, less can be achieved in such situations. It is then reasonable to employ the techniques built around artificial intelligence which at least allow to exploit as much knowl­edge of the process as available. In the extreme case where only a bare minimum of sensors is at hand and the process is extremely uncertain, as for example in complex chemical processes, only a common sense strategy may be practica­ble, a method that is still in its infancy (Howell 1991 ) . In all these cases, expert systems, neural nets and fuzzy logic may be best suited to solve the FDI problems. At the same time, these techniques, eventually combined with Petri nets, can be used to implement the general fail-safe management for the overall supervision of the system.

In many practical situations, a combination of both the analytical and knowledge-based methodology may be the most appropriate solution to the FDI problem. Clearly, the inclusion of the analytical model, if available, provides the most condensed expertise of the plant possible and its inclu­sion helps a lot to overcome the known difficulties of filling the knowledge-base of the expert system and to simplify • h!' reasoning program of the inference engine of the ex-

pert system. The general configuration of an expert system combining the analytical and knowledge-based strategy for FDI is shown in Fig. 1 .

R l ·I process under consideration I

l _l rules and

I I ( rt) facts data base expe -

experlenc l l es

knowledge base

analytical knowledge heuristic knowledge

analytical process model fault tree

observer scheme fault statistic, history

nominal process behaviour process environment

Inference engine

analytic problem solution heuristic problem solution

residual generation fault recognition

threshold logic fault decision

hypothesis test Petri nets

performance Index etc. fuzzy logic etc.

I explanation component I I

Figure 1 : FDI Expert-system combining the analytical and knowledge-based approach

There exists quite a number of expert systems for fault diagnosis, especially in medicine and engineering systems. From the theoretical point of view, however, the analyt­ical redundancy approach has so far reached the highest degree of maturity, especially as far as linear systems with little model uncertainty are concerned. This applies pri­marily to electrical, mechanical, pneumatic and hydraulic systems. For the latest state of the art and more references the reader is refered to the survey papers of Frank ( 1990, 1991 ) , Gertler ( 1991 ) , Patton and Chen (1991) , Isermann ( 1984, 1991), the books of Patton, Frank, Clark ( 1989), Brunet, Jaume, Labarrere, Rault, Verge ( 1990), and the PhD thesis of Sauter ( 1991 ) .

Because of its maturity we focus our attention in this paper upon the analytical redundancy approach to FDI with due regard of the techniques to enhance the robustness with re­spect to modeling uncertainty. Only the basic ideas of the most important concepts are outlined because of the limi­tations in space. For more detailed description the reader is referred to the literature mentioned above and the literature cited therein.

General Concept of Analytical Model-based FDI

The basic concept of model-based FDI is illustrated in Fig. 2. In general, three kinds of models are required: A model

214

of the nominal process as a reference, a model of the faulty process carrying information about the effect of faults, and

u

RESIDUAL GENERATION

MODEL OF NOMINAL SYSTEM

STATE ESTIMATION

GENERATION OF

• PARITY FUNCTIONS • RESIDUALS

MODEL OF FAULTY SYSTEM

• PARAMETER ESTIMATES

RESIDUAL EVALUATION

FAULT TIME

FAULT TYPE SIZE CAUSE

Figure 2: Basic concept of model-based FDI

a model of the observed process defined by the inputs and outputs taken from the actual process. To achieve a high quality of fault detection with a low false-alarm rate, the nominal model should be tracked with high precision by the unfaulted observation model.

The first step of FD! consits of generating estimates of the outputs and/or parameters of the actual process. The esti­mates are then compared with the corresponding quantities of the nominal model in order to generate residuals or pa­rameter error signals, respectively, or they are used to form fault effected textures such as likelihood functions. The ba­sis for the decision on a fault is a signal obtained from a model of the faulty process defining the effects of faults to be discovered. The final step is to diagnose the fault loca­tion and, if desired, its size and cause.

Concerning the model, one has to admit that the process with input u and output y can in general be nonlinear and may be subject to process disturbances, di , measurement noise, d2, parameter variations, d3 (due to modelling uncer­tainties and process parameter changes), and faults, /, that we want to detect. After linearizing the process around an operating point and grouping d1 , d2 and d3 to the so-called vector of unknown inputs d = [df 4 4JT, the mathe­matical model takes the form:

y

A x + B u + E d + K f

C x + F d + G f ( 1 ) (�)

Here, x denotes the state vector and A, B, C, !':, V, /,· ,

and G are known ma.trices of proper dimensions. Actuator faults are reflected in changes in B, sensor faults in changes in C, and component faults in changes in A. They can a.II be represented by f when K and G are chosen properly. Note tha.t, in genera.I, no assumption can (and should!) be ma.de on the mode (type and size) of d and f.

For the case of nonlinear models see Fra.nk ( 1992) and Seliger and Frank ( 1991 a.,b).

Principles of Residual Generation

The key problem of model-based FDI is the generation of residua.ls, i.e., signa.ls which are a.ccentua.ted by the faults. The residua.ls should be sensitive to faults and insensitive to the known and unknown inputs which ma.y lea.d to fa.lse a.larms.

In the widest sense, a. residua.I generator is therefore defined a.s a dyna.mic system which, fed by the inputs and ava.ilable outputs of the process under consideration, a.ttenua.tes a.II influences except those ca.used by the faults to be detected. In connection with the decision logic, such a system ma.y, in genera.I, be termed a fa.ult detection filter FDF.

The different approaches to residua.I generation can be grouped into two major categories:

• Para.meter identification approach

• Observer-based approach.

Parameter Identification Approach

This approach ma.kes use of the fact tha.t faults in functional units of a process are reflected by changes in the physical para.meters, p, as, for exa.mple, friction, mass, viscosity, re­sistance, capacitance, inductance, etc .. On the other hand, the physica.1 para.meters a.ffect the para.meters of the ma.th­ema.tica.1 model of the observed system, i.e., A, B, C in Eqns. ( 1 ) and (2). The idea. of the para.meter identifica­tion approach is to detect the faults via. estimation of the physica.1 model para.meters, due to the following procedure illustrated in Fig. 3:

1. Choice of a para.metric model of the process, y(t) =

G{u( t ), 8) mostly by theoretical modelling. Norma.lly one uses linear models with lumped parameters in the form of input/output differential equations:

a,.y("l(t) + . . . + a1y(t) + y =

b0u(t) + . . . + bmu(ml(t) (3)

instea.d of the state-spa.ce representations, Eqns. ( 1 ) and (2).

2. Determination of the relationships between the vector of the mathematica.1 model para.meters 8; and of the physical para.meters P; :

(} = f(p) (4) 3. Identification of the vector of model para.meters 8 us­

ing the inputs u and outputs y of the observed process.

4. Determination of the corresponding vector of physical para.meters

(5)

215

u ACTUAL y

SYSTEM

d

PARAMETER IDENTIFICATION 9

e CALCULATION OF SYSTEM PARAMETERS

p = f1 (e) p

FAULT ALARMS

Figure 3: Parameter estimation approach to FDI

5. Ca.lculation of the deviations, t:!.p, from their nomina.l va.lues, Po, determined from 80 of the nomina.l model of the process. t:!.p plays the role of the residua.I.

6. Decision on a fault by exploiting the relationships be­tween faults and changes in the physical para.meters, t:!.p;. For this task one can a.lso use catalogues in which the relationships between process faults and changes t:!.p; have been established.

For the identification of 8 one can ma.ke use of well es­tablished methods of the theory of parameter estimation. Problems ma.y arise from the fa.ct that the inversion 1-1

in Eqn. (5) is in genera.I not unique and only little is known about the robustness to model uncerta.inties, pa­ra.meter variations, disturbances and noise. Moreover, the identification problem may become difficult to solve in the case of high-order systems that are not decomposeable into sma.11 units and/or systems that are nonlinear in the pa­ra.meters. But under favourite conditions a powerful fa.ult diagnosis is possible with this technique (Isermann 1991).

Observer-based Residual Generation

The basic idea of the observer-based approach is to recon­struct the outputs of the process with the aid of observers or Kalman filters and to use the estimation error or inno­vation, respectively, as a residual for the detection of the faults. The procedure of fa.ult detection then consists of the following two steps:

1. Generation of residuals via. output observation

2. Evaluation of the residua.ls by a decision logic.

It is well known from observer theory that for the task of observation one can use linear or nonlinear, ful or reduced­order observers (in the deterministic case) or Kalman filters (when noise is considered). In either case a. ma.thema.tica.1

model of the process is needed. The basic configuration of a full-order observer is shown in Fig. 4. In this case the observer simply consists of a parallel model of the process with a feedback of the estimation error, e = y - y. The feedback is important for several reasons:

1. to compensate for differences in the initial conditions

2. to stabilize the parallel model in the case of an unsta­ble process

3. to provide freedom for the design of the observer, for example, to decouple the desired effects of faults, f, from the effects of unknown inputs, d ("unknown in­put observers" ).

In the case of a process with the state Eqns (1) and (2), the state, x, and output, y, of a full-order observer obey the equations:

(A - H C)x + B u + H y c x

(6)

(7)

where H denotes the feedback gain matrix. With Eqns. ( 1 ) ,(2),(6) and (7) the relations for the state estimation er­ror t = y - y, become:

e (A - H C)t + E d + K f

C t + F d + G J

(8)

(9)

It is seen from Eqns. (8) and (9) that the output estimation error, e, is a function of both, f and d. Hence, e can be used as the residual, r, for FDI. If no fault occurs, i.e. , f = 0, the observer will track the process so that r only depends on the unknown input, d. If, however, f =/= 0, the observer does no longer model the process precisely and r will be increased. Hence, a fault can be detected by checking the increment of r caused by f. In the simplest case this can be done by a threshold logic where the threshold is surpassed as f occurs. The objective of the observer design is to choose the feedback gain matrix, H, such that the fault signature in the residual is decoupled from that of the unknown input and becomes large enough to be detected.

In a similar way one can derive residuals using reduced­order observers, or Kalman filters, or even nonlinear ob­servers in the case of nonlinear systems (Frank 199 1 , 1992).

Generation of structured residuals

For the task of fault isolation one needs structured residuals. They can be generated by observers or Kalman filters that are arranged as observer schemes or banks of observers. The goal of the observer schemes is to generate structured sets of residuals that enable a unique fault isolation. To this end, each observer may be made sensitive to a different fault and insensitive to the rest of faults. This may be accomplished by driving the observers by different sets of inputs or outputs of the process depending on the type of desired fault detection, i. e. actuator fault detection AFD, instrument fault detection IFD or general type component fault detection CFD. The most important types of observer schemes for FDI are briefly outlined in this section.

Innovation Test

A very simple observer configuration for FDI is that of using a single I< a/man filter driven by all outputs of the process. The innovation vector, i .e. , the difference between the mea­surement vector and its estimate is taken as the residual. In normal operation the residual is white noise with zero mean

216

u MEASUREMENTS

y

y +

' '

I ' ' ' ' l _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ J

OBSERVER, KALMAN Fil TER

Figure 4: Basic concept of observer-based FDI: Identity observer

and known covariance. With the occurrence of a fault in the process the character of the noise and the covariance change. Hence, a fault can be detected by statistical tests of whiteness, mean and covariance of the innovation. Ex­amples are the Chi-squared test, the bad data suppression concept and the general likelyhood ratio (GLR) test. The latter approach includes a hypothesis test based on different modes of the faults (Willsky 1976). More robustness of the covariance matrix test with respect to parameter variations can be achieved by a proper time shifting of the compo­nents of the innovation vector, i.e., by inclusion of correla­tion (Frank 1987) .

Fault Detection Filter (FDF)

The so-called fault detection filter (or fault sensitive filter) is a full order observer of Kalman filter designed for the decoupling of the effects of different faults f; in the process (Willsky 1976). Let the process be given by

y A x + B u + I< f

C x

( 10)

( 1 1 )

instead of Eqns. ( 1 ) and (2), i .e., n o unknown input vector d be considered. The corresponding observer equations are

(A - H C)x + B u + H y c x

(12)

( 13)

with the same meaning of the symbols as in Eqns. (6) and (7) . Defining the state estimation error as t = x - x and the residual as r = y - y, the state equation of the residual becomes:

r (A - H C)t + +K f

c f ( 14) ( 15)

Typical for the fault detection filter is that H is chosen such that the residual r due to a particular fault, f; , is con­strained to a single direction or plane in the residual space independent of the mode of f;. This is often not possible unless the state x is accordingly enlarged.

Since the important information about the fault is in the direction of the residual rather than in its time function, the use of a fault detection filter does not require any knowl­edge of the fault mode f;(T), i.e., on the size or time history. Hence, a fault is detected when one or more of the residual projections along the known fault direction or in the known fault plane are sufficiently large. Since unknown inputs are not considered in the design, this approach does not account for the effects of disturbances, model uncertainty, parame-

ter variations or measurement noise. This can, however, be achieved by treating the disturbances of concern like faults to be decoupled.

Parity Space Approach

The parity space approach provides a systematic exploita­tion of the analytical redundancy relations defined by the mathematical model of the process. This is associated with (generalized) parity checks (Chow and Willsky 1984). Par­ity functions are functions of the time histories of the mea­sured outputs that are small (ideally zero) if and only if the process operates normally.

Following the state space representation of Chow and Will­sky (1984), consider the system equations in discrete form

x(k + 1 )

y(k)

A x(k) + B u(k),

C x(k) + D u(k).

(16)

(17)

A redundancy relation for this model is some linear com­bination of present and shifted values of u and y that is identically zero if and only if no faults occur. For the math­ematical specification, consider the subspace of (m + l )q dimensional vectors given by

This is called the parity space of order m with q being the dimension of the measurement matrix C. At any time instant k, every vector y in Eqn. (18) can be associated with a parity check, r(k) :

with

H =

D CB

CAB D

CB D

0

CAB CB

It is evident from Eqns. (19) and (20), that a redundancy relation is simply an input-output model for a part of the dynamics of the process.

Robustness can now be achieved by using primarily the re­lations of the certain part of the model, which can, e.g., be found by a minimax optimization (Lou et al. 1986).

Note that the resulting observer due to Eqn. (19) has all poles in the origin and can thus be interpreted as a dead­beat observer, i.e., a special form of an observer (Frank and Wuennenberg 1989). Gertler (1991) has discussed the parity space method from the ARMA and MA model point of view and has illustrated its crossconnections with the observer-based methodology (see also Patton and Chen (1991) and Frank 1992).

Unknown Input Observer Scheme (UIOS) A most efficient way of creating robustness with respect to modeling errors is to apply unknown input observers UIO. Unknown input observers are therefore gaining increasing importance in FDI schemes. Here the feedback gain matrix H in Fig. 4 is assigned to make the residual invariant to unknown input signals d; whilst being sensitive to faults fk· The resulting state equation of the UIO for a process

217

described by Eqns. ( 1 ) and (2) is:

z = F z + G y + J u (18)

with the residual

(19)

and with r having the following properties

lim r = O for f = O t-oo

and for all K, d and initial conditions x(O) and z(O) and

q f O for / # 0

Moreover, the states z of the UIO are linear combinations of the system states according to the following similarity transformation:

z = T x (20)

which holds in the no-fault case after the transients due to the initial conditions have died out.

The resulting estimation error, e = Tx - z, is governed by:

e = TAx + TBu + TEd + TKf - Fz - Ju - Gy (21)

Evidently, to guarantee that e only depends on the faults f, the following relations have to be fulfilled

T A - F T G C

J T B

T E 0 (22)

T K I 0

L1T + L2C 0

Solutions can be found under certain conditions, as for ex­ample, if the number of measurements is at least as large as the number of unknown inputs (Frank and Wuennenberg 1989, Wuennenberg 1990).

If the prerequisites for the existence of a UIO are not given, the best one can do is to design an optimal approximation such that a norm of the sensitivity with respect to the un­known inputs related to a norm of the sensitivity with re­spect to faults becomes minima.I (Frank and Wuennenberg 1989).

In order to configure robust observer schemes using UIOs that allow the isolation of multiple faults in the face of unknown inputs, one has to partition the faults into subsets of f, specified by vectors f;, with corresponding matrices K; and G; . Each UIO of the observer scheme is then assigned to be sensitive to a particular subset of faults and invariant to the rest of faults. The remaining design freedom can be used to provide invariance to unknown inputs. This is done, in turn, to such an extent that a properly structured set of residuals is obtained which enables a unique decision on the appearance and isolation of the faults. Such an observer scheme is shown in Fig. 5.

Depending on the given circumstances, this unified design philosophy covers a number of established FDI schemes:

• When the system is considered undisturbed and si­multaneous faults in all sensors are to be detected, the design procedure leads to the dedicated observer scheme DOS as shown in Fig. 6 (Clark 1978). Here the ith observer (i = 1 , . . . , p) is driven only by the ith measured variable.

y u Actual System t==�=l>

UI Observer 1 r1

• • I I •

,g UI Observer p r.

Figure 5: Generation of structured residua.ls using an ob­server scheme

Figure 6: Dedicated observer scheme DOS

• When simultaneous sensor faults, component faults or a.ctua.tor faults a.re to be detected and no disturbances ha.ve to be considered one arrives a.t the fa.ult detection filter FDF as described earlier in this pa.per.

• When disturbances a.re considered and only a. single sensor fa.ult a.t a. time is to be detected, the design procedure leads to the generalized observer scheme GOS (Frank 1987) as shown in Fig. 7. Suppose, for example, a. process has p measurable outputs. Then an IFD scheme with p observers is used. The ith observer (i = 1 , 2, . . . , p) is driven by a.II but the ith output. In this case one fa.ult a.t a. time in one of the p sensors can be detected a.nd isolated and the IFD scheme can be ma.de invariant to p - 1 unknown inputs. If, instead, two faults a.t a. time a.re to be detected a.nd isolated, the IFD scheme ca.n be ma.de invariant to only p - 2 unknown inputs, etc.

In the widest sense the simplified observer scheme SOS (Clark 1978) can also be seen as a. special case of this a.p­proa.ch. Here, only a. single fa.ult a.t a. time can be detected

f i )�.· ..

. ···.· .. ·· ALARM

Y 1 -------l�J.-..... L:.JI �

y( i ) ESTIMATOR i

Figure 7: Generalized observer scheme GOS

218

and no disturbances can be considered. However, only a. single observer is needed tha.t is driven by one of the mea­sured va.ria.bles.

Whilst Wuennenberg ( 1990) has used the Cronecker form to design UIOS, an a.lterna.tive a.pproa.ch for the decoupling of the effects of d a.nd f using an eigenstru.ctv.re design was proposed by Patton et a.I. ( 1987). In the no-fa.ult case, the observer can be designed to ha.ve a.n invariant sub­space (Patton 1988). Motions in the inva.ria.nt sub-space a.re rendered completely insensitive to disturbances, whilst the residua.I signal departs substantially from zero during a. fa.ult - thus allowing a. low threshold to be set for robust and rapid fa.ult detection. The methods of Wuennenberg and Frank and of Patton differ in the design a.pproa.ches adopted but lea.d to similar results.

The observer-based a.pproa.ch can readily be extended to nonlinear systems (Frank 1992). For a. certain class of non­linear systems a.n unknown input observer a.pproa.ch was proposed by Seliger and Frank ( 1991 a.,b).

For frequency domain design procedures of FDI observers see Ding and Frank {1991) and Frank (1991 ) .

Multiple Hypotheses Tests

The idea. of FDI by multiple hypotheses test is to define a. hypothesis for ea.ch fa.ult, i.e., Ho : ,,no fa.ult" , H1 : ,,fa.ult in sensor 1", . . . , Hq : ,,fa.ult in sensor q" , a.nd to test these hypotheses by using Ba.yesia.n decision theory. Ea.ch hy­pothesis is associated with a. Ka.Iman filter and a. likelihood computation from the innovations, see Fig. 8. Hence, a. bank of pa.ra.llel Ka.Iman filters is needed. The erroneous sensor is detected with the a.id of m-a.rra.y hypothesis test­ing. A moving window of the innovation of ea.ch Ka.Iman filter drives a. detector tha.t ca.lcula.tes the likelihood ratio for ea.ch hypothesis of a. possible failure mode.

INNOVATION

• .r-KALMAN---F-IL-TE-R--, r O H o

. . .

KALMAN FILTER H q

LIKELIHOOD FUNKTION Lo

LIKELIHOOD FUNKTION Lq

Figure 8: Multiple hypothesis test

Combined Hardware-Software Redundancy

SELECTED HYPOTHESIS

Instead of pure software or ha.rdwa.re redundancy, one can also combine both of them. In the most simple case of e duplex sensor system one uses two sets of sensors, ea.ch set being supervised by an IFD scheme. Once a. fa.ult in one of the sensor sets is detected, the decision logic provides tha.t the system is further operated with the unfa.ulted sensor. Using duplicated sensor sets complemented by dedicated observer schemes leads to the quality of a. triplex ha.rdwa.re redundancy system.

Hierarchical Observer Scheme (HOS)

The isolation of component faults requires more structural insight in the process than the isolation of sensor or a.ctua.tor faults. If no assumption on the fa.ult mode can be ma.de, a. reasonable a.pproa.ch is to decompose the process and apply a. hiera.rchica.l scheme of local observers or Ka.Iman filters

(Frank 1987), see Fig. 9. The difficulty of local state obser-

Process Component faults

u . =t>: . . . . . Component

Coupling

Observer

Coupling

Figure 9: Local observer scheme

ALARM

vation lies in the couplings among the components. If the couplings are sufficiently weak or measurable, malfunctions in the components affect only the estimates of the corre­sponding local observers. A unique fault isolation is then possible. However, if there are substantial non-measurable interactions, then the effect of a fault in a component prop­agates to observers of other components, and the observer scheme fails to isolate the fault. What could, however, be isolated is a fault in a subsystem of coupled components, which has only known interconnections to other similar sub­systems.

The hierarchical observer scheme permits the division of the whole system into an upper level of interconnected subsys­tems with either weak or measurable couplings among the subsystems, and a lower level comprising only components with strong and uncertain couplings. For each of the result­ing configurations in both levels a local observer scheme can be applied. In the upper level the so-called available state coupled observer scheme ASCOS, Fig. 10, can be used. Here the intercouplings of the original system are taken to feed the observers.

In the lower level a coupling network is required to generate the unavailable coupling signals among the observers. As coupling signals one can take the estimated states including the estimation errors. The resulting estimated state coupled observer scheme ESCOS is shown in Fig. 1 1 .

The coupling of the local observers can completely be avoided by using local unknown input observers that are made invariant to the non-measurable coupling signals, see Fig. 12.

Decision and Monitoring

The final step in any FD! procedure is the fault decision and monitoring. The decision logic operates either directly on the residuals generated by the residual generator or on decision functions built of there, as, for example, likelihood functions. The final goal is then to maximize the detection probability while minimizing the false alarm rate. In gen­eral the decision procedure includes either threshold logic or

219

p i�t Xj . . . . ... . . .. . . ...... .. . .. . . . .. .. . .. .... .. . .. ...... i-thcot.1i>oNli�.

·

J;o'I

!&1 : . . . . . . . . . . ... . . ... ..... . . ..... ... . . . . . . . ... . . i:tl.1.��� �� _()_B��-FI'-'.��

Figure 10: ASCOS

p �i1 Ai!

xi · · ········· ··· · ··· · ··················· · · · · · · ··· · · · ·· · · · · · ·i-thcoMPONE1

P i-lh OBSERVE� 81 j�_1 'ij�+Hij<Yf9'� .... .... .. .. ..... .. .. .. .. .. . .. .. . .. . .. . .. . .. . .. . .. . J;o'I

Figure 1 1 : ESCOS

more sophisticated deterministic or probabilistic tests with an increasing tendency towards the application of adap­tive strategies, fuzzy logic and artificial intelligence (Frank 1992).

Our view is that the use of natural intelligence should in­creasingly be used. This means that the evaluation of the residuals should preferably be done by the operators us­ing the residual generator as a proper tool to support their decision in combination with their expert knowledge of the process and the process environment. This strategy may be of particular relevance in connection with lean production.

Conclusions

The paper has outlined the principles and various tech­niques of FD! in dynamic systems based on analytical sys­tem models. Attention has been focused upon the observer­based methodology with due regard to a unified approach

p �t\xi · · · · · · · · · · · · · · · · · · · · · · · · · · · · · -�

il· · · · · · · · · ·i-ihc0t.1PoNE1

,- - - - - - - - - - - - - - - - -·--·- - - - - - - --·- - - - - - - - - -·-·- - - - - -·-·······--·--·-·-- -·-·--·-·-; ' ' ;

i

! '

Figure 12: Local Unknown Input Observer Scheme LUIOS

known as the unknown input observer scheme UIOS which can provide a maximum of robustness with respect to un­known inputs.

Though much research is still going on in this field some of the methods described have already reached a rather high degree of maturity and there are a number of encouraging applications of model-based FDI schemes, especially in elec­trical, mechanical, pneumatic and hydraulic systems as, for example, aircrafts or advanced transportation systems. Yet in cases where only poor analytical models are available, as, for example, in complex chemical processes, the analytical model-based FDI approach is still facing difficulties and re­strictions, and it seems that here it is the knowledge-based method that will have the best chance to be used for model­based FDI in combination with or as an alternative to the analytical model-based approach.

References

Brunet, J., Jaume, D., Labarrere, M., Rault, A. and Verge, M. (1990), Detection et diagnostic de pannes, ap­proche par modelisation, Hermes, Paris.

Chow, E. Y. and Willsky, A. S. (1984), Analytical redun­dancy and the design of robust failure detection sys­tems, IEEE Trans. A .G., AC-29, pp. 603-614.

Clark, R.N. (1978), Instrument fault detection, IEEE Trans. Aerosp. and El.Syst., AES-14, pp.456 - 465.

Ding, X. and Frank, P.M. (1991) , Frequency domain ap­proach and threshold selector for robust model-based fault detection and isolation, Proc. SAFEPROCESS '91, Baden-Baden, Vol. 1 , pp. 307-31 1.

Frank, P.M. (1987), Advanced fault detection and isolation schemes using nonlinear and robust observers Proc. 0th '

1 /FAG World Congr. , Munich, Vol. 3, pp. 63-68.

Frank, P. M. and Wiinnenberg (1989), Robust fault diag­nosis using unknown input observer schemes, in: Pat­ton, Frank, Clark, Fault Diagnosis in Dynamic Sys­tems, Theory and Application, Prentice Hall.

Frank, P.M. (1990), Fault detection in dynamic systems using analytical and knowledge-based redundancy -A survey and some new results, Automatica, Vol. 26,

220

No. 3, pp. 450 - 4 72.

Frank, P.M. (1991) , Enhancement of robustness in observer-based fault detection, Proc. SAFEPRO­CESS '91, Baden-Baden, Sept. 10-13, pp. 275-287.

Frank, P. M. (1992), Robust model-based fault detection in dynamic systems, /FAG Symp. On-Line Fault De­tection and Supervision in the Chemical Process In­dustries, Newark, Del., 22. - 24. April.

Gertler, J. (1991), Analytical redundancy methods in fault detection and isolation, Proc. SAFEPROCESS '91, Baden-Baden, Sept. 10-13, pp. 9-21.

Howell, J. ( 1991) , Model-based Fault Diagnosis in Infor­mation Poor Processes, PhD Thesis, University of Glasgow, Dept. of Mech. Engg.

Isermann, R. (1984), Process fault detection based on modeling and estimation methods - A survey, Auto­matica, Vol. 20, pp. 387-404.

lsermann, R. ( 1991), Fault diagnosis of machines via pa­rameter estimation and knowledge processing, Proc. SAFEPROCESS '91, Baden-Baden, Sept. 10-13, pp. 121-133.

Lou, X. C., Willsky, A. S. and Verghese, G. L. (1986), Optimally robust redundancy relations for failure de­tection in uncertain systems, Autom. 22, pp. 333-344.

Patton, R. J. , Willcox, S. W. and Winter, J. S. (1987), A parameter insensitive technique for aircraft sensor fault analysis, A/AA Journal of Guidance and Control and Dynamics, pp. 359-367.

Patton, R. J. ( 1988), Robust fault diagnosis using eigen­structure assignment, in: Patton, R. J., Frank, P. M., Clark, R. N. (Eds.) Fault diagnosis in dynamic sys­tems, theory and applications, Prentice Hall, London.

Patton, R.J., Frank, P.M. and Clark, R.N. (Eds) ( 1989), Fault diagnosis in dynamic systems, Theory and ap­plication, Prentice Hall.

Patton, R.J. and Chen, J. (1991), Parity space approach to model-based fault diagnosis - A tutorial survey and some new results, Proc. SAFEPROCESS '91, Baden­Baden, Sept. 10-13, pp. 239-255.

Sauter, D. (1991 ) , Contribution a l'etude des methodes de detection de rupture de model, These de Docteur es Sciences Plysiques, Universite de Nancy I, CRAN.

Seliger, R. and Frank, P.M. (1991a), Robust component fault detection and isolation in nonlinear dynamic sys­tems using nonlinear unknown input observers, Proc. SAFEPROCESS '91, Baden-Baden, Sept. 10-13, pp. 313-318.

Seliger, R. and Frank, P.M. ( 199lb), Fault diagnosis by disturbance decoupled nonlinear observers, Proc. 30th

CDC, Brighton, Vol. 3, pp. 2248-2253.

Willsky, A. S. ( 1976), A survey of design methods for fail­ure detection in dynamic systems, Automatica 12, pp. 601-611 .

Wiinnenberg, J. ( 1990), Observer-based fault detection in dynamic systems", Ph.D. thesis, University of Duis­burg, Fortschrittberichte VD/ 8 Nr. 222, VDl-Verlag, Diisseldorf.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

ON-LINE RESIDUAL COMPENSATION IN ROBUST FAULT DIAGNOSIS OF DYNAMIC SYSTEMS

R.J. Patton and J. Chen

Department of Electronics, University of York, York, YOJ 5DD, UK

Abstract: This paper deals with the robust fault diagnosis problem for systems with unstructured uncertainties, for which disturbance de-coupling methods are not applicable. A technique for compensating the residual is proposed. By compensation, the effects of modelling errors on the residual will not adversely affect the detection and isolation of faults. The idea is to estimate approximately the bias term in the residuals due to modelling errors, then compensate it on-line. These estimates are used to form a compensated residual to decrease the effect of modelling errors on the residuals. The compensated residuals are then used to make the fault diagnosis decision. Simulation results illustrate the effect of incipient faults in sensors of a complex jet engine can be reliably detected with the method developed.

1 Introduction

Modelling uncertainty is the main problem impeding the progress of applying model-based fault diagnosis (FD) techniques to real systems. All model-based FD methods employ system models to generate fault indicating signals (residuals) to detect and isolate the presence of faults. Here, we consider that fault diagnosis includes the detection, isolation and estimation of each fault in the components of a dynamic system. Residuals are normally based on a comparison between the measured and anticipated responses. The anticipated response is obtained using a model of the monitored system. Fault diagnosis would be straightforward if an exact system model were available and if the system could be considered noise-free. Exact modelling of real systems however, is impossible. Hence, a practical and applicable fault diagnosis scheme must be made robust with respect to modelling errors and uncertainties. As a definition, the robustness of an FD scheme is the degree to which its diagnosis is unaffected by (or remains insensitive to) modelling uncertainties (Frank, 1991; Patton & Chen, 1991a, 1992; Gertler, 1991).

In recent years, a great deal of research effort has been paid towards the improvement of robustness in FD problems. Up to now, the most successful ways to achieve robustness in FD is the use of "disturbance de-coupling" ideas (Frank, 1991; Patton & Chen, 1991a, 1992; Gertler, 1991). In these approaches, all uncertainties are considered as disturbance terms acting on a nominal model of the monitored system. Although the magnitude of the uncertainty is unknown, its distribution into the

221

system dynamics is assumed to be know a priori (Frank, 1991; Patton & Chen, 1991a, 1992; Gertler, 1991). This is often referred to as structured uncertainty. For unstructured uncertainty, no mature robust FD methods are available. Perfect solutions for this problem are almost impossible, although an approximation solution can be achieved. For example, one way (Patton & Chen, 1991b, 1991c) is to estimate an approximation structure of uncertainties and then to deal with this using disturbance de-coupling methods. Another way is to make use of adaptive thresholds via so­called "threshold adaptors" or "threshold selectors" (Emami-Naeini et al, 1988; Ding & Frank, 1991).

In practical situations, the residual is never zero even when no faults occur. A threshold must then be used in the residual evaluation stage. Normally, the threshold is set slightly larger than the largest magnitude of the residual evaluation function for the fault-free case. The smallest detectable fault is a fault which drives the residual evaluation function to just exceed the threshold. Any fault which produces a residual response smaller than this magnitude is not detectable. From our point of view, the purpose of the robust design is to decrease the magnitude of the fault-free residual and maintain (even increase) the magnitude of faulty residuals.

This paper deals with unstructured uncertainties. An on-line compensation method for residuals is presented. The idea is to estimate approximately the bias term in the residuals due to modelling errors, then compensate it on-line. These estimates are used to form a compensated residual to decrease the effect of modelling errors on

residuals. The compensated residuals are then used to make the FD decision. The proposed method has been used to detect faulty sensors in a simulated jet engine system. The results demonstrate the effectiveness of this approach.

2 Basic concepts of residual generation

The model-based FD process consists of two stages: (1) Residual generation: In which, outputs and inputs of the system are processed by an appropriate algorithm (a processor) to generate residual signals. (2) Decision making: The residuals are examined for the likelihood of faults, and a decision rule is then applied to determine if any faults have occurred. The residuals are quantities that represent the inconsistency between the actual plant measurements and the mathematical model outputs. If multiple faults may occur and have to be isolated, a set of structured residuals is required, so that different faults which are reflected in the residuals in different ways can be isolated.

Now, we consider the mathematical description of the diagnosis problem. Though the plants are usually continuous, the diagnostic computations are normally performed on sampled data. Hence, we consider discrete (discretized) plant models. Note that most of the diagnostic methods can be applied to both discrete and continuous models. Plant linearity will be assumed throughout; in the case of a non-linear plant, this implies model linearization around an operating point.

The discrete-time input-output description of the monitored system is:

�(z) = Gu(z)y(z) + Gr(z)f(z) (1)

where � is the mxl output vector and y is the rxl input vector, whilst f is a qxl fault vector. The transfer function matrix G (z) represents the nominal system model which

u is assumed known.

Each element fi(k) (i = 1, 2, .... , q) corresponds to a special fault mode. From a practical point of view it is unreasonable to make further assumptions about the characteristics but consider these as unknown time functions. The transfer function matrix Gr(z) represent the effect of faults on the system which is normally known a priori.

Residual generation plays an important role in FD. In order to be useful indicators of ·faults, the residuals should be small in the absence of faults, and one or more of them should become large in the presence of a fault. The residual generator is shown in Fig.1 which involves the processing of the input and output data of the system.

222

!J.(z) System

r(z) ' ' '

--: • H Jz) i Residuals ' ' ' ' � --- -- - - - -- -- - - - - --- --- - ___ _: Residual Generator

Figure 1 : The transfer function structure of residual generator

A general form of the residual generator can then be expressed as:

r(z) = [ Hu(z) �(z) ] [ y(z) ]

�(z)

= Hu(z)y(z) + Hy(z)�(z) (2)

Here, Hu(z) and Hy(z) are transfer function matrices which are realizable using stable linear systems. The residual must be independent of the normal operating state of the system. In the fault­free and no uncertainty case, the residual is zero (or at least very small), i.e.

r(z) = O and �(z) = Gu(z)y(z) (3) In order to satisfy this requirement, the transfer functi�n matrices Hu(z) and �(z) must satisfy the equation:

or

(4)

(5) Equation (2) is a unified and generalized representation of all residual generators. The design of the residual generator results simply in the choice of the transfer function matrices H (z) and H (z) which must satisfy equation (4). Differe6't residual generation methods correspond to different parameterizations of H (z) and H.,(z). The observer residual structure is

uan exampfe of

the parameterization of Hu(z) and H (z). One can obtain other residual generators J!mg different forms for Hu(z) and H (z), designed to meet any performance specificatiJn.

When faults occur in the monitored plant, the response of the residual vector is:

r(z) = HyCz)Gr(z) f(z) (6)

In order to detect the i-th fault in the residual r(z), the i-th column [H (z)G�z)]· of the transfer matrix [�(z)Gr(z)] lhoulcf be 1 nonzero, especial for steady �alues, i.e.

and

If the above conditions are satisfied, the i-th fault can be said to be detectable using the residual. This is the detectability problem. The fault detection problem can be stated in terms of some decision function, J(r), and threshold, Jth·

J(r) s Jth J(r) > 1th

for

for

f(k) = 0

f(k) ;t 0

Evidently, the ideal case would be Jth = 0 which is however, normally impossible because of the presence of admissible errors.

In practice, no nominal models can be describe a physical plant perfectly, the model uncertainty is inevitable and should be taken into account. Model uncertainty refers to the mismatch between the nominal model and the actual system. An uncertain system can be expressed by:

:y(z) = G(z)y(z) + Gr(z)f(z) (7)

where G(z) is the actual transfer function matrix which can not modelled exactly. For multivariable systems, there are three commonly used forms of representing uncertainty:

G(z)

G(z)

G(z)

Gu<z) + .1Ga(z)

Gu(z)(I + .1Gi(z))

(I + .1G0(z))Gu(z)

(8a)

(8b)

(8c)

where AGiz), .1Gi(z) and A G0(z) represent additive, mput multiplicative and output multiplicative perturbations, respectively.

When we apply the residual generator (2) to the uncertain system (7), the actual residuals are:

r(z) = H/z).1Ga(z)y(z) + H/z)Gf(z)f(z)

r(z) = H/z)Gu(z).1Gi(z)y(z) + H/z)Gf(z)f(z)

r(z) = H/z)AG0(z)G/z)y(z) + H/z)Gf(z)f(z)

These three situations can be summarized as:

r(z) = H/z).1G(z)y(z) + H/z)Gf(z)f(z) (9)

From equation (9), it can be seen that the residual is not zero, even if no faults occur in the system.

223

Indeed, it can be difficult to distinguish the effects of faults from the effects of modelling errors. The effects of modelling error obscure the performance of fault diagnosis and act as a source of false and missed alarms. Therefore, in order to minimize the false and missed alarm rates, one should design residuals which are insensitive to uncertainties.

For the case where the modelling error can be considered as structured uncertainty (Ding & Frank, 1991; Patton & Chen, 1991a, 1992), i.e.

AG(z)y(z) = Giz)!l(z) (10)

where !l(z) is a unknown disturbance vector, the transfer function Giz) is known. In this situation, the effect of the uncertainty on the residual can be nulled by disturbance de-coupling design, i.e. to make:

(11)

This can be done either in the time domain, e.g. the unknown input observer approach (Frank, 1990; Wiinnenberg, 1990), the eigenstructure assignment approach (Patton & Chen, 1991a, 1991b, 1991c, 1992), or the frequency domain approach (Ding & Frank, 1991).

Unfortunately, most uncertainties are unstructured. In this situation, one way to achieve reliable fault diagnosis is the threshold selection or adaption method ((Emami-Naeini et al, 1988; Ding & Frank, 1991)). In this method, assuming that:

then, an adaptive threshold is assigned as:

T(z) = 6H/z)y(z)

We have classified this approach as a passive approach for robust fault diagnosis (Patton & Chen, 1992) as no effort is made to achieve robustness in the residual design. Because the threshold is relatively large in this method, the smallest detectable fault is also large. This cannot meet the requirement of incipient fault diagnosis

which is the special concern in the current fault diagnosis literature. So-called incipient faults may

not be very serious when they occur but might lead to serious situations. To be specific, this class of

faults is quite small in magnitude and the developing speed is slow. In order to deal with the unstructured uncertainty, Patton & Chen (1991b, 1991c) proposed the approximate de-coupling

approach. In their approach, an (estimated) approximate structure is used to describe the unstructured uncertainty. Hence, approximate de­coupling is achievable.

3 On-line residual compensation

From Section 2, it can be seen that the modelling uncertainty gives rise to the following term in the residual:

(12)

which is not zero and called the bias tenn. This term is related with the input. Assume that this bias term can described as:

(13)

where G (z) is an unknown transfer function matrix wh1fch represents the combination of all the effect of all uncertain factors on the residual, eg. parameter perturbations, dynamic errors (e.g. model reduction error) etc. This relationship can also be described in the time domain as:

r1(k) + a1r1(k-1) + ... + anr1(k-n) = bQl!(k) + b1y(k-l) + ... + bny(k-n) (14)

or (15)

where the parameter vector e is:

<f>(k) = [-r1(k-l) ... -r1(k-n); y(k) y(k-1) ... y(k-n)]T

If 9 is known, i.e., the transfer function G1iz) is known, the bias term r1(k) in the residual can be estimated on-linely as:

(16) where:

¢(k) = [-r'i(k-1) ... -r1(k-n); y(k) y(k-1) ... y(k-n)JT

_;J_. Primary r u Residual ' _,. .... Generation On-line

Residual Compensation

.... Bias t Estimation r 1 r*

Figure 2: The on-line residual compensation

Hence, a compensated residual is defined as:

r•(k) = r(k) - r1 (k) (17)

224

which will be used for robust fault diagnosis. As the residual compensation can be done on-line, this approach for robust fault diagnosis is called the on-line residual compensation approach. This idea is illustrated in Fig.2. As the effect of the modelling uncertainty on the

residual has been compensated, the compensated residual r•(k) is only affected by the faults and can be used for robust incipient fault diagnosis.

The problem is that the parameter vector 9 is unknown. Based on equation (14), the least­squares method (Goodwin & Payne, 1977) can be used to identify this parameter vector. When the system is in the normal condition, the bias term r1(k) is equal to the residual r(k). Where r(k) is a primary residual which is generated using any normal residual generation method (e.g. observer­based methods, parity equation methods). The fault-free residual r(k) {k= l, 2, .. ., N) will be used to identified the parameter vector 9. This stage is called as the training stage. Then, the estimated parameter 9* is used to compensate the residual. The model order n is not known a priori which is determined in the identification procedure. In practice, a reasonable model order is less than 5 (Goodwin & Payne, 1977).

The parameter identification can be also carried out adaptively based on the recursive least-squares equation as follows:

S(k) = S(k-1) + K(k)[r1(k) - S(k-l)<f>(k)] (18a)

P(kf1 = P(k-lf1 + <f>(k)<f>T(k)/a(k) (18b)

K(k) = P(k)<f>(k)/a(k) (18c)

where a(k) is a forgetting factor. The tracking speed can be improved by changing the forgetting factor.

The question arising here is that the effects of modelling uncertainties and faults are mixed up in r(k), i.e. r1(k) is a part of r(k). Hence, the residual compensation method is divided into two stages:

(1) Adaptive training stage: In this stage, the system is assumed normal. The residual is only due to the modelling uncertainty and r1(k) = r(k). This residual is used for identifying the parameter vector 9 based on equations (18). After the .... estimation 9(k) converge to a constant value 9*, the procedure will move to the next stage. The convergence can be tested using:

ll r1(k) - r1(k) ll $ €

or ll e(k+ 1) - e(k) ll $ µ

where € and µ are small positive constants which are chosen a priori.

(2) On-line residual compensation stage: In this stage, equations (16), (17) and the estimated parameter e• will be used to compute the compensated residual r•(k).

The idea of the adaptive parameter identification and the on-line residual compensation method is illustrated in Figure 3.

y Primary

u Residual Generation

Adaptive On-line Parameter .--.... Residual Identification r 1 Compensation

r*

Figure 3: Adaptive parameter identification and on-line residual compensation

When the system operating conditions change or the system characteristics vary, the parameter identification will be started again.

Frank, Ding & Wochnik (1991) used the adaptive observer approach to generate robust residuals for unstructured uncertain systems. A parameter identification procedure is also involved in their method. This is a re-identification of the system model. The disadvantage of their method is that it is only useful for the parameter variation situation as they considered that the modelling uncertainty is only due to parameter perturbation. In this paper, we consider the combined effects of all uncertainties on the residual which includes: parameter perturbations and model reduction errors etc. For a range of operating conditions, we can use a fixed system model together with a residual model, the latter may vary according to the system operating conditions.

For all adaptive methods, a problem is that the fault effects may be compensated as well as modelling error effects. This makes the detection impossible. Hence, the adaptive parameter identification procedure must be switched off before the possible faults occur otherwise the

225

incipient faults may be mis-interpreted as a model variation. For the hard faults (the magnitudes are relatively large and occur abruptly), the detection is also possible even if the adaptive parameter identification is not switched off as the compensated residual and/or the parameter estimation may jump rapidly.

4 An example: Robust detection of incipient faults in jet engine sensors

A complex thermodynamic simulation model of a jet engine is utilised as an example to illustrate the method developed in this paper. This model has 17 state variables; these include pressures, air and gas mass flow rates, shaft speeds, absolute temperatures and static pressure. This is a highly non-linear dynamic system which has grossly different steady-state operation over the entire range of spool speeds, flow rates and nozzle areas. The jet engine has the measurement variables N

L'

NH, T7, P6, T29• N denotes a compressor shatt speed, P denotes a pressure, whilst T represents a measured temperature. The main engine fuel flow rate is considered as a control input. The linearized 17th order model at one operating point has been used to simulate the system. For practical reasons and convenience of design, we choose to employ a 5th order model to approximate the 17th order model. The model reduction errors and other errors are inevitable and present a real challenge to fault diagnosis. The simulation data are generated using 17th order linear model with 10% perturbation in the model matrices. The input is a step signal combined with a muti-frequency sinusoid signal. In order to give meaningful magnitudes in the final results a per-unit scaling of the engine dynamics has been used.

An observer based on the 5th order model is used to generate the output estimation i(k). The primary residual is defined as:

r(k) = W�/k) = W(:Y(k) i(k))

where the weighting matrix is W = [1 1 1 1 1]. In this case, the primary residual is a scalar variable.

The Fig.4 shows the primary residual for the fault­free case. It can be seen that the primary residual is too large and a small threshold cannot be used to detect faults.

This primary residual is now used as training data to identify the parameter vector 9. In this paper, a 2nd order model has been chosen, i.e. n = 2 (in equation (14). Using the MATLAB Identification Toolbox, we obtain the identification results are: a1 = -1.430808 � = 0.432895 b0 = -0.002161 b1 = 0.002153 b2 = o

primary residual -30 �---=-.--------.---�

-35

-40

-45 L__ ___

c__ ___ c__ __

__,

0 5 10 15 time (seconds)

Figure 4: The primary residual for fault free case

These parameters have been used for residual on­line compensation. In turn, the compensated residual will be used to detect faults. A particular emphasis is the power of the method to detect soft or incipient faults which are otherwise unnoticeable in the measurement signals. These attributes are well illustrated in the following graphical time response results. As the fault detection scheme has been made robust against modelling errors, the scheme is able to detect incipient faults under conditions of modelling uncertainty.

Fig. 5 shows the faulty output of sensor TT The fault signal is very small compared with the output signal, and consequently, the fault cannot be detected directly in the output.

.:1T7 (oK) 150 �---,-.:..__--.-------�

100

50

5 10 15 time (seconds)

Figure 5: The faulty output of the temperature sensor (T7)

primary residual -30..--���-,--���-.-����

-35

-40

time (seconds)

Fig.6 (a) primary residual

226

compensated residual 4���������������

2 0

-2

time (seconds)

(b) compensated residual

Figure 6: The primary and compensated residuals when a fault occurs on the temperature

sensor T7

Fig.6 shows the faulty residual signals. It can be seen that the compensated residual has a very significant increase when a fault has occurred in the system, a small threshold then can easily be placed on the residual signal to declare the occurrence of faults. But, one cannot be sure whether a fault has even occurred in the system when using the information from the primary residual.

&>6 (KPa) so �����-=-���.--����

60

40

20

5 10 15 time (seconds)

compensated residual 2 r-��---o;:==:::::-����----,

0

-2

15 time (seconds)

Figure 7: The faulty output the compensated residual when a fault occurs in the pressure

sensor P6

A fault signal with the same time profile is now added to the pressure sensor signal for P 6 in order

to assess the fault detection performance further. The result is shown in Fig. 7.

All simulation results demonstrate the efficiency of the compensated residual in the role of robust fault detection.

5 Conclusion

This paper has provided a study of the on-line residual compensation method for robust model­based fault diagnosis. Using an identification approach, the combined effects of all uncertainties on the residual are modelled as a transfer function between the residual and the input. Then, the effect of uncertainties can be compensated on-line. The compensated residual provides a basis for robust fault diagnosis.

The paper has also provided an interesting simulation of the application of the residual compensation approach to detect sensor faults. The approach used considers robustness in terms of the modelling uncertainty present when a low order model is used to approximate a complex non-linear high order system. The results have shown that an incipient fault which has a barely detectable effect on any one measurement, can be detected very easily using a compensated residual. This illustrates the potential of using a model­based method which does not actually require a detailed and accurate model of the dynamic system considered. Further studies are being carried out to evaluate the effectiveness of the approach applied to real engine data. Especially, the stochastic case will be considered. This may involve noise modelling etc.

6 Acknowledgements

The authors acknowledge the funding support for this research from the UK Science & Engineering Research Council through grant (GR/G2586.3). Thanks are extended to Professor H. Y. Zhang for helpful comments during his sabbatical leave at the University of York.

7 Reference

Ding X & Frank P M (1991), Frequency domain approach and threshold selector for robust model-based fault detection and isolation, Proc. IFAC/IMACS Symposium SAFEPROCESS'91, Baden-Baden, Sept 10-13, Vol.1, 307-312

Emami-Naeini A E, Akhter M M & Rock S M (1988), Effect of model uncertainty on failure detection: the threshold selector, IEEE Trans. Aut. Contr., AC-33 (2), 1106-1115

227

Frank P M (1990), Fault Diagnosis in dynamic system using analytical and knowledge -based redundancy - A survey and some new results, Automatica, 26 (3), 459-474

Frank P M (1991), Enhancement of robustness in observer-based fault detection, Proc. IFAC/IMACS Symposium SAFEPROCESS'91, Baden-Baden, Sept 10-13, 1991, Vol.1, 275-2S7

Frank P M, Ding X & Wochnik J (1991), Model based fault detection in diesel-hydraulically driven industrial trucks, Proc. of 1991 Amer. Control Conf., 152S-1433, Boston, USA

Gertler J (1991), Analytical redundancy methods in Failure detection and isolation, Proc. of IFAC/IMACS Symposium SAFEPROCESS'91, Baden-Baden, Sept., Vol.1, 9-21

Goodwin G C & Payne R L (1973), Dynamic system identification: Experiment design and data analysis, Academic Press, 1977

Patton R J (1991), Fault detection and diagnosis in aerospace systems using analytical redundancy, IEE Computing & Control Engineering Journal, £ (3), 127-136

Patton R J & Chen J (1991a), A review of parity space approaches to fault diagnosis, Proc. IFAC/IMACS Symposium SAFEPROCESS'91, Baden-Baden, Sept.10-13, 1991, Vol.1, 239-255

Patton R J & Chen J (1991b), Robust fault detection of jet engine sensor systems by using eigenstructure assignment. Proc. of A/AA Guidance, Navigation & Control Conf., New Orleans, August, AIAA-91-2797

Patton R J & Chen J (1991c), Optimal Selection of unknown input distribution matrix in the design of robust observers for fault diagnosis, Proc. IFAC/IMACS Symposium SAFEPROCESS'91, Baden-Baden, Sept.10-13, 1991, Vol.1, 221-226, also to be published in Automatica

Patton R J & Chen J (1992), Robustness in model­based fault diagnosis, In Concise Encyclopedia

of Simulation and Modelling, (Eds: D. Atherton, P. Borne), Pergamon Press, January 1992, 379-392

Patton R J, Frank P M & Clark R N (1989), Fault Diagnosis in Dynamic Systems, Theory and Application, Prentice Hall

Wiinnenberg J (1990), Observer-based fault detection in dynamic systems, Ph.D. Thesis, University of Duisburg, Germany

Copyright © IFAC Anificial Intelligence in Real-Tune Control, Delft, The Netherlands, 1992

GEOMETRIC TOOLS FOR AN OBSERVER-BASED APPROACH TO RESIDUAL GENERATION

J.-F. Magni, P. Mouyon and M.I. Arsan

CERT-DERA, B.P. 4025, F-31055 Toulouse Cedex, France

Abstract. This paper emphasizes on the basic geometric tools necessary for the design of a failure diagnosis system, where the diagnosis is based on the residua.I generation by using elementary observers. In order to improve the sensitivity of the residua.ls, various methodologies a.re proposed. A realization over a. physical example is presented.

Keywords. Failure detection, Observers, Ana.lytica.1 Redundancy, Diagnosis, Eigenstruc­ture Assignment

1 INTRODUCTION

Analytical redundancy approach has become one of the major research areas over the last two decades, in the design of a failure diagnosis system, see Frank and Wunnenberg ( 1 ) , Gertler (2), Patton and Chen (5) and the references therein. This approach pre­sumes the observation of certain variables ca.lied the residua.ls, which a.re equal to zero as there isn't any admissible failure occurred. These residua.ls can be arranged in such a. way that their scheme permits the decoupling of ea.ch admissible failure from the other failures and/or from the causes of false alarms.

The work described in this paper considers firstly, the generation of residua.ls by using well-defined elemen­tary observers. An easy to realize residua.I genera­tion procedure is depicted by using these elementary observers. For most of the mathematical demonstra­tions, one can apply to Magni and Mouyon (3) and (4). These references describe a stepwise procedure for the design of observers, including diagnostic ob­servers.

The decoupling of each event is achieved by using the notion of structured residua.ls. This concept is ex­plicited by making calls to the so-ca.lied geometric ap­proach, but it is essentially realized by the classical eigenstructure assignment. A necessary and sufficient condition of a. structured residua.I is also given.

The sensitivity of a structured residua.I is studied and it is related to the choice of the eigenvalues. If there are not too many decoupling requirements, the de­gree of freedom on the eigenvectors is also used for improving the sensitivity.

Finally the utilization of these concepts in a. fa.ult de­tection scheme is illustrated over a significant physical example.

229

2 RESIDUAL GENERATION

2.1 Observer design

The basic step is the design of what we have called "elementary observers" , which are one-dimensional in the real case and two-dimensional in the complex case. We sha.11 consider a linear system with n-dimensiona.l state space and p-dimensiona.l measurement space :

x = Ax + Bv + 11., y = Cx + Dv + 1111 v = v + llv

( 1 )

where C is not assumed t o b e o f full rank. The signals 11., , 11., and 1111 stand respectively for: actuator failure or disturbance on the input (v), component failure or state disturbance, sensor failure or disturbance on the measurement (y) (See Figure 1 ) .

At first, i t is assumed that 11., , 11., and 1111 are a.II equal to zero. Under this assumption, the derivation of the following lemmas are straightforward :

Lemma. 2.1 : The dynamic system is defined by :

i = /3z - tT y + (uT B + tT D)v (2)

is an observer of z = uT x , where u, t, /3 are such that :

(3)

The observation dynamic corresponds to the real eigenvalue /3.

Lemma. 2.2: The dynamic system is defined by :

[ !: ] = [ � -:: ] [ !: ] - [ !f ] fr+

[ =� ] Bv + [ !� ] Dv (4)

Fig. I. µ is the estimate of µ. = Q.,v + Q11y + Q,,z.

is an observer of Zr = !R(u*x) and z; = 9(u*x), where the subscripts "r " and "i" stand for "real" and "imag­inary" parts, and u, t, f3 are such that :

u*A + t*C = iJu* (5)

The observation dynamics correspond to the eigenval­ues f3 and iJ.

If a set of elementary observers is used at a time, we can build matrices U, T and IT where the rows of U and T are the vectors satisfying (3) (or the real and imaginary parts of vectors satisfying (5) in the complex case) and where IT is a diagonal matrix with the dynamics in the diagonal (2 x 2 blocs as in (4) for the complex case). Clearly these matrices satisfy

UA + TC = ITU (6)

Finally, to estimate a desired signal we have at our disposal: v (input without disturbance), y (measure­ment with disturbance) and z (estimation of z = Ux through elementary observers). Therefore we can only estimate the combinations of the form Q.,v + Q11y + Qzz, for Q.,, Q11 and Qz varying. Figure 1 depicts the device to be used for estimating a signal in the form of µ = Q.,v + Q11y + Qzz.

2.2 Generalities on observer-based residual gener­ation

Observer-based residuals are signals generated from v, ii and z which are identically equal to zero when there is no failure or disturbance (11., = 0, 1111 = 0, llz = 0). If a failure occurs, the value of the residual is no longer equal to zero. To make a diagnosis relative to a failure, we must consider structured residuals, i.e. residuals that remain zero when some failures of a prespecified set occur.

Let us describe an approach for the structured resid­ual generation. In order to simplify the presentation, it will be assumed that there is no actuator failure (11., = 0, see (4) otherwise). The possible failures are modelized as follows :

where ii represents the failures that must have no ef­fect on the considered residual and where ii signifies the failures which must be detected. Let us state a procedure for designing such a residual.

230

Procedure 2.3: . Structured residual generation {as­suming that D = 0) :

o Solve for 111 , . . . , flr the following equation

'Ir ] [ g��:l ] = O

U(f3r)

(7)

where [ U(f3;) T(f3;) ] are matrices of maximal rank, such that they satisfy

( U(/3;) T(/3;) ] [ A 1;1 � ] = 0 (8)

o Find the matrices U, T and II given by, II = Diag{/31 , . . . , /3r} and

U = [ 111U

:(f3i ) l ; T =

[ 111T�/31 ) l (9)

'Ir U (f3r) flr T(f3r)

o and set

Q., = 0 ;

Q11 = 0 j Qz = [ 1 . . . 1 ] (10)

The device giving the structured residual jJ. is depicted in Figure 1.

For complex values of {3, obvious amendments are to be done, for instance: if f32=P1 we must be careful to attain 112=tji , etc . . . From now on, it will be assumed that all {J;'s are real.

Justification of the procedure. The assumption of D = 0 is not important, it is made only for simplifying the residual generator as it induces the fact that Q., can be made equal to zero. The fact that Q11 = 0 is not a necessary condition. Here we have decided to present a residual generator which does not use directly the measurements (so, measurements will be filtered). See, ( 4) for a general presentation without these simplifying assumptions.

To justify the procedure we must check that the trans­fer function between ii and jJ. is equal to zero. From Figure 1 and Equation (10)

p.(s) = [ 1 . . . 1 ](s/ - IT)-1 (U Bv(s) -TDii(s) - TC(sI - A)-1 (Bii(s) + Bv(s)))

A special form of Equation (6) is needed. Subtract the matrix sU from both sides, then multiply the left hand side by (sl - IT)-1 and the right hand side by (sl - A)-1 , so we obtain

So

-(sl - IT)-1TC(sl - A)-1 = U(sl - A)-1 - (sl - IT)-1 U

p.(s) = -[ 1 . . . 1 ]( s/ - IT)-1 (U B + TD)ii(s) and using (8), it is clear that p.(s) = 0.

It remains to study the sensitivity of the residual µ to the failure ii.

!.9 Senaitivity of atructured reaiduala

For studying the sensitivity of the residual µ obtained by using Procedure 2.3 a subspace is introduced in ( 4) which is similar to the infimal complementary observ­ability subspace extensively used for decoupling (rf. Geometric Approach). We recall this definition and a lemma that will answer to the questions concerning the sensitivity.

Definition 2.4: • .6. n NA,o =

{t'!;i!zero of (A,A,C,D)} Ker (U (/Ji) T(/Ji)) (11)

where the number of {3; ia large enough and where U ({J;) and T({3;) are given by ( 8).

Lemma 2.5: The event with aignature fJ and D affecta the reaidual µ(a) computed by Procedure !.9 if and only if

Im [ � ] (l'. Afk,b The proof of this lemma can be found in (4). Assuming that the signature B and D is as in Lemma 2.5, the residual µ is not decoupled from the failure ii, however, it remains to optimize the coupling to make the failure detection more reliable. For this purpose, we are going to propose an amendment to Procedure 2.3 which enables to maximize the steady state gain between ii and µ (with a normalization because the residuals are defined according to a multiplicative co­efficient).

For this purpose, consider the degrees of freedom ap­pear while solving (7). Let X = [X1 . . . Xr] be a matrix with maximal rank such that [ U(/J1 ) l U(f32) x . = 0

U(f3r)

(12)

a priori the degrees of freedom for choosing f11 • • • fir correspond to a vector e which yields

[ '11 It will be shown in Lemma 2.6 that some of these "degrees of freedom" might be redundant.

The transfer matrix between ii and the residual is, [1 . . . 1] Diag{l/(s - f31 ), . . . , 1/(s - f3r)} (U lJ +TD).

therefore, if we only consider the steady state re­sponse, the criterion to be minimized with respect to e. is the angle :

, (ce ;e,E.i ;; [U(P;) T(P;)])T , [ � ] ) c1a)

231

Let us simplify the notations by rewriting the criterion in (13) as follows : J = Angle( (eP)T,Q ). Minimizing J means that We want pT eT as "colinear" as possible to Q. For example we can look for the least square solution of Q = pTeT. Finally, we state an important result concerning the minimization of the criterion in (13). Lemma 2.6: The number of true degrees of freedom in the vector e is limited from above by the rank defi-

ciency of the matrix [ � Z ] . Proof. To prove this lemma, it suffices to show that

L ;j [U(f3i) T(f3,)] [ � z ] = 0 jE{l, . . . ,r} 1

From (8), it is clear that

[U(f3i) T(f3i)] [ z ] = 0

Again from (8), we have U(f3i)A+T(f3i)C = f3iU({3j), so

. L ;; [U(Pi) T(f3,)] [ � ] =

JE{l, . . . ,r}

L x,u(p,) jE{l, ... ,r}

then (12) concludes the proof of the lemma.

This result is very important as it shows that, it is of no use to increase the number of elementary observers to obtain more freedom for making the residual sen­sitive. Moreover, if there is enough number of such obervers so that, all the left kernel of the matrix in Lemma 2.6 is spanned, the optimal value of J becomes independent of the chosen observation dynamics.

3 PHYSICAL APPLICATION

9.1 Description of the system

The following mass-spring device example demon­strates, how one can realize a fault detection mech­anism by using observers on residual generation. The system is modelized as :

0 1 0 0 0 0 0 0 _..!1.. _.=!.. ..!1.. .=!.. 0 0 0 0 m1 m1 m1 m1 0 0 0 1 0 0 0 0 ..!1.. .=!.. � c1+c2 � � 0 0

A = m2 m2 -m2 -m2 m2 m2 0 0 0 0 0 1 0 0 0 0 � � !l.±!a. c2+c3 .!a. s. m3 m3 -m3 -m3 m3 m3 0 0 0 0 0 0 0 1 0 0 0 0 .!a. s. _.!a_ _s. m4 m4 m4 m4 c - [ i 0 0 0 0 0 0 n 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1

Fig. 2. Mass-spring system.

where m1 , m2, m3 and m4 are the four masses and their positions are given by x1 , X3, xs and x1 (entries of the state vector x ) , respectively. The spring con­stants are k1 , k2 , k3 and the damping coefficients are c1 , c2 and c3• For numerical applications, we shall take m1 = m2 = m3 = m4 = 10 kg ; ki = k2 =k3 = 1 kg/sec2 ; c1 = c2 = c3 = 1.5 kg/sec (see Figure 2). We have chosen arbitrarily, to detect which one of the three dampers is defective. Here, it is assumed that in case of a breakdown, the damping coefficient of the corresponding damper will be altered from its nomi­nal value. This leads to the modelization of damper failures as follows: for example if the nominal value of c1 is altered, we have :

Hence, we can write :

- T [ 1 0 1 0 0 Bc1 = O - ml ';;i2 - T [ 0 0 0 1 0 1 Bc2 = m2 - m3 - T [ 0 0 0 0 0 1 0 Bc3 = m3

Dc1 , Dc2 , Dc3 are 4 x 1 zero matrices.

3.2 Number of elementary observers

0 0

0 0

1 - m4

The number r of elementary observers is fixed by two objectives. First, there is a minimum in order to find a nonzero solution to (7) (-+ decoupling). Second, there is a maximum if the criterion in (13) is to be minimized, because, in view of Lemma 2.6, using ad­ditional elementary observers yields redundancy (-+ coupling).

Once we have fault signatures, we can start with the so-called structured residual generation. Here, our aim is to generate a residual for each damper in such a way that, the corresponding residual is decoupled from the others. This scheme will permit to decide directly, which one of the dampers is defective in case of a breakdown. For example for c1 , its fault signature IS:

and it must be decoupled from

�c3 ] Dc3

232

The number of observers r, is determined during the search of the matrix [U(P) T(P)]. From Equation (8), U(P) is expected to have two rows. But our system is not generic and by a simple computation it can be easily checked that, the special structure of the system yields U(P) to have three rows. Therefore, in order to be sure of a nonzero solution to (7), it suffices to consider three elementary observers (r = 3). Solving (7) leads to numerical values for 711 , 112 and 713 . Hence, we can write the corresponding residual, which is zero in normal operation (the choice of the /j;'s will be discussed later) :

To = L: 71;U(P;)x iE{l ,2 ,3}

( 14)

Now that we have decoupled a residual ro, from an event [BT bT]T, it is interesting to know whether or not an event with signature [.BT DT]T affects the residual. This can be checked by using Lemma 2.5. That is to say, if the space spanned by the event [BT DTY is not a subspace of the infimal comple­mentary observability subspace spanned by the event [BT bT]T, then the residual is affected. We have :

0 0 0 0 0 -0.9 0 0 0 0 -3 0 0 0 0 0 -20 3.1 1 0 0 0 1 0 0 0 0 1 0 -2.2 N• -1 0 1 0 1 0 [ iJ Li

0 0 0 -1 20 0 jj 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -6 0 1 0 0 0 3 0 -1 0 0 0 3

Hence it can be concluded that, six events are decou­pled from [BT bT]c1 T where two of them correspond to the fault signatures of c2 and c3, and the other four don't have a clear physical meaning. The vector [iF .i)T]c1 T is not in this subspace, moreover, the an­gle in-between is calculated as 53.8°, which signifies a sufficient coupling between the considered failure and the residual, provided that the criterion in (13) is op­timized. For this purpose, we can consider the degrees of freedom appear while solving (7) (or equivalently (12)) together with the rank deficiency of the matrix in Lemma 2.6. This rank deficiency is clearly equal to two. So from Lemma 2.6, it is not worth choosing a large number of /J;'s in order to increase the num­ber of rows of the matrix X in (12) because as far as there are enough of /J;'s so that X has two rows, the criterion in (13) cannot be further optimized. With three p, 's, it appears experimentally that X has two rows. Therefore no more p, 's are needed.

In the sequel, we shall study the residual generation by using three elementary observers. The P's will be chosen in such a way that, they must be quick enough for a rapid detection and slow enough for filtering the measurement noise. For such a given triple, the opti­mal residual will be studied. It is worth noting that the minimal value of the criterion will be indepen­dent of the triple and will correspond to 36.2° (notice that the optimal angle given above as 53.8° is the 90° complement of the optimal angle found by (13)) .

1 .1

1 .2

0 .7

0.2

-0 .3 1 00

Fig. 3. /3={-0. 75, -2.25, -6.75}

'.l.4

1 .9 1 .4 0.9 0.4

- 0 . 1 -0.6

so 1 00

Fig. 4. /3={-0.75,-2.25, -6.75}

3.3 Results and Discussion

The simulations that have been carried out are made under the following prescriptions: the system is push­ed and then pulled back, each for 10 seconds of time with the same amount of force. At 40th second a. breakdown occurs at the first damper and the move­ment of the system is examined over a. period of 100 seconds. The measures are sustained to the same level of white noise with unit spectrum. The solu­tions of Equations (7 and 8) impose the utilization of at least 3 observers for each damper. The ma.trices fl found from (8) have one degree of freedom, even so it suffices to see the effects of optimizing the angle given by (13) . For example a non-optimized solution yields to 80.76° of aperture from [BT .l)T]ci T where decou­pling to the residual is worse than the optimized case {36.2° of aperture) . In Figures 3-6, we present the normalized residual sig­nals of the defected damper. Figure 3, illustrates the results of the optimization with respect to e and of the well placement of the 3 eigenvalues. The detection is easy and quick enough as the noise level is sufficiently suppressed and the signal level changes abruptly af­ter 401h second. Figure 4 is the result of the same choice of eigenvalues but without optimization. The corresponding case is obtained for 80.76° of aperture of the angle described by (13) . Figure 5 , is the re­sult of choosing one of the eigenvalues as very large, hence we can conclude to the non-filtering effect of the eigenvalues. tn Figure 6, the eigenvalues are chosen so small that the measurement noise is filtered, but the detection is much more slower. It is evident that the choice of the eigenvalues must be also opt.imizf'<l for a fnrl her stu<ly. for t.hi" pnrpo�, we can say that the eigenvalues must be chosen as distinct as possible. This follows from the fact that:

233

3 . 0

2 . 0

1 .0

0 . 0

- 1 .0

-2.0

I . I 0 . 9 0 .7 o.s 0.3 0 . 1

- 0 . 1

0 1 0

Fig. 5. /3={-1.5, -9, -54}

I 0

Fig. 6. /3={-0.1 , -0.2, -0.3}

if the eigenvalues are chosen to be equal, the residual generator becomes degenerate as it produces a. zero signal for all cases. So by the continuity principle, if the /3;'s are too close the residual will be highly sensi­tive to parameter perturbations. Therefore a. compro­mising solution must be found in-between two cases: On the one hand, filtering and quickness qualities of the eigenvalues induce the clustring of the poles, while on the other hand, in order to improve the robust­ness to parameter perturbations, the poles must be spread ed.

REFERENCES

[1] P.M. Frank and J. Wunnenberg. Robust fault di­agnosis using unknown input observer schemes. Chapter 3, in Patton, Frank and Clark: Fault Diagnosis in Dynamic Systems, Theory and Ap­plication, Prentice Hall, pages 47-97, 1989.

[2] J . Gertler. Analytical redundancy methods in fault detection and isolation. in Proc. 1 •1 IFAC-IMACS Symposium "Safeprocess", Baden­Baden, Germany, Vol. 1 :9-21 , September 1991.

[3] J.F. Magni and Ph. Mouyon. A generalized ap­proach to observers for fault diagnosis. in Proc. of 30th I.E.E.E. conj. Decision Contr., Brighton, UK, December 1991.

[4] J.F. Magni and Ph. Mouyon. On residual generation by observer and parity space ap­proaches. Submitted for 31th I.E.E.E. conj. De­cision Contr., December 1992.

[5] R.J. Patton and J. Chen. A review of parity space approaches to fault diagnosis. in Proc. 1 •1 IFAC-IMACS Symposium "Safeprocess", Baden­Badcn, Germany, Vol. 1:239-255, September 1991.

Copyright © IFAC Anificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

EXAMPLES FOR FAULT DETECTION IN CLOSED LOOPS

R. Delbert and R. Isermann

lnstilule of Automatic Control, Laboratory of Control Engineering and Process Automation, Technical University Darmstadt, Landgraf-Georg-Str.4, D-6100 Darmstadt, Germany

Abstract. Fault diagnosis of closed control loops and its components is a topic which requires deeper inves­tigation. Main problems are the different targets of control and fault diagnosis. Control loops are designed to reduce the influence of deviations of controller, actuator, the process itself and the sensors with regard to the desired input/output behaviour. On the other hand, the aim of fault diagnosis procedures is to detect these deviations in order to decide whether they cause a failure, damage or not allowed process behaviour, and to arrange appropriate actions. State space approaches are first investigated for fault detection in control loops because they need not necessarily excitation, a cirumstance which is given in many control loops. As a first stage of the current investigations, control loops with linear components will be examined.

Keywords: Control loop, model-based, state estimation, parameter estimation

1. Introduction

In recent years the development of tools for fault diagnosis and supervision of technical systems has increased because the requirements on reliability and availability increased and the systems and plants became more and more complex. Hence, the detection and diagnosis of faults in closed control loops has become an important topic. The problem of fault diag­nosis in control loops is that the strategies of fault diagnosis and controller design differ in comparison to open loop pro­cesses. Control loops (controllers) are designed in order to decrease the influence of parameter deviations or signal dis­turbances. However, these parameter deviations may be symp­toms of an incipient or small fault, which has to be detected and localized as early as possible to avoid any damage caused by a failure.

If no possibility can be achieved to match both problems of controller design and fault diagnosis simultaneously, some kind of compromise has to be made. For adaptive control systems a coordination of controller design and supervision with diagnosis abilities seems to be useful, Schumann, Iser­mann, Lachmann(1981), Lachmann and Isermann(1985). In this case, the word intelligent control, Astrom (1991), can also be used for control systems which contain fault diagnosis tools.

State-of-the-art for supervision in control loops is only limit value checking of some important, measurable variables. Deeper diagnosis will be possible using model-based fault detection methods. Most of the research work in the last years dealing with model-based methods for fault detection, use either signal models or process models. An overview is given e. g. in Willsky (1976) or Isermann (1984). Other, more speci­fic approaches using signal based methods are given in Neu­mann(l 991) and Janik(1991). Instruments for fault diagnosis via state estimation are considered in Patton(1989,1991) and Frank(1989,1991). Parameter estimation is used in this sense e.g. by Isermann(1990,1991), Freyermuth(l991) and ReiB/Wanke(1991). A more theoretical introduction of the parity space approach is given by Gertler (1991).

235

Most of the publications concerning fault diagnosis regard only the process itself or even a part of the process but not the closed control loop as total system. One important aspect which occurs in both open and closed loop systems is the problem of sensor faults. Sensor faults and the problems which occur there are treated by Halme and Sel.kainako (1991) and Clarke and Hency(1991).

In the following sections the behaviour of closed control loops in presence of a fault and possibilities for fault detection in control loops will we investigated. After a description of the control scheme typical problems of faulty control loops are treated and approaches for fault diagnosis in control loops are proposed.

2. Models for the closed loop and its components

Fig. 1 shows the block diagram of the considered standard control loop. The single blocks describe the mathematical models of the subsystems controller, actuator, process and sensor in form of differential equations, transfer functions, state space descriptions or simple characteristic curves.

Fig. 1: Standard control loop

Of special interest are the blocks of the actuator and the sensor. The actuator usually consists of several components and represents a control loop itself. Most of these actuator­controllers are position controllers in analog realization. If microelectronics is used, there may be additional workspace for fault diagnosis tools, Raab (1990). These actuators are

called intelligent or smart actuators, Raab(1992). The situ­ation in the field of sensors is similar. Therefore, for all blocks in Fig.I the static and dynamic behaviour has to be con­sidered.

The description of the single blocks in continuous-time­domain is either given by transfer-functions

G (s) = Y/,s) (1) 1 u/,s)

or in state-space-equations

&i<t> = A1�1(t) + B1a1(t) (2) -y.1(t) = c,�1(t) + D1a1(t) (3)

A,B,C,D denote the wellknown state space matrices, .! the states, .!! the inputs, l'.. the outputs in respective dimensions; i denoting subsystems as

R: regulator, e.g. pneumatic PI-controller, digital con-troller

a: actuator, e.g. pneumatic or electric valve p: process s: sensor

For closed loops according to Fig. 1 following relations are valid ( it is assumed that all loop components are SISO­models ):

u8(t)=YR(t), up(t)=y8(t), u,(t)=yp(t), uR(t)=w(t) - y1(t) w(t): command signal u(t)=yR(t): manipulated variable y(t)=y1(t): output signal

With the command signal w(t) as input and YR(t) and y,(t) as measured output signals the state space description for the whole system is obtained with feedback of the sensor output: 0 0 :: =rB��1t :o

x, o B,c. AP x. 0 0 B•CP

( 0 0 0 }l(.{) = c. o o

x.(t)

(5)

Without loss of generality the matrices D;, i=a,p,s may be equal zero. If e.g. a PI-controller is used, DR has to be taken into account. It is also assumed that the subsystems are linear or can at least be linearized according the operating point. It is very important that the parameters of the state space des­cription are known as exactly as possible for the nominal (fault free) case, e.g. via identification methods, Iser­mann(1988). It is first assumed that only the command signal and the sensor signal can be measured. In this case only the first row of eq .( 5) is valid.

3. Fault models

A distinction of faults can be made as follows:

• external faults:

• internal faults:

changes of power supply, contami­nation, collision, external disturb­ance signals. wear(which means deviations in the process coefficients), actuator and sensor faults.

236

Concerning actuator and sensor faults, the nomenclature within state space domain is not unique. It has to be men­tioned that some authors call faults sensor faults if they influ­ence the C-matrix or the output signal y. Similarly, faults related to the B-matrix are called actuator faults. This is, however, too much simplified if real faults of sensors or actuators are to be detected and diagnosed. Additionally, as shown in eq.(4),(5), this nomenclature cannot be valid for the state space description of the closed control loop. Here, actuator and sensor faults are considered, which influence physical existing actuators and sensors and may express them­selves in their own dynamic models in various places. So they can be interpreted as process faults of the actuator or sensor subprocess'

In the following it is assumed that these faults are represented by deviations t:.A, AB or AC and fault vectors L., and 4--

&(t) = (A +.U)�t) + (B + AIJ)a(t)+fL (6) }l(.t) = (C+AC)�t) + I, (7)

The parameter changes t:.A, AB, AC are also called multiplicative faults, and L., and � as additive faults, Gertler(1988).

4. Fault detection in control loops

4.1 Model-based methods

There are two advantages for preferring model-based methods for fault detection in control loops. First, as mentioned above, model-based methods provide much deeper diagnosis as stan­dard limit value checking, and second, one can use the same models of the control loop components for both controller design and fault diagnosis. So, modelling has to be done only once.

There are two groups of model-based methods: parameter estimation and state estimation. Both methods and their vari­ous algorithms are well-known and both have advantages and disadvantages according their usage as fault diagnosis tool:

parameter estimation

requires only the structure of the process model and therefore less a-priori knowledge allows deeper diagnosis, especially when the parameters correspond directly to the physical coefficients computational expense is medium appropriate excitation of the considered system is neces­sary, if dynamic parameters are influenced by faults

state estimation

model parameters must be known rather precisely (more exact a�priori knowledge) the response to occuring faults may be very fast if the noise is low deep diagnosis has not been demonstrated (until now)

Therefore, state estimation seems to be useful for the purpose of a fast model-based fault detection in control loops, although the disadvantage of the exact process knowledge is given. Of course, some new apporaches try to decrease this disadvantage, e.g. unknown input observers, Frank (1989,1991), Wiinnenberg(1990).

4.2 An example

The approaches described in the preceeding sections are often

applied to open loop systems. Here, faults may often be detected by monitoring the measurable signals and limit-value­checking. The information about faults can be increased using analytical redundancy, e.g. modified state estimation or para­meter estimation methods.

For closed loop systems the situation is different because some faults are covered by the control loop. Fig. 2 gives an example. The gain of the sensor changes abruptly at t=lOO s. After a short transient the sensor output holds its old station­ary value so that the output behaviour of the control loop seems to be allright. However, the manipulated variable u(t) = YR(t) shows a deviation.

Simulation Control Loop

FaiJt. no. 1 1.2 400 'E wlU u

n 360 L .. Ci 320 .0 .5 c El 0.8 II) yltl

280 " 240 :ii .. � 0.6 .: 200 .. >

� 0 0.4 .,;

160 " 120 2 .. c .,

E 0.2 E 0 0 0

80 :; a. ·c:

40 .. E

0 0 40 80 120 160 200

time [sec]

Fig. 2 Simulation fault no.1 - measurable signals

One possibility to match this problem is to increase sensor redundancy. Especially for sensor problems, additional mea­surements generated by other sensors are helpful to make decisions whether the measured signal is the right one.

If no additional sensors can be applied, the above mentioned methods of analytical redundancy, especially state estimation, are helpful. Fig. 3 shows the internal states of the control loop according to the fault described in Fig. 2. Comparing both, one can see a difference in the stationary states after the fault has occured whereas the output signal holds its stationary value after a short transient deviation. So, for this kind of fault, a simple Luenberger observer may be appropriate to detect changes in the closed loop, but no deep diagnosis is possible, because similar behaviour is obtained for other faults, e.g. faulty process gain. A next step is to increase the number of measured signals which are fed back to the observer. This leads in the case of a full measurable system (rank(C)=n) to a simple version of a failure sensitive filter, Beard/Jones(l971/1973).

48

'O> 40 i:l ri ; 32 .0 E 4 24 'E u II) 16 ! !! "

0 0

r>...

-

'/

Simulation Control Loop

.state e.stmates - fault. no. 1

,,... ""'

..

/' /

/'

40 80 120

lime [sec]

Fig. 3 Simulation fault no.1 - state estimates

160 200

237

4.3. Fault detection with state estimation

Most of the state space approaches yield the information about faults via so called residuals, see Fig. 4. The only differ­ence is how to design the observer feedback matrix H und the weighting matrix W. In the fault free case the residual equals zero, and if a fault occurs, the residual deviates from zero in a matter which is typical for the specific algorithm used. Fig. 4 shows the common block diagram. According to section 3 state space approaches which are sensitive for sensor faults in the sense of having influence on the C-Matrix or ,!¥. respect­ively, are not useful for control loops, because the C-Matrix of the sensor subsystem occurs in both A-Matrix and C-Matrix of the entire control loop representation.

Fig. 4: Scheme of observer-based residual generation

As mentioned in section 3, a system influenced by multiplicative and additive faults can be described in continu­ous time domain by equations (6) and (7). A state estima­tor(residual generator) for fault diagnosis is described by the equations

i (t) = A�t) + BK(() + H�(t) i(.t) = C�t)

(8) (9)

For simplification it is assumed that rank(C)=n, n=dim(A). Then the differential equation of the residual e(t) follows as

ef.t) = (CAC-1)�t) - CAC-1J1 + CfL + (4CA +CA.A. + 4CA.A. -CAC-14C)�t) (lO) + (4CB +CJ1B + 4Cl111)11.(t) + 11CfL

Eq.(10) shows that additive faults !L and ,!¥ influence the resi­dual directly, that means state estimation is suitable for this case. Tiie appearance of multiplicative faults t:.A, 11B, 11C in the residual depends on the form of the states !_(t) und the inputs u(t). Eq.(10) holds for both, open loop and closed loop systems, so that state estimation for fault detection can be applied to control loops without large modifications. If all states hold a stationary value - which is often the case in control loops, all kinds of faults cause similar residual beha­viour in the case of an abrupt change of a parameter or fault signal, compare Fig. 3. Therefore only fault detection is pos­sible, but no fault diagnosis in the sense of information about location .

4.4 Fault diagnosis with parameter estimation

In the case of parameter estimation the parameters

itT = [a1 • • • a,,. b1 . • . b.,] of a transfer function

G<..s) = B(s) or G<..z-1) = B(z:-') A(s) A(z;-1) are obtained by a Least Square(LS) approach on the basis of

the equation (11)

• consists of the measured input and output signals of the estimated system. There exist convergence conditions which must hold for the LS-solution of eq.(11). Then deviations of the estimated parameters from their nominal( fault-free) values are symptoms for faults. In the case of a fault parameter deviations from their nominal values are fault symptoms. It depends on the chosen system description - that means on the measurable input/output signals - whether these deviations corresponds directly to physical coefficients which provides deep diagnosis. In closed loops, the following problems con­cerning the convergence conditions occur: If the transfer function

G (s) = y(s) ., w(s) is to be estimated, the excitation of the control loop may not be sufficient, and the error signal e(k) may not be uncorre­lated with the elements of the data-vector • because of the feedback of y. So, parameter estimation of the whole control loop using only the same signals as state estimation, w and y, is often impossible and therefore no fault detection and diag­nsosis can be done in this case.

s(t} perl1lballon v(I) noise ------. - .... -Illar Iller

11(1)

w(l) u(t) a:tualor + yro regUatar process+ -- - -- ..,,

Fig. 5: Scheme of identification in closed loops

However, there exist ways to treat parameter estimation in closed loops. They are based on a modificated description of the control loop according to Fig. 5. Assuming that the order of the regulator transfer function is larger than the process order and the regulator parameters are known - which is always possible if a digital controller is used - the parameters of the remaining systems which includes actuator, process and sensor can be estimated using the noise signal n(t) and/or the external perturbation signal s(t), Isermann, Lachmann, Matko (1991 ). The manipulated variable must be measurable and the noise or perturbation signal must provide enough excitation for parameter estimation, this method provides deeper diag­nosis abilities.

S. Simulation results with state estimation

First investigations were made using a simulated level control loop for a tank system, Fig. 6. The controller is designed as a standard PI-controller with the transfer function

G = y,f_s) =KJ..l + -1-) " w(s)-y(s) T.s

(12)

The actuator, a pneumatic or electric valve, is given by a simplified, linearized transfer function

G = Y.(s) =_5_ (13) • yj..s) 1 + T,1

The sensor for the control signal feedback is a simple gain k,,,.

238

w

Fig. 6: Simulated tank system

According to the linearized fluid dynamics of two tanks, the state space matrices for the closed loop is given by

0 0 0

IC"IC• 1 0 T.T. T.

A 0 1

gAt!. A6I..flgH01

0 0 gAt!.

A6zl2gH01

1.

Al>lp

B= K,.JC,k. T,Al>l p

0

0

denoting Ai,; : cross section of tank no. i

� : outlet cross section of tank i �. Tn : regulator parameters K., T1 : actuator parameters

0

0

0

-1

-� A,,zP

-IC"K1k. T,A»p

0

-gA� Al>l..flgHm

Hoi : level of tank i at the operation point k,,, : sensor gain

The state vector !(t) consists of

(14)

(15)

(16)

x1 : internal regulator state, no physical interpretation x2 : valve position x3,x4 : mass flow

The following faults were implemented:

No. l)

No. 2) No. 3)

incorrect sensor gain. It should be noticed that the sensor gain k,,, appears in the A-matrix and not in the C-matrix. incorrect actuator gain decreased outlet cross section of tank 2 (process fault)

All three kinds of faults occur at t= lOO seconds and are simu­lated as a 15-percent deviation from the nominal value. the command signal of the control loops is a step at t=O seconds, afterwards the command signal hold a constant value.

Simulations were made for three different assumptions:

i) command signal w(t), manipulated variable u(t) and output signal y(t) are measurable.

ii) only w(t) and y(t) are measurable. The states are esti­mated with a Luenberger-<>bserver, designed by pole­placement.

iii) the control loop according to eq.(14), (15), (16) is full measurable and a failure sensitive filter is applied. The design of the feedback matrix H=ul is chosen similar to ii)

Fig. 7 and 8 show the output signal in the case of fault no. 2 and 3 respectively. After a short transient starting at the time the fault occurs the output signal goes back to its stationary value, the fault is covered by the control loop.

Ii c

1.2

� 0.8 ..

., .9- 0 6

::> 0 0.4 -u c .,

E 0.2

g ()

0 0

/w{t)

f

I \

Simulation Control Loop

FaUf no. 2

'-< y(t)

ueuzy.m

40 80 120 160

time [secJ

Fig. 7 Simulation fault no.2 - measurable signals

'E u

Ii c

1.2

� 0.8 ..

., 5. 0.6 ., ::> 0

0 4 -u c ., E 0.2

E 0 ()

0 0

/wm

f

I \

Simulation Control Loop

uCU=y,.tu

40

Falil no. 3

(\ 'rm

�

80 120

time [sec) 160

Fig. 8 Simulation fault no.3 - measurable signal

400

360

320

280

240

200

160 120

80

40

0 200

400

360

320

280

240

200

160 120

80

40

0 200

n ... .. ., .5 " :;; .. -.: "' > -0 .'l "' :; c. "1' "' E

n ... .. ., .5 " :;; .. ·;:: .. > -0 .'l "' :; c. c "' E

Fig. 9-14 show the estimated residuals achieved by a standard Luenberger observer and an oberserver designed according the failure sensitive filter approach. The residuals show differ­ent deviations for different faults so that the faults can be distinguished. However, a diagnosis which fault did occur is not directly possible, only the detection. One possibility for fault diagnosis will be to teach the typical residual behaviour for different kinds of faults via simulation.

239

0.8

n Ol 0.6 � ,-; '- 0.4 "' ., � 0.2

� 0 .. � -0.2 -0 ·;;; � -0.4

-0 6 0 40

Simulation Control Loop

I\ /., I\ .,

." ..

/.,

80 120 160

time [sec)

Fig. 9 Simulation fault no.1 - Luenberger residuals

n Ol � ,-; ... " ., .5 � u

.. Ii ::> :Q .. �

1.2

0.8

0.4

0

-04

-0 8 0 40

Simulation Control Loop

LuenbergM observitr - fault no. 2 . T7

/·/·· I " ..

80 120 160 lime [sec]

Fig. 10 Simulation fault no.2 - Luenberger residuals

n 0 Ol "' u -1 ,-; ... � -2 .§ -3 ,-; .5 -4

� -s ::> -0 -6 Ui � -7

-8 0 40

Simulation Control Loop

LtHil'berger oburver - fa&Jt no. 3

/., ". / ..

.,,

/.,

80 120

lime [sec)

160

Fig. 11 Simulation fault no.3 - Luenberger residuals

200

200

200

It should be mentioned that in this simulated case of a fJXed value control parameter estimation methods give no results because there isn't any excitation of the control loop. So either an excitation of the control loop Aw(t) or the method proposed in section 4.4 have to be used for fault diagnosis.

0.6

n g 0 4 ';! " .g 0.2 LI ri .s <ii " .,,

0

'ii) -0.2 " '--0.4

0 40

Simulation Control Loop FaBure sensiUve filter - falit. no. 1

' '2

/1 /•

/' 80 120 1eo 200

time [sec]

Fig. 12 Simulation fault no.1 - residuals failure sensitve filter

0.6

'ti> 0.4 G '2 0.2 " £> E o

LI ri 8 -0.2

� -0.4 .,, 'ii) � -0.6

-0.8 0 40

Simulation Control Loop Falure .seMJtlve filter - faiJI. no. 2

')•

/1 "

'•

/2 80 120

time [sec] 160 200

Fig. 13 Simulation fault no.3 - residuals failure sensitive filter

� 0.12 G � 0.05

Simulation Control Loop Failure sensitive fifer - fai.Jt no. 3

� r, .s 0 k--------------1-----�--------------:§ -0.06 <ii j -0.12 .,, 'ii) � -0.18

-0.24 ��-�-�--'--�-..J'---�---'--�__J 0 40 80 120 160 200

time [sec]

Fig. 14 Simulation fault no.3 - residuals failure sensitive filter

6. Conclusions

Some studies of fault detection of control loops were shown in this contribution in order to give some ideas for fault detec­tion and diagnosis strategies in control loops. With respect to the modem complex components of control loops, model­based methods , especially state estimation seem to be useful. Another advantage of these methods is that the models can be used for both controller design and fault diagnosis. State estimation approaches are useful to detect faults in control loops which occur only a little in the measurable output sig­nals, because they respond rapidly to a fault. However, they provide no deep diagnosis. It depends on the kind of fault to be detected and the nature of the considered control loop which approach is the most appropriate one or whether a

240

combination of different methods will be the best approach. Further investigations have to be made with more complex components of control loops including their nonlinear behav­iour.

7. References Astrom, KJ. (1991); Intelligent Control, European Control

Conference 1991, Grenoble Beard, R.V. (1971 ); Failure Accomodation in Linear Systems

Through Self Reorganization, Rep. MVf-71-1, MA, USA

Clarke, D:W:, Henry, M.P. (1991); A standard interface for self-validating sensors, IFAC-Symposium SAFEPRO­CESS'91, Baden-Baden

Frank, P.M. (1991); Enhancement of robustness in obseiver­besed fault detection, IFACSymposium SAFEPROCESS '91, Baden-Baden

Freyermuth, B. (1991);Knowledge based incipient faultd diag­nosis of industrial robots, IF AC-Symposium SAFEPRO­CESS '91, Baden-Baden

Gertler, J. (1991); Analytical redundancy methods in fault detection and isolation, IFAC-Symposium SAFEPRO­CESS '91, Baden-Baden

Gertler, J. (1988); Suivey of model based failure detection and isolation in complex plants, IEEE Control systems Magazine, December 1988

Halme,A, Selkiiinako,J. (1991); Advanced fault detection for sensors and actuators in process control, IFAC-Sympo­sium SAFEPROCESS '91, Baden-Baden

lsermann, R. (1988); ldentifikation dynamischer Systeme, Band I+II, Springer Verlag, Berlin

Isermann, R. et al.(1990);Model based fault diagnosis and supeivision of machines and drives, 11th IFAC-World Congress, Tallinn

Isermann, R. (1991 ); Fault Diagnosis of machines via parame­ter estimation and knowledge processing, IFAC Sympo­sium SAFEPROCESS'91, Baden-Baden

Isermann, R., Freyermuth, B. (1991); Process Fault Diagnosis Based on Process Model Knowledge -Part II; Journal of Dynamic Systems,Measurements and Control, Vol.113, pp.623-633

Janik, W., Fuchs, A(1991); Process and signal model based fault detection of the grinding process, IFAC Symposium SAFEPROCESS'91, Baden-Baden

Jones, H.L. (1973); Failure Detection in Linear Systems, Ph.D.thesis MIT, MA,USA

Lachmann, K.-H., Isermann, R. (1985); Parameter adaptive control with configuration aids and supeivision functions, Automatica Vol.21, No. 6

Neumann, D. (1991); Fault diagnosis of machine tools by estimation of signal spectra, IFAC-Symposium SAFE­PROCESS'91, Baden-Baden

Patton, Frank, Clark (1989); Fault Diagnosis in Dynamic Systems - Theory and Application, Prentice Hall

ReiB, Th., Wanke, P. (1991); Model based fault diagnosis and supervision of the drilling process, IFAC-Symposium SAFEPROCESS '91 , Baden-Baden

Raab, U. (1990); Application of Digital Control Techniques forthe Design of Actuators, VDINDE-Tagung Actuator '90, Bremen

Raab, U., Isermann, R. (1992); Intelligent Actuators, IFAC­Symposium on intelligent components, Malaga

Schumann, R., Lachmann, K.-H., Isermann, R. (1981); Towards applicabilitiy of parameter-adaptive control algorithms, gth IFAC-World Congress, Kyoto(Japan)

Wiinnenberg, J. (1990); Obseiver-based fault detection in dynamic systems, VDI-Fortschrittberichte Reihe 8, Nr. 222, VD I-Verlag Diisseldorf

Copyright © IF AC Anificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

A METHOD FOR FAULT DETECTION USING PARAMETER AND STATE ESTIMATION

T. Sproesser and G.L. Gissinger

/nstilUl de Recherche Polytechnique, BP 2438, 68067 Mu/house Cedex, France

Abstract. In this paper, fault detection in linear dynamic systems based on analytical redundancy and identification of continuous time models, is considered. Particular emphasis is placed on the realisation of state variable filters by mean of interpolation techniques. Two examples illustrate interpolation for different noise levels.

Keywords. Fault detection, parameter identification, continuous time models, digital state variable filter, interpolation.

1. Introduction

The increasing demand on reliability and safety of technical systems and their supervision led to methods of failure detection and isolation (FDI) based on the use of dynamic models of the system and the inherent analytical redundancy. See for instance the survey papers of Winsky 1 976, Frank , Isermann 1 989, Gertler 1988.

There are essentially two basic concepts. The first one is based on state estimation (observers and Kalman filters), while the second one uses identification techniques in order to estimate process model parameters !l. The key idea of the last concept is that physical parameters l2 of the system are related to the parameters of the process model. Detecting changes in the model parameters can be used for failure detection.

This paper deals with component and sensor fault detection using parameter estimation techniques. In the second section we briefly describe a general procedure of FDI, while in the third section the identification algorithm used for a continuous time model is presented. In order to avoid time derivatives for identification, the state variable filter (SVF) approach has been chosen (section 4). In section 5 we propose an algorithm for the digital realisation of the SVF by means of interpolation techniques. In section 6, examples are used to compare the influence of interpolation for different noise levels.

2. Method

In order to validate the sensor measurements, the Dedicated Observer Scheme (DOS) (Clark, 1 978) can be used. If there are uncertainties due to time varying parameters, the DOS can be achieved using adaptive state observers (Sauter et al. 1991). Another method of performing this task in the presence of time varying parameters is to use the results of the identification part.

241

a) Instrument fault detection using the DOS.

For each of the sensors a single observer is designed which estimates as many system outputs as possible. The ith observer is driven by the ith sensor output and of course by the system input. The observer estimates are compared with the measurements and with the estimates of the other observers. Sensors faults are detected by means of a decision logic : in the no fault case, all of the estimated outputs will be close to the corresponding sensor output. The differences between these estimations and the instruments will not be exactly zero because of the measurement noise as well as the modelling incertainties and inaccuracies. In the case of a fault in the ith sensor, the estimations of the observers will still be close to the other sensor outputs, except for the observer driven by the faulty instrument.

b) Instrument and component fault detection using the results of identification

For the sake of faults detection by means of identification techniques, we identify the transfer function between the system input and a system output from which the considered sub-system is observable. When it is possible to identify the transfer function between the input and another system output and if the resulting sub-systems are not entirely decoupled, some of the physical parameters will be part of both transfer functions.

This redundancy can be used for fault isolation. In fact, two kinds of comparisons are possible. First there is the comparison of parameter estimates issued from successive identification with one and the same sensor. Going on the hypothesis that the identification window is smaller than the time variance of the system, then, in the no fault case, these values will be close together.

The second comparison concerns common parts in transfer functions belonging to different sensors. This can be used to decide if a change in the estimates is the result of either a sensor fault or a component fault. If there is no fault in the sensors, there will not be much difference in the estimated parameters of the common parts of the transfer functions.

The decision part can be performed by a statistical hypothesis test, like the subsequent Bayes Test (Geiger, 1983).

3. Identification

For system identification we consider multi input -single output systems. In the case of multi input -multi output systems, we decompose them into multi input - single output sub-systems, each described by linear differential equations of the form :

(n) (n-1) (m) y (t) + 3n-1 y (t) + . . . + ao y(t) = bm,l u1 (t)

(m-1) + bm-1,1 u1 (t) + · · · + ho,1 u1 (t) + · · ·

(m) · · · + b u... (t) + · · · + ho u...(t) m,p P ,p P where the uj(t) are the system inputs, y(t) the (sub-)system output signal, and where (m) (n) Uj (t) and y (t)

denote the time-derivatives of order m and n of the input-output signals respectively. The � and bi,j are the unknown continuous-time model parameters, which are related to the physical parameters Pi of the system by mostly nonlinear functions. In the case of a time variant system, the model parameters can be represented by (unknown) time functions ai(t) and bi,j(t) respectively.

In order to estimate the non-measurable model parameters equation ( 1 ) is transformed into a more appropriate form :

y(t) = ,ytT(t) !!(t), (2)

with : T

.e. = [a1 . . . 3n b1 ,o · · · b1,m · · · hp,O . . . bp,ml•

T (1) (n) (m) .Yl (t) = [ - y (t) . . . - y (t) u1 . . . u1 (t) . . . (m) � (t)]

Now, using the measurable input and output signals, we can estimate the parameter vector .e._(t) with the Least Squares (LS) method, or any suitable version, like the Instrumental Variable (IV) method, etc. Because of its capability to deal with the problem of time varying parameters, we chose the recursive least squares method with forgetting factor (RLS). For this algorithm, we consider equation (2) at discrete times :

A A T A !!(k+l) = !!(k) + K(k+l) [y(k+l) - .Yl (k+l)�(k)J

K(k+l) = £.(k) ,yt(k+l) I (A. + .YLT(k+l) f(k) ,yt(k+l))

1 T £(k+l ) = i°[l + K(k+l) .Y£ (k+l) f(k)J f(k) (3)

with I the identity matrix and A. the forgetting factor, O < A. � l.

242

3.1 Dlscret Square Root Filter in the Information Form

The use of this standard form (3) of the RLS algorithm can pose numerical problems. Therefore a numericaly improved version of the the least squares algorithm, like the Discrete Square root Filter in the Information form with forgetting factor (DSFI) (Goedecke, 1 987), is recommended. However, the use of this improved algorithm can increase the computational burden. We will not present this algorithm, for more details refer to Goedecke (1987). We will just make a comment on the Housholder transformation used for this algorithm and compare the number of multiplications to that of the RLS (3) which is, under computational aspects, not in an optimized form.

In the semi-recursive version of this algorithm, the calculation of the parameter vector a is based on an upper triangular matrix .S.. This matrix .S. can be seen as the square root of the information matrix :

.e.-1(k) = .S.(k).S.(kr At each sampling time, �(k) is updated with the information vector .!IL,(k+l). The resulting matrix is transformed with the Housholder transformation to upper triangular form, ,S,(k+ 1 ). Because of the upper triangular form of .S.(k), we modifed the algorithm of the Housholder transformation in such a way that only the non-zero elements of ,S_(k) are considered. Therefore the computing time is reduced. Table 1 compares the number of multiplications between the Householder transformation (HH) and the transformation adapted for the DSFI (HHmod). Furthermore it shows the number of multiplications of the DSFI in comparison with the reference algorithm (3). In this table, "n" corresponds to the system order, and "N" to the number of time samples after which an estimation for e_ is required.

4. State Variable Filter

If the system is sufficently exited and if there is less measurement noise, the parameters can be estimated. However, the remaining problem is that the

continuous time model (2), and therefore .Yl T (k) of the algorithm, requires the time derivatives of the normaly noisy systems signals.

One method of circumventing this problem (Young, 1981 ; Homssi, 1989) is the state variable filter (SVF) approach (Kohr, 1967; Isermann, 1987) :

Taking the Laplace transform of ( 1 ) and neglecting the initial conditions leads to :

with : n �(s) = ao + al s + . . . + s

m-1 Bi (s) = bo,i + bi,i s + . . . + bm-1,i s

Then we multiply both sides by a polynomial F(s). This is equivalent to a linear filtering of the input and output signals.

The requirements for the filter F(s) are : - filter order greater or equal to n, with n the order of the system - bandwidth comparable to the bandwidth of the filter

We adopte the following filter :

k F(s) = 2 n fo + f1 s + f2 s + · · · + fn s

If an estimation of the system polynomial A(s) is available, the filter parameters can be chosen as :

/\ fi = ai. Another possibility is to design the filter coefficients via Butterworth - characteristics. Because of the low pass character of the filter, measurement noise will be filtered.

The state space representation of F(s) shows clearly that the states Xi correspond to the ith time derivatives of the output signal zF(t) of the filter (Figure 1) :

z.(t)

where : (i)

0 0

1 0

0 0

0 0

-fo -!1_ . . . -fn - 1 fn fn fn

zp(t) = Xi,

z.(t) +

0 0

z(t)

. x 1 [ xo ]

with x = : , and i = 1, . . . , n-1

(n) fo ZF(t) = - rxo -n

Xn-1 fn-1 k

--r-xn-1 + r z(t) n n

5. Realization of the SVF by digital computers

(5)

When realizing the state variable filter by digital computers, the filter equations have to be discretized. With T as the sampling interval and t(T) as the transition matrix of the filter, equation (5) is given by :

(k+l)T x(k+l) = t(T) x(k) +

k� t((k+l)T-"t) Q. z('t) dt (6)

In practice an analytical solution is not possible. Furthermore the system input and output signals are known only to discrete time samples. If the filter input is constant between two time samples, equation (5) can be solved exactly. This is often true for the system input, but does not hold for the system output. In this case, equation (5) has to be solved approximately. If the samping rate is too slow, the assumption that the system output is constant between two time samples will lead to faulty parameter estimates. When it is not

243

possible to increase the sampling time, a solution can be to approximate those system signals, which are not constant between two time samples, using interpolation techniques (Peter and Isermann, 1989). The accuracy however depends on the measurement noise. Simulations we made have shown that in the presence of a high noise level, the zero order hold can lead to better estimates.

5 . 1 Interpolation

Given N measurements of a signal at discrete times. It is possible to approximate the signal in the given interval by means of interpolation polynomials. For the state variable filter, interpolation for the filter input will be based on the last N measurements (z(k), z(k-1 ), . . . , z(k-N+l )). In the case of interpolation polynomials like Newton or Spline interpolation, an approximation for the signal z(t), (k-l)T S t S kT, is given by the following polynomial of order 11 :

2(t) = <XQ(kT) + al (kT) t + . . . + a,,(kT) t11 (7)

The interpolation order 11 determine the length of the interpolation window. In practice 0 S 11 S 3 will be sufficient. The interpolation coefficients ai(kT) depend on the interpolation interval, but they are constant for an interval given and entirely determined by the type of interpolation chosen.

5.2 Computation of the filter m atrices

The algorithm proposed here is different to the one presented by Peter (Peter and Isermann, 1989) in the way that it works also when the system matrix A. is singular. Furthermore the matrices are computed in a time scaled way in order to improve numerical properties.

Rewriting (6) yields : kT

/\ /\ f /\ z_(k) = t(T} X(k-1) + t(kT-"t) .12. z("t) cit (k- )T

or : T

�(k) = t<T)S.(k-1) + Jt(T-"t) d"t J! a0(k) + . . .

T + Jt(T-"t) "tTl. d"t <Xi,(k)

�(k) = i<T) S.(k-1) + [o(T) <XQ(k) + . . . + ITJ.(T) <Xi,(k)

Approximating the transition matrix t(T) by the trunceted time series of the exponentiel leads to the following form :

" r (AT)v tm = :L -

v=O v ! (8)

In the same way, an expression for the matrices I.i(T) can be found :

T T

t(T) = J 't i i(f-'t) d't l2 = ±A.� J 'ti (T-'t)v d't 12. 0 V=O v.

and after i partial integrations : II r · 1

.I:·(T) = L (AT)v . i . Ti+l h i

v=O (1+v+ 1 ) ! (9)

However, when computing (8) and (9) in this form, the convergence of these algorithms is not guaranteed. One method of circumventing this problem is the "time scaling" (Plant, 1 968). In fact, it can be show that the smaller the matrix norm

llATll = l lAlrf the better the series convergence. The idea is to determine the transition matrix as a function of T/m using (8) and computing the original transition matrix according to :

According to this idea, Kallstrom (1973) presented a numerical stable algorithm to compute (8) and (9) for a zero order hold, i.e. 11 = 0.

In order to apply the principle of time scaling also for the matrices .[i(T), we define the following matrix :

A =

A_ Q. Q_ Q_ . . • Q_ Q_ Q_ l .Q. . . . .Q. Q_ Q... Q... L · · · �

.Q_ Q_ .Q_ .Q_ • • • l .Q_ Q_ .Q_ .Q_ • • • .Q_

Calculating i,_T/m for the matrix A using (8) leads to :

- T t(-) = m

Sl( T � m i:o<!� Q_ l

Q_ Q_ Q_

l.. ( T)11I

11 ! m -

1 ( T)11- 1 -- - I (11- 1 ) ! m -

l

where Sl�� is the scaled transition matrix of the filter,

and with .I:i<!� the according to (9). Calculating

- - T S1(T) = t(:'.jm leads to the unscaled matrices of the m

filter. Chosing m = 2µ reduces the computational burden.

244

In order to perform the computation of these matrices, a two step computer algorithm can be found in the appendix :

1 ) computing the scaled matrices t( T � and m

.I:i(� with algorithm 1 , then with these results

2) computing ,Sl(T) and .I:i(T) with algorithm 2.

6. Examples

a) The first example is a real second order system with a pure low-pass characteristic :

1 Y(s) = _ 5 _ 8 U(s) 1 + 5 .94· 1 0 s + 7 . 29 · 1 0 s2

After measuring (sampling time T = 5 · 1 0-5 sec), we identified this system for a large v ariety of SVF coefficients. Go(s) is the best identification result we obtained for a zero order hold, while G1 (s) is the result using interpolation of order one and the same SVF.

-5 G ( ) -

0.92 + 2 .2 · 1 0 s 0 s - -5 -8 1 + 5 .3 1 · 1 0 s + 6 . 05 · 1 0 s2

- 6 G ( ) - 0. 94 - 1 .5 · 1 0 s

1 s - -5 -8 1 + 5 .40 · 1 0 s + 7 .20 · 1 0 s2

With these results (in a low noise level case) the interest of interpolation becomes clear. Using interpolation of higher order did not increase the precision of the parameter estimates.

b ) In order to show the influence of noise on the choice of interpolation, we simulated the following second order, non-minimal phase testfunction proposed by Isermann ( 1 987), (sampling

1 - 4 s Y 0(s) = 2 U(s) 1 + 1 4 s + 40s

The system output was corrupted by zero mean white noise :

y(t) = y 0(t) + n(t)

The state variable filter was chosen to : 1 F(s) = 2 ( 1 + Tes)

where T f is a constant which determines the bandwidth of the filter.

With a PRBS as input signal, we identified the following models Gx%,z(s), where x% indicates the noise level 11. and z the order of interpolation.

G 0 . 9 9 - 4 . l s l%,o(s) =

1 + 1 0 .4s + 29 . l s2

G 0 . 99 - 4 . l s l%, l(s) =

1 + 1 3 .9s + 3 9 .4 s2

In the case 11 = 1 % , T f = 2, the interpolation of order one leads to much better estimates than the zero order

hold. Increasing the order of interpolation does not increase the precision of estimation. In the low noise level case, identification using a zero order hold is much more sensitive to the filter coefficients of the SFV than for identification with interpolation of order one. However, when increasing the noise level, one can observe, that interpolation of order one (and of higher order) leads to poor estimates of the slowest time constant and the choice of the filter coefficients is more critical than in the case of the zero order hold :

Tf = 9 :

Tf = 50 :

G 1 .0 - 4 . l s

10%,o(s) = 1 + 1 4 .4s + 3 9 .2s2

G 1 .0 - 4 . l s

l 0%,1(s) = 1 + 1 4 . l s + 3 6 .3 s2

G 1 . 0 - 4 . l s

20%,o(s) = 1 + 1 4 .4s + 3 9 .2s2

G ( l .0 - 4 . 2s

20%,1 s) = 1 + 1 3 .9s + 3 2 . 8 s2

7. Conclusion

For the realisation of digital state variable filters by mean of interpolation techniques, a numerical improved algorithm has been proposed. This algorithm works in a time scaled manner and is applicable also for singular system matrices. Two examples showed that in a low noise level case interpolation can increase estimation results. However, in the second example, when increasing the noise level, the zero order hold provided better estimates.

R eferen c e s

Clark, R . (1978) Instrument fault detection. IEEE Trans. on Aerospace and Electronic Systems. Vol. AES-14, No. 3

Frank, P.M. (1990). Fault detection in dynamic systems using analytical and knowledge-based redundancy.

Automatica, Vol. 26, No. 3

Geiger, G. (1983). On-line fault detection and localisation in electrical DC-drives based on process parameter estimation and statistical decision methods.

IF AC Control in Power Electronics and Electrical Drives, Lausanne, Switzerland

Gertler, J.J. (1988). Survey of model-based failure detection and isolation in complex plants.

IEEE Control Systems Magazine 8, No. 6

Goedecke, W. (1987). Fehlererkennung an einem thermischen Prozess mit Methoden der Parameterschlitzung.

VDI Fortschrittsberichte, Reihe 8, Nr. 130

Homssi ; Tittli ; Despujols (1989). Identification of continuous-time process for failure detection and diagnosis.

AIPAC '89, IFAC Symposium, Nancy, France

Isermann, R. (1987). Digitale Regelsysteme.

245

Springer Verlag

Isermann, R. (1988). Identification dynamischer Systeme.

Springer Verlag

Isermann, R. ( 1989). Process fault diagnosis based on process model knowledge.

France AIPAC '90 - IFAC Symposium, Nancy,

Kohr, R. (1967). On the identification of linear and nonlinear systems.

Simulation, Vol. 8

Peter ; Isermann, R. ( 1989). Parameter adaptive pid­controler based on continuous time models.

IFAC Symposium, Glasgow

Sauter ; Cecchin; Brie ; Aubrun (1991). Adaptive detection and accomodation of sensor faults.

ECC 91, European Control Conference, Grenoble, France

Willsky, A (1976). A survey of design methods for failure detection in dynamic systems.

Automatica, 12

Young, P. ( 1981). Parameter estimation for continuous-time models - a survey.

Automatic� Vol. 17, No. 1

A pp e n d ix

Algorithm 1 : Initialisation :

io = !. � = ! for i = 1, 2, . . . , l1

Xo,i = !

Algorithm : for v = l, 2, . . . , r

AT �v = �v-1 -=--; v

.mv = .mv-1 + �v 1

Xo·v = �v ­v+l .Yo·v = .Yo·v-1 + Xo·v for i = 1, 2, . . . , l1

Xi•v = Xi-l•v --­(v+i+l) Yi•v = Yi•v- 1 + Xi•v

for i = 0, 2, . . . , l1

Algorithm 2 : Initialisation :

T i+l Ii,T = Yi•r B. (�

io = ti'!m for k = 0, 1 , . . . , l1

Ik,O = Ik,T/m 1 T k

Mk,O = k ! � I

Algorithm : for i = l, 2, . . . • µ

for k = 0, 1, . . . , Tl

z

r:k,i = [�-1 + ll r:k,i-1 +

k + l�l M.1,i-l .[k-1,i- 1

k Mk,i = 2 M.k,i-1

2 i.i - 1

n = 2

n = 3

n = 4

n = 5

n • 8

HHrnod 63,6

55,3

50,5

47,5

42,4

Number of multiplications : Comparison bc:tween HH and lffimod (HH=lOO)

(p) ZF

N = l N = lOO N = lOOO

n = 2 124,2 1 13,0 1 12,9

n = 3 1 11,1 102,6 102,5

n = 4 98,8 92,3 92,2

n = 5 90,0 84,7 84,7

n = 8 75,2 71,9 71,9

Number of multiplications : Comparison between DSFI and RLS (RLS=lOO)

Table 1

(p-1) ZF

Figure 1

246

(2) ZF (1) ZF Zp

Copyright @ IF AC Artifkial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

SUPERVISION AND CONTROL OF AN EXOTHERMIC BATCH PROCESS

R. Perne

Process Control Systems, Bayer AG, Lever/cusen, Germany

Abstact- A m odel based superv Isl on and control system has been designed for exotherm i c chem i cal re­act ions, and batch processes In particular. Adaptive, extended Kalman f i l ters reconstuct process states as we 1 1 as react I on parameters and a Bayes-Markov process al lows to d1scr 1 m l nate between norma l and unwanted process states. The new concept cons1derab ly reduces the t !me for one batch and w arns of ha­zardous states at a very early stage, leav i ng enough t 1me for counter act ions.

Keywords· Exotherm le React I on, F ault Detecti on, Kalman F l l ter1ng

l ntroduct 1 on

Uni form qua l i ty, h igh product y ie lds, low energy consumpt ion and m inimal effects on the environ­m ent are the main demands on superv ision and contro 1 systems for chem I ca 1 reacti ons. I nexpen­s lve process computers are I ncreasingly being used to fulfi 1 these demands. Such computers per­m it not only the implem entation of a P I O control algorithm equiva lent to analog control lers but a l­lows the app 1 !cat I on of advanced process contro 1 technology.

Thi s technology I nc ludes observers, extended Kal­man fi lters and adaptlve control algorithms. As shown in prac� tee, the use of these control proces­ses ls successful If chem ical engineering know led­ge of the reaction concerned ls I nc luded In the con­trol concept as a priori know l edge [ 1 ]. Jn the ap­pl lcatlon presented here a pr ior l I nformation ls provided to the control by slmulat ing m athematical mode 1 s of the non 1 1 near process dynam I cs para 1 1 e l to the actual process on a computer. This a l lows the on l ine estimation of signif icant process varia­bles, such as concentrat ions of the reactants or reacti on rate, which are difficult or Impossible to measure on l i ne. The I nformation of these estimates form the basis for an I mproved superv is ion and control performance: replacement of unmeasura­ble var lab l es by est ! mated variables or adapt I on of control !er parameters accord Ing to the estimated process states.

247

The examp l e, presented I n thi s paper, ls the su­pervis ion and control of an exotherm lc process w 1tha potent1a l ly hazardous autocatalytlc decom­posltion. Here i t ls essentia l to detect the onset of an autocata lyt le decompos It Ion at a very early sta­ge, in t ime to take counter act ions. Mult l-Kalman­F 1 1 ter techn I ques as proposed by K Ing, Schu ! er & G I l les [2-3] are app 1 1 ed and sui tably m od 1f led a l­low ing a detect Ion of unwanted process states hours before a runaw ay of the reaction. Furthermore, w ith the lnformat I on from the f i l ters control ler parameters optim a l ly adapted to the process dyna­m 1cs reduci ng considerably the t ime needed for one batch. This concept has resulted In t ime-optimal and safe operat Ion of the chem !cal reactions under a l 1 process condit Ions.

The Problem

The process In the case at hand ls an exotherm le chem ical reaction, described by the fol low lng slm­P le stoich iom etry:

[A] + [Bl ( I )

and a macrok inet lc reaction rate k:

k = ko* exp(-E0/ < R*T >}*[AJµ1* [ B ]µ2 <2>

w i th A, B : reactants, C : product, ti.hR : react i on

enthalpy, k0 : pre-exponent ia l factor, E0 : act iva­

tion energy, R : gas constant, T : reaction tempera­ture, [Al and [BJ ... concentrations of A and B and the exponentsµl and µ2, w hich are a l l ow ed to be rat i ona I numbers. Inc J ud ing energy and mass ba­lances one arrives at the fol l ow I ng mathematical mode I of the process dynam i cs :

d[A]/dt = -k (3)

CM: the tota l react ion m ass, cp : the specif ic heat,

kF : the heat transfer coeffic ient between the reac­

t ion vessel and the jacket coo l i ng, F the area of he­at exchange and TM : the temperature of the coo I ing

med ium . )

Beside the normal reaction, product C m ay decom­pose autocatalyt ical ly :

C -> D • E • ( -ti.hs> start react ion

C•D -> 20 • E•(-ti.hA) exotherm i c decomposition

The start of autocatalytic decomposit lon Is favou­red by h igh temperatures. To avoi d a dangerous runaway of the exotherm ic decomposi ti on of the react ion product C, an upper l im i t is set for the reaction tern perature T and care has to be taken to ensure eff icient removal of reaction heat so that the critical temperature is never reached. I n the convent ional control concept temperature was control led by a P IO regulator w ith f ixed parame­ters acting on the jacket coo I i ng system. Even s I i gh t changes in process parameters, how ever, have signif icant effect on the overal I behaviour of thi s chem ical p lant, due to the h ighly nonl i near dependence of the reactor behaviour on the process state. As a consequence, a regul ator w i th f ixed pa­rameters does not work opt imal ly in a l l process states.

Because of this diff icu lty, the slope of the tempe­rature set point ramp was taken to be very sm al I i n order to avoi d unwanted rap id changes i n the reaction pow er. On the other hand, th i s m easure l eads to a l arge increase in react i on t ime and a subsequent l oss of productivity w ithout bei ng suf­ficient to e l im inate total ly the occurrence of dan­gerous peaks i n react i on power fol l ow ed by tempe­ra I shut-down of the reacti on. T hus a new control concept was ca 1 1 ed for, us I ng advanced process control technology.

248

Furthermore, a short l ocal temperature peak i n some sma 1 1 part o f the reactor can start the auto­cata Jyt le decomposlt I on which has hardly any ef­fect on the control led temperature and m ay go by unnoticed. Once started, the decomposition w I 1 I not ext lnguish In the norm a I operat Ion m ode and even­tua I ly l ead to a runaway of the react Ion. Thus, a supervising system I s needed for the early detecti­on of a begiMing autocatalytic decomposition.

The New Control Concept

To i mprove the control behav iour of the exother­m i c batch process, a new contro 1 strategy was de­veloped contro I I 1 ng the reaction pow er dOreacl dt

rather than product temperature. React i on power, the m ost sens itive variable for safe operation is then under direct contro I .

Simulation tests demonstrated the d isadvantages and I nadequacy of a f ixedparameter control l er and showed, that the dynam ic response of the system changes m arkedly w i th the varyingheat product i on w ithin the reactor. With a P l control structure for the reaction power control l er, computer s imulati­ons showed that the control l oop m ai ntains 1 ts cha­racterist ics only i f the ga i n ls changed in accor­dance w Ith the changing dynam ics.

A gain-schedul ing strategy is therefore adopted whereby the value of the galn-schedul ing factor i s adjusted s o a s t o keep the overal I loop gai n con­stant:

(5)

where kP and kc represent the gai n of the process

and the contro l ler respective l y. The gai n has then the fol low i ng form:

As shown by equat ion 4, react i on power i s a func­t ion of unknown concentrat i ons [A] and [B]. To provide the control w i th a value of the react ion power these variables are est imatedby an extended Kalman f i l ter based on the mathematica l model of the process as described by equat ion 3. The overa 1 1 block diagram for the control l oop i n quest ion i s shown i n F ig. 1 .

F ig. 1 : Overal l B lock D iagram

As an integral part of the control design process, simulation tests of the control system m ust be performed to ensure that transi ent performance speci ficat ions are m et. F ig. 2 shows reactions to set point changes for two different temperatures: in the upper diagram the react i on temperature i s c lose t o the lower l i m i t and i n the l ow er diagram i t close t o the higher l im i t o f the a l l ow ed temperatu­re range. The resul ts demonstrate that, in contrast to the ear l i er temperature control , the relevant variab le for safe operation, the react i on power, i s now contro I led direct ly ensuring satisfactory transient behaviour for a l l process state.

0

I I

0

I I

High Temperature State

. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . ,,, . . ____ .....,.

Norm.atzed Time

O-Aotu.a Value Q-Setpolnt

Low Temperature State

_., ...... . . . . . . . . . . . . . . . .

Normalized Time ,_

F ig. 2: Transi ent behavi our of the react i on power control l oop

249

Typical experim ental results are shown in F i g. 3 and 4. T he product temperature trajectory fol low­ed by the conventional control differs significantly from the m ore eff ic ient trajectory of reactt on po­wer control.

...... .... · ·

.·

······ ··········7\ .... \ . .....

, .. •· wlflaul AIMlbl PoMl'Comal

F i g. 3 : Product temperature trajectori es for conventional and advanced control

strategy

r J

Normallr.ed Time

F ig. 4 : Frequency of norm a l i zed product ion t ime

Early Detect i on of a Hazardous Secondary React i on

The detect ion princ ip le appl ied here i s based on propos i t i ons of King & G i l l es [ 3 J and G i l ies & Schuler [ 2 ], who suggest to construct extended Ka Iman Fi 1 ters for the norm a 1 reacti on and each type of disturbed process. A decision stage based on a Bayes-Markov process discr i m i nates between the different process states: norma l and type of di­sturbance. Thereby, probabi l i t ies derived from the Kalm an f i l ters <F ig.5) are used to update a Markov process which m odels the prob ab i l i t i es to be i n one of the different process states and gives a priori est i mates for these probab i l i t ies. This mo­del contains rates for the transit ion between the d ifferent process states - an example i s the tran­sition rate from normal reacti on to autocatalytlc decomposit ion which is a function of temperature and concentrations.

I n contrast to King and G i l les, only two m ode l s are used: one for the norma l react i on and one for di­sturbed processes. The second mode 1 contains pa­rameters, which are est imated a l ong w lth the pro­cess states and can describe different types of di­sturbances at the same t ime. Much of the e ff ort gained by reduci ng the number of f i l ters has to be rei nvested ln construct ing and calculating a more compl icated f l l ter. However, thls approach w i l l automatlcal ly deal w Ith commonly observed mode 1 devlat ions.

The abl l i ty of the Bayes-Markov forma l i sm to de­tect unwanted process states depends crucial ly on

. the cho ice of the covariance m atri x of process noi­se a. Whereas the covariance m atrix of measure­ment no ice R is chosen such that l t corresponds to the actual m easurement no i se, a and the In it ia l va­lues of the covar iance matr ix of the states P 0 are

considered as designvar lab les for the Kal man f i l­ter. p0 i s chosen such that the desired speed and

necessary degree of model adapt ion is achieved at the start of each batch. O for the norma l react i on i s a comprom ise between speed o f process tracking and accuracy of esti m ati on. Care has to be taken choos ing this var i able for the adaptive fi lter which inc ludes the decomposit ion andparameters to be estimated along w l th process states.

250

For the normal react i on both mode ls should be equivalent and give si m i Jar resul ts. It has been observed, however, that the h igher d imensi on of the second mode 1 l eads to a much broader estimated probab i 1 i ty densi ty d istribut i on p for the m easu­red vari ab les effecting the abl l l ty of the subse­quent decision logic to dlscri m inate between the two cases.

f t ;�--

D T.._ue

Tl

F i g. 5: Probab i l ity dens ity d i str ibut i on pi for two ·model s

F ig: 5 shows the probab l l i ty densi ty distr ibution for two model s. E1 and E2 are expected values, T 0 i s the observed va lue. p1 i s a funct ion of the i nno­

vat i ony1< k > = E i-T 0 and the error covar i ance m a­

trix P 1<klk- 1 ) of the Kal m an f i l ter < H: Jacobi an

of m easurem ent equat ion, m: d imensi on of R>:

(7)

The si tuat i on shown i n the Fig. 5 has to be avo ided. Although the observed temperature is much c loser to the expected va Jue of m ode I 2 1nc Juding decom­posit ion, for the gtven probabi l i ty densi t ies the decision log1c w 1 1 1 choose model 1 . A steeper pro­babl I ity density d1stribut Ion can be obtained by assum i ng sma l lerva l ues for the "process noi­se", which, however w 1 1 1 reduce the speed of model adaptation. The opt tmum a of the Kalman f i l ter I s a comprom ise between speed of detecti ng autocata ly­t ic decomposit ion on one side and certainty of dis­crim inat ion and accuracy of est tmat ion on the other side.

-

l I

...... �·····

-

/

,_ -

-

l I

- -

.... -

F ig. 6 : Test resul ts from an i ndustr ia l p lant

This detect ion m echanism has been implemented in a process w i th a react ion m echanism s im i Jar to the one shown above. F ig. 6 shows resul ts for different batch samples: I n the f irst case, the reaction pro­ceeded normal ly, in the second case, deviation of the start concentrattons required the add1t Ion of one component during the heating phase. The re­sult ing he.at of m ix ing is i nterpreted by the detec­tionmechanism as an addit ional potent ia l ly dange­rous heat source and a w arni ng Is given. At this point the temperature i s st i l l l ow and a autocata­lyttc decomposit ion not very probable.

Conclus1on

The performance of the supervision and control system for exotherm ic batch react I on ls encoura­ging for further practical app l i cations. I t shoul d be m entioned, however, that models accurate enough to discrim i nate between different process states are not readi ly ava i lable and often difficult to establ ish 1 im i t ing a straightforward extension of thi s approach to other react I ons. These restric­t ions are not as stri ngent for the react i on power control w here someti mes a good model of the reac­tor w ithout an expl ic it model of the react ion can lead to considerable improvement.

R ef erences

[ 1 ] 6 1 1 /es, E.D. ( 1 983)

Moderne Methoden der Me13- und Automat i­s ierungstechni k und ihre Bedeutung fOr dle Automat is ierung verfahrenstechntscher Pro­zesse Chem log Tech 55, pp. 437-446

[ 2 ] G i l les, E.D., Schuler, H. < 1 98 1 > Zur frOhzei t igen Erkennung gefahr l i cher Re­akt tonszustande i n chem t schen Reak toren. Chem Ing Tech 53, pp. 673-682

[ 3] King, R., G i l ies, E.D. ( 1 986)

251

Early detect ton of hazardous states i n chem i­cal reactors. Prepri nts of the I FAC Work­shops "Faul t Detection and Safety in Chem ical P lants" , S ept. 1 986, pp. 1 37- 1 43

Copyright © IF AC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

MARKOVIAN RELIABILITY ANALYSIS OF STATE-ESTIMATOR-BASED INSTRUMENT

FAULT DETECTION SCHEMES

D. van Schrick

Department of Safety Control Engineering, University ofWuppertal, D-5600 Wuppertal J , Gauss-Strasse 20, Germany

Abstract. Concerning their reliability, several state-estimator-based schemes for deterministic and stochMtic instrument fault detection and isolation {IFDI) are analysed. Based on the Markovian the­ory, these schemes and a classical hardware-realized majority voting system are modeled. The resulting models make possible a comparison of the different schemes by calculating their survival probability, their mean life, their availability or other characteristic quantities of reliability. To allow a uniform c.omparison, an intelligent measuring system (IMS) with three different input variables to be super­vised is taken 88 a basis. For this example, numerical and simulation results show the advantages and disadvantages of each estimator-scheme also compared with the hardware-realized voting system. Additionally, the influence of the quality of estimators will be investigated.

Keywords. State-estimator schemes; analytic redundancy; instrument fault detection; reliability analy­;fs; Markovian theory.

INTRODUCTION

The on-line detection of faults in technical systems is a prere­quisite to run reliable, economic and ecologically beneficial plants. There are many different ways of supervising such systems, cf. the survey papers of Willsky ( 1976), Isermann ( 1984), Gertler ( 1988) and Frank ( 1990) or the books of Bas­seville and Benveniste ( 1985), Viswanadham et al. ( 1987) and Patton et al. ( 1989). The way we are looking at is founded on analytic redundancy realized by state-estimators. These state-estimators are used to generate quantities, called residuals, which carry informations on faults in the system. Just like the duplication of critical components of a plant with hardware redundancy, state-estimators form a software­realized redundancy of the plant or parts of it .

The study of literature shows that there exists a number of so-called state-estimator schemes not only for the genera­tion of residuals but often also for the evaluation of residuals, mostly by means of a threshold logic. These fa ult detection and isolation (FDI} systems are also known as estimator banks. In both cases, generation and evaluation of residuals, a lot of work has been done and is done, cf. lsermann ( 1991). All these design efforts must result in a very high reliability of the different supervising systems.

In this paper such estimator schemes are regarded that are used for the Instrument Fault Detection (IFD) based on (Luenberger) observers or Kalman filters which in several ways are connected to a system. The term estimator scheme {ES) has been chosen because some schemes, originally de­signed for observers only and therefore called observer sche­mes, allow the application of both, observers and filters de­pending on a deterministic or stochastic environment. The schemes regarded are the duplex sensor DSES, the dedicated DES, the simplified SES, the generalized GES, the sensiti­vity discriminating SDES, the innovations-based !BES and the multiple model estimator scheme MMES. As a reference, one hardware-redundant voting scheme is also investigated.

253

The reliability analysis method is based on the well-known theory of Markov processes. After the fundamentals of the method have briefly been discussed, it is applied to the eight !FD-schemes. In order to form a uniform basis for the analy­sis, it is necessary to define a general !FD-task to be fulfilled by each of the schemes. It is important to note that we are not interested in the overall reliability of a dosed-loop sy­stem where the !FD-scheme is integrated and additionally the complete switching part for reconfiguration or fail-safe actions has to be considered. We consider only those IFD­schemes with a fixed number of measurements of a system as inputs to be supervised and an appropriate number of alarm quantities as outputs regardless of its deterministic or stochastic environment. This general !FD-task, the resulting structures of !FD-schemes and the reliability modeling are il­lustrated by one example. The modeling results in reliability state-graphs and appropriate transition rate matrices for the transition from one to another state the scheme can take on. Some important aspects of this modeling are also addressed. The last step deals with the calculation of several reliability relevant quantities and contains the results of the compari­son of schemes which make clear that it is worthy of going on with the intensive work in the more and more important field of fault detection with analytic redundancy. Based on Boolean structure functions, first attempts to reliability ana­lysis of state-estimator-based !FD-schemes are described by van Schrick ( 1990, 1991 ) .

DESCRIPTION OF ESTIMATOR SCHEMES

Over the years, a number of different !FD-estimator schemes has been proposed in the literature. Depending on the appli­cation, these schemes differ in the number of estimators, the number of measuring quantities used as inputs to t.he esti­mators, the order of estimators and the regarded goals at the design of estimators. The logic for residual evaluation can be another feature where mainly a threshold logic is used.

In the following brief description of !FD-schemes, we are concentrating on those schemes that can often be found in the literature and are based on certain classes of measuring configurations. The classes can be distinguished in simple:r:, duple:r: and triple:r: sensor configurations. This means, there exist one, two or three sets of instruments for measuring the quantities of interest, e.g. for control purposes. Each set contains a fixed number of instruments and its duplica­tion leads to a single or double hardware redundancy of the instruments. Fitted on the application example IMS (in­telligent measuring system} for our reliability investigations, one of the resulting structures of schemes will be given. For deeper informations on the schemes, the reader is referred to Frank and Keller ( 1984) or to the list of publications in Patton et al. ( 1989).

We only use the double hardware redundant configuration (triple:r: sensor configuration) for comparative purposes. One realization of this structure is the well-known 2-out-of-3 ma­jority voting system that works correctly, if at least two out of three components (sensors) are not. faulty (Meyna, 1982). This structure is the simplest fault-tolerant structure, irre­spective of the realization of its evaluation logic in hardware, software or firmware. In the following, the interest is directed to the completely hardware-realized version of the 2-out-of-3 structure marked with HWR (hardware redundancy).

The best known representative of the class of systems with a duple:r: sensor configuration is the duple:r: sensor esti­mator scheme (DSES} optimized by Stuckenberg ( 1981 ). In this scheme, there are two independently act.ing paths con­sisting of one set of instruments and one observer. Each set of instruments drives one observer that generates an appro­priate set of residuals. Because this scheme is based on two independently working observers, it allows a separate loca­lization of faulty sensors in each path. The detection of in­strument faults is carried out by a classical hardware-realized comparison between each sensor output in one path and its redundant counterpart in the other path. When a faulty sen­sor is detected, the residuals are used to determine the path in which the faulty sensor is located. Originally, this scheme takes into account the robustness against parameter uncer­tainties and unknown inputs within the evaluation logic by e:r:tended thresholds and with the design of observers.

The class of software-realized !FD-schemes based on the simple:r: sensor configuration can be generally described by the general structure estimator scheme (GSES} illustrated in Fig. 1. This scheme consists of b fa ult detection estima­tors (FDE} each driven by the system inputs !!(t) and the

y(t) I ! t(tl 1 I 1!'.(t)-

I System 1 I Sensors 1 a,

ij f.-I

FDE 1 . r1(t) � I IFD

It i:,(t) I FDE 2 : I Logic

Clb ij"

f.-

I FDE b : r.(t)

I �

Figure 1: General structure estimator scheme (GSES).

measurements y(t) and provides b residuals r.;(t), e.g. each for one of the -;ensors to be supervised. All residuals and possibly all measurements are then treated in the residual evaluation logic (REL). The result is reflected by the alarm signals a1,2, . . . ,b· All following schemes can be derived from this general structur·e estimator scheme {GSES) and repre­sent special cases of it.

As an example, we only consider estimator schemes ori­ginally designed for stochastic environments. It is obvious

254

that these schemes consist of only one estimator that is a Kalman filter generating an innovations sequence. Additio­nally, there is a logic for the generation of statistics based on the innovations with a following evaluation of these stati­stics for fault detection and isolation. Such schemes can be treated as the group of innovations-based estimator schemes (!BES). This group is founded on the robust covariance ma­tri:r: test (RCMT) of Belkoura ( 1983) for example, or on the entirety of generalized likelihood ratio (GLR} methods, may be the one of Tanaka and Muller ( 1990).

In our investigations, we consider the residual evaluation logic (REL) as a well functioning part of the !FD-scheme. Under special conditions, its influence onto the !FD-scheme is not of interest to us. In opposition to that, the influence of the quality of estimators (and other components) is of high interest. This does not mean that we try to formulate modern estimator design techniques in terms of reliability. But more to that is presented later.

Table 1 summarizes the features of the eight schemes re­lating to the estimators. Feature "1" is the sensor confi­guration, "2" the environment, "3" the number of estima­tors, "4" the order of estimators, "5" the number of sensors per estimator, "6" the original robustness by estimators, "7" the original robustness by the evaluation logic elements, "8" the possible robustness by estimators with respect to para­meter variations, "9" the possible robustness by estimators with respect to unknown inputs, " 10" the possible robustness by evaluation logic elements and feature " 1 1" the maximal number of faulty sensors. Additionally, "tx", "dx" and "sx" stand for triplex, duplex and simplex, "det" and "sto" for deterministic and stochastic, "f" for full, "m" for the num­ber of instruments and "m*'' stands for m-out-of-n.

I Feat. I/ HWR I DSES I DES I SES I GES I SDES j IBES j MMES j 1 tx dx sx sx sx sx ax sx 2 det det det det det det sto ato 3 2 m 1 m 2m 1 m+l 4 - { f f f { { f 5 - m 1 1 m-1 1 m m 6 - no no no no yes yea no 7 - yes no no no no no no 8 - yes yes yes yea yes yea yes 9 - yes no no yes no yes yes

10 - yea yes yes yea yea yes yes 11 m• 2/3 m-1 m-1 1 m-1 m-1 m-1

Table 1: Features of the !FD-schemes.

BASIC THEORY OF MARKOV PROCESSES

Our investigations are founded on the theory of homogeneous Markov processes with a finite number of states and conti­nuous parameter domain. The properties of the processes that are of primary interest in analysing the models of the !FD-schemes will be presented in this section. Proofs of the properties are omitted. The main properties of such a ran­dom process are (Barlow and Proschan, 1965): If a system to be modeled can take on only a finite number N of states then the Markov process can take on only a finite number N of discrete values. These discrete values are labeled with the integers 1 ,2, . . . ,N. Thus, a transition i to j means a change from a state labeled i to a state labeled j, and the proba­bility that the next state to be occupied by the process is j depends only on the current state i that is occupied. This independence of the future process transitions from the past is called Markov property.

The probabilistic behaviour of a finite state Markov pro­cess is completely characterized by the initial distribution of its value and the history of the state transition rate matri:r: that describes the probabilities per unit of time of occupy­ing each of the states at the next transition given the current state that is occupied. The probability that the process ta-

kes on the state i at the instant t is called state probability and labeled with p;(t) . The entirety of all state probabilities p;( t), i = 1, 2, . . . , N fulfills the differential equation

'f!_( t) = Ar( t) ( 1 )

where A is a constant matrix of the constant transition ra­tes, i.e. we have the case of a time-invariant process. The solution to this equation can be represented by

(2 )

where p( 0) i s the given initial distribution of the value of the process and T a constant time interval. The vector p(t) and the matrix A have some properties that are important to note, e.g. the elements of p(t) sum to unity for every instant t , with known p(t) the pro-;;ess is completely known for every t in future and the column elements a;j of A sum to zero.

We already noted that the transition matrix A is con­stant. That is, the failure rate A and the repair rate µ of each component of the !FD-schemes are assumed to be constant. Constant rates can be used, if the components regarded are electronic devices with preaged and picked out elements. In this case, we can use the exponential distribution

F(t) = 1 - e -•t, r E {A, µ} (3)

as a description of life L and repair K. Now, the question arises whether i t i s possible to use this

exponential distribution for software-realized components. In the !FD-schemes, software-realized components are obser­vers, filters and the different parts of the residual evaluation logic (REL) which all are regarded as single software com­ponents. One prerequisite should be fulfilled: The software used for !FD-tasks is well-tested and there is no aging of software. This results in constant failure rates. With regard to Markov processes, we have to limit the class of systems in­vestigated to those that are memoryless. That is necessary for both, the estimators and the logic elements. Residual generators such as observers or (stationary) Kalman filters are not problematical because they fulfil the Markov pro­perty. But in general, informations from the past are used when statistical tests, such as the one of Bayes or the GLR test, both possibly with a window of the time series of in­novations, are applied to the residual evaluation. Strictly, programs for such tasks cannot be described by the expo­nential distribution F(t). Nevertheless, we think the expo­nential distribution is justified because the memory depends on the expansion of time of the program or on t.he time con­stants of the controled or supervised system, respectively. In the general case, these time constants amount some hours, but due to the fact that the periods interesting to reliabi­lity are lying in the range of months or years, the failure behaviour of continuously running programs can be approxi­mately well described by the exponential distribution F( t ) . It is important to regard the calculation time to failure as an independent variable instead of the calendar time.

With this background, we do not make any difference between hardware-realized and software-realized components where all estimators and the evaluation logic units are reali­zed as tasks used for real-time processing.

Corresponding to a unit of time UT = 106hrs, the nomi­nal transition rates are given in Table 2. These transition

I Component Instrument Hardware Vot.er A/D-Converter Computer Task

Failure Rate I Repair Rate AJ=50/UT µ1=200/UT

AHv=6/UT JtHv=1670/UT AAv=20/UT µAv=500/UT

Ac=l5/UT Jtc=670/UT Ar= l/UT M=lOOOO/UT

Table 2: Chosen nominal transition rates.

255

rates are the basis for the reliability investigations. After modeling, the following characteristic reliability va­

lues will be calculated for each of the eight !FD-structures: The scheme reliability

Nn Rs(t) = L P;( t ) (4)

i=l

where Nn is the number of non-absorbing states, i.e. states that can be left, the mean scheme life

00

E(Ls) = j Rs(t)dt, (5) 0

the scheme availability

N. As(t ) = L P;( t ) (6 )

i=l

where N,, is the number of the states where the scheme is available, the mean scheme availability

T - 1 I As(t ) = :;: As(t)dt (7 )

0 where T is the end value of the interesting time interval and the stationary scheme availability

As = Jim As(t) = lim A5(t). t-oo t-oo

MODELING OF ESTIMATOR SCHEMES

(8)

Based on the theory of Markov processes described in the previous section, we develop the Markov models for the eight !FD-schemes mentioned earlier. For that, an intelligent mea­suring system (IMS) with two types of inputs and 3 outputs is defined. The inputs are the system inputs !!( t ), assumed to be ideal, and 3 different measuring quantities Yi, e.g. of a. motor current or a. force. The outputs of the IMS a.re 3 quantities which provide informations on the condition (non­faulty, faulty) of the sensors used for measuring the input quantities Yi. The outputs a.re called alarm signals a; and may serve as information carriers for a following diagnosis and/or reconfiguration. The IMS must be able to detect and isolate faulty sensors at lea.st. It is very important to mention that the 3 ala.rm signals a1,2,3 are necessary for a correct operation of the IMS in order to have informations on the sensors and other components, such as estimators, tasks or computers, at any instant. Additionally, we do not examine a. closed-loop (control) system, therefore we do not have to take into consideration switching elements necessary for reconfiguration or fail-safe actions that would make the reliability modeling of the IFD-schemes more complicated. Figure 2 shows the black box intelligent measuring system (IMS). The question that has to be answered runs as fol-

l!(t) System t(t) .--------------, <======="" Sensors

"' Intelligent Measuring System

Which is the

most reliable IFD-scheme?

Figure 2: Black box intelligent measuring system (IMS).

lows: Which of the eight fault-tolerant !FD-schemes is the most reliable one ?

Before we pass on to modeline:. additionally to the as­sumpt.ions on Markov models, different assumptions have to be made: Single faults are allowed (one sensor or one conver­ter); faults have to be distinguished, two faults at the same time are not considered, because their probability of appea­rance is neglectible, two time-shifted faults are only consi­dered, if the second fault appears before the repair of the first faulty component gets started (during repair no fault occurs) ; faults of software-realized components (tasks) are treated as fault of hardware-realized ones; each component can take on 2 states: non-faulty and faulty; faults occur in­dependently; external events, such as power supply distur­bances or electromagnetic fields are not taken into account (no common mode failures); immediate repair, no inspection, no simultaneous repair of more than one component; no ad­ditional load of components; input quantities :!!:( t) (control signals) of the estimators are ideal; the observability requi­rements are fulfilled, e.g. DES and DSES require strong observability (the system is observable by each measuring quantity) , all other estimator-based schemes require general observability; if only one out of three alarm signals a; fails, the complete IMS is failed; the chronological order of faults is considered through the addition of appropriate states, and an absorbing state, e.g. a state that represents the condition of unacceptable system performance and cannot be left, is defined through the failure of the residual evaluation logic (REL), in that case, the IMS is lost.

This list shows the complexity of a reliability analysis where especially the operation in nominal and faulty situa­tions of a system must be investigated carefully.

As one example, the 5 resulting modeling steps are explai­ned with the help of the innovations-based estimator scheme (IBES). The resulting st.ructure is given in Fig. 3. There are 3 sensors, 3 A/D-converters and one computer with 3 tasks

!!(t) System 11'(t ) Y1.2.3(t ) Sensors IFD a,

a,

Logic a,

r(t) FDE

Figure 3: Resulting structure of IBES.

(estimation, detection and isolation) resulting in 210 = 1024 possible states. Modularization leads to 3 sensor unit modu­les SE1,2,3 and one module M1 consisting of one computer with 3 tasks. Thus, only 24 = 16 possible states remain. The modeled scheme can take on 5 chosen states, Table 3. The

I No. II Description 1 all components are working, no fault indication 2 one sensor unit fails 3 second sensor unit fails 4 third sensor unit fails, system unavailable 5 logic modul M1 fails, system unavailable or lost

Table 3: Chosen states of IBES.

state flow graph is given in Fig. 4 and the transition matrix A1sEs in Fig. 5.

It is useful to mention that the evaluation logic can be for example the GLR test or the RCMT one with time shifted covariance matrix.

We think, there is no point. in presenting all resulting structures, state definitions, state flow graphs and transition matrices of all eight schemes. Therefore, Table 4 reflects the

256

3AsE

µsE

2AsE 2 4

2µsE

AMI

µMl

Figure 4: State flow graph of IBES.

main data of the eight resulting models. The numbers in the first column have the following meaning: "1" stands for the number of sensors, "2" stands for the number of hardware-[ •u µ,,

3AsE a22 0 2AsE 0 0 AMI AMI

0 2µsE aaa AsE AMI

0 µM, l 0 µMl 3µsE /LM1 a44 0 0 a55

Figure 5: Markov matrix A1BES·

voters, "3" stands for the number of A/D-converters, "4" stands for the number of computers, "5" stands for the num­ber of tasks, "6" stands for the number of states before mo-

I No. II HWR I DSES I DES I SES I GES I SDES I IBES I MMES I 1 9 6 3 3 3 3 3 3 2 3 - - - - - - -3 3 6 3 3 3 3 3 3 4 - 2 4 2 4 4 1 5 5 - 4 6 3 5 9 3 6 6 210 2'" 2'" 2'" 210 2" 2ll 2'"

7 1 8 7 5 4 7 2 8 8 2'" 2" 2' 2' 2' 2' 2• 28 9 6 1 1 1 4 6 10 14 5 10

10 5-6 9-1 1 1 1-14 4-6 7-10 1 1-14 4-5 7-10

Table 4: Features of the resulting models.

deling, "7" stands for the number series-modules, "8" stands for number of states after modeling, "9" gives the order of the resulting model and " 10" gives the numbers of the states where the scheme is unavailable.

COMPARISON OF ESTIMATOR SCHEMES

The comparison of the eight IFD-schemes is carried out on the basis of the characteristic quantities of reliability ( equa­tions (4) - (8)) where all failure and repair rates are related to the instrument failure rate AJ . This leads to the pseudo transition rates in Table 5, i.e. the simulation time scale is a

I Component II Failure Rate ) Repair Rate ) Sensor A1=1.0 µJ=4.0 Hardware Voter AHv=0.12 µHv=33.4 A /D-Converter AAv=0.4 µAv=l0.0 Computer Ac=0.3 µc=13.4 Task AT=0.02 µT=200.4

Table 5: Resulting pseudo transition rates.

multiple of the mean life E{L1} = l/A1 of the instruments and results in the simulation time T = t * AJ that is dimen-

sionless. Additionally, we only regard p(O) = fu i.e. with all probabilities equal to zero but the first.

The first quantity we evaluate is t.he mean scheme life E{Ls}, equation (5 ) , where the faulty logic defines an absor­bing state. The Table 6 shows the quantities E{Ls} related

I E{L,} II HWR I DSES I DES I SES I GES I SDES I IBES I MMES I UT 0.70 3.36 2.83 3.26 3.11 2.83 2.81 3.08 Years 1.59 7.67 6.46 7.44 7.10 6.46 6.42 7.03 T31% 0.32 1 .55 1 .32 1 .5 1 1.44 1.32 1.31 1.43

Table 6: Mean scheme lifes of the !FD-schemes.

to the unit of time UT, the mean scheme life in years and the instant r373 where only 37% of all schemes are functio­ning at all. It is to be seen clearly, the HWR is the scheme with the shortest mean scheme life that is smaller than the mean life 1/ >.1 of the sensors. The DSES is the best, be­cause its mean scheme life is the largest and together with SES, GES and MMES it forms a group with a mean scheme life more than 3 times larger than the mean life of the sen­sors. There a two groups which lie between the DSES and the HWR. The first group after DSES consists of SES, GES and MMES and the second group consists of DES, SDES and !BES. So, this comparison shows that the duplex sen­sor estimator scheme (DSES) is to be expected the scheme with the longest life. If we now reduce the time observed, we can determine the long-time behaviour by calculating the reliability function Rs( T ) , with T between 0 and 5, i.e. for a time of 1 1 .46 years. Figure 6 shows this behaviour in terms of the failure function Q s( t) = 1 - Rs( t) that reflects the

1 . 000

Q < T Ollu l

1 . 00 2 , 00 3 . 00 4 . 00 5 . 00

Figure 6: Failure functions of 8 schemes, T, = 5.

same order of schemes as with the mean scheme life E{Ls} in Table 6. In this and the following Figures, the numbers 1 ,2, . . . ,8 mark the !FD-schemes appropriate to their order in Table 6, e.g. "1" symbolizes HWR and "4" symbolizes SES. It can be seen that there are no intersections of the reliability courses and that all estimator-based schemes show a relia­bility behaviour that is much more better than the one of HWR. If we now analyse the time behaviour in the interval O :S T :S 3 (not shown), that is a maximum of 6.85 years, we can realize that the reliability curves of the estimator-based schemes split up at the instant T = 0 . 1 into the three groups DSES and SES, GES and MMES as well as DES, SDES and !BES. This is dearly illustrat.ed wit.h t.he Fig. 7 that shows the courses of the scheme reliabilities (without HWR) for T between O and 1, i.e. for a time of 2.28 years equal to the mean life of a sensor. Figure 7 also illustrates that the short­time behaviour of all schemes but of the HWR is quite the same compared with the long-time one shown in Fig. 6.

Due to the fact that there are no intersections of the reliability courses, the mean lifes of the schemes reflect the

257

.20 ·'° .60 .90 1 . 00

hu ( t / [ ( L 1 } l

Figure 7: Failure functions of 7 schemes, r, = 1 .

reliability behaviour for short and long times. This may not be the case for some systems, because their long-time and short-time behaviour can be quite different.

We can summerize the results of the reliability compari­son based on nominal transition rates given in Table 5 for the 8 !FD-schemes with a nonrepairable logic that repres­ents an absorbing state. Independent of time, the hardware redundancy (HWR) is the most unreliable scheme. The best behaviour offers the duplex sensor estimator scheme DSES followed by SES, GES and MMES, the last two with approa­ching the same behaviour. The curves of the group DES, SDES, !BES show identical behaviour. This scheme order does not depend on T. The DSES and the SES can be recom­mended for the intelligent measuring system {IMS), but with a quite different repair strategy due to the time behaviour of the first state p1 ( T ) , in which the SES stays two times longer than the DSES. The selection of one of the 7 software-aided schemes depends on practical aspects, such as the number of faulty sensors, implementation efforts, repair strategies or robustness against uncertain system parameters.

Robustness is a very important topic we are interested in. The question we are know following is whether the ro­bustness property influences the reliability behaviour of the schemes. In sense of reliability, robustness is modeled as a special value of failure rate >.T of the estimator task. We as­sume that the nominal value of >.T given in Table 5 reflects the non-robustness of the estimator used. If now the estima­tor task failure rate is set to >.T = 0.01, an approvement in the behaviour of the estimator schemes without the one of the simplified estimator scheme (SES) is ascertainable. If >.T is set equal to the sensor failure rate >.1, without the !BES, no change in the behaviour takes place. Figure 8 shows the

3 . 366

£ (La}

2 . 693

2 . 020

1 . 346

.673

-.

- -

. • o .90

-

--

1 . 20 1 . 60 2 . 00

La111bda Ta•k

Figure 8: E{Ls} depending on >.T.

robustness behaviour characterized by the mean scheme life depending on the estimator failure rate 0 ::; AT ::; 2. Here we can observe that the mean scheme life of !BES only decre­ases very fast with increasing AT and that the mean lifes of the other estimator schemes remain constant, with the same order as in Fig. 6. Consequently, all estimator schemes but the !BES are not influenced by the robustness quality of the estimators. This is also the case if the repair rate µT varies within the interval 0 ::; M ::; 400.

If we consider the failure rate AT of all tasks (estimator and logic) varying, than the curves of all estimator-based schemes decrease with increasing failure rate in the shape of the curve of !BES in Fig. 8. Similar results are obtained by varying the computer failure rate Ac. In that case, the results in van Schrick ( 1991) are confirmed.

The second part of our investigations is the study of the availability behaviour of the schemes. Figure 9 illustrates the unavailability U( r) in the interval 0 ::; r ::; 0.3. The group DES, SDES and !BES turns out to be the most available one. The largest unavailability is reached by HWR followed by SES. Up to the instant T = 0.23, SES is the most un­available one. Another intersection is at T = 0.24 for the

•10-1 .60 1 ,20 1 .80 2.40 3.00 Tau [t/E!L1 l l

Figure 9: Unavailabilities of 8 schemes, r. = 0.3.

availability curves of the group DES, SDES and !BES. The DSES becomes worse than the !BES at T = 0.045, worse than the MMES at T = 0.21 and worse than the GES at T = 0.29, but it never becomes more available than DES or SDES. The HWR is of no interest.

The order of the schemes depending on the availability As(r) is the first quantity of Table 7. The others are the values of the mean scheme availability As(r) at T = 0.5, the mean scheme availability As( T) at T = 1, the mean scheme unavailability Us(r) at T = 1 and the stationary scheme availability As. This table reflects the high quality of the schemes in the group DES, SDES and !BES.

I Qtty II HWR I DSES I DES I SES I GES I SDES I IBES I MMES I Order 8 6 2 7 5 2 1 4 As(.5) 0.91 0.96 0.99 0.92 0.96 0.99 0.99 0.96 As(l) 0.90 0.94 0.98 0.92 0.95 0.98 0.98 0.96 Os( I) 0.10 0.06 0.02 0.08 0.05 0.02 0.02 0.04 As 0.89 0.93 0.98 0.90 0.94 0.98 0.98 0.95

Table 7: Availability characteristics of the !FD-schemes.

These results and such not shown here in this paper make clear that it is valuable to deal with instrument fault de­tection and isolation from the control theory point of view. With this reliability comparison, the first results of van Schrick ( 1990, 1991) , in sense of "software-realized is more re­liable than hardware-realized", have been confirmed in spite of completely different transition rates chosen for investiga-

258

tion. Moreover, it is easy to recognize that the different schemes require different repair strategies when applied to the intelligent measuring system. But in general we can say the group DES, SDES and !BES results in the highest re­liability gain of all eight schemes investigated, if repairable schemes are required. Otherwise, the DSES and the SES seem to be applicable.

CONCLUSIONS

In this paper, we have run through the feedforward part of the reliability control-loop consisting of analyzing the sy­stem behaviour, reliability modeling, data collection (rates) and reliability analysis by calculation and simulation in or­der to investigate the reliability behaviour of eight different !FD-schemes. Research continues on the modeling of semi­Markov models and on concepts only using one or two com­puters at all.

REFERENCES

Basseville, M. and A. Benveniste ( 1985). Detection of Abrupt Changes in Signals and Dynamical Systems, Lecture Notes in Control and Information Science, Vol. 77, Springer Verlag, Berlin, Heidelberg.

Barlow, R.E. and F. Proschan ( 1965). Mathematical Theory of Reliability, The SIAM Series in Applied Mathema­tics, John Wiley & Sons, Inc., New York, London.

Belkoura, M. ( 1983). Entdeckung von lnstrttmentenfehlern mittels Kalman-Filter, Ph.D. Dissertation, University of Duisburg, Germany.

Frank, P.M. ( 1990). Fault Diagnosis in Dynamic Systems Using Analytical and Knowledge-Based Redundancy · A Survey and Some New Aspects, Automatica, Vol. 26, pp. 459 . 474.

Frank, P.M. and L. Keller ( 1984) . Entdeckung von Instru­mentenfehlanzeigen mittels Zustandsschatzung in tech­nischen Regelungssystemen, VDI-Fortschrittberichte, Reihe 8, Nr. 80, VDI-Verlag Diisseldorf.

Gertler, J.J. ( 1988). Survey of Model-Based Failure Detec­tion and Isolation in Complex Plants, IEEE Control Systems Magazine, Vol. 8, pp. 3 - 1 1 .

Isermann, R . ( 1991) . Preprints of IFAC/IMACS-Symposium on Fault Detection, Supervision and Safety for Techni­cal Processes -Safeprocess '91-, Sept. 10-13, Baden­Baden, Germany.

Meyna, A. ( 1982). Einfiihnmg in die Sicherheitstheorie, Sicherheitstechnische Analyseverfahren, Carl Hanser Verlag, Miinchen, Wien.

Patton, R.J., P.M. Frank and R.N. Clark ( 1989). Fault Dia­gnosis in Dynamic Systems, Prentice Hall.

Stuckenberg, N. ( 1981 ) . Ein Beitrag zur Erkennung und Isolation von Sensorfehlern in Flttgregelsystemen un­ter Verwendung von Beobachtern, DFVLR-FB 81-26.

Tanaka, S . and P.C. Miiller ( 1990). Fault Detection in Linear Discrete Dynamic Systems by a Pattern Recognition of a Generalized Likelihood Ratio, Trans. ASME, Jour­nal of Dynamic Systems, Measurement and Control, Vol. 1 12, pp. 276 . 282.

van Schrick, D. ( 1990). Reliability Analysis of State-Estimator Schemes for the Instrument Failure Detec­tion, Proc. !MACS Symposium on Mathematical and Intelligent Model in Systems Simulation, Brussels, Bel­gium, pp. IV-A 4-1 - IV-A 4-70.

van Schrick, D. ( 1991) . Investigations of Reliability for Instrument Fault Detection State-Estimator Schemes, Diagnostic et Surete de Fonctionnement, Vol. 1, pp. 63 . 78.

Viswanadham, N. , V.V.S. Sarma and M.G. Singh ( 1987) . Reliability of Computer and Control Systems, North Holland System and Control Series, Vol. 8, North Hol­land, Amsterdam.

Copyright © IF AC Anificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

NEURAL NETWORK MODELS AND STATISTICAL TESTS AS FLEXIBLE BASE FOR INTELLIGENT

FAULT DIAGNOSIS

E.A. A verbukh INCOLAB, Research Industrial Firm, P.O. Box 26125, Tver, 170026, Russia

Abstract . The increasing complexity of industrial control systems and industrial processes makes it necessary to frequent use tools and techniques for reliability and safety analysis , particularly

to early detection and localization of faul t s . By applying con­ventional approaches to diagnose faults via both dynamic process and signal models and parameters estimation and knowledge pro­cessing the inherent redundances can be used to make it more ef­fective and to detect faults earlier . But in many cases , it is not enough to design the unique fault diagnosis procedure , but it is also essential to provide its flexible adaptation to changes of envir.onment of the controlled system, including structures , pa­rameters , tasks of the operators , their ( changing ) knowledge , cogni­tive capabilities etc . The major efforts have to be made to deve­

lop new generation of knowledge-based fault detection (FD ) systems with both analytical and heuristical knowledge to be easily ada­pted to the changes in the system ' s environment . The paper de­sribes integrated approach to the "homogeneouc>'' introducing the human-like thinking neuron schemes in all the stages of the mo­del based fault diagnosis . Several examples are discussed.

Keywords . Failure detection; parameter estimation; knowledge-base ; neural nets ; model-based fault diagnosis .

1 . INTRODUCTION

Modern control systems are often large and complex and if some faults occur , consequences can be extremely dangerous in terms of human mortality and safety, environmental impact and economic loss . To ensure reliable operation, a newest fault monitoring and diagnosis schemes need to be available , especially for the processes

and systems with high potential risk . The detection of changes in the dynamics of systems has a strike growth during the last two decades and is comprehensively documented in the survey papers and books of Willsky ( 1 976 ) , Isermann ( 1 984 , 1 991 ) , Basseville ( 1 988 ) , Basseville and Benveniste ( 1 985 ) , Watanabe and Himmelblau ( 1 982 ) , Walker ( 1 983 ) , Gertler ( 1 988 , 1 991 ) , Frank and Keller ( 1 984 ) , Frank ( 1 991 ) . This

259

paper further develops an integrated approach to combine model-based fault detection schemes with flexible knowledge-based techniques , particularly with neural nets schemes .

2 . CONVERSION TO FLEXIBLE FAULT DIAGNOSIS

TECHNIQUES The motivation of the study particular arises from the increasing interest in the field of so-called "conversion" of military systems and technologies to the civil ones , which fortunately p icks up speed over the world and especially in Russia . Conversion processes - are one o f the most complex and dangerous innovation processes , which can be considered from the system analisys point of view as the cyclic multistage dynamic processes of

transforming the military INITIAL SYSTEMS to the civil FINAL SYSTEMS using CONVERSI­ON SYSTEMS . All these SYSTEMS depicted in Fig . 1 are complex hierarchical non­

homogeneus man-machine systems with unique material , information and energy flows and

principal goal - to develop civil SYSTEMS

of the maximum safety, reliability and humanity, with the best quality and cost­

effectiveness .

rhese SYSTEMS have unique specific features to be necessary considered due to the following reasons : o TECHNICAL

• non-traditional "raw material" -High Technologies

• non-homogeneity

• complexity • multiple dimension • high demands on safety and reliability

o ECONOMICAL • goal oriented and "secured" marketing

strategies choice

• high demands on the quality of the CONVERSION SYSTEMS under time pre­ssure and restricted financial support

o ECOLOGICAL • high damage of the CONVERSION PROCESS

for the man and the environment at all levels "space - air- surface -ocean - well"

o COGNITIVE • multiple choice of the conversion

strategies

• decision making - non-trivial problems - multidisciplinary - cooperative problem solving - under mal-function, stress , danger

o PSYCHOLOGICAL • destroy of the products of the per­

sonal intellectual work

• requalification

Therefore much effort should be done in order to develop new comprehesive theory and methodology of the intellectualization of the CONVERSION PROCESSES in the widest sense via the man-machine interaction and flexible knowledge based technologies . And, of course , these technologies are of paramount importance for the monitoring and fault diagnosis for it occurs to be one of the basic functions, which is general to all the -stages of the CONVERSION PROCESSES ;

260

-objects and "subjects" (operators ) ,

including the environment ; -types of the SYSTEM operation (on- and

off-line ) ; -types of transformation.

It is also rather obvious , that such FD technologies have to support the unique combination of the necessary features : -flexibility;

-robustness ; -reliability o f both hardware , software and man decision making ; -activity of the new information perception , i . e . readyness to the quickly adap tation to the new information inputs together with catalyzing the sources of

information, including the creative problem

solving e . g . by experts ; -hymanity in problem solving. Then we possibly can discuss the new generation of the diagnostic knowledge­based systems ( see e . g. Patil et al , 1 981 ,

1 982 ; Nevins et al , 1 987 ; Tzafestas , 1 990, 1 991 ) instead of the first generation systems ( e . g . Murdoch , 1 987 ; Clansey, 1 983 ) ,

particularly with flexible techniques providing analytical redundancy of the fault diagnosis scheme . In this matter one of the basic require­ments is to set up a hybrid knowledge­

based concept , which overcomes the unbalance in flexibility between the two main parts of the process knowledge base ( see Isermann, 1 991 ) : a ) analytical knowledge

- analytical process models - estimation methods fo parameters or

state variables - normal process behaviour

- process history and fault statistics b ) heuristic knowledge

- fault trees , i . e . connections of symptoms and faults

- process history and fault statistics , it only qualitatively known.

The main reasons of this unbalance are still rather "conservative" separate de­velopment of control theory, artificial intelligence and computer science in general ( see e . g . Yong-zai Lu et al , 1 990 ) . Only meeting development of both analytical redundance FD schemes and artificial intelligence approaches within the unified knowledge engineering philosophy can lead to considerable improvement of the FD systems reliability and flexibility as well .

J . QUASI - NEURAL ANALYTICAL KNOWLEDGE FOR THE INTELLIGENT FAULT DIAGNOSIS SYSTEMS

Even brief analysis of the modern artifi­

cial intelligence techniques shows that neural nets are one of the perspective "candidates" to improve todays analytical

knowledge presentation and processing. That

is because of it ' s closeness to deep reasoning, learning and human-like

thinking . Moreover , it has many very

useful properties : they are rather noise

tolerant , can handle nonlinear and underdetermined processes and lead to data

reduction in the learning phase ( see Naidu, Zafiriou and McAvoy , 1 990; Vaidyana-than and Yamamoto , 1 990; Sorsa and Koivo , 1 991 ) •

The most widely studied network architec­ture today i . e . multilayer perceptron net­work , which mimics the adaptive distributed architecture in the human brain is shown in Fig . 2 . It is composed of many simple computatio­nal nodes locally interacting across weighted connections . The output function for every node j is e .g. a sigmoid logistic funct ion f (aj ) , and it acts as a weighted sum of the inputs given by linear function

( 1 )

where U denotes nx1 measured inputs or in­

puts pattern vector ; W denotes 1 xn weight j or gain vector. Thus we receive very flexible mechanizm, which can be well adapted to the environ­

ment by choosing appropriate network to­pology e .g . leading to the following re­lashionships between inputs U and outputs Y expressed by

Y=f (WTH ) ; H=f (wTu ) 0 h ( 2 )

where H is the output vector of the hidden layer, and its learning. The back-propaga­tion learning ( Jones and Hoskins , 1 987 ) is one of the most popular approaches and it is oriented to minimize the mean square error between the desired network outputs Y and the real ones Y for all input

p patterns P

J (W ) = E 1 12 II Y - Y 11 2 p p p

p

( 3 )

Now let us analize the fundamental methods of the model based fault detection and the processes of their learning from the "mult i-layer" point of view . We can easily identify seven traditional"layers" between

261

inputs U and outputs Y, i . e . "symptoms " in

change detection schemes and "causes" and " locations " in the further fault diagnosis schemes as shown in Fig. J . They are

i ) selection of the - model ( of the proces s , changes and

faults ) ;

- method for the inputs segmentation; - method for the parameters (or state

variables ) estimation; - method for the residual generation; - method for the statistical test de-

s igning ; - method for estimation of the thres­

holf for the statistical tests ;

- method for the models validation; ii ) selection of the nodes in the layers ; iii ) learning of the FD network ; iv ) performing of the FD network . Now we can see , that to meet the two approaches under consideration it is neccessary to provide representation of all the nodes in all the FD " layers" in a way similar to e . g . ( 1 ) - (2 ) . But it does not cure the trouble in the full

compatibility of these two approaches of knowledge presentation and processing. The radically difference between the traditional elements of the neutron network layers and the FD "nodes" lies in the fact , that not all the connections

between the selected FD layers and their nodes are permissible . We can conclude from this , that the main trends in developing quasi-neural FD schemes are the following :

- try to derive in a systematic manner FD nodes represented in the traditional for the neural network form (see Fig . 2 and equations ( 1 ) , (2 ) ) ;

- formalize the necessary and sufficient conditions of their possible applica -tions and multiple connections , e . g . a s answers for the questions "what "­"when"-"where"-"how" ;

- build multy-story FD neural net s , where four special floors provide the support for the permissible and appropriate selections , interconnections and learning both on-line and off-line of the proper FD layers and nodes , which form the "pent-house" ( see Fig . J ) .

Now we shall "visit " the above pent-house in order to estimate its completeness based on the classical FD knowledge and possible spin-offs .

4 . A BETTER INSIGHT INTO THE QUASI-NEURAL FAUL DIAGNOSIS "PENT-HOUSE"

The only way not to build castles in the air and to make the hybrid approach become reality in the nearest future is to re­strict ourselves to the closed space of the traditional FD systems environment , i . e . sturctures of the models and tasks to be performed under FD . This limiting process presents no special problems for the majority of layers ( see Fig . 3 ) due to the following reasons : a It is well known from the control theory and particularly, from the publications on FD that a broad class of even nonlinear dynamic processes models can be rearranged to the linear in parameters form similar to ( 1 ) , (2 ) ( see e . g . Middleton and Goodwin, 1 989 , Ljung , 1 990, Isermann , 1 991 , Frank , 1 991 )

I Y= E a <wT 8 i i i i

+ e ) i

where ill - are known ( or assumed to i known) functions of inputs and time ,

( 4 )

be 8 -i

are the vectors of the unknown sets of parameters , ei - denotes zero mean nearly white noise signals with known estimates of their covariance matrixes v ' a - de-i i notes switching function, which is equal to 1 for the model structure under con­sideration and to zero for all other pos­sible structures . a Traditional models of the changes and faults ( see Isermann, 1 991 , Gertler , 1 991 ) are similar to ( 4 ) , where a denotes i non-zero weghting coefficients . a One of the most popular method for the parameter estimation is given also by linear function of the outputs of the previous "layer"

( 5 )

a For the detection of changes the esti­mated quantities e sillgly or in the i weighted combinations are compared with corresponding quantities of the nominal ( i . e .previous ) model resulting in changes 6e , 6e = � a 6e or by observing error i. i. i. i. A

signals or residuals e= Y- � 15 ill"' 8 . i. i. i. i. These functions are also similar to tra-ditional layers (see Fig. 2 ) . a The above residuals e and changes 6e i i are then the symptoms and are used in de-s igning statistical tests ( the 5th layer in Fig. 3 ) . The most popular and tradi­tional likelyhood test approach leads to designing various quadratic forms of the changes 6e

262

( 6 ) o r by analogy o f the residuals ei . In this case one additional hidden layer will fit the neural network scheme .. 0It is necessary to say, that in FD stra­tegies the decision usually is made be­tween two or several hypothesis , parti­cular between H and H : 0 , H : 8=0 and H : &.-!O (7 ) 0 1

under which the distribution of the above test statistics t8 could be well approximated( some time only in asymptothy ) by X2 ( � ) , where 1 and � are functions of

1 our models (process , changes and faults ) , assumptions . To make the thresholds for the tests more robust to the uncertain­ties in the models and to the violation o f the assumptions and at the same time to adapt them to the standard for the neural networks form we can do the fo­llowing ( see Averbukh , 1 990 ) : - to decide between the hypothesis e .g. H : 8=c and H : &.-!c ( 8 ) 0 ,

where c�O in general , which leads to additional bias in the appropriate sta­tistics distribution x2 <� + C ) ; 1 - to rearrange the thresholds to the tra-ditional for the neural nets form using approximation of Patnaik ( 1 949 ) :

x2 <�+c > � p x2 < o ) <9 > 1 1

,

a As to methods for model validation, the traditional for the neural nets cri­teria ( 3 ) is not flexible enough to be well adapted to the changes in the systems environment . It is rather obvious , that this " layer" in the quasi-neural FD net should be itself multi-layer subnet consisted of the majority of the tradi­tional criteria . Designing such flexible criteria for the quasilinear models validation in the sta­ndard form ( 1 ) , (2 ) is theoretically also possible for switching the structure of the process model ( 4 ) or the model of the changes 68 , varying methods for the inputs segmentation and /or for residual generation, combining several simple hy­pothesis to be checked ( 8 ) into a complex one etc . lead to the quasi linear changes in the resulting mean squared error ( see Middleton and Goodwin , 1 990, Averbukh , 1 990, 1 991 a ) . Such criteria should become the basis for the back propagation learning of the whole Fault Diagnosis neural net only after their preliminary adjusting to the systems

environment . It is also a matter ot

special research , tor the appropriate

support based on the analytical and

heuristical knowledge is also needed to be developed under the unified trame shown in Fig. 3 as well as possible strategies ot direct and back propagation multistep learning.

5 . EXAMPL:&s The proposed approach can be well

illustrated by the specific cases ot deve­loping quasineural subnets for the last FD

"layer" criteria for the model validation.

We· shall take as a prototype a , modified BIVAR criteria ( see Young , 1 982 ) based

on a weighted sum predictive variance

set

ot squared bias and tor the training data

H ( p ) = 0 JJfuTtl -¢T M[tl J ) V- 1/:. j\1 z j z �j z j z j + pzOJ��M[tl) -ili� 8J V� �\\1( 1 0 )

where z=j -denotes that training data set ( z ) and examine data set ( j ) are similar ; ¢ - real j inputs for the concrete model structure under

consideration. Even this criteria unifies se­

veral traditional criteria e .g . Akaike ( 1 978 ) .

Taking into account possible ditterences

in the training and examine data sets

( z� j ) appropriate to traditional in FD

schemes methods for the inputs

segmentation leads to a second node in

the first layer ( see Fig . 4 ) and consequent

ly to the new criteria ( see Averbukh , 1 990,

1 991 a ) H = � � a H (p ) ( 1 1 ) z j z j z z j

and to the hidden layer in the FD subnet .

Our next step can b e turning to the more

robust models of changes ( 8 ) , which also

will demand the appropriate evaluations

in the above criteria and statistical tests

and certainly lead to the new layers and

so on.

First prototypes of such quasi-neural

nets were successively implemented in the

fault diagnosis systems tor the oii and

gas reservoirs exploration , where environment of the systems changes very rapidly both in the direct and in the broad sense ( see Averbukh , 1 991 b ) . But of course , conversion processes rise the discussed problem to a radically new le­vel of importance and provide enormous market for such quasi-neural FD nets

implementation.

263

6 . CONCLUSION

We consider this paper as a call for col­laboration in coordinated development of the !lexible FD knowledge-based schemes by the scientists , researchers and engineers working in the neighbouring fields of the control theory, mathematical statistics , artificial intelligence and man-machine systems as well .

As we see , the whole concept is very close to the creating of the Common House

starting from the almost ready pent , which

will provide our safety and reliability.

LITERATURE

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gresive model titting , Research Memo . N 1 26 , The Institute of Statisti­cal Mathematic s , Tokyo .

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Averbukh , E . A . ( 1 991 b ) . Theory and practice of the quasioptimal regression models selection during the control system identitication, when the classical assu­p tions are violated. 2nd Doctoral Thesis. Moscow Power Institute , 353p . (unpublished )

Basseville , M . ( 1 988 ) . Detecting changes in signals and systems- A survey, Automatica.24 . 3 , 309-326 .

Basseville , M . and Benveniste , A . (Eds . ) ( 1 985 ) , Detecting changes in signals and dyna­

mic systems , Lecture Notes in Control

and Information Sciences, Vol . 77 . Springer Verlag.

Chandrasekaran, B . and S .Mittal ( 1 983 ) . Deep

versus decomp iled knowledge approache

to diagnostic problem-solving , Int . J .

Man-Machine Studies , 12.i. 425-43 6 .

Clancey, W . J . ( 1 983 ) . Methodology tor buildin,

an intelligent tutoring system , In :

Methods an d Tactics in Cognitive Scien

(Kintsch ,Polson and Miller, eds . )Law­

rence Erlbaum Publ .

Frank , P . M . and Keller, L . ( 1 984 ) . Entdeckung

von Instrumententehleranzeigen mittels

Zustendsschaetzung in technischen Re-

gelungssystemen, VDI-Fortschrittsbe­richte, Reiche 8, Nr . 80 , VDI-Verlag Duesseldorf , Germany.

Frank , P . M . ( 1 991 ) . Enchansement of Robust­

ness in Observer-Based Fault Detec­

tion . Proceedings SAFEPROC:ESS ' 91 IFAC

/I'. IACS S;l!'lposium, Baden-Baden, 1 ,

275 - 287 . Gertler , J . J . ( 1 988 ) . Survey of model-based

failure detection and isolation in

complex plants . IEEE Control Systems Magazine, 1i_ 1 1 .

Gertler , J . J . ( 1 991 ) . Analytical redundancy methods in fault detection and isola­t ion - Survey and Synthesis . -Procee­dings SAFEPROCESS ' 91 IFAC/IMACS Q:nn= P-OSium, Baden-Baden, 1 , 9- 2 1 .

Isermann , R . ( 1 984 ) . Process fault detec­tion based on modelling and estimati­on methods . - A survey, Automatica,20 677-688.

Isermann, R. ( 1 991 ) . Fault diagnosis of machine via parameter estimation and

knowledge processing , Proceedings

S.AF:EPROC:ESS '91 IFAC/IMACS �osium, Baden-Baden, 1 , 1 2 1 -1 33 ,

Keravnou, E . T . and J . Washibrook , ( 1 989 ) . What is a deep expert system? analysis of the architectural requirements of second generation expert systems . The Knowledge � Rev . , No 4 : 3 , 205-233 .

Kramer, M . A . and Pavlovich B . L. ( 1 987 ) .A rule-based approach to fault di agnosis using the signed directed graph , AICHE Journal .

Lennart Ljung . ( 1 987 ) . System Identificati­on: Theory for the User. Prentice-Hall , Inc . ,New-Jersey.

Middleton R . H . and G . C . Goodwin. ( 1 990 ) . Di­

gital Estimation and Control : A Unified Approach . Prentice Hal l , Inc . , New-Jersey.

Murdoch , STR. ( 1 987 ) A review of the inter section of expert systems and database systems : Expert/Database systems , Int . J. Syst . Res . and Inform. Sci . , 1_._ 1 1 1 -1 1 9 .

Naidu , S . R. , E . Zafirou, and T . J . McAvoy ( 1 990) Use of neural networks for sensor fai­lure detection in a control system. IEEE Control Systems Magazine , 1 0. 49-5 5 .

Nevins , J . L . , D . E . Whitney and A . C . Endsall ( 1 987 ) . Intelligent systems

in Manufacturing , Preprints 1 0th IFAC World Congress on Automatic Control . Munich , 4 , 1 30-1 39 .

264

Patil , R . et al ( 1 981 ) . Causal under­

standing of patient illness in

medical diagnosis , Proc . AJCAI-81 , 893-899 .

Patil , R . , P . Szolovits and W . Schwarrtz

( 1 982 ) . Information acquisition in diagnosis , Proc . AAAI-82 , 3 45-348 .

Patnaik , P . B . ( 1 949 ) . Non-central X2 - and F­distributions approximations , Biometrica,

.2.2...,_g_,_ 2 02-2 32 •

Sorsa , T . and H . N . Koivo , ( 1 991 ) . Neural

networks in process fault diagnosis . IEEE Transactions on Systems. Man and

Cybernatics, 2 1 .

Tzafestas , S . ( 1 990 ) . AI techniques in compu­ter-aided manufacturing systems , In Knowledge Engineering (H . Adeli , ed. ) , McGraw-Hill , Vol . 1 1 , 1 61 -2 1 2 .

Tzafestas , S . ( 1 991 ) . Second generation diag­nostic expert systems : requirements , architectures and prospects , Proceed. SAFEPROC:ESS ' 91 IFAC/IMACS �osium, Baden-Baden, g , 1 -6 .

Walker , B . K . ( 1 983 ) . Recent developments in fault diagnosis and accomodation, AIAA Guidance and Control Conference.AA.IA �er No . 83-2358-CP,Gatlinburg Tene­ssee .

Watanab e , K . and Himmelblau , D . M . ( 1 982 ) , Instrument failure detection in sys­tems with uncertaintie s , Int . Journal System Sci . , 1l.... 1 37-1 58 .

Willsky, A . S . ( 1 976 ) . A survey of design me thods for failure detection in dynamic

systems , Automatica, 1.£.._601 -61 1 . Yong-zai Lu, Qi-zhong Fang and Li-wei Bao

( 1 990 ) .Novel methodology and strategies for complex industrial systems control . Preprints 1 1 th IFAC World Congress on Automatic Control . Tallinn , 8 , 56-61 .

INITIAL SYSTnifS CONVERSION SYSTnifS rans orma ion

L..+r+ Utilisation '-+ Liquidation

l_.r+Annihilation '-+ Burial

I diagnosis I

FINITE SYST1!1f5

Fig. 1 . Extended Stucture of the Man-Machine Systems for Diagnosis and Control of the Conversion Processes

OUTPUT LAYER

HIDDEN LAYER

INPUT LAYER

T T T T w

x 1 1 '--. f (a )

Wn y---- a = E w1"- x"-x <- - 1

n

neuron f (a )

- 5 - 4 - 3 - 2 - 1 0

Fig . 2 . Neural network

Models of the

2

1 :t' ( a. ) -1 + e

3 4 5

- process , changes , faults

-a

a

- Methods for inputs segmentation - Methods for parameter estimation

- Methods for residual generation - Methods for test designing

Fig. J . Multy-story quasi-neural FD nets

265

L_ _ _ _ _ _ _ _ _ _ _ J - - - - - - , r - - -(Young , 1 982 ) I r - -

IAkaike, - 1 L ias ariance 1 97S - -r- - - - -r- - - - J

Training data set Examine data set

Fig . 4 . Quasi - neural subnet for the FD criteria for model validation

266

OUTPUTS

INPUTS

Copyright © IFAC Anificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

MULTIVALUED LOGIC VOTING SCHEME FOR RESIDUAL EVALUATION IN FAIL URE DETECTION AND

ISOLATION SYSTEMS

J.P. Cassar, M. Staroswiecki and R. Ferhati

LAIL (URA 1440 D)ILAFA, Universite des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq, France

Abstract. This paper deals with Failure Detection and Isolation procedures using the generalized Parity Space Approach. The decision scheme uses the structural properties of the residuals and leads to the analysis of fault events signatures. In a classical approach, these signatures are binary words. We propose a multivalued voting scheme, which allows to follow some specifications connected with false alarms and miss-isolation. The performances of the proposed approach are compared with these of the classical one using two examples.

Keywords. Failure detection, Threshold logic.

I - IN1RODUCTION

Model based failure detection and isolation (FDI) systems currently use either state estimation tech­niques (including the parity space approach) (Chow, 84)(Patton, 89)(Staroswiecki, 9 1a)(Frank, 88)] or parameter estimation ones (Iserman,84)(Patton, 89).

In a first step, those systems create residuals (which are in fact the estimation errors) and in a second step proceed to their analysis through a decision procedure, in order to detect and isolate the failures. For the FDI purpose, the quality of the residuals may be expressed in terms of robustness with res­pect to the model errors and the unknown inputs (Wiinnenberg, 88), in terms of sensitivity to the failures (detectability) and in terms of isolability of their different primary causes. The decision step is currently performed via the ana­lysis of the neighbourhood to zero of the residuals vector. The isolation step is solved by the use of specialized filters or logic voting schemes (Gertler, 88)(Cordier, 91). In the first case, each failure event is associated to a given direction in the residual space, so the isolation step consists in the recognition of the direction of the residual vector computed at each time t. In the second case, the coherence of each residual is first determined {0/1 output) and a binary word, cal­led the coherence signature of the process is thus created. The isolation step consists in the recogni­tion of the word which is associated to a given fai­lure event. Logic schemes are based on the consideration of the structure which links the set of the computed resi­duals and the set of the failure events.

267

However, such a structural approach does not take into account the sensitivity of the residuals with respect to the different failure events, and the practi­cal signatures may be far from the theoretical ones, when the sensitivities of the residuals influenced by a given event are very different from each other. Moreover, if one residual is considered, its sensiti­vities to the different failures which intervene in its structure are different, thus leading to poor detecta­bility for certain events and/or large false alarme rates caused by those events for which the sensiti­vity is important. A first way to handle with this problem is to create optimal residuals with respect to structural conside­rations, via combinations of the original ones(Cocquempot, 9 1 )(Staroswiecki, 9 1b). Note that this approach can also be used in order to solve the robustness problem, with respect to modeliza­tion errors or unknown inputs (Frank, 9 la, 9 1b)(Cassar, 92). However, since the number of de­sign parameters is limited and the number of speci­fications may be large, this approach may be limi­ted. We propose a second approach, which can be used either directly or as a complement to the first one. It is based on the use of multivalued logic for the expression of the process' signature, instead of bi­nary logic. The coherence of each residual is no longer expressed as the 0/1 output of the decision procedure, but takes its values in a finite set, allo­wing a more precise isolation of the event which has caused the detection. The isolation procedures in both the binary and the multivalued logic voting schemes are compared and their respective performances are discussed.

II - SYS1EM DESCRIPTION

II.I - State space description Let us consider a system described by a linear dy­namic model talcing into account the measurement errors and the modelisation errors, under the follo­wing form :

x(t+l) = A x(t) + B u(t)+ E T}(t) y(t) = C x(t) + F . �(t)

with x(t), the n-dimensional system state vector at time t u(t), the r-dimensional system input vector y(t), the m-dimensional measurement vector T}(t), the s-dimensional modelling error vector P(t), the q-dimensional measurement error vector E(nxs) and F(mxq) represent the distribution ma­trices of Tl and � in the system. The matrices A , B , C , E, F are assumed to be known. At any time t+p, the measurement equation can be written on a p-sized temporal window as :

-o[P] clP](B) Y(t,t+p)- X(t) + U(t,t+p) [p) [p) R + c (E) Tl(t,t+p) + F P(t,t+p)

with dim olP] = (p+l)mxn ;

dim cf PJ(B) = m(p+l) x r(p+l) ;

dim cfPJ(E) = m(p+l) x s(p+l) aOO

oCPl =

for z E {

c

C A

C A2

C AP

,U,T},� }

0 .. .. .. [p] C K ' ........

C(K) = CAK C K' .. ,

z (t,l+p)=

.. .. .. ..

I ', CAP-IK - - - - CK b

for K e {E,B}

Il.2 - Residuals generation

z(t)

z{t+l)

z(t+p)

The projection of the measurement equation on the parity space [2] leads to a new equation given by :

n I y(t,t+p) = n I olP] x(t) +

n I c f Pl(B) u(t,t+p)+

n . cf Pl(E)T1(t,t+p) +

Q I F[p] �(t,t+p) with n. the z.m(p+ 1) dimensional projection ma­trice.

268

When n satisfies n I olP] = 0, the residual vector is expressed by :

r(t+p) = n I y(t,t+p) - n I o lP] x(t) +

n . cf Pl(B) u(t,t+p) This z dimensional r(t+p) vector may be directly computed because it only involves available infor­mation.Due to the modelization and measurement errors this vector talces the value :

r(t+p) = P T}(t,t+p) + Q �(t,t+p)

with P = n . c f PJ(E)

and Q = 0 . F[p]

Gathering the error vectors, we obtain : r(t+p) = R e(t,t+p)

'th [ ( ) ]

[ T}(t,t+p) ] Wl e t,t+p = �(t,t+p) and R = [P Q] p That can be written as : r(t+p) = I. R1 . e(t+l)

1=0

11.3 - Moc1elization of failures

The vector of failures e(t+p) can be decomposed into two components. The first one represents the deterministic part of the signal and the second one is the stochastic part which applies to the measu­rement and the system equations. e(t+p) = d(t+l) + e{t+l) Then r(t+p) becomes :

p p

r(t+p) = I. R1 d(t+l) + I. R1 e(t+l) 1=0 1=0

In order to settle the specifications of the FDI sys-tem some assumptions are performed about the vec­tor of failures. The deterministic components are supposed to be biases and their influence on the re­siduals values are studied in the steady state condi­tions. So d(t+l) = d 'rt l e [0, p] . The noises are assumed to follow a gaussian distri­bution with zero mean . Under these conditions, the vector of the residuals be expressed as : r(t+p) = cr . d + e*(t+p) (1)

p where cr = I. R1 is the matrice of the steady state

1=0 p sensitivities and e*(t+p) = I. R l . e*(t+p) is a

1=0 gaussian vector with zero mean which represents the distributions of the components of r(t+p).

III - DE1ECTION PROCEDURE

III. I - Detection rule choice

The detection procedure aims at the detection of re­siduals deviations which can reflect an abnormal behaviour. It must thus realize the discrimination

between two hypothesis. The hypothesis Ho is as­

sociated with a normal behaviour, that means a be­haviour which is consistent with the chosen model. The hypothesis H 1 implies a abnormal behaviour.

Each residual value is directly compared with a thre­shold. A value beyond the threshold leads the hypo­thesis H 1 to be validated, in the other case the hy­

pothesis Ho is chosen.

Let 1lc be a residual value, i-e the kth component of the vector r(t+p), and Tk be the associated decision threshold :

1lc < Tk ::::) Ho and 1lc � Tk ::::) H 1 A binary value can be associated as result of this de­tection procedure. Ho ::::) O H1 ::::) l

IIl.2 - Detection probability

From equation (1), the statistical distribution of a residual 1lc· can be derived. mk = crk . d constitutes its mean and vk its va­riance. Equation (1) shows that the statistical distribution of a resiudal rk is gaussian, with means mk = crk .

d and variance vk· The probability of detection related to this residual, using a threshold T k is then :

Tk-mk Pd(mk, Tk ) = 1 _ __2_1 ./Vk J-tkJt (2)

fiit -Tk-mk ./Vk

For a given threshold Tk, this probability is a func-

tion of mk.

III.3 - Statistical performances specifications

111.3.1 - Probability of false alarms. The false alarm probability is often calculed by supposing that all the deterministic deviations are equal to zero. A most realistic case is to bound these deviations and to define the false alarm probability for the maximum residual deviation derived from them. Let d be the vector of the feature deviations. d is supposed to belong to a sub set D. The specification imposes that the Pea be below a

limit value Pfa whatever the value of d belonging to D.

max Pd (crk . d, Tk) :s; Pfa d e D

• Let T k be the value of the threshold for which the equality holds.

III.3.2 - Probability of misses. If we settle the single failure hypothesis, a failure on the jth

269

component can be expressed by a vector dj such that dj = bj . lij. Where bj is the amplitude of the

failure and li j is the vector whose jth component is

equal to 1 , the other ones remain equal to zero. •

1lc = <'.rjk . bj + Ek(t)

crjk is the sensitivity of the jth failure event in the

kih residual. The failing case corresponds to a value *

of lbj I over a limit bj . Let Bj be the set of these values. The specification imposes that the probability of

detection be over a limit value Pj whatever the va­

lues of bj in Bj.

�n . Pd (<rjk . bj> Tk) � Pj bJ e BJ

* Let Tjk be the value of the threshold for which the equality holds. Remark : It is obvious that the specifications rela­ted to the probabilities of false alarms and misses must be coherent. That implies that : \:;/ bj e Bj dj e D

IV - BINARY LOGIC CASE.

The isolation procedure aims to provide the faulty element from the binary information of the detec­tion procedure. We restrict the study in the case of a single failure occurence.

IV .1 - Signature of a failure

Logic schemes are based on the consideration of the structure which links the set of the computed resi­duals and the set of the failure events (Gertler, 88). Let :

R = f(E) be a concise representation of the relations between the set of the residuals (R) and the set of the failure events (E). \:;/ ej e E R(ej) is the set of those residuals

which are influenced by the event ef V' pk e R E(pk) is the set of those failure

events which influence the residual pk.

The signature of the event ej is then the binary word : s(ej) in which sk(ej) = 1 if pk e R(e)

sk(ej) = 0 otherwise

This definition can be related with the sensitivities fo the failure events in the residuals: sk(ej) = 1 if

<'.rjk * 0

IV.2 - Binary logic voting scheme

The detection procedure provides a binary vector c as result of the tests of coherence performed on each residual.

When no miss of detection or false alarme occurs, a failure ej with bj e Bj leads to a coherence vector equal to s(ej)·

The isolation procedure will search the failure event whose signature is the closest to the c vector. The distance between a signature s( ej) and the coherence vector c is choosen as :

N L1· = I, sk (e-) ED ck J

k=O J

Where ED denotes the exclusive or. L1j represents the Hamming distance between the two binary vectors and N the cardinal of R. A comparizon is also performed with the signature of the normal behaviour which is the null vector. If this one is the closest signature to the coherence vector c, no failure is declared.

IV .3 - Single threshold choice

From the choice performed in III. I , each residual value rk is compared with a threshold 'tk in order to indicate which hypothesis about the state of the system this value reflects, and thus the binary value to be affected to ck.

The specifications impose that the choosen thre­shold 'tk be :

- over T� to respect the condition probability of false alarms

- under each Tjk to respect the condition proba­bility of misses

A necessary condition is that :

* . * If it is verified, then T k < 'tk � � Tjk ej e E(pk) In the other cases, the specifications are not realizable. A practical choice is to take:

* 'tk=� Tjk ej e E(pk)

IV .4 - Discussion

For a failure event ej in a residual Pk such that the

value of Tjk * is upper than 'tk, a value Ujk can be

found such that PdL is reached for this value. That means that Pd (crjk . ajk• 'tk) = PdL with

* Ujk � bj We can deduce from this fact that : if bj < ajk then ck = 0 with a probability 1 -

Pd(crjk·bj, tk ) 2:: 1 -PdL

if bj ;::: Ujk then ck = I with a probability Pd ( <Tjk

bj , 'tk ) 2:: PdL

The figure 1 depicts these limits values of bj for several thresholds.

270

Pd(crJk·bJ,tk) 1

Pdl - - - -

0 <lj l <lj2 <lj3 Figure 1 .

As bj varies from 0 to bj different values of the vec­tor c will be obtained, which reflect normal opera­ting conditions. The normal case signature is no more equal to the null vector. A set of signatures reflecting normal condition must be associated with each failure event Some of these new signatures may be close to si­gnatures of other failure events and us lead to bad detections and miss isolations.

V - MULTIVALUED LOGIC CASE

In order to handle with this problem, we propose to extend the basic detection procedure described in III.I to a multiple thresholds based detection and thus to define a multivalued logic decision proce­dure.

Y.l - Multiple thresholds based cJetection For each couple (k, j) such that Pk e R(ej), we choose as threshold Tjk• the threshold which gives

the PdL value as the detection probability when bj . b"' T"' 1s equal to j : jk Each residual fk is then compared with all the resi­duals 'tjk· Under this condition, each comparison leads to a binary result Cjk·

* If bj < bj then Cjk = 0 with the probability I - Pd

(crjk . bj, 'tjk) > 1 - PdL

* If bj 2:: bj then Cjk = I with the probability Pd

(crjk . bj, 'tjk) ;::: PdL

The isolation procedure becomes :

- d.Q the hypothesis of a failure on the lh event, - test the residuals of R(ej) with the thresholds Tjk• - if all the cjk are equal to 1 , � j i s declared faulty

else repeat for the j + 1 th event.

This procedure leads to examine sequentialy the set of the failure events and thus may be time consu­ming. Another possible approach leads to associate to each residual a value mk taken in the set { 0, I , ... Jk} where Jk = IE(Pk)I. The thresholds 'tjk associated with the residual Pk being sorted by increasing values, mk is equal to the serial number of the last threshold which stays under the residual value.

V .2 - Multivalued voting scheme

The detection procedure provides a multivalued vec­tor c whose components are the values mk. The signatures s becomes then multivalued vectors. If Ojk refers to the rank of the threshold 'tjk• a fai­lure on the jth event will be then associated with a set of signatures Sj. Sj = {s I Jk � sk � Ojk if Pk E R(ej) and sk = 0 otherwise} The distance between c and the set Sj is defined by the shortest distance between c and any element of Sj . It is calculated as following :

N L1 · = L. o· k

J k=O J where if Pk E R(ej)

if mk � Ojk then ojk = 0 else Ojk = Ojk - mk

else Ojk = mk

I 2 3 4 c 01 1 100 121 021

Multi- el valued e2 x x

e3 x !:J.i 3 3 1 2

Binary e l x x e2 x x e3 x x !:J.i 0 1 0 0

5 1 1 1 x x

2 x x

0

6 1 12 x

1 x x

0

N !:J. j = L, mk expresses the distance between c and

k=O the normal operating signature. As for the binary scheme, the isolation procedure provides the decision which corresponds to the mi­nimal distance.

VI. DISCUSSION

The two procedures described above are here tested on a simple example and their results are then dis­cussed. The set of residuals contains three elements and involves three failure events. Let the matrice of the steady state sensitivities a

be equal to [�O is �O ] and the measurements 10 5 15

have a variance equal to 0.001 .

We impose as specifications P};.=1-PJ = 0.01 and

the biases to be detected b t * =5, b2 * =5, b3 * =4. These specifications are realizable. Under these conditions, the matrice of the thre­sholds can be computed:

T= [i� .3 � .2 �8.2 ] 48.2 23.3 58.2

The multivalued and binary signatures are derived from T: SI = (2, 1, 2)T ( 1 , 1 , ll s2 = ( 1 , 3, I)T ( 1 , 1 , l)T

s3 = (0, 2, 3)T (0, 1 , l)T

The results of the tests are provided in the table I in order to show how the decision procedure deals whith small, standard and large deviations. For example, the signatures of tests 3,8 and 10 are deri­v e d respect i v e l y fro m d e v i a t i o n s dT =(0.4,4,0.2),dT =(6,1 ,-0.5),dT =(-0.2,6,1 .5)

7 8 9 10 1 1 12 1 3 022 222 131 1 32 223 233 333

x x x x x x x x

x 2 0 0 0 0 0 0

x x x x x x x x x x x x

x 0 0 0 0 0 0 0

Table I The tests number 1 and 2 show how the multiva­lued logic voting scheme avoids some false alarms in the case of very small deviations. The tests from 3 to 7 depict that the multivalued logic based decision provides an additional information whith the value of the distance. This one being different from 0 indicates that the deviation is below the fixed value. By the test 3 and 6 and for the more

271

important failure the isolation ability is better for the multivalued method, even if it decreases when the failure becomes more important ( 12 and 13).

Remarks : The binary signatures of el and e2 are identical. That explains why the binary logic voting scheeme is unable to isolate el from e2.

A means to increase the isolation performances of the binary logic based decision is to increase the number of residuals in order to obtain new exten­ded signatures which will be different. In another hand, if the multivalued signatures were S I = ( 1 , 1 , 2)T s2 = (2, 2, 3)T s3 = (0, 3 , l)T the distance between s 1 and s2 would be equal to zero and thus the isolation procedure would always give e1 as failing event even if e1 was deviating.

Geometrical intemretation : The multiple thresholds constitute for each failure event ej an approximation of its failure direction defined by the oj vector whose components are the crjk sentivity coefficients. When the direction are well separated (example 1) the multivalued signa­ture based procedure can isolate the failure event and then avoids additional residuals generation. In the other cases, some residual must be found in or­der to separate the directions. A criterion of isolability between two failure events is to check whether one of the two multi­valued signatures si belongs the Sj set of signa­tures defined for the other. In the case of a positive result, the failure event will be not correctly isolated and ej will preferencially be given as faulty event. Thus the proposed approach will be successfully used as a complement of a combination on the re­siduals to optimize their directions.

VII. CONCLUSION

The multivalued logic voting scheme constitutes a simple procedure to perform better detection and isolation of failure events. It can be related to a fai­lure direction check and then its association with the optimization of the residuals set may be very powerful!.

REFERENCES :

Cassar,J .P., M. Djeghaba, M. Staroswiecki, V. Cocquempot (1992) Sensitivity robustness tradeoff via the generation of optimal resi­duals in the parity space. S ic ic i '92 , Singapore, Feb. 17-2 1 , 1992.

Chow,E.Y. , A.S. Willsky ( 1984) Analytical re­dundancy and the design of robust failure de­tection systems. IEEE Trans on Automatic Control , AC-29 n° 7, July, 1984.

Cocquempot,V. , J. Ph. Cassar, M. Staroswiecki (199 1) "Generation of robust analytical re­dundancy relations". in Proceeding of the conference ECC91 , Grenoble, France, July 2-5, 199 1 , pp 309-314.

Cordier,B. , J.P. Cassar, M. Staroswiecki (199 la) "Supervision system design for a petroleum application" .IFAC Safe Process Symposium, Baden Baden, Germany, Sept. 1991 .

272

Franck,P.M . . ( 1988) Fault Diagnosis on the B a s i s o f D y n a m i c Proc e s s Models.Proceedings !MACS. 12th World Congress on Scientific Computation, 18-22 July 1988, Paris, France.

Frank,P. M. , B. K5ppen, J. Wunnenberg (1991a) "General solution of the robustness problem in linear fault detection filters". in Proceeding of the conference ECC91 , Grenoble, France, July 2-5, 199 1 , pp 1407- 1412.

Frank,P. M. ( 1 99 1 b) . "Enhancement of robustness in observer-based fault detection". in Proceeding of the SAFE PROCESS'91 IFAC/IMACS Symposium. Baden Baden, Germany, September 10-13 , 1991, pp 275-287.

Gertler,JJ. (1988) "Survey on model-based failure detection and isolation i n complex plants" .IEEE Control System Magazine, pp 3-1 1 , Dec 1988.

Hamad,M. ( 1986) Validation des Mesures et Detection des Capteurs Defaillants dans un Systeme de Controle Commande.These de Doctoral, Universite de Lille 1 , 1986.

Iserman,R. (1984) "Process fault detection Based on Modeling and Estimation Methods. A survey",. Automatica , vol. 20 n°4, pp 387-404, 1984.

Patton,R.J. , P.M. Frank, R.N Clark, ( 1989) Fault diagnosis in dynamical systems, theory and application.Prentice Hall, 1989.

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Copyright © IFAC Anificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

KNOWLEDGE-BASED DIAGNOSIS IN INFORMATION POOR PLANTS: A MATERIALS ACCOUNTANCY APPLICATION

J. Howell

Department of Mechanical Engineering, University of Glasgow, Glasgow G12 BQQ, UK

Abstract A knowledge-based approach is proposed to tackle the uncertainty surrounding the diagnosis of anomalies in the materials account of a solvent-extraction and concentration plant of a nuclear fuel reprocessing facility. Such plants can be described as being information poor because there may be a bare minimum of sensors available to operate the process without recourse to analytical redundancy, the sensors may output at frequencies which are low relative to the dynamics of the plant, a complete set of possible failure modes may not be identified and there may be considerable uncertainty surrounding any models that are available. It is unlikely that these features are unique to these plants and it is therefore argued that a similar knowledge-base approach should be appropriate for the diagnosis of anomalies in other plants which are thought to be information poor. The approach is to fuse conclusions drawn by the application of statistical detectors, by recourse to surface knowledge, based on previous experience, operator intuition and plant peculiarities, and from model-based reasoning. Keywords. Fault diagnosis; nuclear plants; information poor processes; nuclear safeguards; knowl­edge based systems.

INTRODUCTION

A knowledge-based system has been developed to diagnose anomalies in the near-real time materials account of the solvent-extraction and concentration plant of a nuclear fuel reprocessing facility. The ap­proach should also be applicable to the diagnosis of faults as there is no conceptual difference between a fault and an anomaly. The paper first describes near-real time materials ac­countancy (NRTMA) and its application to reprocess­ing plants. An explanantion of why such plants are information poor follows and the proposed approach to diagnosing faults in this type of plant given. The knowledge-base structure and implementation is then described. The contents of each knowledge-source is outlined and a test case presented.

BACKGROUND

Introduction to NRTMA Nuclear materials safeguards (IAEA 1987) are the steps taken by the nuclear community to ensure the security of nuclear materials. One of the main ways that this is achieved is through the application of material accountancy.

273

Nuclear materials accountancy is based on the follow­ing structure. The plant is divided into units called materials balance areas, which are used as a basis for balancing all transfers of nuclear material. The plant is usually operated continuously for 2 months to a year's duration, at the end of which the plant is com­pletely cleaned out and a physical inventory is taken. This operational cycle is known as a campaign. A balance is now obtained and the material unaccounted for, denoted by MUF, derived on the basis of

Total Change in MUF = Net Transfer - Physical Inventory This quantity should be zero if all the estimates are error free.

This procedure suffers from a lack of timeliness. The question therefore arises as to whether these balances could be formed more frequently by measuring the physical inventory in situ. This approach is known as near real time materials accountancy (NRTMA).

NRTMA in Fue1 Reprocessini Facilities

Nuclear fuel reprocessing can be divided into 2 stages: a discrete stage where spent fuel assemblies are broken apart and the irradiated fuel dissolved in nitric acid and

a continuous stage where the solution is converted into separate streams of plutonium nitrate, uranium nitrate, high active, medium active and low active wastes as its outputs. The first stage takes place in what is known as the head-end whilst the second is performed in a

solvent-extraction and concentration plant A separate materials balance area is identified with each stage. In the past near real time materials accountancy as applied to fuel reprocessing plants has involved the formation of material balances at relatively large in­tervals of time (eg every day or every batch). This has been fully implemented on operational plants in the

UK (Jones and Gordon, 1986) and Japan (lkawa and co-workers,1983). Here we focus on the hypothetical solvent-extraction and concentration plant shown in Fig. 1 .

Such Plants are Information Poor It is difficult to define, succinctly, what one means by a plant being information poor. The term has largely been derived from inferring what the plant is not, that is information rich. Searl and co-workers (1987) use the term sensor-rich to describe an environment with an abundance of on-line instrumentation. Himmelblau (1978) describes the temporary need to install addi­tional sensors and to perform special tests to diagnose

certain faults in chemical plants, that is to increase the quantity and quality of the information flow from the plant So far as materials accountancy is concerned, repro­cessing plants can be viewed as being information poor because they have one or more of the following properties.

A. Poor quality measurement systems. The composition of the dissolved fuel will vary considerably and although attempts may be made to monitor it, there will always be the possibility

that the monitoring process might not have been designed to detect certain features or chemicals. One of the key features of a reprocessing plant is

Accountancy

Tank

Solvent·Extraction Plant A

Solvent·Extraction Plant e

that each plant item is designed to minimise the risk of criticality and this can result in poor mixing within a particular component. Difficulties may then arise when trying to measure its internal state. Other problems might arise because the plant oper­

ator and materials accountant have very different

objectives with the former largely dictating the type, quality and frequency, of the data collected. Thus the operator might not need to record, accur­ately, the times at which certain plant activities take place but such information will be needed as input to a simulation for model-based diagnosis pur­

poses.

B. Relatively low frequency data collection.

A significant proportion of the data needed to form an account might be derived from chemical ana­lyses performed off-line in laboratories. It might be some time before these results become available. Hence the term near real time. Obviously this also has a considerable bearing on the frequency at which the account can be taken. The feedstock might vary at a rate which is significant relative to this frequency. It might be difficult to increase this frequency because this might necessitate the pur­chase of considerably more expensive on-line in­strumentation. One consequence of this might be that there could be a considerable discrepancy in

estimates obtained from a linearised model which is only re-linearised at infrequent periods of time. In addition, it might be difficult to ensure that there is sufficient information available to perform identification in a reasonable timescale; that is before a fault has had time to develop.

C. Incomplete set of fault hypotheses.

D

Materials accountancy is to do with ensuring that the flow of material through a plant, as measured

or estimated, balances. A fault is therefore deemed to be anything that upsets this balance; that is, any occurrence in time that results in the plant deviat­ing from its intended mode of operation. Faults

Volume and concentration

measurements taken

Concentrator

� Flowmeter

Product Storage A

Product Storage B

Fig. l : Plant Layout

274

may therefore not only arise because of instrument

or actuator failures but also because of, for in­

stance, the build-up of crud (ie solids), a leak in a

pipe or the development of a set of circumstances

which affects the outcome of a particular chemical

process. In their review paper on the subject, Speed

et al ( 1986) have given a reasonable description of

some of the sources of error that might arise: 'Systematic errors can arise through a wide range of reasons such as plugged probes, solid buildup in tanks, miscalibration of measurement devices and so on, whilst non-measurement errors may include error due to operators misreading mistran­scribing or miscalculating; and random errors are presumably unavoidablee rrors that are left over a ter all other possible explanations have been ex­hausted.'

D. Inaccurate models.

Even the most detailed non-linear model might not

be able to predict, for instance, the flow patterns,

chemical processes or failures that might ensue.

Even if it did, the financial investment needed to

develop such a model may not be justifiable. In

addition, there might be a lack of realistic meas­

urement models.

DIAGNOSIS IN NRTMA

The diagnosis system described here has been de­

veloped in the belief

i) that the only sensible way to handle the

uncertainty described above must be to

diagnose from every possible viewpoint and

to fuse the various conclusions that are drawn

and

ii) that only aspects of the measurement model

that are truly known should be incorporated in

the test procedure.

The former implies a knowledge-based approach, the

latter results in smaller variances and a resultant higher

false alarm rate. The intention is that the system should

then improve this false alarm rate by diagnosing most

of the false alarms without recourse to operator inter­

vention. Thus credibilty will be maintained, diagnosis

performed and a case history of non-random errors

built up, thus improving the capabilities of, for in­

stance, statistical detectors.

Overview of Knowledge-Based System

Its Structure. Fig. 2 summarizes the system. Knowl­edge is represented in two forms: knowledge-sources

and a plant simulation. Both symbolic and numerical

inference techniques are included to assess the knowl-

275

edge present There are four main knowledge-sources

arranged as shown in the Fig. 3.

Inference

Engine

SIMULATION

Analysis

Routines

Numerical

Routines

Q Lisp Programs

CJ Fortran Programs

Fig. 2 : Proposed Knowledge-based System

Fig. 3 : Knowledge Sources

The Fault Detection and Partial Isolation knowledge­

source is invoked everytime a set of plant measure­

ments become available, that is at the end of every

period. Its primary role is to detect the occurrence of

a fault and having done so, to output two lists: a list of

discrepancies and a list of assertions which point to

possible classes of faults that could account for the

patterns observed. It would be unusual to identify a

fault uniquely.

The Supervisor is driven by the resulting data. Its

overall objective is to explain discrepancies observed.

The basic mechanism is as follows. On receipt of a list

of fault scenarios, each fault scenario is taken in turn

and one or more of three options are invoked: an

analysis based on a simulation, a reference to history

or its own assessment Each option returns either a

statement of its deliberations or nothing at all. The system is implemented in a hybrid lisp/Fortran environment with the lisp environment acting as host

calling Fortran routines when necessary. A hybrid

implementation is preferred because this combines the

numerical affinity of Fortran with the list and symbolic

processing powers of lisp.

Knowledge Representation. Individual knowledge­sources are represented in lisp or productions or some combination of the two. Lisp tends to be used only where a specific task is procedural. The productions are of the form

if antecedent then consequent

or antecedent � consequent

Inference Engine. In diagnosis, the inference process is either one of building-up an explanation to describe

the symptoms observed or one of trying out various fault scenarios until a particular scenario correlates with the symptoms. The second option is not a suitable approach for information poor plants because of the generic difficulty in obtaining a complete set of fault hypotheses. The inference process must therefore be

one of building-up or forward chaining explanations until a fault is identified. A production-based forward chainer has been developed specifically for this appli­cation. Based on a unification algorithm described in Charniak and McDermott (1985), its performance has been enhanced by Lam (1989) who has incorporated various pointers and data structures.

fault Detection and Partial Isolation Specification and Interpretation of Detectors. A large number of statistical tests have been proposed in the past to detect a significant MUF (see, for instance,

Speed, 1986). It is envisaged that, at least during the infancy of the plant, the only sensible test statistics will be those of MUF versus time and various forms of its

cumulative sum because of uncertainty surrounding the measurement models. Furthermore, it is well­

known (see, for instance, Howell, 1987) that, when plotted against time period, these statistics will exhibit patterns peculiar to the various categories of fault that might be present. These categories are based, primar­ily, on the effect of serial correlation caused by the presence of the same physical inventory in consecu­

tive balance periods. A number of rules can be derived to explain the pat­terns observed. The approach (Howell, 1991) is to apply the tests to the relevant time series and to corre­late the resulting (binary) alarm sequencies with the (binary) sequencies that would arise if the same tests were applied to patterns generated by the various fault

categories.

Model-Based Reasonin� Both analytical and production based approaches can be brought to bear in diagnosing symptoms generated

by comparing plant data with estimates obtained from

a mathematical model based simulation.

276

The system contains an analytical method which has been developed for the model-based diagnosis of faults in information poor plants. There is insufficient space here to expand on this and the reader is referred to Howell (1991,1992) for further details.

Productions can be added with experience. For in­

stance, a number may be derived from the fact that a tank is simply a storage device. If a particular tank is suspected on a particular period and if the simulation is accepted as being correct, then the following can be applied to investigate whether the measurement model is in error,

if [(simulation_analysis > measured_analysis) & (measured_tank_inventory < simulated_

tank_inventory) & (simulation_analysis > maximum_

analysis_ input) �(stratified?)

This is oflittle use by itself because of uncertainty over the simulation. However if

if [ (stratified?) & (! (perturbation_required 'analysis)

<simulation_analysis) ] �(measurement_model_error)

where the method perturbation_required calcu­lates that analysis which would explain the symp­tom,

also holds then both (stratified?) and (measurement.

model_error) can be returned to the Supervisor as evidence.

The above may also be repeated for the case where the measured tank inventory is greater than the simulation

tank inventory.

The History Knowled�-Source This knowledge source contains data describing any peculiarities pertaining to the plant, either currently or recently and rules of thumb which relate this type of data to possibile fault scenarios. It is largely applica­tion specific and is likely to expand with time.

General assertions are typically of the form, (measurement_maintained period measurement) (suspect feedstock period)

whilst rules are of the form,

if [ (net_transfer_bias_from period)

& (measurement_maintained period

measurement) & (measurement e net_transfer_

measurements) ]

� (poor_maintenance period measurement)

A typical set of rules pertains to problems in the

detennination of the physical inventory of the solvent­extraction plant It is usual operational policy to run at one flowsheet, ie one load, for extensive periods of time so that physical inventory changes are infrequent The Fault Detection and Partial Isolation knowledge­

source should identify a particular pattern (denoted by Pattern 4) when a flowsheet change is invoked and the physical inventory is estimated incorrectly. Rules can therefore be applied to correlate this pattern with known plant activity, thus

if (Pattern 4 m n) j I (look_at_solvent_ext_history m n+l)

if [ (flowsheet_change ?sol_ex_a m) & (flowsheet_change ?sol_ex_b n+ 1) & (no_flowsheet_change m+ 1 n) ]

� (sol_ex? ?sol_ex_a ?sol_ex_b m n)

where look....at.solvenLext.Jiistory is a method which generates the assertions needed by the subsequent rule.

AN EXAMPLE

The following example, where the plant feed tank volume is measured erroneously on a particular peri­od, is given merely to elaborate on system perfor­mance and to demonstrate its potential. Considerably

more development is required before the system can be viewed as being operationally viable. At present, the consequences generated by the Fault Detection and Supervisor knowledge-sources are ap­

pended to the top of a common assertion base, goals. Model-based reasoning and History have their own assertion bases, sim_asserts and co"_asserts. All the assertion bases are initialized with background data like

(INV _TYPE PFT I_ TANK) (INV _TYPE SOL_EX_l SPECIAL)

(Those shown here associate each plant item to a

particular type of inventory). The following additions were made to the various assertion bases when the system was asked to analyse data pertaining to the simulated plant assuming that a volume error of 10 litres had occurred on the previous period (ie day). Note that an incomplete list of addi­tions is provided; the list selected simply gives a

flavour of what happened.

goals - as produced by the control charts

(INV _LOSS+SIM_OUTYESTERDAY)

(INV _LOSS YESTERDAY)

(SINGLE_TRANSFER_ERROR YESTERDAY) (SINGLE_INV _ERROR YESTERDAY) (CUSUM_P YESTERDAY) (MUFIEST_P YESTERDAY 3 16.498) Statistical tests produced the bottom 2 assertions.

277

The top 4 assertions point to possible categories of anomaly.

These top 4 were then interpreted by the Supervisor, producing

goals - generated by the supervisor,

(V ALUE_REQ S_T_E YESTERDAY PROD _STOR_B

((VOLUME 1.0e6 1 .0e6) ANALYSIS 73.8536 3 .113602) (INI_ VOL 106.1241 4.474106)))

(V ALUE_REQ S_T_E YESTERDAY_ACCN_T ((VOLUME -8.36588 9.865882)

ANALYSIS 29.20196 -2.87804) (INI_ VOL 101.6041 -9.86589)))

(LOOK_FOR_FAUL T S_I_E YESTERDAY

(YESTERDAY YESTERDAY)) (LOOK_FOR_FAULT S_T_E

YESTERDAY (YESTERDAY TODAY))

LOOK_FOR_FAUL T I_L YESTERDAY (YESTERDAY TODAY))

The LOOK-FOR-FAULT assertions are generated as requests to model-based reasoning to look for

an anomaly YESTERDAY by perfonning a simu­

lation between the 2 periods (first_day last_day). The Supervisor also perfonns its own assessment

For instance, VALUE_REQ assertions are gener­ated to specify the measurements together with

their respective perturbations that would be needed to individually explain the MUFTEST_P. These

would be of interest if model-based reasoning sus­

pected either the accountancy tank or product stor­

age tank B. Each LOOK-FOR-FAULT was now assessed by the

model-based reasoning knowledge-source. The fol­lowing were generated by looking for a S-1-E (single

inventory error) anomaly.

sim_asserts - as produced by the analytical approach, (S_I_E ((PFTVOL_MEAS -9.20707)) NIL 1) (INTERPRET_MODEL S_I_E

((0 NIL (((1 -0.492931) (991 -9.20707)))

(0.965009))))

Only one possible explanation was generated. A

reduction of -9.21 in the simulated volume in the

plant feed tank would explain the measurements.

That is, there was a measurement error of -9.21 as

compared to an actual error of - 101. An insignifi­cant error in the volume input to the plant was also needed to explain the discrepancies.

The model-based reasoning knowledge-source also

applied productions to look for various effects. For

instance, it attempted to assess whether any of the

tanks were stratified but failed to identify any. The consequence (stratified ... ) would have appeared if it had been successful. Three suspect components were

identified by comparing the simulation output with the measurements.

sim_asserts -(ERROR YESTERDAY

BUF _T ANK_C -38.5993) (ERROR YESTERDAY

BUF _TANK_B_53.93359) (ERROR YESTERDAY PFT -327 .456) (PROBLEM_INV YESTERDAY

BUF _TANK_C) (PROBLEM_INV YESTERDAY

BUF_TANK_B) (PROBLEM_INV YESTERDAY PFT)

These were then analysed as follows.

(ANAL_REQ PFT 30.28288) (MIN_INPUT_ANAL PFT YESTERDAY

28.69) (MAX_INPUT_ANAL PFT YESTERDAY

37.07) (INPUT_ANAL_HIST PFT YESTERDAY

((32.08 37.07 28.69))) (ANAL_REQ BUF _T ANK_B 33.56335) (MIN_INPUT_ANAL BUF TANK B

YESTERDAY 28.84)

{MAX_INPUT_ANAL BUF _TANK_B YESTERDAY 35.68)

(INPUT_ANAL_HIST BUF_TANK_B YESTERDAY

((33.34999 35.68 28.84) (33.18 35.29999 29.05999)))

(SIM_ANAL_HIGH?? YESTERDAY PFT

-327.456

33.25375 33.20999) (ANAL_REQ BUF _TANK_C 34.7864) MIN_INPUT_ANAL BUF _T ANK_C

YESTERDAY 28.84) MAX_INPUT_ANAL BUF_TANK_C

YESTERDAY 35.68)

(INPUT_ANAL_HIST BUF _T ANK_C YESTERDAY

((33.34999 35.68 28.84)

(33.18 35.29999 29.05999))) (SIM_ANAL_HIGH?? YESTERDAY

BUF_TANK_C

-38.5993 35.0352 35.18999)

278

(SIM_ANAL_LOW?? YESTERDAY

BUF_TANK_B 53.93359 32.76209 32.59)

CONCLUSIONS

A knowledge-based system structure has been de­

scribed which incorporates and subsequently analyses the outputs of statistical detectors by recourse to both surface knowledge, based on previous experience, operator intuition and plant peculiarities, and on model-based reasoning. The system is still in its em­bryonic state and considerable work has still to be

done.

REFERENCES

Chamiak, E. & D. McDermott (1985). Introduction to Artificial Intelligence. Addison-Wesley. Himmelblau, D. M. (1978). Fault Detection and Di­agnosis in Chemical and Petrochemical Processes. Elsevier.

Howell, J. (1987). An Intelligent Knowledge-Based Approach to Near-Real_time Materials Accountancy. 9th ESARDA Symposium on Safeguards and Nuclear Material Management. London.

Howell, J. (1991a). Model-Based Fault Diagnosis in Information Poor Processes. PhD Thesis, University

of Glasgow. Howell, J. (1992). Model-Based Fault Diagnosis in Information Poor Plants. Submitted to Automatica. IAEA Safeguards Glossary (1987). International Atomic Energy Agency, Vienna, IAENSG/INF/l (rev. 1).

Ikawa, K., H. Ibara, H. Nishimura, M. Hirata, H. Sakuragi, M. Ido, T. Sawahate, M. Tsutsumi, N.

Suyama, M. Iwanaga & J. Lovett (1983). Study of the Application of Near-Real Time Materials Account­ancy to Safeguards for Reprocessing Facilities. Japan Atomic Energy Research Institute PNCT N841-33-26. Jones, T. L. & D Gordon (1986). Near Real Time

Nuclear Materials Accountancy at Dounreay. IAEA­

SM-293/22, Nuclear Safeguards Technology, Vol 1. Lam, L. Y. (1989). Lisp Production System. Submitted

as part of an MSc in Information Technology, Univer­sity of Glasgow. Searl, E. A., J. R. Jamieson & C. I. Delaune (1987).

Diagnosis and Sensor Validation through Knowledge of Stucture and Function. IEEE Trans Systems, Man, and Cybernetics, SMC-17(3), pp 360-368.

Speed, T. P. & D. Culpin (1986). The Role of Statistics

in Nuclear Materials Accounting: Issues and Prob­lems. Journal of the Royal Statistical Society A, 149, part 4.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

LOGIC-BASED PROCESS DIAGNOSIS UTILISING THE CAUSAL STRUCTURE OF DYNAMICAL

SYSTEMS

J. Lunze and F. Schiller

Technische Universitilt Hamburg-Harburg, Arbeitsbereich Regelungstechnik, EijJendorfer Strafle 40, D-W2100 Hamburg 90, Germany

Abstrac t . A method for logic-based process diagnosis is propos�d that utilise the causal structure of the dynamic syst�m unter consi­deration to restrict the search space of the resolution system • . The basis for this is given by a qual itative model of the dynamical process which is formulated in assertional logic formulae , as well as a ca�sality graph, which describes the direc�ions .of the cause­effect relations . It is shown that the overall diagnosis probl�m can be decomposed into a series of subproblems such that the s?lution of the subproblems is necessary and sufficient for the solution of t�e overall problem. This decomposition reduces the search space con�i­derably and makes the diagnosis algorithm applicable under real-time constraints .

A p di' agnosi· s , knowledge-based systems , dynamical Keyvor�• · rocess systems , causality, real-time expert systems

IllTRODOCTIOR

Process diagnosis concerns the problems of detecting abnormal states of a dynamical system and of finding the ultimate faults that have caused this perturbation . In the control engineer ing l iterature , these steps are also cal led fault detection or fault isolation, respectively. The maj ority of diagnosis methods, which have been elaborated and tested in practi­ce until now , starts from an analytical model of the process under consideration , which is usually brought into the form

. x = f (x , u , a) , y = g (x , u , a) ( 1 )

where x , u and y are the vectors o f the system state , input or output , respective­ly . S ince the fault is reflected in this model by changes of the parameter vector a, the diagnosis problem can be solved by means of parameter estimation methods or by state observers , cf (Patton , Frank and Clark, 1988 ) , ( Isermann , 1989 ) . However , a lot of diagnosis problems are characterised by one or more of the follo­wing features: * The fault yields structural perturbati­

ons of the process , which cannot be reasonably descr i bed by parameter changes . For example , a valve is bloc­ked, or a pipe is broken .

* The on-line information available is not given as quantitative measurements of the system output y (t ) but by qualita­tive assessments ( eg . "water level is high/ low" ) or by alarm messages . Then the model ( 1 ) cannot be used for pro­cessing this information .

279

* The model ( 1 ) is not available . In this situation , the diagnosis problem must be solved by means of knowledge about discrete cause-effect relations occuring in the process rather than by the model ( 1 ) . This provides the motivat ion for using knowledge-based systems for proc�ss diagnosis , since knowledge repres�ntation formalisms and knowledge processing me­thods provide an appropriate bas i s for dealing with qualitative descriptions of the system under consideration . However , it is sti l l a problem of current research to adapt the rather genera� �etho�s dev�­loped in the f ield of artifical intelli­gence cf ( Puppe , 1986 ) , (Milne , 1987 ) , (de Kleer and W i l l iams , 1 9 87 ) , t� the specific circumstances encountered in . on­line supervision and control of dynamical systems . It is the aim of this paper to contribute to this step . A severe open question asks how to make knowledge-based diagnosis applicable under real-time constraints . Knowledge proces­sing and , in particular , theorem proving by means of the resolution method leads to search problems with extensive search spaces ( cf Lunze and Schwarz 1990 ) , which cannot be solved sufficiently quickly for processes with rapid dynamical phenomena . Hence knowledge processing methods have to be1 elaborated that uti l ise specific features of dynamical systems in order to restrict the search space and to accelera­te the diagnosis algorithm. Onl y a f ew papers have concerned the methodological background of knowledge­based diagnosi s . Lunze ( 19 9 0 , 1 9 91 ) has proposed a method in which a l l search problems are solved before the first alarm

occurs . It became obvious that the logic description of the cause-effect relations that become effective within the process after faults have occured makes a more detailed description of the process possi­ble than classical event trees , which have been used , for example , by Narayanan and Viswanadham ( 1 9 8 8 ) . Sticher and Tolle ( 1 9 9 0 ) solved the diagnosis problem by interval analysis . In the following , a completely new way is used where the causal structure of the dynamical system under consideration is used to restrict the search space of the resolution system so that the diagnosis algorithm becomes applicable under real­time constraints . The paper is organised as follows . The diagnosis problem given in Section 1 is solved by means of an assertional-logic description of dynamical systems that will be introduced in Section 2 . on this basis the diagnosis problem can be reformulated in assertional logic as exp l a ined i n Section 3 . A s discussed i n Section 4 , the direct app l i cation o f the resolution method to this problem is impossible for practical applications where the process model consists of hundreds of logic formu­lae and , thus yields a huge search space of the resolution system . This is the reason for introducing the causality graph in Section 5 i n order to ut i l i s e the structure of the system during the diagno­sis . The basis of the diagnosis algorithm is provided by the decomposition principle described in Section 6 . This principle is used in the diagnosis system whose struc­ture is explained in Section 7 . An example given in Section 8 illustrates the propo­sed method .

1 . TKE DIAGNOSIS PROBLEM

The paper concerns a typical situation of process supervision where the existence of faults is indicated by alarm messages and where the fault isolation problem has yet to be solved . The problem is to find the primary fault that has brought about such deviations of the process s ignals from the ir nominal traj ectories that a given set of alarms has been alerted . Since the fault and the a larm messages refer to discrete phenomena , the process has to be described as a sequence of these and other symptoms independently of whether the process under consideration is really a discrete or a continuous system . For this reason , control actions and the general operating conditions are also described in terms of such symptoms ( Fig . 1 ) . The set of a l l symptoms is denoted by �. Alarm messages ai , control actions ui , faults fi and operation conditions z i form disjoint subsets of � :

A c �, !1. c �, E c �, z c � . ( 2 ) The remaining symptoms are denoted by ki � = {k1 , k2 , . . . } = �\ CA u !1. u E u £) . ( 3 ) I t is assumed that the current process state and control activities , which occur prior to the appearance of the faults , are described by the sets

( 4 )

and that these sets are known . After the faults fi £ .f:o have occured , the process

280

signals change dynamically and , eventual­ly , activate a set of alarms

( 5 ) The problem is to find the fault set ,E0 ( Fig . 1 ) .

Diagnosis Problem : For given sets !lo and z of control actions and operation cgnditions find the fault set f'.0 c E for which the process yields a given set A0 of alarm messages .

2 . TKE ASSERTIONAL-LOGIC DESCRIPTION OF TKE PROCESS

The basis for the diagnosis is provided by a logic-based description of the process . This section describes how this model has to be set up .

2 . 1 . A logic-based qualitative description of dynamical processes

The model refers to qualitative phenomena that occur within the dynamical process . These phenomena are characterised typical­ly by the fact that signals or parameters exceed given bounds or have values of a precribed interval . If such conditions are satisfied , it is said that a symptom si occurs . A symptom exists or does not exist . So it is possible to assign a literal assertion si ( l iteral ) to each symptom: The validi­ty of a symptom is represented by assig­ning the truth value "true" to the lite­ral , otherwise the truth value "false" . With these literal assertions , well-formed formulae of assertional logic can be set up . Thi s w i l l be explained now for two classes for formulae that are referred to as general relations or cause-effect­relations , respectively . General relat ions . Relations among sym­ptoms can be written down as arbitrary well-formed formulae . For example ,

p3h v p3m v p31 -p3h v -p3m -p3h v -p3 l -p3m v -p31

( 6 )

mean that exact one of the symptoms p3h , p3m and p3 1 has the truth value "true" , which is reasonable if these literals say that a level p3 is e ither high or medium or low. Particular but important forms of general relations describe the current control dctions or states . These formulae have the simple form

( 7 ) that say that the control action ui i s active and the state has the qualitative description zj . Cause-effect relations . A special symbol "<-- " is introduced in order to simplify the model creation . Cause-effect relations have the general form

s <-- si & sj & • • • & -sk & • • • & -s1 ( 8 )

where the set on the right-hand side Q = {Si , Sj t • • • t Skt • • • t Sl } ( 9 )

describes the symptoms whose simultaneous occurrence makes the symptom s to occur . For instance ,

a <-- b & c a <-- d ( 10 )

mean that the symptom a is the effect of another symptom d or of the simultaneous existence of the two symptoms b and c .

2 . 2 . Reformulation of th• ao4el in asser­tional loqic

At first sight, the arrow notation ( 8 ) can be interpreted as implications , e .g .

a <== b & c a <== d . ( 11 )

However , if it is known that the right­hand sides of ( 10 ) or ( 1 1 ) describe All causes that may bring about the effect a (closed-world assumption (Nilsson 1982 ) ) , then the arrows or implication signs have to be interpreted as equivalence

a <==> (b & c) v d . ( 12 ) Hence, the process model , which i s set up with the notation ( 8 ) , can be reformulated as a set of equivalences like ( 12 ) . Note that eqn ( 12 ) does no longer show in which way the symptoms a, b, c, d are connected as causes or effects , respecti­vely. Therefore , from the arrow notation ( 8 ) another formula is derived that has the form

s = W (Q) . ( 1 3 ) It is referred to as the causal structure of ( 8 ) saying that s is the effect of the simultaneous occurrence of all sym­ptoms included in Q. For the example ( 10 )

a W ( {b , c} ) a W ( {d} )

holds . Th• overall ao4el . In summary, the logical description R cons ists o f formulae B coming from the cause-effect-relations ana of formulae � describing a l l general relations :

( 14 )

With the definitions above , the alarm set ( 5 ) can be represented by

ai & . . . & aj & -ak & . . . & -a1 , ( 15 ) and the fault set .f:o by

fi & • • . & fj & -fk & . . . & -fl , ( 16 ) where both positive or negative assertions on ai f A or fi f E can be made.

3 . STATBKDIT OJ' TRB DIAG•OSIS PROBLBK I• ASSBRTIOSAL LOGIC

The diagnosis problem described in Section 1 can be stated now as a problem of theo­rem proving:

281

Given : ( 1 ) General relat ions l ike ( 6 ) or ( 7 ) describing the sets Yo and � of the current control actions and operation conditions

( 2 ) Process model B of the form ( 1 2 ) ( 3 ) Formula ( 1 6 ) describing a tentative fault set .f'.0

Find : A proof that the assertion ( 15 ) follows from this given set of formulae . If such a proof exists , the tentative fault set Ee described by ( 1 6 ) is a solu­tion to the diagnosis problem.

4 . DIRECT SOLUTION OF THE DIAGNOSIS PROBLEM BY MEANS OJ' THE RESOLUTION METHOD

In principle, the diagnosis problem can be solved by means of a resolution system . After all formulae have been brought into clause form, the negation of the assertion ( 15 ) has to be added to the clause set and it has to be proved that the resulting set of formulae is contradictory (Fig . 2 . ) . However , this way of solution includes a complex search problem . The resolution method consists of resolution steps . Each step connects two clauses of the whole clause set in order to eventually produce the empty clause , which makes the elemen­tary contradiction visible . As it is not known which sequence of resolution steps wil l generate the empty clause , the pro­blem of f inding the proof is a search problem . Two properties of this search problem are important for diagnosis : * The d im e n s i on o f the search space

increases rapidly with the number of model formulae . Hence , the diagnosis problem is NP-complete .

* structura l properties of the set of formulae Be are not utilised .

Therefore , another way of solut ion is proposed now , which exploits the causal structure of the formulae ( 8 ) that is described by formulae of the form ( 1 3 ) . The basis for this is provided by the causality graph , which will be introduced now.

5 . THB CAUSAL STRUCTURB OJ' DYNAMICAL SYSTEMS

s . 1 . The causality graph

The causality graph of a dynamical system has been introduced by Lunze and Schiller ( 1 9 9 1 ) for dynamical systems that are described by implications in assertional logic . Its definition is briefly surveyed here . Definition �: consider a dynamical system, which is described by the model B intro­duced in Section 2 . The causali ty graph of this system is defined to be a directed graph G (�� with the following proper­ties :

1 . For every symptom S · f S there is exactly one vertex in lhe graph . Both the symptom and the vertex are denoted by the same symbol si .

2 . There e x i st s a d i rected edge

3 .

( s · , S · ) E � from si towards S · ( i�j ) J i f there is a cause-effect relation of the form ( 1 3 ) with the structure

with There e x i s t d i rected edges

( si , s - ) E � and ( s · , si ) E � ( itj ) i f the!e is a gene�al relation that refers to both symptoms si and sj .

Fig . 3 . gives an example . Every vertex s E � i s associated with all general relations in which s occurs and with all formulae ( 8 ) that have the causal structure s = W (�) for some set � . The causality graph shows in which way the effects of the faults propagate through the system . Although the graph represents less information about the system than the model R., it makes several important pro­perties obvious : * A given fault f E f: yields an alarm

message Ao E A only if there is a path within the causality graph from f towards all ai E A0 •

* I f there i s a path from some node s i E § towards some node sj E � via the nodes sk , s 1 • • . sm , than the symptoms si , sk , s1 , • . • , sm , sj occur exactly in this order i f the cause­effect relations among these symptoms as described by the graph become effec­tive .

s . 2 . The aqqreqated causality qraph

The causal ity graph can be analysed by graph-theoretic means in order to obtain an aqgregate description of the causal structure . Two nodes s · , S · E � ( s · ts · ) are strongly connected i� i� G (§,E) lhete exist a path from si to s; and a path from sj to s i . It is known in graph theory , that the property of strong con­nection constitutes an equivalence relati­on . The set § of nodes of G (§,E) can be partitioned into equivalence classes

n u §i = §,

i=l ( 17 )

such that any two nodes s1 , s2 E s are stron�ly connected if and only if thev belong to the same set §i in ( 17 ) . The partition ( 17 ) brings about a partiti­on of the graph G rn, fil into subgraphs Gi (§i , Ei ) where

l:i = { ( sk , s1 ) E E I sk , sl E §i} . If these subgraphs are aggregated to hyper nodes , the aggregated causality graph is constructed. Definition L.,: For a given causality graph G£�•Jl the a ggrega ted causal i ty graph G (§ , Ea) is defined as follows : 1 . For each equivalence class §i in eqn

( 1 7 ) there exists one node s ia E §a ( th i s corre lat ion is visible by the same index) .

2 . There exists a directed edge ( s · a , s . a ) E Eia , if and only if there exfsts Jat

282

least one pair s� E Si and sj E §j for which ( si , sj J E � holds . 3 . With e a c h node s i a of Ga a l l

formulae Rk E R are associated that belong to some node S · E �· of the causality graph . This set is denoted by Bia ·

Henc e , the aggregated causal ity graph gives rise to a decomposition of the model B into n disjointed subsets Bia :

n u R · a = _R, R · a n R · a = � ( i�J· ) ( 18 )

i=l-1 -1 -J Y T

Note that the aggregated causality graph doe s not have any loop as the example shown in Fig . 3 .

6 . A DBCOKPOSITIOH PRIHCIPLB POR THB DIAGNOSIS PROBLEM

Lunze and Schiller ( 19 9 2 ) have shown that the whole diagnosis problem can be broken down i�to several subproblems in such a way that the whole problem has a solution if and only if the subproblems have solu­tions . The basis for this is given by the model decomposition ( 18 ) and the following theorems . These theorems use the notation

Kl (Ri ) = { si I either si or -si is a literal of formula Ri }

to indicate which symptoms occur in the model formula Ri . Theorem 1 . Consider the aggregated causa­lity graph

Ga ( { fa , ga , ha } , { ( fa , ga ) , (ga , ha ) } ) , where fa , ga , ha represent the sets � g_, H o f symptoms . Assume that the sets of formulae

Bf , Bg• Rh are assigned to the nodes fa , ga and ha . Consider further a clause Th with

A clause Tf with Kl (Tf ) Q .E

can be deduced from the set of formulae

Bf U Bg U Rh U {Th} , if and only if it is possible to deduce a clause Tg with

Kl (Tg) Q Q from

and the clause Tf from

That i s , the search of the resolution sys t em can be l imited to a search in subsets B,., and Rh , respectively, without restrictilig the solvabi lity of the pro­blem.

Theorem .2...... Consider the aggregated causa­lity graph

Ga ( { fa , ga , ha } , { ( fa , ga) , ( fa , ha) } ) , where fa , ga , ha represent the sets .L §... R of symptoms . Assume that the sets of formulae

Bf , Bg • Bh are assigned to the nodes fa , ga and ha . Consider further a clause Tgh with

Kl (Tgh) Q � u fi. A clause Tf with

Kl (Tf ) Q .E can be deduced from the set of formulae

Bf u Bg u Bh u {Th} , if and only if it is possible to deduce two clauses Tfl and Tf2 with

Kl (Tn) Q _E, from

respectively , such that Tf = Tfl v Tf2

holds .

The s e theorems have a nice intuit ive interpretation . They say that the problem of finding the cause described by Tf for the known e f f ect Th or T h can be decomposed i f the efrect re�ults from series or parallel cause-effect relations . Then the deduction can be reduced into succeeding or parallel deduction problems . Since the aggregated causal ity graph is fre e o f loops , the overa l l d i agno s i s problem can b e decomposed completely into ' series or parallel problems • .

7 . THE DIAGNOSIS SYSTEM

The architecture of the diagnosis system is dep icted in Fig . 4 . The process is described by the model R and the causa­lity graph . For a given alarm message ( 15 ) the diagnosis systems finds the fault set .E0 described in the form ( 16 ) . The figure shows that the diagnosis algo­rithm consists of two parts . The first part concerns the model preparation phase , which can be accomplished before the first alarm occurs . In this phase , the aggrega­ted causality graph is determined and the model R decomposed accordingly . This step includes graph search problems , but since these search problems can be solved before the a l arm occurs , they are not time-critical . The execution phase concerns the solution of an actual diagnosis problem after a set of alarms have been alerted . The algorithm consists of two interconnected parts . The • upper level a lgorithm ' decomposes the whole diagnosis problem into subproblems ,

283

which are described by a theorem to be reformulated and that part B i of the model which has to be used for this re­formulation (cf Theorems 1 and 2 ) . With the answer to the subproblems , new subpro­blems are determined until the result is a formula of the form ( 16 ) in which exclusi­vely literals fi € .E occur .

8 . EXAMPLE

The diagnosis algorithm will be illustra­ted now by considering the water supply system dep icted in F ig . 5 . The system con s i st s o f three water tanks . Level control loops , which operate on the valves ensure that the water levels are indepen­dent of the consumed amount of water . As system output the operator receives the following alarm messages :

al "Level of tank 1 is too low" a2 = "Level of tank 2 is too low" a3 = "Level of tank 3 is too low"

The following faults are be considered : f l f 2 f 3

"Valve 1 is closed and blocked" "Valve 2 is closed and blocked" "Pipe is blocked"

The process can have one of the following qualitative states :

zl Z2 Z3

"Tank 3 has low water level" "Tank 3 has medium water level" "Tank 3 has high water level"

Further symptoms , which have to be consi­dered , are kl "Level of tank 1 sinks below limit" k2 "Level of tank 2 sinks below limit" k3 "Level of tank 3 sinks below limit" Then , the system model R has the follo­wing formulae :

General relations BR : zl v z2 v z3 -zl v -z2 -z2 v -z3 -zl v -z3

Cause-effect relations Be : fl --> kl kl --> al f2 - - > k2 k2 --> a2 kl & k2 --> k3 k2 & f3 --> k3 k3 --> a3 (kl v k2 ) & ( zl V Z2 ) --> k3

( 19 )

( 20 )

From the cause-effect relations in arrow notation the fol lowing set of logical formulae is obtained :

fl <==> kl ( 21 ) kl <==> al ( 2 2 ) f2 <==> k2 ( 2 3 ) k2 <==> a2 ( 24 ) ( kl & k2 ) v (k2 & f3 ) v ( (kl v k2 ) &

& ( z l V Z 2 ) ) <==> k3 ( 25 ) k 3 <==> a3 ( 26 )

The causality graph consists of ten sub­graphs with which the following formulae are associated :

Graph consisting of nodes

fl kl zl , z2 , z3

Formula

no formula ( 21 ) ( 19 )

If the alarm message al & -a3 & -a2 is received the diagnosis algorithm steps forward in the f o l lowing way ( cf the causality graph) . 1 . The first subproblem is to replace the assertion -a3 by some assertion concer­ning k3 by means of ( 2 6 ) , s ince a3 is the vertex at the right of the graph , with this vertex the formula (26 ) is associated and the only way towards the vertex a3 comes from the vertex k3 . This subproblem has the solution -k3 , which replaces -a3 in the alarm message , i . e . the new asser­tion is al & -k3 & -a2 . 2 . The next subproblem is to replace -k3 by some assertion that includes the sym­ptoms kl , z l , z2 , z3 , k2 , f3 by means of ( 25 ) . The result is -zl & -z2 & z3 & -k2 and , hence , the new assertion al & -zl & -z2 & z3 & -k2 & -a2 . 3 . Now, three ' parallel ' problems occur :

-zl & -z2 & z 3 have to be resolved by means of ( 19 ) , since this hyper node has no antecedent . Obviously, this assertion does not contradict ( 19 ) .

- a 2 h a s to be r e p l a ced by a term including k2 by means of ( 2 4 ) , wh ich results in -k2 .

al has to be replaced by a term inclu­ding kl by means of ( 22 ) , which results in kl . The resulting assertion is -k2 & kl · 4 . -k2 has to be replaced by a formula including f2 by means of ( 2 3 ) , which results in -f2 . 5 . kl has to be replaced by a formula inc luding f l by means of ( 2 1 ) , which results in f l . The final assertion

-f2 & fl

has the form ( 16 ) . It says that the single failure fl has caused the alarm message .

RBPBRDCBS

de K l e e r , J . ; W i l l i a m s , B . C . ( 1 9 B 7 ) ' Diagnosing mu l t i p l e faults ' , Artificial

Intelligence 3 2 , 97-13 0 . Iserma n n , R . ( 1 9 8 9 ) ' Be i s p i e l e filr d i e Feh le r d i agnose m i tte l s Parametersch�t­zunq ' , Automatisierungstechnik 37, 3 3 6-34 3 ond 4 4 5 -4 4 7 . Lun z e , J . ( 1 9 9 0 ) ' Ein Verfahren zur Pro­zeBdiagnose auf der Grundlage der Aussa­genlog i k ' , Hessen, Steuern, Regeln 3 3 , 530-5 3 6 . Lun z e , J . ( 19 9 1 ) ' A method for logic-bas· � fault diagnosis ' , IFAC-Symposium on Fault De t e c t i on , Superv i s i on and Safety for Technical Processes, Baden-Baden , Vol . 2 , 4 5- 5 0 . Lunz e , J . ; Sch i l l e r , F . ( 19 9 2 ) ' Logikba­sierte ProzeSdiagnose unter Nutzung der kausalen Struktur dynamischer Systems ' , Automatisierungstechnik, Hefte 2 und 3 . Lunze , J . ; Schwarz , w . ( 19 9 0 ) KUns t l i che Intelligen z . Verlag Technik, Berl i n .

Narayanan, N . H . ; Viswanadham, N . ( 19 8 7 ) ' A methodology f o r knowledge acqu isition and reasoning in failure analysis. IEEE Trans . SXC-17, 274-288 . Ni lsson, N . J . ( 19 8 2 ) Principles of Artifi­cial Intelligence . Springer-Verlag , Ber­lin-Heidelberg-New York. Patton, R . ; Frank , P . M . ; Clark, R . ( 198& 1 Fau l t Diagnosis o t Dynamic Systems, Pren­tice-Hal l , London. Puppe , F. ( 1986) Diagnost isches Problemlo­�en mit Expertensystemen . Springer-Verlag, berli n .

284

St.icher, T . ; Tolle, H . ( 19 9 0 ) ' Alarmbe­hendlun9 aittels wissensbasierter Inter­vallanalyse • , Autoaatisierungstechnik 3 8 , 292-298.

Control U o Process State Z0

Alarm

Fig l . Dynam_ical

process

with fault message A0

Alarm message (15) 'yes'/"no'

I Fault (16)

i l Model B Resolution system

Fig 2 . Solution of the diagnosis problem by resolution m@�,0�

�- k2

Fig 3. causality graph and

aggregated causal ity graph

!'reoaration phaae Set of formulae B

Determination of the

aggregated

causality graph

Aggregated

causality graph

Structured

k nowledge base a

R • U R

Execution ohaae Alarm message

(15)

Fault

(16)

Decomposition of the

diagnosis problem

Subproblem Solution

Modified resolution system

Fig 4 . Diagnosis utilising the causal structure of the process

11

f2

tank 1 f3

a1

tank 2

l a2

Fig 5 . A tank system

B�w··� l Consumer

a3

285

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

KNOWLEDGE BASED SENSOR FAULT DETECTION FOR GAS TURBINES UNDER

CONSIDERATION OF MODEL BASED METHODS

R.A. Lunderstaedt and Th. Hillemann

Institute of Automation, University of German Armed Forces, Hamburg, Germany

Abstract. The gas path analysis is a useful tool for modeling jet engines and stationary gas turbines, respectively. Such models a re used for diagnosis that means that measure­ment values as inputs deliver state variables as outputs from the model. The measure­ment values are not fault free. They are disturbed by noise and by systematic sensor er­rors. Therefore algorithms have to be implemented which filter and compensate these er­rors; furthermore the modeling is not exact. Thereby the algorithms must be extended and adapted to this case. I n alternation to the model based procedures the diagnosis problem can also be solved by knowledge based methods using an expert system. Such an expert system is developed a nd presented in this paper. It i s an efficient tool - also in connection with the model based procedures - for detecting faults in the states of the engine and faults in the sensors as well. The diagnosis software package is applied on military and civilian jet engines and it is used in power plants for stationary gas turbines.

Keywords. Modeling; gas turbines; diagnostics; �as-fath-Analysis (GPA); failure detection ; sensor failures; expert system; fault tree; correlation procedures; fuzzy logic.

INTRODUCTION

The high requirements both in the civil and military field of air traffic as well as in the operation of power plants, which may be cha racterized by the keywords of "safety, reliability and economy" have led at an early stage to the development of methods of engine condition monitoring.

Back in the early thirties, visual inspections were carried out. Later on. operational tests, u ltrasonic tests, and lubricant checks as well as vibration analyses came up. The first automated diagnostic systems were introduced in the early sixties. Those systems were designed to supervise mainly the life cycle of important engine components by counting load cycles and temperature strains. A detailed compilation here­to can be found among other subjects in the investigations of de Hoff and Hall (1978). System theory regarding diag­nostic procedures for jet engines/ gas turbines was first con­sidered in the early seventies (Barschdorff (Ed.) , 1984). Those considerations were based on steady-state models for engine dynamics, having been obtained from working proce­dure data processing. Special achievements in that field have been contributed by Urban (1972, 1980) who was the first to develop analytical programs which have stood the test of practice and allow a high-quality diagnosis with the aid of the digital computer. They are being used with success for example by several airline companies. The procedure of modeling the engine is based on a thermodynamic cycle process which is known as �as-fath-Analysis (GPA).

Based thereon a nd moreover on the investigations of Roesnick (1984) a nd Fiedler and Lunderstaedt (1985), as an example of a diagnostic procedure for up-to-date one-, two­and three-shaft jet engines have been composed and some power plants were automated. Due to measuring noise and also due to systematic measuring errors, the diagnosis com­prises the employment of estimation procedures. Referring hereto, algorithms for state evaluation were developed and checked on their reliability. Especially for the systematic sen­sor errors a new theory was developed theoretically, which is outlined in detail by Lunderstaedt (1988). In combination with filtering the noise, the basis of fault detection is given also by Lunderstaedt (1990). The corresponding applications on two- and three-shaft jet engines and on an appropriate gas turbine with different workin!! points was published by Lunderstaedt and Hillemann (1991).

The diagnosis on the basis of methods referring to mathe­matical models is one way for detecting faults in a system. Another one is to use knowledge based methods as a com­petitive software tool or to combine both methods in order to use the advantages of both of them . For the diagnosis. that means the estimation of the state variables of the en­gines, this is done very successfully by Willan (1990). Finding

287

out the sensor faults is now outlined in the paper presented. The significant advantage in comparison with the only use of model based methods is the fact that now only one working point of the plant is necessary. This is especially important so far as gas turbines in power plants possess only one work­ing point because the rotational speed is fixed by the fre­quency of the electrical net.

The procedure outlined operates knowledge based with an expert system. This is worked out on a UN IX-workstation in a development environment on the basis of the programming language C.

The application of the theory is the engine LARZAC of the Alpha Jet fighter airplane. This engine has two shafts and it is diagnosed by 9 state variables which are derived from 13 measurement quantities. Some representative results of the diagnosis are given in tables and are depicted in some graphs. Furthermore, hints a re lined out using uncertain knowledge for diagnosis.

MODELING

As stated in the introductory context, a diagnosis oriented towards system theory requires a detailed model develop­ment. I n the following, this is briefly indicated, based on working process computations. The derivations can be found in detail in the fundamental works of Fiedler and Lunderstaedt (1985, 1988).

Corresponding to an up-to-date concept of jet engines/gas turbines, a modular structure of the engine is assumed. The modules to be considered are: the compressors, the combus­tion chamber, the turbines, and in some cases the thrust nozzle.

Different characteristics serve at describing the conditions of those components. In the sense of the terms related to con­trol technology, they a re referred to as state variables. For the turbo engines, they a re efficiency and mass flow rate, for the combustion chamber, efficiency and relative pressure loss, and for the nozzles, efficiency a nd cross section of out­let. Those characteristics and state variables a re not d irectly measurable, but they must be calculated from measured values. Those measured values are the pressures and temper­atures at inlet and outlet of each module, furthermore the speeds of rotation of the turbo engines, the fuel flow rate and, as a desirable further magnitude, the thrust and the power for stationary plants, respectively. If parts of the jet engine a re of variable geometry, the position indicators de­scribing the change of geometry are comprised with the measured values.

The correlation between measured values a nd state variables is established by reference to thermodynamics and the char­acteristics of the components with the aid of similitude theo­ry. Those linkages are in general non-linear, and procedures of system theory would not be applicable therewith . For that reason , the describing equations in the a rea of a predetermi­ned operational point a re linearized, and only the changes in that working point, as referred to nominal state, are consid­ered.

If a variable of state Xi is a function of m measurement values Yj, the total differential of Xi is

( 1 )

wherein dY. = Y. - YfJ and dX. = x. - x.0, the nominal J J I I I

state being identified by index 0. For later evaluation as well as for generalization , it is of advantage to pass over to a non-dimensional description. This is reached by referring the variations to the nominal state itself. At the same time, there shall be considered that finite deviations A from the nominal state are allowed.

wherein

The coefficients

( 2)

= I , . . . , n ; j I , . . . , m

are now to be determined by a thermodynamic cycle process calculation (Fiedler and Lunderstaedt, 19S5) a nd by this one gets the linear system of algebraic equations

m Ax . = }; q . . . /iy . l j=l l J J i = l , . . . , n (3)

which connect the n state variables of the engine with the m (normalized) measurement values. I n Eq. (1) to (3) it is suggested that the various sensors are placed such that from system theory the engine is observable, which means that E�I: (3) is solvable. In vector and matrix notation from Eq. (3) follows

x .!l . Y.. ( n�l) ( n ,m) (m, l ) (4)

where for Ax and Ay it is x and y rewritten. All the informa­tion of the engine model is now included in the system matrix Q.. In some cases it may be more suitable to write Eq. (4) in terms of a real measuring equation. Then one gets

( 5)

288

with

(6)

as (m,n) dimensional measuring matrix, which results from Q. in the case m > n as the right-hand side pseudoinverse matrix r,#. The formal connection of Eq. (6) is not appro­priate to calculate the matrix r, explicitly from Q.. This lies in the fact that the least squares solution r,# is not unique and may injure the physical conditions on which Q. and r, a re basing. Because of this the measurement matrix r. is deter­mined in the following way: After Q. is known from thermo­dynamics there exist vector pairs (x)k and (�)k. k = 1, . . . , r linked by Eq. ( 4) and Eq. (5) . For the j-th row of Eq. (5) one gets

which can be rewritten as

(7b)

where .!;j is a column vector representing the j-th row of r,. For all k = 1, . . . , r connections Eq. (7b) goes over in

Yj , l

Yj , r ( r , l )

, n , I ['I I . . . '

xl , r . . . x n , r ( r , n)

from which it follows for r � n

·�j (Sa)

( n , l )

(Sb)

M is thereby an abbreviation for the coefficient matrix in �q. (Sa). Goin� fro!'l j = 1 till j = m the m times applica­tion of tq . (Sb) delivers all row vectors of s; and by this the complete measurement matrix C is known. C is needed later and used for sensor fault detection.

-

The pure model based sensor fault detection consisting of filtering the noise and compensating the systematic sensor faults is investigated and completely solved by Lunderstaedt and Hillemann (1991). Because of this here this problem is not considered. I n this paper model based procedures a re only used in connection with knowledge based methods.

KNOWLEDGE BASED METHODS

From the measurement quantities Yf j = 1 • . . . , m one gets by application of Eq. (4) the states of the engine. These state variables a re mainly the mass flows and the efficiencies of the different turbo engines as mentioned before; all states are normalized such that in the fault free case they are all equal to zero. That means that states representing efficien­cies cannot be positive for physical reasons. If this case oc­curs, there must be one or more sensor faults. These physi­cal circumstances can be put in rules of a n expert system. The expert system gives hints for the sensor faults or ex­cludes in which sensor no fault can occur. By this, one dis­criminates between two types of rules,

- state based rules, - sensor based rules.

The state based rules look for the consequences on one special state xi by all the sensors Yj which have an influence on xi via Eq. (4).

In the case of the sensor based rules the situation is contra­ry. One looks for the consequences in all states x. if in one J special sensor yi a fault happens. In both situations there exist a fault tree which is walked through in one way forward and in the other way backward. Fig. 1 shows as an example a pa rt of the rules.

,. ,. ...... C- t.llM .-t ...... - --- - -

/ ·., / ""' x7> 0 >te> 0 x4> 0

,· ""' , /""' / ·, x1> o x1 > o

/ ' /' · , - · __. .,

/'"·, /' · , - n ....., ,

Fig . I . Part of a fault tree for sensor based rules.

It is depicted a fault tree for the sensor based rules of the LARZAC engine where the different logic connections are given by the elements (positive/negative/zero) of the system matrix Q in Eq. (4) .

In both types of rules the expert system finds out the sets of faulty sensors

- A, set of faulty sensors in the state based rules, - B, set of faulty sensors in the sensor based rules.

From both sets A and B the new set D is derived which con­tains all sensors being in A and B simultaneously and which have an influence on the states if there are faults in the measurement device. This set is given by

where cf is a certitude factor (Hetzheim, 1990) set by expe­rience here equal to 0.7. By this, the expert system is capa­ble to reduce the number of possible faulty sensors from m to p, with p < m. Then these remaining p sensors are inves­tigated by model based methods in order to get quantitative results.

Correlations

Another way of a knowledge based procedure is the use of correlation methods. Combining Eq. (4) and Eq. (5) one gets

( 10) The input vector XE is now chosen such that

0

0

means that in the sensor k; 0 < k < m a fault of - 1 % is sim­ulated. This is done for all m sensors and the m patterns (xA)k; k = 1, . . . , m are stored in the knowledge base of the expert system. Basing on the assumption that the best sim­ilarity between a real measurement vector x and one of the stored patterns (xA)k exists then, if the sensor faults includ-ed in x and (xA)k a re placed in the same sensor, those sen­sors are used which are indicated by the set D of Eq. (9) . They are compared with the real measurement vector x via Eq. (10) where a criterion for the similarity is chosen by

289

l m ck • -· E m j·l ( 1 1 )

The similarity coefficient ck lies i n t he region of O to 1; V is an emperical constant chosen as 10. In the sense of a hy­pothesis test, now all patterns (y A)k with k from (9) togeth-er with XA from Eq. ( 10) are put in Eq. (1 1) and one gets by this p similarity coefficients ck. The value ck = (ck)max leads to the right location of the fault in the sensor k. By using the principle of superposition this procedure can also be applied if there are more than one sensor fault. For this case an example is given in Fig. 2 and Table 1 . For the LARZAC engine three sensor faults are simulated for a real measurement data set coming from a test stand. The faults are set to 1 % in sensor 3 (dynamic pressure in the inlet). -4 % in sensor 7 (temperature in the high pressure compressor) and -2 % in sensor 11 ( rotational speed of the low pressure shaft). The sensor combinations calculated from Eq. (9) for the example, that means the set D, are now investigated by Eq. (11) and a following model based proce­dure. The result is depicted in Fig. 2. There a re ten combi­nations of sensor faults, whose explicit numerical values are given below in the Figure. They are represented by the different beams, the figures for the sensor combinations are placed on the bottom below the beams. The similarity coefficient is drawn above.

.. .. 71) .. .. .. JO ,. 1lJ "'

-UJ -20 .... ... ... ... -70

Diap9s F1<q<rn Lhi Bw H 1931 Oda Slt= -27. S3= 1?. S7= --4% Ode: Sui Feb 23 15:33'.32 l!m

-I / .....

........ 'S. ,,... +---

. 1 1 I I 1 1 I II 1 11 II II 1 1 I II I ll II II 1 1 I I I 1 • I I •

........ ·-

. 1 1 -11 I ll I II 1 11

I 1 1 . , .

, . .. " Q1 ..

7 t n 2 1 11 7 1117 5 7 n 3 7 11 e 7 n 4 7 t1 1 a n 1 1 11 1 11u

Se:m y

F ig . 2. An example for using the correlation method for sensor fa ult detection.

The numerical results are placed in Table 1. On the left there are the different sensor combinations, then follows the similarity coefficient ck, and on the right there a re the diffe�" ent sensor faults belonging to the combinations on the left . In the table, two things are important: The coefficient ck discriminates the different combinations sufficiently, and the values of the faults are found exactly confined to the accura­cy of the modeling.

Table 1 Similaritx coefficient and sensor faults

Sensor Comb i ­nations

3 7 1 1 6 7 11 5 7 11 4 7 1 1 7 1 1 1 2 7 8 1 1 2 7 1 1 l 7 11 7 9 11 7 1 1 13

0.999666 0 .878888 0 . 763218 0 . 752469 0 . 710125 0 . 688288 0 . 654657 0 . 652981 0 . 643421 0 . 610098

Sensor Faul ts

+I .018440 -3.988014 -0 . 133008 -3 . 914870 +0 . 539603 -3 . 557838 +0 . 399144 -3 . 688141 -3 . 769018 - 1 . 990477 -3 . 929749 +0 . 398300 -0. 146535 -3. 566043 -0.314025 -3 . 350986 -3 . 467725 -0 . 145278 -3 . 370373 - 1 . 919671

- 1 .991667 - 2 .078325 - 2 . 014111 - 1 . 983945 +0. 242410 - 2 . 093815 - 1 . 963322 - 1 .876718 -2 . 026340 -0 . 195149

Model based minimization

If in Eq. (10) the input measurement vector XE is fault free then the output vector XA is equal to XE· For faults Ax in XE one gets from Eq. ( 4)

( 12a)

and consequently from Eq. (5)

YA z £· (!E+A!) = £·Q· (yE+A.y) ( 12b)

That means XA # XE· This fact can be used to calculate the sensor faults. Let us at first assume that there is one sensor fault in the set D of Eq. (9). The location and the amount of the fault are unknown. then the unity vector

0

( 13 )

0

is formed, where the k-th element is equal to one, all others are zero. For �k from Eq. ( 13) one gets via Eq. (4) and Eq. (5)

( 14a)

For the real fault affected measurement vector it follows

( 14b)

From Eq. ( 14) one gets the quadratic difference sum

( 15)

In Eq . ( 15) the index k represents the unknown location of the fault and the coefficient ak its amount. Now one mini-mizes

( 1 6a)

for all k taken from Eq. (9) and all ak with the necessary condition

which leads to

m E YA · ·Yk .

* j= l , J , J a k = m

E y2 · j=l k , J

and finally to

( 16b)

( 16c )

( 16d)

290

The variation over all sensors from Eq. (9) yields the absolute minimum of Eq. ( 16a), that means Eq. ( 16c) and Eq. (16d ) are evaluated p times, with p from Eq. (9). If there a re more than one sensor fault, the theory derived can also be used because of the validity of the superposition principle. Jn an a nalogous generalization to Eq. ( 15) the quadratic difference sum is now given by

m r 2 s = E [y . - E ak l " Yk l ' ] ( 17a) kl , 2 , . . . , r�p j= l A,J l =l , , ,J

and the minimization rule is read

m i n s kl , 2 , . . . , r ( 17b) ak , l ; l = l , . . . , r

The efficiency of the procedure is proven for two examples, which are taken both from test stand data of the LARZAC engine. In the first example two sensor faults are simulated: in sensor 7 (temperature in the high pressure compressor) -2 % and in sensor 8 (temperature behind the low pressure turbine) 3 %. The results are outlined in Fig. 3 and Table 2. Fig. 3 , which is very similar in its composition to Fig. 2, shows for ten different combinations of sensor faults the evaluation of Eq. (17a). The sensor faults a re given by the different beams, the combinations of the faults are the fig­ures below the beams. The sum sk is depicted on top of Fig. 3 .

1 1'1 "" .. "' 10 "'

40

10

"' -10

_,. -JD

Dicgms FTOJan Lhi S.. H 1'.lll Oda S7= -2% ::8= 3% l)1e: M:ri FEb 24 16:1()19 1992

o= f-fl-I-a_ -\

'\ ,,.., u

I I I

. I 1

/

II ., I I I 11 I l I I I 11 . .

- -"""" u

I II 11 n II 11 . -

• 7 2 7 5 7 7 !0 7 1 $ 1 J 7 7 9 7 12 7 tl

"""" y

Fig. 3. Sensor fault detection by minimization for � faults.

The numerical results of the example are presented in Table 2. On the left , there are the different sensor combina­tions then the sum sk is coming, and on the right side the different sensor faults are outlined. The table illustrates very clearly the high precision in finding the location and the amounts of the simulated faults.

Table 2 Sum sk and � sensor faults

Sensor-Combi nat i ons sk Sensor Faul ts

7 8 0.00000013 -2 .000081 +3 .000499 6 7 0 . 00045043 - 1 . 651909 -2 . 236190 7 10 0 . 001 13012 - 2 . 1 77355 +2 . 451460 3 7 0 . 001 15779 +3 . 620769 -2 . 103500 5 7 0 . 001 19201 +0 . 412501 - 1 . 859 1 1 7 7 9 0 . 001 19203 -2 . 109456 - 1 . 063221 2 7 0 . 00130122 -0 .432868 -2 . 151290 7 1 2 0 . 00136680 - 1 . 924538 +0 . 536697 4 7 0 . 00151212 - 1 . 068876 - 2 . 066185 7 13 0 . 00152322 - 2 . 190137 - 1 . 200646

The second example is figured out in Fig. 4 and Table 3. It is a simulation of three sensor faults: 2 % in sensor 4 (static pressure between the low and high pressure compressor), -3 % in sensor 8 (static pressure behind the low pressure tur­bine) and -2 % in sensor 9 (temperature behind the low pressure turbine). The composition of the Figure is ana­logous to Fig. 2 and Fig. 3. The main result is the fact that also for three sensor faults the locations as well as the amounts are detected by the algorithm exactly. This is additionally confirmed by Table 3, where the numerical results are placed and which is prepared similar to Table 2.

• 1'1 "' ., "' ID "' .. .. .Ill

2D

1D "' ·1D

·2D

·.Ill .... _,,., ... ·7D

Diop::r;is Prcqan lti S. H 1!!ll Wa 54= 2% SB= -3% 59= -2% [):le Moo Fit 24 16:1753 19.lZ

r-s._ ..,.__ --Vo

� a rn a I � I 1 � .� 1 1 1 1 � I I 'I I H r-I I I 1a . I I I I

-:ii ,a-'

e 1 1 1 1 � .

II � I ' '6 I I

7 10\J ! IO\J 2 10tJ 101213 4 8 9 • IHJ ! !013 3 1013 ! a t 5 1013

\l'l

Sirs:< y

Fig. 4 . Sensor fault detection by minimization for three faults.

Table 3 Sum sk and � sensor faults

Sensor Comb i - sk Sensor Faul ts nations

4 8 9 0 . 000000 1 1 +2.007988 - 2 .996289 -1 .999680 4 10 13 0 . 00003569 +0 . 786854 - 2 . 819230 +2 . 086968 1012 13 0 . 00005023 - 3 . 211847 +0 . 508773 +2 . 096190 6 10 13 0 . 00006481 - 0 . 19821 2 - 3 . 265136 +I . 956928 2 10 13 0 . 0000871 7 - 0 . 4 16164 - 2 . 738580 +2 . 168421 3 10 13 0 . 00009184 +0. 980457 - 2 . 640593 +2 . 036897 8 10 1 3 0 . 00012323 +0 . 582361 - 3 . 351912 +I . 944332 6 8 9 0 . 00013277 - 0 . 785693 - 3 . 969879 - 1 . 671 529 7 10 13 0 . 00014417 +0 . 805204 - 2 . 725881 +1 . 896259 5 10 13 0 . 00017490 +0 . 735180 - 2 . 382746 +1 . 925039

THE EXPERT SYSTEM XSD

The knowledge based procedure described above and the analytic algorithms are realized in the expert system XSD (E�pert System for S.ensor Fault .Qetection). This expert system is implemented on a SUN-workstation under UN IX in the development environment N EXPERT-OBJECT. This environment, basing on the programming language C was chosen. because it makes the implementation of own pro­grammes possible, which are particularly written in C, and by this the communication with the environment, that means the data exchange by the different interfaces, is made easier. A further advantage is based on the fact that the expert system, developed on a fast and efficient workstation, can be transferred without great expenditure because of its com­puter independent codes (ASCII-files and C source code) on PC's which are normally used in industry.

The expert system starts, as depicted in Fig. 5, after the be­ginning with the initiation of the data and the different interfaces. After reading the measurement quantities the state variables a re calculated from the system equation, gi­ven by Eq. (4). After passing the rules of the expert system the inference machine gives a ranking of possible fault affect­ed sensors and the user is asked, whether he wants the application of analytic algorithms for a more exact detection . These algorithms deliver the results i n form of tables, from which possible sensor faults can be extracted declared by its location and amount. Furthermore, the expert system yields

291

graphic representations. Basing on the results of the expert system the user is in position to make corrections on the sensor data, whereby the following diagnoses will become fault free. The whole procedure ist done in real time, which is necessary for its use in practical applications.

EXPERT SYSTEM for SENSOR FAULT DETECTION

x s D

I Me•eurement V•lu•• I T

Knowtedg�. I lnld.llzotlon I I Stmte Value• I Base (! . g Ill yt

I Rules :=j Inference Mechine \

I I Rooking by

Certltudefactor

I Pattern H Correlation I

H Minimization I ' I Results I I Graphics I

Fig. 5. Principal flow chart of the expert system XSD.

USE OF UNCERTAIN LOGIC

Because of uncertainties in the measurement device all diag­nosis data are affected with faults which can be interpreted by fuzzy logic. These faults a re transferred to the states. Additionally, there are further uncertainties in the system matrix Q basing on defects in the modeling. Therefore a possibility is considered to describe the relations between the state variables and the measurement quantitites by u ncer­tain logic.

The state xi ; i = 1, . . . • n is a function of the different measurement quantities y .; j = 1, . . . , m or in the usage of the fuzzy logic (Zimmer�ann, 1988) the state belongs to the measurement quantities Yf j = 1, . . . • m , such that

x1 • f[µY1 (x1 ) ,µY2 (x1 ) , . . • ,µym(x1 ) ] ; i • 1 , . . . , n ( 18)

is valid, where the µ �x-) are certain influence functions . . YJ I

bemg an uncertain measure of the dependence of xi(y .) . As shown in Fig. 6 for the state � of the LARZAC engin!. the influence function is chosen as a triangular function, where the slope of the triangle straight lines follow from the ele­ments q. · of the system matrix Q. The maximum value of l,J an influence is - as in the fuzzy logic used - set to 1. This means that large values q . . lead to a dependence x.(y.),

. . 1,J I J which 1s broad , and small values q. . have only a little 1,J dependence xi(Yj), which means in Fig. 6 only a narrow strip on the x2-axis. For the special example in Fig. 6 the measurement quantities y1, y2• y4. y5 and y11 influence the state �- By this, one gets the set

Xz • {µy1 <x2 ) ,µy2 <x2 ) ,#y4 (Xz) ,µy5 (xz) ,µy1 1 <x2) }. ( 19)

For the other states similar sets are held so that for all states the sets J{i; i = 1, . . . • n are available. Now, the set

( 20a)

is derived and by this this set

(�Ob )

Under the assumption th:?t the diagnosis is fault free i n the states, a measurement value with faults wili have a very high influence in the set 5{. which gives a criterion to separate this value from the others. The future work will be concentrated especially on this fact.

1.0 µY. µy µy4 µy 5 1 1 1 µy 0.9 I o.e 2

0.7 0.6

µ 0 5 � 0.4 0.3 0.2 0.1 0."._5 3 4 5

X2 [/.]

Fig. 6. I nfluence functions for a special state in the case of fuzzy logic.

CONCLUSIONS AND OUTLOOK

I n the paper presented knowle<!ge based pr�cedures in con­nection with model based algorithms are derived for the sen­sor fault detection imbedded in the general diagnosis prob­lem for jet engines and gas turbine�. resp�tively. The algo­rithms base on a model of the engine. which comes from a thermodynamic cycle process calculation. For the know!edge based procedures different ways are offered alternatively. The future work will be focussed on fuzzy methods and on instationary models in order to investigate the jet e�gine !n flight. In this direction, there is already much experience in the institute as can be seen from the work of Willan (1990) and Schmidt (1991). Willan developed an expert system for the diagnoses in the de�riefin� of a Ger!flan !ORNADO squadron, and Schmidt investigated the mstat1onary heat transfer in a helicopter engine for load chan�es a�d gave first results to describe these phenomena analytically in �he sense of Eq. ( 4 ). It is intented to have an expert system. improved by some analytic methods in the near fut�re, which 1? a ble to deliver a full diagnosis in the state variables and m the measurement faults as well. Furthermore the diagnosis will be extended by this expert system on instationary operating conditions.

292

REFERENCES

Barschdorff, D. (Ed., 198�). Verfahren und Systeme zur technischen Fehlerd1agn05e. GMR-Bencht 1 zum Ausspra.:hetag "Diagnosesysteme" . :...angen.

De Hoff, R.L., and W.E. Hall {1978). Advanced f�ult de-. tection and isolation methods for aircraft turbine engines. Office of Naval Research. Report ON!t-CR-215-245-1, Arlington, USA

Fiedler, K., and R. Lunderstaedt (1985). Zur systemtheoretischen Diagnose von Strahltriebwerken. A m i i run h ik t 33, 2"l2-279, 313-317.

Hetzheim, H. 1990 . Wissensbasierte Diagnosesysteme u nter Ausn:itzung von Wahrscheinlichkeit und Unsch:ir:fe. Messen-Steuern-Regeln 3�, S. 73-76.

Lunderstaedt, R., and K. Fie ler (1988). Gas path Modeling, Diagnosis a.nd S'ensor Fault Detec­tion. AGARD-Conference Preprint Nr..448. Ouebe�. Ca.

Lunderstaedt. R. (1988). Zur Kompensat1on systemat1scher Sensorfehler. A tom ti iePJngstechnik. c:t 36, 282-289.

Lunderstaedt R.. 1990 . Zur Elimination von Sensorfeh­lern und Beseitigung von Modelldefekter.. Automatisie­rungsstechnik. at 38, 223-230.

Lunderstaedt, R. , a nd Th. Hil!emann (�991). Model Based Diagnosis of Gas Turbines Including Sensor Fault De­tection. P reprints I FAC-Symoosium SAFEPROCESS' 91. Baden-Baden.

Roesnick. M. (1984). Eine system�hE?ret!sche L!jsu�g des Fehlerdiagnoseproblems am Be1sp1el emes Flu_gtneb­werkes. Dissertation. Department of M�cha.mcal En ineerin German Armed Forces Umvers1t , Hamburg.

Schmidt, !(,�J. 1991). Experimentelle und theoretische Unterst.ichungen zum instation:iren Betriebsverhalten von Gasturbinentriebwerken. Dissertation. Department of Mechanical Engineering. German Armed Forces University. Hamburg.

Urban, L.A. (197_2). Gas-P�t�-Analysis _ap�lied turbine engine cond1t1on monitoring. AIAA-Paper 72-1082.

Urban, L.A. (1980). Gas-Path-Analysis - A tool for engine condition monitoring. 33rd Annual International Air Safet eminar, Christchurch, N .Z.

Willan , U . (1990 . I ntegration von mode!lb�zoge�er und wissensbasierter Diagnose am Beisp1el emes T ur�o­flugtriebwerkes. Dissertation. Departm.ent ?f Mechanical Engineering, German Armed Forces Umv��s1ty. Ha!11burg.

Zimmermann, H.J. ( 1987). Fuzzy Sets. Dec1s1on Making and Expert Systems. Kluwer Academic Publishes, Boston .

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

TOWARDS A GENERAL MULTI-MODEL-BASED METHODOLOGY FOR DIAGNOSIS SYSTEMS

C. Badie*, C Castel* and 0. DufTaut••

*CERT-DERA, 2 Avenue Edouard Belin, BP 4025, 31055 Toulouse Cedex, France **ACT/A, 4 Chemin de Pouvourvil/e, BP 4215, 31432 Toulouse Cedex, France

ABSTRACT

The paper concentrates on a Petri-net approach to fault diagnosis. The framework which is proposed allows the preconditions, logical links and mutual influences of the activities and states of functions and equipments to be naturally described, and a simulation-based fault isolation reasoning to be im­plemented. It is also a basis for a multi-model-based approach, since Petri nets and behavioral models can be easily connected. The framework is illustrated with the example of a pneumatic suspension system.

KEYWORDS

Diagnosis - Models - Multi-model-based diagnosis -Petri nets - Simulation - System failure -

INTRODUCTION

Dealing with diagnosis problems means defining what kind of information is necessary and how it has to be organized, according to the kind of result expected. The approach which is outlined in this paper is a generalization of dedicated solutions we proposed for two aeronautical applications, namely the validation of aircraft flight recorders (Badie and others, 1992) and the diagnosability assessment of helicopter sys­tems (Badie and Castel, 1991). Both of them proved the need for modeling system activities and states, involving functions and equipments, and for clearly describing influences. Moreover, as one of our con­cerns is to perform on-board (i.e. on-line) diagnosis, the idea is to concentrate on a Petri net approach, which has proven to be very valuable in modeling, analysis and on-line monitoring of systems. What is proposed therefore is to extend this concept, i.e. to use Petri net - based models of normal and abnormal behaviors of functions and equipments as a starting point for a general fault diagnosis reasoning.

This work can be connected with the extension of Petri net controllers for error .recovery in manuf ac­turing systems (Zhou and Dicesare, 1989), the appli­cation of Petri nets to safe process control, involving

fault detection and isolation via dedicated test tran­sitions (Dhalluin, Gabillard and El Koursi 1987) and event-graphs used as a representation of procedural knowledge in the diagnosis/recommendation level of a real-time expert system (Benini and others, 1991; Gallanti and others, 1985).

A PETRI NET BASED MODEL FOR FAULT DIAGNOSIS

On-line Petri net - based diagnosis means supervi­sion, i.e. real-time simulation of the system ope­ration: it can be performed either within the Petri net itself, through abnormal states marking (Dhalluin, Gabillard and El Koursi 1987) , or through a two-step process involving fault detection by discrepancy ob­servation between the current marking and the actual state of the system, and fault isolation via an off­line simulation-based reasoning. What is emphasized here is Petri net design and use for fault isolation.

A Petri net (Peterson, 1981) is a directed graph with two types of nodes - places and transitions - con­nected by directed arcs. Places are linked to system activities or partial states (e.g. chassis raising, elec­trical supply on) and transitions correspond to instan­taneous events (e.g. beginning or completion of an activity). The presence of a token in a place (marked place) indicates which activities are in progress or what the states of the corresponding devices are. The set of all marked places (current marking) defines the state of the whole system. The marking of the Petri net evolves through transition firing: a transition is fired as soon as all its input places are marked and the corresponding event occurs; the output places are then marked.

The basic knowledge we use involves first, a des­cription of normal and abnormal states that can be reached by functions and equipments and second, a description of the possible state changes, which is not far from a planning-like approach to diagnosis

(Pastor, 1991). The main interest is the explicit modeling of preconditions, either for normal or faulty states.

293

Consequently, the model we propose is based on a preliminary analysis of the functions and equip­ments involved in the system and of the possible corresponding failures at a given level of descrip­tion. This knowledge essentially stems from system specifications (e.g. SADT-based specifications (IN­RIA, 1986)) and FMEAs - Failure Modes and Effects Analysis (Jordan and Marshall, 1972). It is organized as follows:

• Each function is associated with a Petri net whose places describe normal and abnormal states. Some of these states are observable: normal states de­liver normal observations whereas abnormal states deliver symptoms. The transitions may be associ­ated to control orders, state changes of the equip­ments involved in the function achievement or state changes of other functions in the system. They may be also associated with external events (e.g. environmental interactions).

• Each equipment involved in the function is also as­sociated with a Petri net whose places describe nor­mal and faulty states. Usually these states are not directly observable (unless tests are performed). The transitions are linked to events, which are most often related to physical variables (e.g. a variable exceeds a given threshold).

The resulting model is a set of connected Petri nets, highlighting both the logical linking of states or ac­tivities within functions and equipments, and the in­fluences between those states and activities. This or­ganization is illustrated on Fig. 1 .

Function G is achieved through equipments 1 and 2. The preconditions for G achievement are therefore "function G idle", and "equipments 1 and 2 OK". Function H is achieved only if equipment I fails. Maintenance actions MA 1 and MA2 are introduced so as to keep the reversibility (reinitializability) pro­perty of the Petri nets.

A FAULT ISOLATION REASONING

The model is a basis for the following fault isolation reasoning:

• Fault detection is assumed to have been performed, either through on-line marking of abnormal states (which implies that the relevant variables are mo­nitored) or discrepancy (i.e. inconsistency) obser­vation between the marking and the state of the actual system. As fault isolation is obvious in the first case, reasoning only deals with the second one, and is performed off-line (possibly with the system still operating if it is fault-tolerant).

variable v 1 exceeds

threshold thl

equipment 1 failure

M.A.l

equipmenJ 2 breaks down

equipment 2 failure

M.A.2

or equipmenJ 2/ailure Q function G non achievement j_ equipmenJ 1 OK / ""-·., .. / and equipmenJ 2 OK

' ./ ............ _,./ ..... _·-............... ,. .. .-'"

function H idle

equipmenJ I failure / function H achievement

equipmenJ 1 OK ? Fig. 1: A Petri net - based

model of functions and equipments

• The observable states of the system after detection (namely symptoms and possible normal observa­tions) are memorized. As an example, let us consider the following obser­vations: "function G non achievement" (symptom) and "function H idle".

• Fault isolation is a return to consistency, through fault hypothesis setting. What is looked for here is a minimal explanation to observations, which is performed through a simulation of the Petri nets from the initial marking and under hypotheses of abnormal events or states. If the places marked at the end of the simulation match all the memorized states, the hypotheses hold, i.e. are consistent with the observations; therefore, faults are identified. Otherwise, other hypotheses have to be contem­plated.

294

Example: the simulation starts with the initial marking of Fig. 1. "Control order On" of func­tion G is supposed to have been fired, therefore "function G achievement" is marked.

First hypothesis: "component 1 failW"e"; the corres­ponding transitions of function G and H are fired, therefore "function G non achievement" and "func­tion H achievement" are both marked, which does not match the observations; this hypothesis does not hold. Second hypothesis: "component 2 failW"e"; the corresponding transition of function G is fired, and only "function G non achievement" is marked; this hypothesis holds.

This Petri net approach to diagnosis has got several major advantages:

• it allows the functional aspect of a system, which is essential to the mission and to the user, to be emphasized,

• equipments are naturally linked to the functions they are involved in,

• preconditions, states and state changes are natu­rally described,

• influences, such as in (forasso and Console 1989), between functions and between equipments and functions are taken into account within a well­defined framework,

• as it is explained in the next section, it is a basis for a multi-model-based approach to fault diagnosis.

TOWARDS A MULTI-MODEL-BASED MEIBODOLOGY

General

The Petri net approach to fault diagnosis can be easily combined with numerical or qualitative behavioral models (e.g. electrical, thermal, mechanical models), which are necessary to refine diagnoses. This is particularly worthwhile when operational (i.e. func­tional) failures have physical consequences or con­versely (e.g. pump stalling leading to fuse blowing (Hunt and Price 1991)).

The organization which is contemplated is a joint use of both types of models, with information being sent from behavioral models to Petri nets transitions and from Petri nets places to behavioral models. Rea­soning on behavior can therefore lead to transition firing, whereas a token in a place can trigger a given behavioral model. This is illustrated with the exam­ple of a pneumatic suspension based on that used in the automotive industry.

The Pneumatic Suspension System

The pneumatic suspension system allows the chassis of a vehicle to be set at a given height. It mainly con­sists of two electro-valves: electro-valve 1 is linked either to a compressed air reservoir or to the open air, whereas electro-valve 2 transmits the air coming from electro-valve 1 to the suspension bellows. The chassis height can be varied with a remote control by operating the ''raising" and "lowering" push-buttons, which respectively result in air being admitted in or vented from the bellows. The main raising and lo­wering function can be split up into a control sub-

function, two electrical and pneumatic supply sub­functions.

The comected Petri nets described here are a res­tricted and simplified part of the entire functional model of the system (see Fig. 3).

An electrical model of the system is also available, which gives the possible effects (through variables such as tensions and currents) of electrical equip­ments failures. Effects on variables are then trans­lated into aggregated states that can be taken into account by the functional model (Fig. 2)

El.E.Cl'RICAL MODEL FUNC1lONAL MODFL

Ohm's law, node law, •••

� i Translation

V1tiables: V,I, .•• .------ States

Fig. 2: Linking functional and behavioral models

As an example, let us consider the case of the chas­sis not being able to be raised, the lowering function being OK. Let us assume that an electrical failure occured (e.g. failure of the connection between the source of tension and the electrical supply of electro­valve 1). Under this hypothesis, the electrical model concludes that there is no current and no tension across electro-valve 1 . This is translated into the ag­gregated state "open circuit 1 ", which results in the corresponding place of the functional model being marked. If the "raising" function is considered, places "EVl not supplied" and "EV2 live" are marked, and con­sequently, places "EVl inoperative" and "EV2 un­locked". Therefore "chassis lowering" is marked. If the "lowering" function is considered, EVl stays idle whereas "EV2 live", "EV2 unlocked" and "chas­sis lowering" are marked. The electrical failure is an explanation to the symp­toms.

CONCLUSION

What is outlined in the paper is a Petri net framework for fault diagnosis. The main advantages of this approach are the following:

• as an extension of the standard use of Petri nets in modeling and monitoring, it is a sound basis for on-line diagnosis,

• the activities of a system, the functional aspects, so as their links with equipments, are naturally taken into account; furthermore, influences can be clearly described,

• the Petri net framework is a starting point for a multi-model approach to fault diagnosis, as it can be easily combined with other types of models, such as behavioral models.

295

An object-oriented implementation of this framework has been realized. Our future research will concentrate on the following points:

• the refinement of the fault identification reasoning, especially in the multi-model case (systematization of information exchanges), and extension to multi­ple failures (the possibility of a de Kleer-type (de Kleer and Williams, 1987) reasoning will be stu­died),

• how to take advantage of theoretical properties of Petri nets in fault diagnosis,

• how to extend the framework to test-related pro­blems: tests modeling, best setting up of test points, assessment of system testability.

REFERENCES

BADIE, C. and C. CASTEL (1991). Tests integres des systemes avioniques sur helicopteres Rapport '!1_0 3{7778 CERT-DERA Aerospatiale, Dec 1991

BADIE, C., A. BUCHARLES A., C. CASTEL, G. CAUBET, P. FERRETTI and M. PORTAL (1992). Automatic validation of Flight Data Recorders European Telemetry Conference ETC92, Garmisch-Partenkirchen, May 1992

BENINI, M., M. GALLANT! and R. TARLI (1991). An intelligent on-line diagnosis system for cy­cle chemistry control in thermal power plant F.u­ropean Conference on Industrial ApplicationSOf Knowledge-based Diagnosis, Milano, Oct 1991

DHALLUIN, J.F., R. GABILLARD and M. EL KOURSI (1987). Application des reseaux de Petri

a la commande-controle de processus en securite APII n°21, pp 531-551

GALLANT!, M., G. GUIDA, L. SPAMPINATO and A. STEFANINI (1985). Representing proce­dural knowledge in expert systems: an applica­tion to process control Proceedings UCAI 1985 pp 345-352

HUNT, J. and C. PRICE (1991). Diagnosis of electromechanical subsystems using multiple models Second International Workshop on Prin­ciples of Diagnosis, Milano, Oct 1991

INRIA (1986). SADT: une methode d'analyse des systemes de production

JORDAN, W.E. and G.C. MARSHALL (1972). Fai­lure Modes, Effects and Criticality Analysis An­nual Reliabilitity and Maintainability Symposium, San Francisco, Jan1972

de KLEER, J. and B.C. WILLIAMS (1987). Diag­nosing multiple faults Artificial Intelligence, Vol 32, Nr 1

PASTOR, P. (1991). Modele de changement d'etat pour le diagnostic de pannes DEA ENSAE, Toulouse Sept 1991

PETERSON, J.A. (1981). Petri net theory and the modeling of systems. Prentice Hall Inc.

TORASSO, P. and L. CONSOLE (1989). Diagnos­tic problem solving. North Oxford Academic

ZHOU, M.C. and F. DICESARE (1989). Adaptative design of Petri nets controllers for error recovery in automated manufacturing systems IEEE SMC, Vol 19, Nr 5

296

EVJ idle

EVl eledrlcal supply

EVl idle

EVl live

Open circ11il 1 / EVl not supplied

.i.. M.A.

EVl equipment

EVl connection to open air

EVJ live / EVl connection to air reservoir

EVJ not supplied/ EVl inoperative

.l M.A.

EV2 idle

Raising/Lowering function

EVJ connection to air reservoir

AND EV2 unloclced ' Chassis raising

EV2 locked OR EV2 inoperalive

.t M.A.

EV2 electrical supply

EV2 idle

HraisingH OR HloweringH

EV2 live

Open circuit 2 / EV2 not supplied

M.A.

EV2 equipment

EV2 locked

EV2 live / EV2 unlocked

EV2 not S"fJplied/ EV2 inoperative

..t.. M.A.

Chassis lowering

/ EV2 locked OR EV2 inoperalive

Fig. 3: The pneumatic suspension system - Functional model

297

Copyright © IF AC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

AN ADAPTIVE DECISION SYSTEM USING PATTERN RECOGNITION

B. Dubuisson

U.RA. C.N.R.S. Heuristique et Diagnostic des Systemes Complexes. Universite de Technologie de Compiegne. France

�- Pattern recognition is a well adapted set of methods in order to solve diagnostic problems. One of the main problem of diagnosis is to have a set of data corresponding to the different possible system faults in order to learn the decision rule. This set being not generally complete, we propose a decision rule based on the concept of reject : this rule does not need a complete learning set at the beginning because the learning is done iteratively when observing the physical system. The reject concept is divided into two possibilities : ambiguity reject and distance reject. Each one is adapted to a different situation. We develop main differences between these two rejects and exhibit their interests. At last, some methods are given about removing a reject decision.

Keywords. Diagnosis ; pattern recognition ; learning ; reject decision.

INTRODUCTION

There are many methods one can use to solve a diagnostic problem. All of the methods are model based, that means one needs some knowledge about the physical system on which the diagnosis is done, but the model is different from one method to another of the problem. This paper is based on a pattern recognition approach. The model for this method is not the same as the one is used in automatic control, i.e. a state variable model, but a statistical one using a data basis recorded on the system. In a first part, we present how pattern recognition can solve a diagnostic problem ; then, we exhibit general problems which arise in diagnosis. In a third part, a modified decision rule will be proposed in order to solve these problems. Properties of this rule will be given and, then, a complete adaptive system will be presented.

DIAGNOSIS AND PATTERN RECOGNITION

A decision system can be built by using pattern recognition, so it is a diagnostic problem. Let us consider that the state of the observed physical system is characterized by d features or parameters. This set of parameters will be called the pattern vector x. Its choice is a difficult problem, linked with the knowledge about the physical system one has studied. Then, let us also suppose that the physical system may be in M states : the problem of the diagnostic system is to recognize a state, using the pattern vector observed at time t. To do the link with pattern recognition, each state is called a class and the problem becomes a classification problem : a lot of useful decision rules exist in statistical pattern recognition to classify the patterns. The general problem can be written as follows : knowing M possible classes ro1, ro2, . . . COM and observing a new vector x, decide upon the class it comes from. The best rule is the Bayes optimal rule but it needs a complete knowledge about the probability laws

299

to perform the classification. Let us call P(roi) the

a priori probability of class COi and f(x I COi) (i = 1, . . . , M) the probability law of vector x in class COi. We have the relation :

M L, P(roi) = I i=l

( 1 )

We decide upon a set of costs C(COi I COj) (cost associated to the decision COi when x is a vector

from COj (i = 0, 1 , ... , M; j = 1 , . . . , M). If no decision is more important than another one, one chooses the { 0, 1 } costs:

C (Oli I Oli) = o c (COi I COj) = 1

i = l , .. . , M (2) i, j = I , . . . , M i if' j (3)

This classical rule is given by :

x is associated with COi if P(roi) f(x I COi) = Maxj=l , M P(COj) f(x / COj) (4)

When these probability quantities are unknown, many non-optimal rules have been proposed in the litterature (see for example Fukunaga, 1990). The main one is the k-nearest neighbor rule : a new vector is associated whith the class which is in the majority among its neighbors. But in this case, it is necessary to dispose of samples of each class in order either to learn the parameters of the decision rule or to find the neighbors of the observed vector. This set of data is usually called the learning set. The more representative it is, the more pertinent the decision rule is. Pattern recognition has allowed to solve many diagnostic problems on different physical systems (Gonzalez, 1977, Dubuisson, 1990a).

USUAL PROBLEMS IN DIAGNOSIS

In practical applications, the number of classes or system states is unknown and any record about some states cannot be done. For example, because of security problems, it is unsafe to run the system under dangerous states, therefore no data from these states are in the learning set. Also, anyone would not like the process to work in an abnormal state because of bad production quality . . . So, in most of the cases, the learning set is only composed of some classes out of a set of possibilities. Another comment concerns the number of states or classes : this number is usually very important. Think, for example, of a transport system for which you want to build an on-board diagnostic system. This system can run (or cannot run) under a lot of different states : some of them are normal ones, some of them are abnormal. The number of states is very important and the discrimination problem becomes difficult because it needs samples from each class. Some ones propose to consider only two states : the normal one and the set of abnormal ones. With this simplification, the recognition of abnormal states is impossible and the accuracy of the diagnostic system is less. In order to conclude, a diagnostic problem is always difficult to solve because of the number of system states or classes and/or because it is impossible to record observations on some states : the learning set (i .e. the set of observations on each possible class) is never complete and it is impossible to discriminate using the usual rules. As we are interested in a pattern recognition approach, we have to modify the usual rules (4) in order to take into account the above mentionned problem.

DECISION WITH REJECT

The model is the following : • the pattern vector is composed of the d parameters considered as relevant to the problem, • each pattern class is associated with a different fault. Let us suppose we have to decide between M

classes WJ, coi, . . . WM in a d dimensional space, M is the number of known states for the observed physical system. Let us suppose the complete knowledge about the different probabilities : relation { I ) is still true. We will introduce a modified decision rule which includes two reject options : - the first one called ambiguity reject concerns points lying between classes, i.e. points which can be associated to more than one class. - the second one called distance reject concerns points which belong to another class which is not, at this time, included in the learning set. A new vector is said to be classified if it is associated with one of the M classes. So, one has to define a decision rule d(x) so that d(x) = i

means that x belongs to class Wi.

Ambiguity reject Let us consider the ambiguity reject. We add a new class wo to the M ones (Chow 1970) · this class is called the reject class.

·

We h�ve now to d«?cide among (M + I) classes and bulld up the decision rule d{x) so that :

d{x) = I x '.s assoc'.ated with w 1 } d(x) = 2 x 1s associated with w2

d{x) = M x is associated with WM

is classified

d(x) = b x is associated to wo

x

(5)

300

x is rejected (6)

To the costs given by (2) and (3), we add a constant reject cost Ca :

C (WO I Wj) = Ca j = ! , . . . , M (7)

Let us define the a posteriori density P(Wj I x),

P(Wj / x) = �(x I Wj) P(Wj)

L. f(x I Wi) P(Wi) i=l

(8)

The optimal decision rule corresponds to the rule for which the conditional error probability is minimum. It can be written :

d(x) = i X � Wj if

P(Wi I x) = Maxj=l,M P(Wj I x) � I - Ca (9)

d(x) = 0 x � wo if

1 - Ca > MaXj=J,MP(Wj I x) ( 10)

It is easy to establish that an ambiguity reject option cannot exist if :

( 1 1)

This decision rule separates the representation

space 0 (Rd :2 0) into (M + 1 ) areas Oi (Fig. I ):

ni = ( x : MaXj:J,M P(Wj / X) = P(Wj / X � I - Cal

i = l , M ( 1 2)

0o = ( ( x: Maxj=l.M'P(Wj I x) < I - Ca ) ( 13)

Fig. 1 . Decomposition of the representation space.

In the case where the two known classes obey a Gaussian law with respective means M1 and M7,

and respective covariance matrices :E1 and :I;i, the

logarithm of the likelihood ratio, A(x), is given by :

A(x) = f(x/w1)

f(x/coi) ( 14)

This expression has to be compared to two thresholds (Dubuisson, 1 992):

A1 = Log{P(0>2) �} P(w1) Ca ( 16)

(17)

Figure 2 represents the case of two Gaussian classes in R (the two Gaussian laws have the same variance): the reject area is situated "between" the

two acceptance areas !21 and !22.

- �or probability

Fig. 2 Ambiguity reject with two gaussian laws in R .

It is well known that greater is the reject probability, smaller is the error probability .

Distance reject This ambiguity reject is not sufficient to solve a diagnostic problem (Du buisson, I 990b), particularly when the number of possible classes is not known as explained above. In fact, a new vector can be observed in an area of

the representation space n where no vector of the learning set were previously observed. It means that this new vector might be an element of a new class, for which there is no information at this observation time. This second kind of reject, that we have called "distance" reject, has been introduced to avoid to associate a vector, far from previous analyzed areas, with one of the M classes ; if we had used usual statistical decision rule, even with an ambiguity reject option, this point would be associated with one of the M known classes and an error would be made (Fig.3).

Fig. 3. Problem of points far from the learning set The distance reject being activated only for points situated "far from" the known classes centroids, we propose to base this reject on a simple threshold upon the probability law f(x) of the observed point x. A point x will be distance rejected if:

f(x) < Cd ( 18)

Cct is called the distance reject threshold. So, two rejects have to be included in the decision system : - ambiguity reject, - distance reject. Figure 4 gives an example of the different regions by considering two Gaussian classes in R.

301

.!lo lit 6I] A.mbipity rojoct Fig. 4. Comparison of the different reject options.

Some properties can be exhibited (Dubuisson, 1992) : - greater Cct is, greater the percentage of distance rejected points is, whatever the value of the distance between classes is. - if the value Cct is big, the ambiguity reject may be null when the classes are close together.

- error probability and correct classification probability have opposite variation. - greater Cd is, smaller the error probability is. We have described a decision rule with two kinds of reject in the parametric case, i.e. when the different probabilities are known. It is also possible to develop the same kind of rules in the non parametric case, using the K nearest neighbor rule (Dubuisson, 1 992). A learning set, that is a set of samples from each a priori known class, is now necessary but this set have not to be complete.

IMPROVEMENT OF THE DIAGNOSTIC SYSTEM

The reject points must be analysed in order to improve the a priori knowledge. But we must distinguish ambiguity rejected points from distance rejected points.

Ambiguity rejected points

On one hand, we have to decide about points which have been ambiguity rejected : they must be assigned at the end to one of the M classes in order to take a decision on the process. In order to do this classification, other informations must be added to the one coming from the observed point at time t ; so we propose to use a sequence of decision and to analyse it. Let us consider a sequence composed of (n + m + n') points : the n first points have been associated

with COj, then m points have been ambiguity rejected and the last n' points have been associated

with COj (j may be �qua! to i) ; Ienght �f t�e sequence is m + n + n . One can then modehze m the representation space this sequence of points : using the n first points, the parameters of a chosen model can be identified. Using this model, a prediction system can be built corresponding to the sequence of m points, using, for example, a Kalman filter or an extended Kalman filter (Frelicot, 1 992) : when the error between predicted and observed point is below a threshold,

the corresponding point is associated with Wj, otherwise this point remains rejected. We do the same thing in reverse time, using the points of the second sequence of n' points. After these two computations, only a few points remained ambiguity rejected, and so one would rather not take a decision about of them, because their information does not seem sufficient enough. A last possibility, we have tried, is to add expert rules to the decision system for removing this ambiguity. Of course, this expert system is dependent on the process.

Distance rejected points

Treatment is different for points that have been rejected by a distance reject because these points are far from the area containing the learning set.

These distance rejected points correspond to new classes or states. So, we propose to use a clustering algorithm in order to analyze them and to exhibit these new states. Any clustering algorithm will exhibit new classes by analysis the inter point distances : a best solution will be found using a criterion, based generally on the distance between points in a class (minimization) and the distance between new classes (maximization). Many cl ustering algorithms can be found in the litterature, see for example (Diday, 1 973), and the solution of a clustering algorithm is not unique : so, the obtained solution may correspond to non physical system states and it must be validated by analysis from a physical point of view. This part of the method, which is a real adaptive part, must be done all the time during the decision process. In fact, the new M' exhibited classes have been created after the analysis of 1 distance rejected points : it is a partial information. Then, the decision system uses (M + M') classes and new observed points have to be associated with one of the (M + M') classes or rejected. Suppose l' new decisions have been taken. According to these l' new decisions, the geometry of the M' classes may be modified and some classes among these M' ones have to be merged or splitted because the information on them increased. After this analysis, the decision system is composed of (M + M') classes and the previous decision rule is modified in order to take them into account. A new observed vector x can be - associated to one of the (M + M') classes, - ambiguity rejected if it is located in a region situated between two (or more) classes, - distance rejected if it is located far from the region where the samples of the (M + M') classes are situated.

CONCLUSION

The complete adaptive system is indicated in figure 5.

Fig. 5. General scheme of a diagnostic system.

The advantages of such a system are : - the ability of learning new states of the physical system, and so, we are not limited to two states (normal and abnormal), - the ability to decide completely about a new point by using past and future infonnation. This kind of decision system has been tested on differen t physical systems for different applications. I ts adaptive property gave very interesting results for physical systems, on which the normal state was only known.

REFERENCES

Diday, E., J. C. Simon ( 1 976), Cluster Analysis in Digital

Pattern R e cogn i t i o n , K . S . Fu (ed.), Springer-Verlag,

Berlin. Dubuisson, B . ( 1 990a), Diagnostic et reconnaissance <les

�Hermes, Paris. Dubuisson, B. ( 1990b), Decision with reject options, Sigrul1

Processing Y · Theories and Applications, L. Torres, E.

302

Masgrau, M.A. Lagunas (eds), ed. Elsevier Science

Publishers, pp. 1 7 1 5- 17 1 8. Dubuisson, B., M. Masson, ( 1 992), A statistical d e c i s i o n r u l e

with incomplete knowledge about classes, � Recognition. To be published. Chow, C.K. ( 1970), On optimum recognition e r r o r a n d r e j e c t

tradeoff, IEEE Trans. on Information Theory. IIJ..n. 41-

46. Frelicot, C., B. Dubuisson ( 1 992), K-step ahead prediction in

fuzzy decision space, IEEE International Conference on

Fuzzy Systems, FUZZ-IEEE'92, San Diego. Fukunaga, K. ( 1 990), Introduction to statistical �

recognition, Academic Press, San Diego. Gonzalez, R.C. , L.C. Howington ( 1 977) , Machine

recognition of abnormal behavior in nuclear r e a c t o r . I E E E

Trans. on System Man and Cybernetics. l.Q, 717-728.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

INTELLIGENT REAL-TIME CONTROL OF A MULTIFINGERED ROBOT GRIPPER BY LEARNING

INCREMENTAL ACTIONS

K. Kleinmann, M. Hormel and W. Paetsch

Darmstadt University of Technology, Department of Control Systems Theory and Robotics, Darmstadt, Germany

ABSTRACT Learning control systems are expected to have several advantages over conventional approaches when dealing with complex, high-dimensional processes. One example is the task of controlling grasping operations of a multifingered, mul­tijoined robot gripper, which has been designed and implemented at our robotics lab (the Darmstadt-Hand) . The Advanced Gripper Control with Learning Algo­rithms -AGRICOLA- presented in this paper is able to maintain a stable grasp even if disturbances are applied. Also it works for objects of different sizes for which the grasping has not been learned. Compared to the conventional stiffness approach the performance of the learning system is equal but the design is much easier, since less knowledge about the gripper-hardware has to be taken into account . The main part of the learning control loop is an associative memory storing the grasping behaviour as determined by the choice of an objective function.

KEYWORDS high-dimensional nonlinear process, stable grasp, object manipulation, associative memories, learning control loop

INTRODUCTION

Within the last years industrial robots played a major role in industrial automation and their increasing flexibility showed new ways for auto­mated assembly. In order to improve the ma­nipulation capabilities of todays robots several dextrous hands have been developed as research tools.

In contrast to standard robot effectors like e.g. two-fingered grippers the multifingered robot hands are able to grasp a large variety of differ­ently shaped objects and to make small changes to orientation and position without moving the whole manipulator. Thus a robot equipped with it operates much more flexible and is able to imitate human dextrous manipulation. Ne­vertheless, the increased flexibility is accompa­nied by an increased complexity of the control system, since these grippers are highly nonlin­ear systems with a large number of inputs and outputs. The implementation of conventional control algorithms (e.g. Salisbury and Mason

303

( 1 985)) requires detailed knowledge about me­chanical design and the dynamics of the grip­per in order to determine precompensation fac­tors for the decoupling of position- and torque­control loops. On the other hand learning con­trol loops have proven to be applicable for the control of nonlinear unknown or only partially known systems. Therefore a gripper control sys­tem has been designed at which grasping oper­ations are controlled exclusively by associative memories and learning control loops (fig. 3) .

The paper is organized as follows: After a short description of the implemented gripper hard­ware we introduce to the neurobiologically mo­tivated Associative Memory System AMS , an enhanced version of the CMAC. Then the learn­ing coordination of the three fingered gripper by applying incremental actions is discussed and some results are given which have been car­ried out using the Darmstadt-Hand (Paetsch and Kaneko, 1990} . The paper concludes with some statements concerning the efficiency of the learning approach and further research topics .

BASICS

Gripper System

The 0-version gripper system used for the ex­periments was developed and built at the Tech­nical University of Darmstadt (Germany) . It is a three fingered tendon driven gripper with three joints per finger, see fig. 7. Each joint has a joint torque sensor as well as a joint po­sition sensor. Therefore joint torque and joint position control loops can be set up . A simpli­fied blockdiagram of a conventional joint torque control for one finger is shown in fig. 1 .

The input values are the desired joint torques and the output values are the actual joint torques. The innermost blocks represent the dynamic behavior of the DC-motors. The non­linear block in each joint control loop describes the effects within the bowden wires which under certain circumstances produces stability prob­lems in the control loops.

Because of the wire guiding within each finger there exist some coupling effects between the control loops. These coupling effects are rep­resented by the factors K,i; ( i, j E [1 , . . . , 3]) . The factor K,12 for example means that joint two will move (joint angle 8;2) when a motion in joint one (joint angle 8; 1 ) appears. A sec­ond type of coupling is a torque coupling repre­sented by the factor Kta2 for example, which means that if a certain torque is applied in joint three an additional joint torque, beside the regular torque transmitted by radial forces in the joint bearings, is produced in joint two be­cause of the wire guiding. The respective decou­pling blocks are represented by K11pij and K11tij ( i, j E [1 , . . . , 3] ) . Every conventional control has to decouple the joint loops because other­wise the fingers have a very different behaviour in the different directions in cartesian space due to the kinematic coupling effects. This would lead to large problems in stable grasping un­der disturbance forces because the finger motion due to a disturbance force is sometimes ampli­fied by the kinematic coupling effects so that the fingers can loose the grasped object . Therefore the coupling effects have to be considered.

One can see that the gripper is a comparatively complex, nonlinear process therefore being a

304

good canidate for applying a learning control scheme

Learning Elements

The Associative Memory System AMS dis­cussed below is a suitable system for storing a nonlinear input-output relationship and for a fast recall of the stored information. AMS is conceptually based on CMAC (Cerebellar Model Articulation Controller) , which was orig­inally proposed by Albus ( 1975) as a model for information processing in the human cerebellar cortex.

Figure 2: The basic mapping mechanism of AMS

AMS can be represented mathematically by the overall mapping (see fig. 2)

f : ! --+ ?:. (1)

where ! is an n-dimensional input vector (stim­ulus) and ?:. is an m-dimensional output vec­tor (response) . An encoding procedure selects a constant number of cells (memory locations) p out of p (p < p) memory cells depending on the contents of the input information !· The output value is determined by the mean value of the p selected memory locations (active weights) . During the learning phase (training) , the gen­erated output f. is compared with a desired out­put ?:.· The correction value (?:. - t.) can then be determined and added to each active weight .

Joint & environment

Figure 1 : Simplified blockdiagram of the joint torque control for one finger

One of the characteristics of the encoding mech­anism is that similar input vectors are mapped to similar sets of activated memory cells. This yields the AMS most fundamental feature of generalization, i.e. similar inputs generate sim­ilar outputs. The response for untrained stim­ul'ils vectors in the neighborhood of trained points is calculated by an automatic multidi­mensional interpolation over the output values of the trained points, for details see e.g. Tolle and Ersue { 1992) .

AGRICOLA ADVANCED GRIPPER CONTROL WITH LEARNING ALGORITHMS

In general a grasping operation can be charac­terized by the four phases approach, contact,

305

grasping and handling.

During approach, the geometrical data of the target are used for preshaping the gripper i.e. for opening the hand wide enough not to col­lide with the target. This involves the determi­nation of joint angles so that the finger tips can be located at prespecified points of a cartesian space:

(2)

where q represents vectors of joint angles and p the cartesian positions of the finger tips, respec:

tively. Also 1-1 represents a mapping from po­sition to joint coordinates, the so called inverse kinematics function.

We trained an AMS-block off-line using p as stimulus {!) and q as response (?:) vector. The

Context Layer (object form, object position, grasping strategy, ... )

Learning control loop LERNAS inverse kinematic

learning coord i n ation graap­preparat ion

learning Joint torque control

loop 8

learning Jo int torque control

loop 1 1---+-<1-1

motors 2 ----

motors 3 ----­rd palm qd

s t i f f d

Figure 3 : AGRICOLA - Advanced Gripper Control with Learning Algorithms

joint vectors q were selected by a random num­ber generator:- Based on the .forward kinematics relationship

f = l('l) {3)

which can be simulated easily, one can compute for each given q the corresponding p values. As a result of storing q and p in AMS, the asso­ciative memory learns the correct inverse kine­matics after sufficient training. By a recall, the AMS-block can subsequently be used to provide the joint angles for a given finger tip position within the workspace.

After the approach phase the hand is closed un­til all fingers detect a contact with the object . We implemented the detection by a continuous supervision of the joint forces.

During the grasping phase the fingers have to exert coordinated forces to the object in order to ensure a stable grasp. Stability with respect to the grasping operation is defined as keeping the object at rest with respect to the hand co­ordinate system and to move the object back to

306

its original position after it has been shifted due to external forces. The coordination mechanism is based on the learning control loop LERNAS {Ersue, 1984) , which imitates human problem solving behaviour. A blockdiagram of this im­plemented approach is shown in fig. 4.

It consists mainly of two AMS-blocks. Theo­retically other implementations of associative memories are also applicable, but as is shown in Mischo, Hormel and Tolle {1991) AMS has some major advantages with respect to convergence and computational complexity. Comparable to the conventional stiffness control approach one associative memory AMS maps joint position errors tlq to desired joint torques 'Ll · The op­timal control strategy is determined by plan­ning control actions using a nonlinear, unstruc­tured, predictive process model and evaluating the predicted reactions according to a certain performance criterion. The predictive model -giving an estimate of the joint positions q at .:.a time (k+l)To (To sampling time) in dependence of the desired joint torque values Ll and joint positions q at time kTo - is generated on-line by observ�g the input and output values of the

.,..

-

q ,

Figure 4 : Learning finger coordination (shaded boxes denote AMS-units)

gripper and storing this relationship in another AMS-block.

The continuous updating of the model mem­ory and the on-line optimization ensures that the system is able to follow slow time depen­dent variations in the process parameters. Ex­ternal forces as they occur during accelerations of the robot arm may be considered as fast changes in the environment . The learning con­troller can deal with this time variant behaviour by the implemented learning of incremental ac­tions which are added to the currently effec­tive values. In a conventional control loop a linear mapping from situations to incremental actions would lead to stability problems (inte­grating behaviour) . However, the implemented mechanism which is comparable to human con­trol strategies is nonlinear and stable! It should be pointed out that the controller-AMS could also learn absolute joint torques, but the incre­mental method improves the performance sub­stantially.

In fig. 5 the desired joint torques Li of one fin­ger during the grasping phase are shown. The

307

constant values after every manually applied disturbance prove the stability of the grasping operation .

0.4 joint 1 ;::; � 0.2 joint 2 Ill .§: :::: o joint 3 II

! -o.2 ... -0.4

sampled time

Figure 5 : The calculated joint torques of one finger (disturbances are manually applied)

Our learning approach is also suitable to learn the finger coordination for object manipulation . The handling task depends only on the trajec-

tory of desired joint angles. Figure 6 shows the actual joint positions and the desired joint torques during a peg-in-hole manipulation, re­spectively.

I o� I O ""-"�----�---�_,.��----��-"!

-G.l '---.......... �L--'-�L-.......... �L-.......... �L-.......... __, 0

0.27 ;; � 0.11 f ::; 0.00 • � 0 .s

-0.00

IO 190 240 sampled time

320 400

Figure 6: The joint positions and joint torques of one finger during an object manipulation

CONCLUSION

The presented learning gripper control system is able to achieve a stable grasp and to realize object manipulation.

In contrast to a conventional algorithmic con­trol scheme the implementation effort is less. Details about the gripper JTtechanics, internal parameters for decoupling or precompensation are not necessary. The learning system is able to learn a control behaviour specified by an ob­jective function in contrast to a heuristical set up of the stiffness matrix by trial and error. The

308

learning system stores the process behaviour in­stead of identification and modelling. The in­verse kinematic is learned off-line in contrast to the on-line computation of the algorithmic ap­proach.

The performance of the system can be improved by a VLSI-chip for AMS which is currently un­der development at our department . Further research activities are concerned with the ex­tension of the system to a learning hand-arm control.

REFERENCES

Albus, J . S . ( 1975) . A new approach to ma­nipulator control : The cerebellar model articulation controller (CMAC) . '.lransac­tions of the ASME, 97(9).

Ersue, E. ( 1984) . A new concept for learn­ing control inspired by brain theory. Pro­ceedings of the 9th IFA C World Congress, Budapest , Hungary.

Mischo, W. S . , Hormel , M . , and Tolle , H. (1991) . Neurally inspired associative memories for learning control : A com­parison. Proceedings of the International Conference on Artificial Neural Networks - ICANN91, Espoo, Finland.

Paetsch, W. and Kaneko, M. ( 1990) . A three fingered, multijointed robot grip­per for experimental use. Proceedings of the International Workshop on Intelligent Robots and Systems - IROSDO, Tsuchiusa, Ibaraki, Japan.

Salisbury, J . K . , and Mason, M. T. (1985) . Robot Hands and the Mechanics of Ma­nipulation. MIT Press , Cambridge , Mass . , USA.

Tolle, H., and Ersue, E. ( 1992) . Neurocontrol - Learning Control Systems Inspired by Neuronal Architectures and Human Prob­lem Solving Strategies . Lecture Notes in Control and Information Sciences No. 1 71. Springer-Verlag, Berlin, Germany.

Figure 7: The Darmstadt-Hand

309

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

SYNTHESIS OF OPTIMAL CONTROL USING NEURAL NETWORK WITH MIXED STRUCTURE

Y. Yokoyama, T. Kohda and K. Inoue

Department of Aeronautical Engineering, Faculty of Engineering, Kyoto University, Kyoto (J()6, Japan

Abstract. This paper proposes firstly to use a neural network with a mixed structure for learning the system dynamics of a nonlinear plant, which consists of multilayer and recurrent structure. Since a neural network with a mixed structure can learn time series, it can learn the dynamics of a plant without knowing the plant order. Secondly, a novel method of synthesizing the optimal control is developed using the proposed neural network. Procedures are as follows: (1) Let a neural network with a mixed structure learn the unknown dynamics of a nonlinear plant with arbitrary order, (2) after the learning is completed, the network is expanded into an equivalent feedforward multilayer network, (3) it is shown that the gradient of a criterion functional to be optimized can be easily obtained from this multilayer network, and then (4) the optimal control is generated by applying any of the existing non-linear programming algorithm based on this gradient infonnation. The proposed method is successfully applied to the optimal control synthesis problem of a nonlinear coupled vibratory plant with a linear quadratic criterion functional.

Keywords. neural network; optimal control synthesis; feedforward multilayer network; recurrent network; nonlinear plant; identification; learning.

INTRODUCTION

Multilayer neural networks are applied for learning the system dynamics, and the optimal control input can be determined using them. This kind of method has been reported to obtain good results(Uno et al 1989, Nguyen and Widrow 1990). However all these methods require that the plant order is given, even though they assume that the characteristics and structure of the plant is unknown. This contradiction is due to the fact that the learning of the system dynamics by multilayer networks using time �lay units requires that the number of time delay units must be more than the plant order. This paper develops a novel method to synthesize the optimal control for non-linear plants with unknown dynamics, which does not require their plant order. A neural network with a mixed structure is proposed to learn the dynamics of a plant, which is composed of multilayer and recurrent structure. A kind of Back Propagation algorithm (Rumelhart et al. 1986) is shown to be applied to learning the system dynamics. Firstly, the property of a neural network with a mixed structure is given to explain the learning algorithm . Secondly, It is shown that after learning the system dynamics the network gives the optimal control input in a simple way.

output relations very well using Back Propagation algorithm, but they require the spatial representation of time using time delay units to learn the system dynamics. The number of time delay units requires that the order of the system dynamics must be given beforehand. Another type of neural networks, interconnected networks, are able to learn time series, but they cannot represent input­output relations not so easily as multilayer networks. To learn the system dynamics of an unknown non-linear plant, a neural network with a mixed structure is proposed here. Figure 1 shows its structure, where only hidden units have an inter-connected structure. For the neural network given in Fig. l, activation values of input, hidden, and output units are calculated sequentially as:

NEURAL NETWORK WITH MIXED STRUCTURE

Multilayer neural networks can learn the static input-

3 1 1

111 r

where netHp> = E ai1u1(t) + E bi1H1(t-1) i•l l•l

where r

net0(t) = E c;1H/f) ' j•I

(1)

(2)

(3)

Thus, the input-output relation represented by the neural network can be expressed as:

, .. , X;(t) = f0(L c;/H(L a11u1(t) + E b11H1(t-1))) (4)

j•I l-1 l•I

Eq. (4) shows the possibility of learning the system dynamics by feedback of activation values at the previous time.

LEARNING ALGORITHM

In considering a learning algorithm for any neural network. it is necessary to obtain the gradient of an error criterion with respect to its weights. For this purpose, two types of algorithms are considered: one is application of Back Propagation algorithm to the equivalent multilayer network. the other is to obtain gradients by differentiating the input-output relations directly.

Back Propagation to Equivalent Multilayer Network

As shown in (Rumelhart et al. 1986), for every recurrent network. there is a feedforward multilayer network with identical behavior over a finite period of time. Thus, the equivalent multilayer network. which is transformed from a neural network with a mixed structure, can learn the system dynamics over a finite period of time by Back Propagation algorithm. This method is suitable if some input-output data over some period of time are available, which can be considered as an off-line learning algorithm.

Real-Time Recurrent Leaming

Several learning algorithms have been proposed for a neural network with a recurrent structure (Jordan 1986, Pineda 1987, Williams and Zipser 1989). Here, the real­time recurrent learning algorithm (Williams and Zipser 1989) is applied to learning the system dynamics, where the derivative dependencies of hidden units are represented as simultaneous linear equations. Derivatives of square error function at time t: E,(t) with respect to al"l' bl"l' and cpq are represented as:

1 � -E,(t) = -E ( X;(t) - X;(t) ) 2 i-1

CJE,(t) = t CJ�,(t) CJ.i1(t) � i•I dX;(t) �

= (.iP(t) - x/t))f01(net0 (t))Hq(t) '

where dnetH (t)

-...,.._' _ = H (t-1)8 db q pj pq

(5)

(6)

' CJnet (t-1) + E b., JH'(netH(t-1))

H, /•! I ' dbpq

312

f> = { 1, if p=j pj - 0, if J#i CJE,(t) = t CJE,(t) CJ.i,(t) =EEfo'<neto (t)) <ra;;- i•I dX1(t) -aa;:- 1•1 J•I

'

where

dnetH (t) X(.i1(t) -X1(t)}c1JH1(netHy)}

da 1

pq

(8)

Now, defme error signals for output and hidden units as:

(9)

(10)

and defme derivatives of activation values: BJpq(t) and AJpq(t) as:

dnetH(t) B (t) = ' jpq - db pq

(11)

(12)

Using BJpq(t) and AJpq(t), the gradient of the error function can be calculated as:

(13)

(14)

(15)

and BJpq(t) and AJpq(t) must satisfy the following relations:

BJpq(t) = Hq(t-l)f>PJ , + E b1, f,/(netH(t-l))B1P,(t-1)

/•! '

AJpq(t) .. uq(t-l)f>PJ , + E b11 f,/(netH (t-l))A1pq(t-1)

l•l I

(16)

(17)

Here, the activation derivatives at initial time are given as B1pq(O'J=O and AnJ,O'J:=O if the initial states of the network are given. To obtain the gradient using Eqs. (9)-(17), it is necessary to store the derivatives of active values of hidden units with respect to weights only at the previous time. In this sense, this method is not the same as the

Back Propagation algorithm. However, since Eqs. (13)­( 17) show that the method obtains the gradient by propagating errors through previous active values, the method is considered as a kind of Back Propagation algorithm. The method is suitable for a case where the teaching signals are obtained directly from on-line sensors of the plant.

Based on the above derivatives, the learning is completed using a gradient method. Note here that 1) the criterion functional can be evaluated only by the current error, 2) at any time the gradient calculation only needs the activation derivatives at the previous time, and further 3) this calculation does not include any approximation.

SYNTHFSIS OF OPTIMAL CONTROL

Problem Formulation

Consider the following optimal control problem for a plant expressed in a discrete-form.

[Problem] The plant to be controlled has a relation such as:

�ft) = ffJ!{t), Et-1), !,(t-2), ... , !fO) )

t=l , ... , T !,(0) = :!ii

Obtain an optimal control input !,,p,(t), t=l, .. ., T, that minimizes criterion functional L(!t y), where e= (!(1). !f..2), .• ., @)), J!-=<!f(l). ]!(2). .•• , ,!!(I')). ,!!(i) denotes input signals at time i, and x(i) denotes output signals at time i.

Here, the characteristic of this problem is that an explicit form of system equation! is not given. Instead, the neural network which has learned the plant dynamics is given. In other words, the input-output data over a finite period of time are available.

Equivalent Multilayer Network

Assume that the network in Fig. 1, which has learned the system dynamics, gives output data x(t) in response to input data u(t), t=l, ... , T. Now consider a multilayer neural network in Fig. 2, whose weights are composed of a;1, biJ' and ciJ of the network in Fig. 1. Input units l;(t) is connected to an uniform input source by weight Ui(t). Hidden unit H;(t) gets input from �(t) j=l,. .. ,m and Hi,.(t-1), k=l, .. ., r, through branches whose weights are a;i and bikt respectively. Output unit O;(t) gets input from hidden units Hj(t), j=l, .. ., r through branches whose weights are cii' If weights U;(t) are set as plant input, for t=l, ... ., T, then the output X;(t)=O/t) can be equal to plant output for i=l, .. ., n. Thus, this network is an equivalent multilayer network to the network with a mixed structure in Fig. 1 . For the network with a mixed structure which has learned the dynamic behavior of the subjective system, the output signals of the plant can be also calculated easily from the input signals using its equivalent multilayer network

representation.

Optimal Control Input

In the equivalent multilayer network representation of a neural network with a mixed structure, assume that the only adjustable weights are u,(1), u,(2), .... u,(T) i=l,2, .•. ,m and the other weights au. bil' and c11 are fixed. Let lJ.b 19 be the criterion functional to be minimiud. The derivative of criterion functional lJ.b 19 with respect to U,('t) can be obtained as:

313

CJL = CJL (x,u) au,('t) au,('t) - -.f. � CJL CJx1(t) + .LJ .LJ (x,u) "'° l•l ax,(t) - - au, ('t)

(18)

Since this network is a multilayer network, the second term in the right side of Eq. (18) can be calculated using Error Back Propagation algorithm. Error signal at output unit i with time t can be given as:

(19)

Similarly, error signals for hidden units can be calculated as follows backward from time T to 1 .

• 88 (T) = f,/(net8(T))L 80 (T)c11 I I i•l a • 88 (t) = f,/(net8(t))(L 80(t)c11 I I l'.•t l

, + L 8H(t+l)bl/ ) for t�T

l•l l

(20)

Using the above error signals, error signals at input unit ltft) can be also obtained as:

(21)

From Eqs. (19)-(21), the following equation holds:

Using the above result, the second term in the right side of Eq. (18) is reduced to:

t t CJL (x,u) CJx,(t) • 8 ('t) 1-0 1•1 dX1(t) -- au,('t) 1• (23)

Thus, the gradient of criterion functional � can be represented as:

�(!,.U) + 81 ('t) ou,(-t) - • (24)

This equation shows that the derivatives of any criterion functional L(!.19 with respect to its input parameter U,('t)

can be obtained using a simple calculation and Back Propagation algorithm. Thus, the optimal conttol problem can be reduced to a nonlinear optimization problem, whose gradients with respect to decision variables are given by the equivalent neural network.

ILLUSTRATIVE EXAMPLE

Consider a nonlinear vibration system composed of two output variables x1, Xi and one input u. The system equations are:

.£1 +2.5i1 -� +0.3i13 +0.8x1 -0.3x2 = 0

.£2-.:X1 +�+0.2i23 -0.2x1 + 85

x2= u 3 3 1

and the initial condition is:

Xi(O) = 0.4

i1(0) = 0.0

x,_(0) = 1 .0

�(0) = 0.0

(25)

(26)

The problem considered here is to obtain optimal input u.,/t) that minimizes criterion functional L{!J�.W represented as:

Here the continuous-time expression in F.q. (25) is ttansformed into a discrete-time expression with a sampling time 0.1 in F.q. (27).

If the explicit form of the system equation is given as F.q. (25), then we can obtain an optimal conttol using the Differential Dynamic Programming (DDP) method (Gershwin and Jacobson 1970). However, in the problem considered here, we do not assume that the system state equations are given as F.q. (25). Therefore, first we apply the learning method to a neural network with a mixed structure to obtain the system model. Since the neural network is expressed in a discrete form, the continuous system is ttansformed into a discrete system with sampling time 0.1. Since the system has two outputs and one input, a neural network is composed of one input unit, two output units and fifteen hidden units. For learning the plant dynamics, a random stepwise signal as shown in Fig. 3 is input to the plant, where the mean time width is 20 sampling periods and its range is randomly selected from -5.0 to 5.0. Input-output data over 500 time units: input data { u(l), ... , u(500) } and output data {xi(l),xz(l), ... , xi(500). l2(500)}, are obtained, and so the learning method using an equivalent multilayer network expression is applied with Broyden-Fletcher­Goldfarb-Shanno (BFGS) method (Fletcher 1970) as a gradient method. Error function E;.

is minimized using the BFGS method until it results in a sufficient small error. This operation is called one-step off-line learning. The real-time recurrent learning is not applied here because it is not be suitable to be used with a gradient method.

314

To consider the effect of learning times on the accuracy, compare two neural networks with one-step (N.N.l) and two-step off-line learning (N.N.2), where the sampling period is 500 and the error threshold is 0.0001 . Figure 4 shows their differences in the frequency response of X1 to a sine wave input with an amplitude 0.3. The neural network with two-step learning (N.N.2) is closer to the plant as it is expected. The difference between neural networks and the plant is more evident in higher frequency. This shows that a criterion to examine the learning accuracy should utilizes a high range of frequency response.

Now, obtain the optimal conttol input using the above networks which learn the plant dynamics with one and two ttaining data, respectively. In the proposed method, we obtain the optimal conttol input using the BFGS method. The optimal conttol input obtained by the DDP method is also shown in Fig. 5, which can be considered as the exact optimal solution. The optimal conttol input obtained by N .N .2 is equal to the optimal conttol input obtained by the DDP method in Fig. 5. Values of criterion functional L{!J�.!) are 6.70 for N.N.l and 6.68 for N.N.2. Comparing the results of two networks, it can be found that the more the network learns, the better solution the network can obtain. Thus, as in other types of mathematical models, the quality of optimal conttol input depends on the accuracy of a neural network to use.

CONCLUSIONS

This paper shows that the optimal conttol input can be obtained for a nonlinear plant with unknown order of degree by use of a neural network with a mixed structure, which is composed of multilayer and interconnected networks. The proposed method is successfully applied to the optimal conttol synthesis problem of a nonlinear coupled vibratory plant with a linear quadratic criterion functional. The proposed method has some problems to be resolved in the future: 1) the learning process of network needs much time to learn the plant dynamics and 2) a plant may exist, whose dynamics cannot be learned by the proposed network and which requires more complex structure with such a sigma-pi unit.

REFERENCES

Uno, Y., M. Kawato, Y. Maeda, and R. Suzuki (1989) Repetively structured cascade neural network model which generates an optimal arm ttajectory, Proceedings of the 28th JEEE Corif erence on Decision and Control, 3, 1750-1751

Nguyen, D.H., and B. Widrow (1990) Neural network for self-learning conttol system, IEEE Contt. Syst. Magaz., 10-3, 18-23

Jordan, M.I. (1986) Atttactor dynamics and parallelism in a connectionist sequential machine, Proceedings of

the 8th Annual Conference of the Cognitive Science Society, 531-544

Pineda, FJ. (1987) Generalization of back-propagation to recurrent neural networks, Physical Review Letters, 59-19, 2229-2232

Williams, RJ., and D. Zipser (1989) A Leaming algorithm for continuously running fully recurrent

Inputs

Input Units

neural networks, Neural Computation, 1, 270-280 Rumelhart, D.E., and G.E. Hinton, RJ. Williams (1986)

Learning internal representation by error propagation, Parallel Distributed Processing, 1, The MIT Press, 318-362

Fletcher, R.,(1970) A New approach to variable metric algorithms. Computer Journal, 13-3, 317-326

Outputs

Output Units Hidden Units

Fig. 1 Neural network with mixed structure

Group of Input Layers

Group of Hidden Layers

Group of Output Layers

Fig. 2 E.quivalent multilayer neural network

315

i'(O)

�

u ..... �����������������-

. . ------------ ------i----- --- -------- :--- ---------------:--- - - ------- i ------ - -- ----

+.l' : : :

! ··· : : r ••········ ········: ·· - ·· · ··· · · ·•• I U.uft0

Sampling Times 500

Fig. 3 Random stepwise signal used in learning of plant dynamics

-40.0 - - - - - - - - -

Plant

N.N.2 N.N.1

w Frequency

1.0 w0 = 0.1 ( 1/sec)

Fig. 4 Frequency responses of NN.1, NN.2, and plant

0.4������������������������ 0.0 --------- - - - - - - - - - - - -L - - - - -�-�-=- - -=- - -=- - -=- -=- - -=- - --r-. ---- ·

]' ' ' :

i -o.4

· · ·::.:::::::::::::::::I : : :::::::::: :::1:1::�:::�:�:�:;::��:::�:�::1 -1 .20 50 100

Sampling Times

Fig. S Comparison of optimal control inputs

316

bD <Ii

Copyright @ IF AC Anificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

LEARNING TO A VOID COLLISIONS: A REINFORCEMENT LEARNING PARADIGM FOR MOBILE ROBOT NAVIGATION

B.J.A. Kr0se and J.W.M. van Dam

Faculty of Mathematics and Computer Science, University of Amsterdam, Kruislaan 403, NL-1098 SJ Amsterdam, The Netherlands

Abstract The paper describes a self-learning control system for a mobile robot. Based on sensor information the control system has to provide a steering signal in such a way that collisions are avoided. Since in our case no 'examples' are available, the system learns on the basis of an external reinforcement signal which is negative in case of a collision and zero otherwise. We describe the adaptive algorithm which is used for a discrete coding of the state space, and the adaptive algorithm for learning the correct mapping from the input (state) vector to the output (steering) signal.

Keywords self-adapting systems, learning systems, neural nets, vehicles.

INTRODUCTION

Self-learning and adaptive controllers, which map sensor information into motor signals, have found a growing application in autonomous (mobile) robot systems (Touretzky and Pomerleau, 1989; Kuperstein, 1987) . These controllers are often based on some sort of neural network, which can be trained by presenting learning examples con­sisting of input and corresponding output pairs. Learning samples are either provided by an exter­nal teacher (Touretzky and Pomerleau, 1989) (su­pervised learning) or are generated by the system itself (Smagt and Krose, 1991) (self-supervised learning). Not always there are correct output values known for each input: sometimes the only information available is a binary evaluation of the current state of the system (reinforcement sig­nal). In this case a reinforcement learning proce­dure must be used (Barto, Sutton and Anderson, 1983).

In our application we studied a reinforcement learning method for a mobile robot. The robot is equipped with 8 sensors distributed on a semicir­cle on the front of the vehicle, each of which gives the distance d, to the nearest obstacle in its field of view. The robot has to learn how to avoid a collision with an obstacle o�e it is in its prox­imity. A constant speed has to be maintained, but no other tasks are imposed on the vehicle. The only feedback is given upon collision, when

317

a negative reinforcement signal is generated.

The control problem can be regarded as find­ing a correct mapping between the sensor input J of the system and the steering signal u. In most "neuro-computational" approaches, a func­tion u = F(d) is approximated by a weighted summation of basis functions z0(d}. These can be sigmoid functions, such as in the standard multi­layer feed-forward networks (Rumelhart and Mc­Clelland, 1986), radial basis functions (RBF's) (Moody and Darken, 1989) , or non-overlapping functions which discretise the input-space and as­sign an output signal explicitly to each region in the state-space (Michie and Chambers, 1968; Barto, Sutton and Anderson, 1983).

Similar to Barto and co-workers (1983) we use a discrete representation of the input space, where for each region the corresponding ac­tions are learned with the reinforcement learning method. However, experiments which we carried out with the mobile robot application showed that it is very difficult to find a good a-priori selection of the resolution and region boundaries of the state space. In most solutions a number of regions were hardly ever activated, while other regions were too coarse, with (for example) as a result that approaching a wall from two opposite directions was coded as the same state z0•

Self-organising schemes for quantisation of the input space have been presented (Rosen,1990) and seem to be able to overc..ome this problem.

In the first section of this paper we describe how such a self-organising algorithm can be used to quantise the input space of our neural controller. The second section of the paper describes the neural network which gives the steering signal as a function of the (discrete) sensor input, as well as the algorithm for training the network. Exper­iments and results from a simulated robot system are discussed.

SELF-ORGANISING STATE-SPACE QUANTISA­TION

The 8 sensors of the robot system provide range values di. Since we want the sensor system give high values when the obstacles are close, the range vector lis transformed to an 8-dimensional vector 8, with components

- � Si = e " , (1)

with a a scaling constant. A self-organising quan­tisation algorithm maps this vector 8 onto a set of N discrete input states

As a vector quantisation scheme we used a method described by Kohonen (1984). In this approach an array of "neurons" is defined which forms a topology-preserving map of the input do­main. Each neuron j is responsible for a sub­set Si of the input space S, which means that if a vector s E Sk is presented, the Kohonen method will "activate" a single neuron k, result­ing in Zj = 1 if j = k and Zj = 0 otherwise. This neuron k is now called the winning neuron.

A neuron k is defined by its 8-dimensional 'weight' vector 4. The winning neuron is the neuron of which the weight vector 4 is closest to the input vector 8:

k : I I wk - 8 1 1� 1 1 wi - 8 1 1 Vj. (2)

We used a 2-dimensional grid of 8 x 16 = 128 neurons. The reason for using the topology pre­serving mapping instead of other self-organising methods, such as the Competitive Learning or Learning Vector Quantisation is that the topolog­ical structure of the discrete state space is used in our reinforcement learning method.

Learning patterns are generated by position­ing the vehicle at random locations in the envi­ronment, which means that at time t a sample 8(t) is presented to the network. The Euclid­ian distance between 8 and the weight vector 4 is calculated for all neurons j and the neuron k closest to the current state vector is determined. Next, the weight vector of this winning neuron k as well as its neighbours are shifted toward the input using the learning rule

ij(t + 1) = tf(t) + 11Gkj {8(t) - tf(t)) Vj. (3)

318

Figure 1: The sensor state 8 is mapped onto a layer of neurons of which :z: i = 1 if the system is in state j and :Z:j = 0 otherwise. This layer serves as input for the Associative Search Element, which determines the steering output u, and the Asso­ciative Critic Element which gives an evaluation r as a function of the changing state and of the external reinforcement r.

Gkj is a Gaussian function of the distance d(k,j), measured in the grid-coordinates, between neu­ron j and the currently active neuron k, with a O' decreasing with time as used by Ritter and co­workers ( 1989):

Gki = exp(-d(k,j)2/20'2 (t) ) (4)

Also the learning parameter 1/ decreases with time. After 20000 learning patterns a mapping has been made which reflects the probability den­sity function of the entire state space. On pre­sentation of a state vector 8 the discrete state is given by neuron j, of which the weight vector is the nearest neighbour of 8. :Z:j = 1 if the system is in state j and zero otherwise.

LEARNING THE CORRECT ACTIONS

Once an optimal discretisation of the sensor state space has been found, the mapping between the discrete state z and the steering signal u has to be learned. A "trial and error" method is used based on the theory of reinforcement learning (Barto, Sutton and Anderson,1983; Sutton 1 984) . Such a method makes the steering action corresponding to a given state j more or less probable depending on an evaluation of the action. For the evaluation function the expectated change in future external reinforcement is chosen.

In our system the action or steering signal is generated by the "Associative Search Element" or ASE (see Fig. 1 ) and is probabilistic function of the state z. If the system is in state j, an action Ui is selected according to a Boltzmann distribution, as used by Sutton ( 1990):

(5)

where u; is drawn from the set

U = {left, right} and w;; denotes the "weight" between state z; and the ASE.

The external reinforcement signal r is in our application equal to -1 upon collision and 0 oth­erwise. However, the collision signal is a conse­quence not only of the last action, but also of actions taken at previous states. The "credit as­signment" problem is how to assign this external reinforcement signal to earlier states in the se­quence.

Rules from Temporal Difference Learning (Sut­ton,1984) are used to define an "internal rein­forcement" signal f which is available for each state of the system. The basic idea is that for each state z; an evaluation value p(t) = p(i(t)) has to be learned by the "Adaptive Critic Ele­ment" (ACE) . This evaluation should be the ex­pectation of the discounted sum of external rein­forcement

Pdes (t) = E (L 'Yt' -

tr (t' + 1)) (6) t' 2'.t

with 0 < 'Y < 1 . From this we can derive that, if p( t) is correctly learned:

p(t - 1) = r(t) + 'YP(t). (7) An error signal can now be defined for training the ACE:

f(t) = r (t) + 'YP(t) - p(t - 1) . (8) p(t) is implemented as a series of "weights" v; to the ACE such that

(9) if the system is in state k at time t, denoted by zk = 1. The function is learned by adjusting the v; 's according to a 'delta-rule' with an error term c given by f(t) :

�v; (t) = {3f(t)h;(t) . (10)

{3 is the learning parameter, and h;(t) indicates the "trace" of neuron z; :

h; (t) = >.h; (t - 1) + (1 - >.)Gk; (t - 1) . (1 1)

This trace is a low-pass filter or momentum, through which the credit assigned to state j in­creases while state j is active and decays expo­nentially after the activity of j has expired. Gk; is a Gaussian function of the distance between neuron j and winner k as introduced in the pre­vious section. Note that the trace is not only de­pendent on the history of state z; but, because

319

of the Gauss-function also on the history of the neighbours in the Kohonen grid. In this way the winning neuron spreads it's credit to neighbour­ing neurons which should result in a faster learn­ing.

If f (t) is positive, the action u of the system has resulted in a higher evaluation value, whereas a negative r(t) indicates a deterioration of the system. r(t) can be considered as an internal reinforcement signal, which can be used to learn the correct mapping u = F(i). This mapping is also implemented as a set of weights, which are updated according to:

w;;(t + 1) = w;; (t) + ar(t)e;;(t) (12) with e;; the 'eligibility trace' of a connection w;; :

ei; (t + 1) = 8ei;(t) + ( 1 - c)Gk; (t)ui, (13) where Ui = 1 if action u; is chosen and Ui = 0 otherwise. Gkj denotes the Gaussian function defined earlier.

Initially all weights are set to zero resulting in a random behaviour. From Eqs.[5] , [12] and [13] it can be seen that r(t) > 0 (reward) increases the probability of the action while f( t) < 0 (pun­ishment) decreases this probability.

The self-organising state space quantisation as described in the previous section distributes the neurons in the grid according to the probability density function of the input. However, we would like to have a higher resolution in the 'critical' areas, where a collision is very likely. This can be achieved by an adaptive process, in which the adjustment of the mapping of the input vector 8 onto the discrete array of neurons is weighted by the internal reinforcement. We used an "adaptive range coding" rule as described by Rosen (1990) : f; (t + 1 ) = f;(t) - 'f/Gk;r(t) (s(t) - f; (t)) Vj. (14)

In the critical areas, r(t) will generally be nega­tive, so that the learning rule will move the region

f; toward the current state 8. In safe areas ( r(t) positive) , the neurons are moved away from the current states.

EXPERIMENTS AND RESULTS

Experiments are carried out in our simulation en­vironment, consisting of a sensor simulation pro­gram (ASSIM (Krose and Dondorp 1987) ) and a simulation program for the mobile robot (CAR­SIM (Albada, Lagerberg and Krose, 1991) ). A 2�-dimensional map of the environment is spec­ified, in which the robot can be positioned at any location. ASSIM simul;ttes outputs of a wide range of sensors such as ultrasonic, laser

4 I v

Figure 2: The training environment and a typical series of trials.

range finders etc. In our experiments we used an ideal type of ultrasonic sensors, which give the distance to the nearest object within their beam. Beamwidth is small for sensors looking forward and increases for sensors looking to the sides. The sensors are oriented ±9° ,±28° ,±49° and ±75° relative to the direction of the vehicle.

Sensor readings are fed into our controller which gives as output the curvature of the mobile robot. This curvature is fed into CARSIM, to­gether with a desired velocity of vehicle. The ve­locity was kept constant during all experiments. CARSIM consists of a simulation of the dynamic behaviour of the vehicle on which a conventional PI controller and inverse kinematics module have been programmed. Given a desired curvature and velocity, CARSIM calculates the position of the vehicle as a function of time. This position serves again as input for ASSIM. The control fre­quency is 2 Hz.

The vehicle was trained in an environment as shown in Fig. 2. A trial consists of a series of steps until a collision occurs. When a collision occurs, the system is returned to a position oc­cupied 30 steps ago and a new trial is started.

At the start of the first trial, the vehicle is po­sitioned at location 1 (see Fig. 2) . When the ve­hicle has learned to move more than 2000 steps without collision it is put in starting position 2, and training is continued. After position 2, posi­tions 3 and 4 are also tested. The performance of the system was expressed as the number of steps which was taken before a collision occured, and is shown in Fig. 3.

From the figure it can be seen that the sys-

320

3000

2500

� 2000 ::l .-j ·r! ell lj..j

� 1500 .j..) i:: ::l Cl) fr 1000 .j..) Cl)

500

pos 1 pos 2 pos 3 pos 4

pos 4 decoder

,.It

\ (r:-:�=-::_-:.�--:-==-��--:_-::.'��------, ' r. · / "

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0 '--�����--'-�����--'��� 0 2 0 t rial nr

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Figure 3: The performance as a function of the number of trials. In this figure also the best per­formance of an a-priori state space quantisation with 28 = 256 states has been plotted

tern learns to drive without collision after about 16 trials. Positioning the vehicle at a different location does not influence the performance.

CONCLUSIONS

As shown by the results the system works well. With the adaptive range coding the performance is better than with a fixed coding of range bound­aries, even though we used fewer discrete states. A quantisation into 256 states was used in the fixed range coding experiments, whereas the re­sults obtained with the adaptive range coding are based on 128 discrete states. Apparently the adaptive coding is able to place neurons where they are needed, i.e. near states where collisions are likely. Because of the topology conserving mapping, neigbouring neurons represent states which are close in state space, which is used in a. faster reinforcement learning paradigm. A dis­advantage of the proposed model is the fixed size of the Kohonen network: for more complicated environments the number of neurons may im­pose a limitation. Furthermore the initial train­ing which is needed for the first discretisation of the state space is quite elaborate (20000 learning samples)

Recent work is done along two different lines. One way is to abandon the disqetisation of the state space and have a distributed representation

of the input. Instead of having a single neu­ron active for each state, the sensor readings can be mapped directly into motor commands, which also has shown to result in a collision free naviga­tion (Verschure, Krose and Pfeifer, 1992). How­ever, this can only be done for linear control rules. A second approach which is studied is to have a discretisation where also the number of regions can be adapted. In this model the neurons Zi are added when needed (i.e. when collisions occur) and trained with a reinforcement learning proce­dure. To limit the size of the network, neurons can be merged with neighbouring neurons when their action probability distributions are similar. This approach has resulted in a control system which has about the same performance as the system described in this paper, but needs less neurons (Krose and Dam, 1992).

The controller described in this paper results in a reactive behaviour of the robot, aimed at avoiding collisions with obstacles. If also a goal directed behaviour has to be learned, basically the same approach can be used. Instead of giv­ing a negative external reinforcement signal upon collision also a positive signal could be generated upon achieving a goal. However, a sensor sys­tem for goal directed behaviour will very likely not consist of a set of range sensors, as used in this paper. Adding extra sensors will thus result in an increase of the dimensionality of the input (sensor) space, but again a trial and error search can be used to find the mapping between sensor input and action output.

REFERENCES

Albada, G.D. van, J.M. Lagerberg and B.J.A. Krose. Software architecture and simulation tools for autonomous mobile robots, Proc.

of Euriscon '91 Corfu, Greece, Kluwer Press (in press) .

Barto, A.G., R.S. Sutton and C.W. Anderson (1983) . Neuronlike adaptive elements that can solve difficult learning control problems. IEEE Trans. on Systems, Man and Cyber­

netics 13 834-846.

Kohonen, T. (1984). Self-Organization and As­

sociative Memory. Springer Verlag.

Krose, B.J.A. and E. Dondorp (1989). A Sen­sor Simulation System for Mobile Robots. In: T. Kanade, F.C.A. Groen and L.O. Hertzberger (Ed.)Intelligent Autonomous Systems 2 pp. 641-649.

Krose, B.J.A and J.W.M.van Dam (1992). Adaptive state space quantisation for rein­forcement learning of collision-free naviga-

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tion IEEE International Conference on In­

telligent Robots and System

Kuperstein, M. (1987) . Adaptive visual-motor coordination in multi-joint robots using par­allel architecture. Proceedings of IEEE In­

ternational Conference on Robotics and Au­tomation pp. 1595-1602.

Michie, D and R.A. Chambers (1968). Boxes: An experiment in adaptive control. In: E. Dale and D. Michie (Ed.) Machine Intelli­

gence 2 Oliver and Boyd pp. 137-152.

Moody, J and C. Darken (1989) . Fast learn­ing in networks of locally-tuned processing units. Neural Computation 1 281-294.

Ritter, H.J., T.M.Martinetz and K.J. Schulten (1989). Topology conserving maps for learn­ing visuo-motor coordination. Neural Net­

works 2 159-168.

Rosen, B.E., J.M.Goodwin and J.J.Vidal. (1990) Adaptive range coding. In: D. Touretzky (Ed.) Neural Information Pro­

cessing Systems 3. Morgan Kauffman.

Rumelhart, D.E. and J.L.McClelland (1986). Parallel Distributed Processing. MIT Press.

Smagt, P.P van der, and B.J.A. Krose (1991). A real-time learning neural robot controller. In: Proceedings of the 1991 Int. Conf. on

Artificial Neural Networks Finland pp. 351-356.

Sutton, R.S. (1984) Temporal credit assignment

in reinforcement learning Ph.D. dissertation at University of Massachusets.

Sutton, R.S. (1990) Integrated architectures for learning, planning and reacting based on ap­proximating dynamic programming. Proc.

of the Seventh Int. Conf. on Machine Learn­

ing.

Touretzky, D.S. and D .A. Pomerleau (1989) What's hidden in the hidden layers? Byte,

August pp. 227-233.

Verschure, P.F.M.J. , B.J.A. Krose and R. Pfeifer (1992) Distributed Adaptive Control: the self organization of structured behavior. Robotics and Autonomous Systems 9 (2).

Copyright © IF AC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

GENETIC ALGORITHMS FOR PROCESS CONTROL: A SURVEY

J.M. Renders*, J.P. Nordvik* and H. Bersini**

*Commission of the European Communities, Joint Research Centre, Institute for Systems Engineering and lnformatics, l-21020 lspra (Va), Italy

**!RID/A - Universite Libre de Bruxelles CP 14916, 50 av. Fr. Roosevelt, B-1050 Bruxelles, Belgium

Abstract. This paper presents a survey of the potential use of Genetic Algorithms (GAs) for process control. GAs are a family of iterative search algorithms based on an analogy with the process of natural selection and evolutionary genetic. Application to off-line control is first en­

visaged, where GAs are used for task scheduling, calculation of optimal set points and design of optimal control strategies. Then application to on-line control is considered, focusing on system identification and enhancement of existing controllers, two problems for which GAs seem to of­fer the most promising results. After the description of possible applications of GAs to supervi­sory problem, the general advantages, drawbacks and limitations of applying GAs to process control are discussed, and further lines of research are drawn.

Keywords. Adaptive Systems, Control System Design, Leaming Systems, System Identification, Genetic Algorithms.

INTRODUCTION Recent interest in paradigms inspired by biological metaphors for adaptive process control stems mainly from the difficulties of traditional control theory to deal with complex varying or uncertain environment. These difficulties mainly lie in the fact that even traditional adaptive control theory requires precise knowledge of the process to be controlled (slow deviation of the proc­ess parameters with respect to the adaptive capacity of the controller, a priori knowledge about the structure of the process and its perturbations) [Astrom and Witten­mark, 1989]. Moreover this knowledge has to be precise and complete: any slight imprecision can degrade dra­matically the quality of the control. On the other hand, several biological adaptive systems, whose principles and mechanisms have inspired artificial computing metaphors such as Neural Networks (NN) [Rumelhardt and Mc Clelland, 1986], Immune Networks (IN) [Allan and Cohen, 1989; Varela, Sanchez and Coutinho, 1989] and Genetic Algorithms (GAs) [Goldberg, 1989; Davis 1991] are characterized by their ability to reconfigure themselves to an unspecified environment in an incre­mental and robust fashion. These adaptive biological systems seem to have less stringent requirements than the traditional control theory - or at least different ones. They therefore constitute a promising approach for proc­ess control, although these biological metaphors are still under development and only partial applications are available.

While there already exists an abundant literature on ar­tificial neural networks applied to process control [Miller, Sutton and Werbos, 1990; Narendra and Parthasarathy, 1990], the use of the IN and GA tech-

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niques for process control is more recent and not so de­veloped [Varela and Bersini, 1991; De Jong, 1980 and 1988]. This paper focuses on the GA technique and pre­sents a survey of its applications to process control, em­phasizing the originality, advantages and drawbacks of the various approaches, and attempts to determine the most promising lines of research.

The paper is organized as follows. First a brief descrip­tion of GAs is given. Then applications of GAs to off­line control, on-line control and supervisory control are described successively. Finally conclusions about the use of GAs in process control are presented as well as some guidelines for further investigations in this do­main.

BRIEF l>FsCRIPI10N OF GAs Genetic Algorithms are a family of iterative search algo­rithms based on an analogy with the process of natural selection (Darwinism) and evolutionary genetics. The search aims to optimize a user-defined function called the fitness function. To perform this task, GAs maintain a "population" of candidate points in the search space, called "individuals". During each iteration, called a "generation", a new population is created. This new gen­eration generally consists of individuals that fit better than the previous ones to the external environment as represented by the fitness function. As the population it­erates through successive generations, the individuals will in general tend towards the optimum of the fitness function. To generate a new population on the basis of a previous one, GAs perform three steps: (a) they evaluate the fitness score of each individual of the old population, (b) they select individuals on the basis of their fitness score, (c) they recombine these selected individuals us-

ing "genetic operators" such as "mutation" and "crossover".

Four major differences from conventional methods are to be noted: (a) GAs encode the parameters which it has to optimize and base its procedure on the codes and not on the parameters themselves; (b) GAs work in parallel on a number of search points (potential solutions) and not on a unique solution, which means that the search method is not local in scope but rather looks globally at the search space; ( c) GAs require from the environment only an objective function measuring the fitness score of each individual; (d) both selection and recombination steps are performed by using probabilistic rules rather than deterministic ones.

OFF-LINE CONTROL When a sufficiently accurate model of the process is available, GAs can be used as powerful search methods for computing optimal set points of the process units or for discovering efficient strategies in complex environ­ments. The availability of a good model allows an arbi­trary number of trials to be performed by simulation, without any danger of damaging the process or degrad­ing its performances. Nevertheless, the availability of a model is not a strictly necessary condition: for all the applications discussed here, it is quite possible to use the real process instead of a model, but in this case, the process must be able to endure a learning phase of sev­eral hundred trials, including completely erroneous ones; this property is obviously rare in industrial practice. In either case, after searching or learning, the solution fi­nally proposed by GA is frozen and used on the real process in the production phase (exploitation mode).

Calculation of O,ptjma} Set Points Set point selection is an optimization problem, based on process and economic models of the plant: plant opera­tions are optimized to maximize daily profits, yields or production rates, while satisfying operational con­straints. The process model is typically a steady state model, obtained by eliciting physical properties or by collecting experimental data. This model relates process variables - such as unit pressures or feed flow rates - to product properties, while an economic model relates product values, costs of production and market objec­tives as functions to operating conditions. After synthe­sizing all information and objectives in a cost function with constraints, GAs are used to minimize this cost function, thereby fmding the optimal set points. GAs can be run periodically to adapt the process set points to changing management decisions or market fluctuations.

Task Schedulin,

GAs, as combinatorial search methods, provide a set of efficient domain-independent heuristics in complex search spaces, without the need for highly domain-spe­cific knowledge. This approach has especial advantages when dealing with computationally complex problems (''NP-complete problems'', e.g. the Traveling Salesman Problem [Grefenstette and others, 1 985]), including scheduling problems, where deterministic and exhaus­tive search techniques often fail because of time con­straints. Nevertheless, several problems arise in these cases: individual's interpretation, coding and evaluation are non-trivial problems, and usually specific genetic operators (in addition to the traditional crossover and

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mutation operators) must be designed in order to give useful results.

GAs have already been used to allocate resources, in a near optimal way, to multiple users - while satisfying re­source and time constraints - by ordering a sequence of tasks in combination with a deterministic schedule builder which acts according to domain-specific knowl­edge [Syswerda, 1991). This application demonstrates that the design and combination of new specific genetic operators can be a very effective tool for solving such problems.

DesifW of O,ptirnal Control Strate,jes

GAs offer interesting advantages when applied to the learning of optimal control laws and of high-perform­ance state-feedback. Contrary to most heuristic algo­rithms, GAs do not require a priori knowledge about the system and can learn from scratch; but GAs can easily include a priori information, for example by designing specific genetic operators, by seeding the initial popula­tion of search points, or by combining them with heuris­tic methods in order to increase the efficiency of the learning. Once learned, the control law is used on-line in a closed-loop mode. This concept of GA-based learning has been applied for controlling a tank [Nordvik and Renders, 1991a], a cart-pole system [Odetayo and McGregor, 1989) and a gas pipeline {Goldberg, 1985).

The performance measure (objective function) is usually related to the error between a reference behavior and the actual output of the process, squared and integrated over a given time interval, and possibly averaged for different initial operating conditions; alternatively it can be de­fmed as the mean time before exiting from a domain of viability, when the control objective is not so precise.

GAs are not limited to "reacting after learning": it may also be applied to "planning", i.e. to sequential decision tasks, and is especially worthwhile when the environ­ment is very complex. In this case, GAs allow to acquire a high-performance strategy, despite the analytically in­tractable properties of the problem (e.g. multi-agent in­teractions, uncertain and noisy environments and de­layed reward systems). From this viewpoint, the main role of GAs are to decrease human design efforts, by automating the generate-and-test cycle in evolving high­performance strategies. Another family of learning methods, based on Dynamic Programming, could com­pete with GAs for this class of problems, but they suffer from requiring stronger assumptions (Markovian deci­sion problems) and from the "curse of dimensionality" -that the combinatorial complexity increases exponen­tially with the number of dimensions of the search space. As an application instance, GAs have been used for solving an "evasive maneuvers" problem, where a decision making agent (a plane) has to learn to escape another decision making agent (a missile) [Grefenstette, 1989 and 1990); GAs effectively explore a space of knowledge structures and discover sets of rules which provide high performance in a variety of environments.

To realize these learning tasks, three ways of implemen­tation can be distinguished: optimizing parameters of a pre-specified controller, evolving "control programs" and combination of GAs with other control techniques.

O,ptimjzjn' parameters of a pre-specified controller, GAs can be used for tuning parameters of a parameter-

ized control law, such as the gains of a P.l.D. controller or the coefficients of linear state feedback [De Jong, 1980].

Evolvin& "control pronams". The term "control pro­gram" must be understood in the computational sense, as the executable code for a control system. One idea could be to apply GAs to evolve PASCAL-like programs (or indeed programs written in any traditional procedural language) until they produce a program which correctly solves the control task. Unfortunately, the processing of such programs with GAs raises inextricable problems because of the context-sensitive interpretation and the importance of the order of the instructions: it is easy to see that the application of the traditional genetic opera­tors has very little chance of giving any meaningful and syntactically correct programs. However, using a tree­structured language such as USP can render this ap­proach successful [Koza, 1991 ]. Lisp programs which computes the optimal switching surface for the control of a cart-pole system have been successfully generated using GAs [Koza and Keane, 1990]. An alternative ap­proach, efficient and widely used, is based on the "Production System" paradigm.

Production Systems as Control Strate&ies. A production system (PS) can be regarded in its simplest form as an unordered set of rules; each rule is of the type "if <condition> then <action>". In control applications, the antecedent part <condition> generally depends on the state variables (all are assumed measurable), while the consequent part <action> gives the control action to be applied to the process. Sometimes - and particularly with the PSs called a "classifier systems" [Booker, Golderg and Holland, 1989] - internal variables, which have no a

priori meaning, are present in both antecedent and con­sequent parts and represent some "internal model build­ing", similar to the concept of estimation or reconstruc­tion of non-measured states in classical control theory.

A PS defines a particular control strategy and amounts to the "control program", as defined above. Processing and evolving a PS with GAs are not as problematic as with procedural language program because of the sim­plicity of the representation; this simplicity is achieved, however, at the cost of a reduction of the expressive power of the items processed.

Two fundamental approaches have been developed for the application of GAs to production systems [De Jong, 1988]. In the first one - called the Pitt approach - GAs try to search for an optimal strategy - represented by a production system - between a population of production systems; in other words, the individual in the GAs meaning is a set of rules constituting a particular strat­egy. Conversely, in the second approach - called the Michigan approach - the individual is merely one rule and GAs attempt to evolve a population of individual rules in such a way that the population finally evolved represents a high-performance strategy.

One method of implementing the Pitt approach is to re­duce the role of GAs to the computation of action values in the consequent part of the rules, all condition parts being already fixed and defined by an a priori partition of the state space [Odetayo and McGregor, 1989; Gold­berg, 1985]. More interestingly and more generally, GAs can be used to search for useful conditions on the state

325

variables or to establish an efficient partition of the state space, in order to give optimal control performances [Nordvik and Renders, 1991a]; in this case, GAs per­form structural search, rather than merely parameter op­timization.

On the other hand, implementing the Michigan approach requires different principles, because GAs must now let several individuals (rules) cooperate and coexist, even though they are not similar. To achieve this goal, GAs usually act in combination with another heuristic optimi­zation algorithm for credit assignment [Grefenstette, 1988]. The credit assignment algorithm is in charge of distributing each response of the environment - often a delayed reward or punishment - to the individual rules concerned, and thus useful sets or chains of rules; GAs have the role of generating new rules by combining and locally perturbing existing ones. Each mechanism has its own dynamics: fast for credit assignment and slow for GAs.

Combination of GAs With Other Control Tecbnjgpes. The underlying principle of combined or hybridized techniques is the following. An initial non-linear con­troller, governed by a parameterized closed-loop control law relating the control vector (action or input of the process) to the state vector, depends on a parameter vector and has a part of its structure allowed to vary. Then GAs are used to help the search for an optimal structure (combinatorial search) or for optimal parame­ter values (numerical optimization).

The initial controller can be some "fuzzy controllers" (controllers based on fuzzy sets theory), "neurocontrol­lers" (controllers using artificial neural networks), or any other types of non-linear controllers. For the fuzzy controllers, the part of the structure allowed to vary could consist of the rules composing the rule base or the set of fuzzy operators used (e.g. AND, ALSO, fuzzy implication, defuzzyfication,) or alternatively the deci­sion table could be considered directly; the parameters vector could be those defining the membership function of the fuzzy reference sets or could be linear coefficients associated with the consequent part of the rules. For the neurocontrollers, the structure to vary could consist of the topology of the network (layout of connections, nodes and layers), while the parameters could be the connection weights.

The combinations GAs/Neural Networks have already been demonstrated to offer significant improvements over neural network techniques alone. For example, GAs have been applied to adjust the connection weights of a network, so as to obtain a pre-defined behavior [Whitley, Starkweather and Bogart, 1990]. In the same way, the discovery of an efficient network topology for a prescribed task has been realized with GAs [Harp and Samad, 1991].

Hybridizing GAs with fuzzy control (FC) is a more re­cent issue. Karr [ 1991] has described how GAs can se­lect high-performance membership functions for a fuzzy controller, which controls a computer-simulated cart­pole system, all fuzzy rules being already defined. On the other hand, Thrift [1991] has applied GAs for build­ing a decision table for a simple cart-centering problem, with a fuzzy partition of the state space already fixed.

Generally, structure optimization is twofold: besides the structure optimization itself, it also includes an embed­ded stage of parameter optimization. The two optimiza­tion processes are normally implemented with very dif­ferent time scales (fast dynamics for parameter optimi­zation and slow dynamics for structure search). GAs seem to offer excellent results for the slow dynamics process, but also for parameter optimization when it is combined with traditional algorithms (e.g. back-propa­gation for neural networks) [Belew, Mcinerney and Schraudolph, 1991].

Finally, it is interesting to mention the combination of GAs with a Kohonen neural network for learning viable strategies [Thierens and Vercauteren, 1990]. The role of the Kohonen network is to reduce the problem size, by automatically extracting useful features of a high-dimen­sional state space, using its self-organization properties; moreover, the network maps the real-valued input space into a discrete structure of units, while preserving the to­pology of the input space. Once the unsupervised learn­ing of the Kohonen network is terminated, GAs are used to search for a viable control strategy, i.e. a set of ac­tions to be applied as a function of the mapped features, rather than of the complete state vector. This combina­tion seems to render the GAs-learning easier and faster.

ON-LINE CONTROL

Adaptive Learnini: of Qptjmal Control Law

Under certain circumstances GAs can be directly used on-line for the applications described in the previous section. These circumstances are:

1 . A process model is available and accurate enough -usually resulting from on-line identification in order to present adaptive characteristics - and the time interval between control samples is sufficiently large to allow meaningful computing (near-convergence) of the genetic algorithm. In this case, GAs can search at each step for an updated optimal strategy, and adaptive control is thus achieved. Yet, for real-time purposes, interweaving a GA-stage (computation of one or several generations, without achieving complete convergence) with a control stage on the real process at discrete times is a quite fea­sible approach.

2. No accurate model is available and indeed it may be the case that nothing is known about the process to be controlled; when directly applying GA-based learning to such process, it must be borne in mind that the process must be sufficiently "robust" to accept non-completely mastered learning and "exploration"; all individual must be sequentially evaluated on the unique process and this implies that the process has to endure possibly erroneous trials and that the process output (product) is allowed to be temporarily of poor quality during the learning and exploration times. In order to insure adaptation, and particularly for abrupt changes of the process, GAs must keep up a constant exploration level (for example, by an increased mutation rate); this operating mode is not the normal one for GAs, which tend towards a convergent behavior by gradually reducing the exploration level. Fortunately, GAs permit to tune easily the balance ex­ploration/exploitation.

In both circumstances, the process is assumed to be so complex that a classical analytic treatment is not realiz­able in practice. Indeed it would be a complete nonsense

326

to use GAs simply to design on-line a linear control law for a given linear process model.

Enhancement of Existini: On-Line Controllers

The idea is to limit the possible dramatic consequences of GAs when applied directly on the real process, by re­ducing its contribution to the process input. Its new role is to refine the performances of an existing on-line con­ventional controller by discovering optimal corrections to be added to the controller's output [Nordvik and Ren­ders, 1991a]. The global strategy of the GA-based auxil­iary controller is to learn to associate with some measur­able variables (features) of the process (state, output er­ror, ... ) the corresponding optimal correction value; to realize this task in practice, the feature space can be partitioned into ''boxes" and the correction space dis­cretized, in such a way that the task of GAs is simply to solve a simple combinatorial problem. The performance measure (cost function) is usually chosen as the integral of the squared error - the difference between an ideal behavior and the actual output of the process, taken over a given time interval, and possibly averaged for different initial conditions.

This approach has two main advantages: (a) it is com­patible with any conventional controller and can there­fore be applied to any existing control systems; (b) it can be implemented in such a way that the performance of the resulting system, after learning and convergence, is always at least as good as the conventional controller alone (in the case where no improvement is possible, the GA-based controller response is to leave the output of the conventional controller unmodified).

Construction and Identification of Models All the approaches described above, when they are di­rectly applied on the real process, suffer from requiring a sequential evaluation of the individuals, which can take a very long time because each strategy represented by an individual must be tried independently on the process; moreover, when the process is time-varying, re­sults given by sequential evaluation have to be inter­preted very carefully, because the optimization problem has changed meanwhile and adaptation becomes deli­cate. This evaluation also involves using individuals of varying quality to control the process, thereby often de­grading it; for this reason, direct on-line application of GAs is rarely realizable in practice.

A way to avoid such drawbacks is to split the control problem into two stages: a modelisation/prediction stage, and a strategy-building stage based on the models thus constructed. Applying GAs for the first stage only -on-line, if adaptation is needed - does not require the successive application of individual strategies; rather, output measurements for arbitrary - but well chosen -inputs are the only requirement and are common for all individuals. Such splitting is not new in control theory: it is closely related to the "indirect adaptive control problem" whose fundamental principle is the on-line formation of an explicit model of the system being con­trolled.

From the GA point of view, each individual now repre­sents a model of the process, and therefore the fitness function no longer measures the quality of control, but rather measures the quality of a model by assessing its ability to predict future states [Nordvik and Renders,

1991b]. This enables computation of the fitness scores (evaluation) to be carried out in parallel and on-line: each individual matches its own predictions to the proc­ess and derives its fitness score, which can be related, for instance, to the error between the predicted output and the real one, squared and integrated over some time interval. The individual with the best score - the best model - is used as input for the second stage which de­termines the action to be undertaken through an analysis of the model represented (e.g. by computing some kind of inverse model or through a real-time dynamic pro­gramming stage). As described in a previous section it is also conceivable that GAs play a role in this second stage by discovering optimal strategies

Three ways of implementation can be envisaged: a) optimizing parameters of a pre-structured model or of a parameterized state-observer; b) evolving "modelisation programs" or "estimation programs", in particular production systems consisting of rules having the following fonn: "if <process inputs> then <process output>" or "if <current state> and <action> then <next state>" (in these notations, "<u>" designates some condition on the vector u); c) combining GAs with other estimation or modelisation techniques, and particularly with fuzzy and neural network-based modeling tech­niques (in this case all the considerations of the section on combining GAs with other control techniques remain valid, replacing the word "control" by "modeling").

Supervisory Control

GAs offer a good compromise between reliability of the search process and computing time in a variety of search problems. Applying GAs in supervisory control tasks, such · as fault detection and diagnosis, therefore consti­tutes an interesting alternative to traditional methods for diagnostic decision-making (exhaustive enumeration, branch-and-bound methods, "greedy" heuristics), espe­cially when the problem size is particularly large: ex­haustive enumeration is impracticable, branch-and­bound methods can result in excessive search time, while greedy heuristics rarely offer reliable results. Combination of GAs with the fonner will probably pro­duce the most effective compromise.

In this vein, Potter, Miller and Weyrich [1990] have shown that such a combination gives significantly better results (in terms of time and reliability) than traditional methods alone for multiple-fault diagnostic decision making - the problem of fmding out a set of elementary component faults which accounts, as well as possible, for the set of observed symptoms.

DlsCUSSION AND CONCLUSION When and How to Use GAs in frocess Control

Fundamentally, GAs are a family of combinatorial search algorithms, which include, besides parallelism­and exploration-based properties, interesting heuristics based on the building-block combination principle. Most of control problems - on-line or off-line - need search methods, and therefore GAs can constitute in certain cases an interesting alternative, when traditional optimi­zation methods (gradient descent, hill-climbing, analyti­cal methods such as least-squares) fail to provide effi­ciently reliable results.

However, most current implementations of GAs nor­mally require an environment (the process or a model of

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the process) with considerable error-tolerance, i.e. one which permits trying and evaluating candidate-solutions which can be mediocre, bad or indeed of dramatic con­sequences. When a sufficiently accurate process model is available, this does not pose any problem in principle and the use of GAs is especially recommended when the problem is too complex to be treated analytically and when nearly nothing is known about the search space. In particular, GA-based learning of control strategies in a complex environment seems to constitute a feasible and useful approach.

When no process model is available, the use of GAs is more problematic, at first glance. If the process is robust enough to offer the error-tolerance needed - intensively during the learning stage, and still occasionally if a con­stant level of exploration is desired (adaptation mode) -then the direct application of GAs remains feasible, al­though this robustness property is rare in practice. It must be kept in mind that a parallel implementation of GAs is generally no longer possible in this case, because the individuals must be evaluated sequentially on the same process. More interestingly, rather than trying to control the process directly, splitting the control problem into a modelisation/prediction stage and a strategy­building phase is a more elegant and more efficient ap­proach in absence of an accurate process model. In this case, GAs have the role of fmding a good model of the process, given a set of actual input-output measurements observed, without acting directly on the process; the in­dividual evaluations can again be perfonned in parallel, using the same measurement set.

GAs, on their owns, are blind search mechanisms, some­times too blind. Therefore, it is often more efficient when it is combined with traditional - usually more local - methods. In the same vein, the combination of GAs with already existing controllers, with a fuzzy controller or with a neurocontroller generally results in perform­ances superior to those using the methods alone, while preventing GAs from acting too dangerously by limiting its direct intervention.

Further Investi&ations

Beyond the restricted framework of process control, theoretical work is still needed to understand properly what is fundamentally new in GAs in the field of opti­mization and in which circumstances GAs offer signifi­cant advantages over other optimization methods. Then, Connally relating control problems to optimization problems would permit a sound analysis of the perform­ances of GAs for process control and the possible hy­bridization with other methods.

Meanwhile, experimental results are necessary as well. They have to demonstrate the feasibility of the GA­based approaches to the control of large-scale complex systems (rather than the traditional "toy-systems"), pos­sibly in combination with other types of controllers. For the on-line control of such systems, real-time considera­tions constitute non-trivial constraints, particularly for GAs which can be very slow if no particular precaution is taken; the interweaving of GA-steps with control steps at discrete time intervals remains an issue to investigate. In the field of GA-based adaptive control, studies have still to be carried out to characterize the process changes the GA-controller is able to cope with.

The indirect control approach, consisting of splitting the control in two stages, seems to be the most promising one, when applying GAs to on-line process control. In this case, efficient combinations of GAs - used as model-builders - with strategy-building methods have still to be discovered. More generally, issues concerning the general design of "biologically-inspired controllers", mixing for example GAs with connectionist techniques both in the modeling and the strategy-building stages, must be considered before applying intensively GAs to process control in a real environment.

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Copyright @ IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

AN ADAPTIVE SYSTEM FOR PROCESS CONTROL USING GENETIC ALGORITHMS

C.L. Karr

U.S. Bureau of Mines, Tuscaloosa Research Center, P.O. Box L, University of Alabama Campus, Tuscaloosa,

AL 35486-9m, USA

Abstract Researchers at the U.S. Bureau of Mines have developed adaptive process control systems in which genetic algorithms (GAs) are used to augment fuzzy logic controllers (FLCs). GAs are search algorithms that rapidly locate near-optimum solutions to a wide spectrum of problems by modeling the search procedures of natural genetics. FLCs are rule based systems that efficiently manipulate a problem environment by modeling the "rule-of-thumb" strategy used in human decision making. Together, GAs and FLCs possess the capabilities necessary to produce powerful, efficient, and robust adaptive control systems. To perform efficiently, such control

systems require a control element to manipulate the problem environment, an analysis element to recognize changes in the problem environment, and a learning element to adjust to the changes in the problem environment. Details of an overall adaptive control system are discussed. A specific laboratory acid-base pH system is used to demonstrate the ideas presented.

Kevwords fuzzy logic, genetic algorithms, process control , adaptive control, pH control

INTRODUCTION

The need for efficient process control has never been more important than it is today because of economic stresses forced on industry by processes of increased complexity and by intense competition in a world market. No industry is immune to the cost savings necessary to remain competitive; even traditional industries such as mineral processing (Kelly and Spottiswood, 1982) , chemical engineering (Fogler, 1986), and wastewater treatment (Gottinger, 199 1) have been forced to implement cost-cutting measures. Cost-cutting generally requires the implementation of emerging techniques that are often more complex than established procedures. The new processes that ·result are often characterized by rapidly changing process dynamics. Such systems prove difficult to control with conventional strategies, because these strategies lack an effective means of adapting to change. Furthermore, the mathematical tools employed for process control can be unduly complex even for simple systems.

In order to accommodate changing process dynamics yet avoid sluggish response times, adaptive control systems must alter their control strategies according

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to the current state of the process. Modem technology in the form of high-speed computers and artificial intelligence (Al) has opened the door for the development of control systems that adopt the approach to adaptive control used by humans, and perform more efficiently and with more flexibility than conventional control systems. Two powerful tools for adaptive control that have emerged from the field of AI are fuzzy logic (Zadeh, 1973) and genetic algorithms (GAs) (Goldberg, 1989).

The U.S . Bureau of Mines has developed an approach to the design of adaptive control systems , based on GAs and FLCs, that is effective in problem environments with rapidly changing dynamics. Additionally, the resulting control lers include a mechanism for handling inadequate feedback about the state or condition of the problem environment. Such controllers are more suitable than past control systems for recognizing, quantifying, and adapting to changes in the problem environment.

The adaptive control systems developed at the

Bureau of Mines consist of a control element to manipulate the problem environment, an analysis

element to recognize changes in the problem environment, and a learning element to adjust to the changes in the problem environment. Each component employs a GA, a FLC, or both, and each is described in this paper. A particular problem environment, a laboratory acid-base pH system, serves as a forum for presenting the details of a Bureau-developed, adaptive controller. Preliminary results are presented to demonstrate the effectiveness of a GA-based FLC for each of the three individual elements. Details of the system will appear in a report by Karr and Gentry ( 1992).

PROBLEM ENVIRONMENT

In this section, a pH system is introduced to serve as a forum for presenting the details of a stand­alone, comprehensive, adaptive controller developed at the U.S. Bureau of Mines; emphasis is on the method not the application. The goal of the control system is to drive the pH to a setpoint. This is a non-trivial task since the pH system contains both nonlinearities and changing process dynamics. The nonlinearities occur because the output of pH sensors is proportional to the logarithm of hydrogen ion concentration. The source of the changing process dynamics will be described shortly.

A schematic of the pH system under consideration is shown in Fig. 1 . The system consists of a beaker and five, valved input streams. The beaker initially contains a given volume of a solution having some known pH. The five, valved input streams into the beaker are divided into the two control input streams and the three external input streams. Only the valves associated with the two control input streams can be adjusted by the controller. Additionally, as a constraint on the problem, these valves can only be adjusted a limited amount (0.5 mL/s/s, which is 20 pct of the maximum flow rate of 2.5 mL/s) to restrict pressure transients in the associated pumping systems.

The goal of the control problem is to drive the system pH to the desired setpoint in the shortest time possible by adjusting the valves on the two control input streams. Achieving this goal is made considerably more difficult by incorporating the potential for changing the process dynamics. These changing process dynamics come from three random changes that can be made to the pH system. First, the concentrations of the acid and base of the two control input streams can be changed randomly to be either 0. 1 M HCl or 0.05 M HCl and 0. 1 M NaOH or 0.05 M NaOH. Second, the valves on the external input streams can be randomly altered. This allows for the external addition of acid (0.05 M HCl), base (0.05 M CH3COONa), and buffer (a combination of 0. 1 M CH3COOH and 0. 1 M

330

CH3C00Na) to the pH system. Note that the addition of a buffer is analogous to adding inertia to a mechanical system. Third, random changes are made to the setpoint to which the system pH is to be driven. These three random alterations in the system parameters dramatically alter the way in which the problem environment reacts to adjustments made by the controller to the valves on the control input streams. Furthermore, the controller receives no feedback concerning these random changes.

.05 II HCl

. 1 11 HCl

.05 II NcJOH

.1 II NcJOH

Control input streams

External input streams

Fig. 1 . Basic structure of the pH system.

The pH system was designed on a small scale so that experiments could be performed in l imited laboratory space. Titrations were performed in a 1 ,000-mL beaker using a magnetic bar to stir the solution. Peristaltic pumps were used for the five input streams. An industrial pH electrode and transmitter sent signals through an analog-to­digital board to a 33-MHz 386 personal computer which implemented the control system.

STRUCTURE OF THE ADAPTIVE CONTROLLER

Figure 2 shows a schematic of the Bureau's adaptive control system. The heart of this control system is the loop consisting of the control element and the problem environment. The control element receives information from sensors in the problem environment concerning the status

of the condition variables, i .e . , pH and .1pH. It then computes a desirable state for a set of action variables, i . e. , flow rate of acid (QAcm) and flow rate of base (Q8AS.J· These changes in the action variables force the problem environment toward the setpoint. This is the basic approach adopted for the design of virtually any closed loop control system, and in and of itself includes no mechanism for adaptive control.

The adaptive capabilities of the system shown in Fig. 2 are due to the analysis and learning elements. In general , the analysis element must recognize when a change in the problem environment has occurred. A "change, " as it is

used here, consists of any of the three random alterations to a parameter possible in the problem environment. (Of importance is the fact that all of these changes affect the response of the problem environment, otherwise it has no effect on the way in which the control element must act to efficiently manipulate the problem environment.) The analysis element uses information concerning the condition and action variables over some finite time period to recogniz.e changes in the environment and to compute the new performance characteristics associated with these changes.

Problem Environment

Control .... a .. Element

updated controller paramatara

Lea rning E lement

ne w ftlue• or anYironmantal parametera

Analysis E lement

Fig. 2. Structure of the adaptive control system.

The new environment (the problem environment with the altered parameters) can pose many difficulties for the control element, because the control element is no longer manipulating the environment for which it was designed. Therefore, the algorithm that drives the control element must be altered. As shown in the schematic of Fig. 2, this task is accomplished by the learning element. The most efficient approach for the learning element to use to alter the control element is to utilize information concerning the past performance of the control system. The strategy used by the control , analysis, and learning elements of the stand-alone, comprehensive adaptive controller being developed by the U. S . Bureau of Mines is provided in the following sections.

Control Element

The control element receives feedback from the pH system, and based on the current state of pH and 4pH, must prescribe appropriate values of QAcm and QBASE· Any of a number of closed-loop controllers could be used for this element. However, because of the flexibility needed in the

33 1

control system as a whole, a PLC is employed. Like conventional rule-based systems (expert systems) , FLCs use a set of production rules which are of the form:

IF {condition} THEN {action}

to arrive at appropriate control actions. The left­hand-side of the rules (the condition side) consists of combinations of the controlled variables (pH and 4pH); the right-hand-side of the rules (the action side) consists of combinations of the manipulated variables (QAcm and QeASE). Unlike conventional expert systems, FLCs use rules that utilize fuzzy terms like those appearing in human rules-of-thumb. For example, a valid rule for a PLC used to manipulate the pH system is:

IF {ph is VERY ACIDIC and 4pH is SMALL} THEN {QaASE is LARGE and QAcm is ZERO} .

This rule says that if the solution is very acidic and is not changing rapidly, the flow rate of the base should be made to be large and the flow rate of the acid should be made to be zero.

The fuzzy terms are subjective; they mean different things to different " experts , " and can mean different things in varying situations . Fuzzy terms are assigned concrete meaning via fuzzy membership functions (Zadeh, 1973) . The membership functions used in the control element to describe pH appear in Fig. 3 . (As will be seen shortly , the learning element is capable of changing these membership functions in response to changes in the problem environment. ) These membership functions are used in conjunction with the rule set to prescribe single, crisp values of the action variables (QAcm and Q8AsE) . Unlike conventional expert systems, FLCs allow for the enactment of more than one rule at any given time. The single crisp action is computed using a weighted averaging technique that incorporates both a min-max operator and the cellter-of-area method (Karr, 199 1) . The following fuzzy terms were used, and therefore "defined " with membership functions, to describe the significant variables in the pH system:

pH Very Acidic (VA), Acidic (A) , Mildly Acidic (MA), Neutral (N) , Mildly Basic (MB), Basic (B) , and Very Basic (VB) ; Small (S) and Large (L) ; Zero (Z) , Very Small (VS) , Small (S) , Medium (M) , and Large (L) .

Although the pH system is quite complex , it is basically a titration system. An effective PLC for

performing titrations can be written that contains only 14 rules. The 14 rules are necessary because there are seven fuzzy terms describing pH and two fuzzy terms describing 4pH (7*2 = 14 rules to describe all possible combinations that could exist in the pH system as described by the fuzzy terms represented by the membership functions selected). Now, the rules selected for the control element are certainly inadequate to control the full-scale pH system; the one that includes the changing process dynamics. However, the performance of a FLC can be dramatically altered by changing the membership functions. This is equivalent to changing the definition of the terms used to describe the variables being considered by the controller. As will be seen shortly, GAs are powerful tools capable of rapidly locating efficient fuzzy membership functions that allow the controller to accommodate changes in the dynamics of the pH system.

Q. I

j E .75 � "; .s ! , .25

VA MA N MB 8 118

I 2 3 4 5 9 7 8 t 10 1 1 1 2 1 3 1 4 pH

Fig. 3. pH membership functions.

Analysis Element

The analysis element recognizes changes in parameters associated with the problem environment not taken into account by the rules used in the control element. In the pH system, these parameters include: (1) the concentrations of the acid and base of the input control streams, (2) the flow rates of the acid , the base, and the buffer that are randomly altered, and (3) the system setpoint. Changes to any of these parameters can dramatically alter the way in which the system pH responds to additions of acid or base, thus forming a new problem environment requiring an altered control strategy. Recall that the FLC used for the control element presented includes none of these parameters in its 14 rules. Therefore, some mechanism for altering the prescribed actions must be included in the control system. But before the control element can be altered, the control system must recognize that the problem environment has changed, and compute the nature and magnitude of the changes .

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The analysis element recognizes changes in the system parameters by comparing the response of the physical system to the response of a model of the pH system. In general , recognizing changes in the parameters associated with the problem

environment requires the control system to store information concerning the past performance of the problem environment. This information is most effectively acquired through either a data base or a computer model. Storing such an extensive data base can be cumbersome and requires extensive computer memory. Fortunately , the dynamics of

the pH system are well understood for buffered reactions, and can be modeled using a single cubic

equation that can be solved for [H30 +] ion concentrations, to directly yield the pH of the solution. In the approach adopted here, a computer model predicts the response of the laboratory pH system. This predicted response is compared to the response of the physical system. When the two responses differ by a threshold amount over a finite period of time, the physical pH system is considered to have been altered .

When the above approach is adopted , the problem of computing the new system parameters becomes a curve fitting problem (Karr, Stanley , and Scheiner, 199 1) . The parameters associated with the computer model produce a particular response to changes in the action variables. The parameters must be selected so that the response of the model matches the response of the actual problem environment.

An analysis element has been forged in which a GA is used to compute the values of the parameters associated with the pH system. When employing a GA in a search problem, there are basically two decisions that must be made: (1) how to code the parameters as bit strings and

(2) how to evaluate the merit of each string (the fitness function must be defined). The GA used in the analysis element employs concatenated , mapped, unsigned binary coding (Karr and Gentry , 1992) . The bit-strings produced by this coding strategy were of length 200: the first 40 bits of the strings were used to represent the concentration of the acid on the control input stream, the second 40 bits were used to represent the concentration of the base on the control input stream, the third 40 bits were used to represent the flow rate of the acid of the external streams, and the final 80 bits were used to represent the flow rates of the buffer and the base of the external streams, respectively. The 40 bits associated with each individual parameter were read as a binary number, converted to decimal numbers (000 = 0, 00 1 = I , 0 1 0 = 2 , 01 1 = 3 , etc. ,) , and mapped between minimum and maximum values according to the following:

c = cm1n + b cc - c� (1)

(2111 - 1) max

where C is the value of the parameter in question, b is the binary value, m is the number of bits used to represent the particular parameter (40), and cmin and c_ are minimum and maximum values associated with each parameter that is being coded.

A fitness function has been employed that represents the quality of each bit-string; it provides a quantitative evaluation of how accurately the response of a model using the new model parameters matches the response of the actual physical system. The fitness function used in this application is:

MOOr I = E (pH,_u, - pHGt:ltM1i· (2)

'"°"

With this definition of the fitness function, the problem becomes a minimization problem: the GA must minimize f, which as it has been defined, represents the difference between the response predicted by the model and the response of the laboratory system.

Figure 4 compares the response of the physical pH system to the response of the simulated pH system that uses the parameters determined by a GA. This figure shows that the responses of the computer model and the physical system are virtually identical , thereby demonstrating the effectiveness of a GA in this application. The GA was able to locate the correct parameters after only 500 function evaluations, where a function evaluation consisted of simulating the pH system for 100 seconds. Locating the correct parameters took approximately 20 seconds on a 386 personal computer. Industrial systems may mandate that a control action be taken in less than 20 seconds. In such cases, the time the GA is allotted to update the model parameters can be restricted. Once new parameters (and thus the new response characteristics of the problem environment) have been determined, the adaptive element must alter the control element.

Leaming Element

The learning element alters the control element in response to changes in the problem environment. It does so by altering the membership functions employed by the FLC of the control element. Since none of the randomly altered parameters appear in the FLC rule set, the only way to account for these conditions (outside of completely revamping the system) is to alter the membership functions

333

employed by the FLC. These alterations consist of changing both the position and location of the trapezoids used to define the fuzzy terms.

14 13 1 2 I I 10 ' •

% 7 G. I 5 4 3 2

l= :: = I

25 so Time, 1

75 100

Fig. 4. Performance of an analysis element.

Altering the membership functions (the definition of the fuziy terms in the rule set) is consistent with the way humans control complex systems. Quite often, the rules-of-thumb humans use to manipulate a problem environment remain the same despite even dramatic changes to that environment; only the conditions under which the rules are applied are altered. This is basically the approach that is being taken when the fuzzy membership functions are altered .

The U. S . Bureau of Mines uses a GA to alter the membership functions associated with FLCs, and this technique has been well documented (Karr, 1991) . A learning element that utilizes a GA to locate high-efficiency membership functions for the dynamic pH laboratory system has been designed and implemented.

The performance of a control system that uses a GA to alter the membership functions of its control element is demonstrated for two different situations. First, Fig. 5 compares the performance of the adaptive control system (one that changes its membership functions in response to changes in the system parameters) to a non-adaptive control system (one that ignores the changes in the system parameters) . In this figure, the pH system has been perturbed by the addition of an acid (at 75 seconds) , a base (at 125 seconds) , and a buffer (at 175 seconds) . In this case, the process dynamics are dramatically altered due to the addition of the buffer, and the adaptive controller is better.

Second, the concentrations of the acid and base the FLC uses to control pH are changed (those from the control input streams) , which causes the system to respond differently. For example, if the 0. 1

MHCl is the control input, the pH falls a certain amount when this acid is added. However, al l

other factors being the same, the pH will not fall as much when the same volume of the 0.05 M HCl is added. The results of this situation are summarized in Fig. 6. In this simulation, the concentration of the titrants is changed at 50 seconds. As above, the adaptive control system is more efficient.

:z: Q.

:z: Q.

1 4 1 3 1 2 1 1 10 9 8 7 6 5 4 3 2

50 100

1 ......... non-adoptive AO-FlC I - adoptive GA-FlC

1 50 200 250 JOO Time, s

Fig. 5 . External reagent additions.

1 4 1 3 1 2 1 1 1-1 0 9 8 1-7 6 5 4 3 2 1 0 0 50

1 ........ non-adoptive AO-FLC I - adoptive GA-FlC r········ ···· I "

r- �-1 00

Time, s 1 50

Fig. 6. Alteration of titrant concentrations.

SUMMARY

Scientists at the U.S . Bureau of Mines have developed an Al-based strategy for adaptive process control. This strategy uses GAs to fashion three components necessary for a robust, comprehensive adaptive process control system: (1) a control element to manipulate the problem environment, (2) an analysis element to recognize changes in the problem environment, and (3) a learning element to adjust to changes in the problem environment. The application of this strategy to a laboratory pH system has been described.

REFERENCES

Fogler, H. S. ( 1986). Elements of Chemical Reaction Engineering. Prentice-Hall , Englewood Cliffs, NJ.

334

Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading, MA.

Gottinger, W. W. ( 199 1) . Economic Models and Applications of Solid Waste Management. Gordon and Breach Science Publishers, New York, NY.

Karr, C. L. (199 1). Genetic algorithms for fuzzy logic controllers. AI Expert, §., 26-33 .

Karr, C . L . and Gentry, E . J . ( 1992, in press) . An Adaptive System for Process Control. U.S . Bureau of Mines Report of Investigations.

Karr, C. L. , Stanley, D. A. , and Scheiner, B. J. (1991) . A Genetic Algorithm Applied to Least Squares Curve Fitting. U.S. Bureau of Mines Report of Investigations No. 9339.

Kelly, E. G. and Spottiswood, D. J. ( 1982) .

l11troduction to Mineral Processing. John Wiley & Sons, New York, NY.

Zadeh, L. A. (1973). Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions 011 Systems, Man, and Cybernetics, SMC-3 , 28-44.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

REAL-TIME ACQUISITION OF FUZZY RULES USING GENETIC ALGORITHMS

D.A. Linkens and H.O. Nyongesa

Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield SJ 4DU, UK

Abstract . The paper presents a Genetic Algorithm(GA)-based system for online acquisition and modification of rules for a fuzzy logic controller. This uses a version of the rule competition production systems, called Classifier Systems, but in which the rules are matched in the fuzzy domain rather than as binary patterns. The GA is operated in the incremental mode whereby only one structure from a population is evaluated in each time interval. To hasten the learning process, the payoff received is used to assign estimates of new strengths to the other classifiers, dependent on the degree of matching with the evaluated classifier. The rule learning is initialized with randomly generated structures to which fairly general heuristic knowledge has been added. The interacting environment has been modelled by a real time simulation of closed loop administration of an anaesthetic drug, but the characteristics of the environment are not known to the GA.

Keywords: Adaptive Systems, Artificial Intelligence, Biomedical , Fuzzy Control, Genetic Algo­rithms, Learning Systems, Self-adjusting systems.

1 INTRODUCTION

Although fuzzy logic controllers (or fuzzy ex­pert systems) have been successfully applied in the control of various physical processes, the derivation of the linguistic rules has remained a 'bottleneck' of fuzzy control design. There is still no generalized method for the formulation of the fuzzy rules and the choice of the mem­bership functions, and the design is usually a trial and error exercise. Several studies have ad­dressed techniques for automated rule acquisi­tion, and self-organizing methods for rule mod­ification. The self-organizing technique intro­duced by Procyk and Mamdani [Procyk, 79] , for example, iteratively reformulates the rules by providing an adjustment using predeter­mined performance indices that indicate conver­gence to a desired trajectory. The derivation of the Performance Index table however, reflects only a common sense approach, and is not op­timal with respect to any criteria. These meth­ods also rely on a certain amount of knowledge

335

of the controlled process, at least in terms of the system time delays or 'weak models' , which can be a handicap in some complex control pro­cesses. One other shortcoming of these tech­niques is the fact that it is usually not possible to incorporate 'expert' heuristic knowledge into the controller. This paper advocates learning algorithms as a means of deriving fuzzy rules. A technique is reported for real-time acquisition and tuning of a fuzzy rule-base for a dynamic process - simulated control of muscle relaxation in Anaesthesia, using a recent type of learning algorithms, called Genetic Algorithms. This is an entirely new technique for real-time learning of fuzzy rules.

GAs have been extensively studied through analysis, and through simulation, and shown to be capable of locating high performance ar­

eas in complex domains without experiencing the problems of 'false optima' associated with standard optimization techniques. Results of these studies have also shown Genetic Algo-

rithms to exhibit learning capabilities in such diverse fields as computer software, control and game playing. Genetic Algorithms appear suit­able for application in fuzzy control, especially for learning rules and the membership func­tions. Of particular relevance is a paper by Karr and others [Karr, 89] which applied GA to the learning of membership functions of fuzzy rules. This used off-line optimizations, and showed the resulting control rules to perform better than those designed using conventional techniques.

2 GENETIC ALGORITHMS: A REVIEW

Genetic Algorithms ( G As) are exploratory adaptive search and optimization procedures that have been designed on the principles of nat­ural population genetics [Holland, 75] . There are four main differences between the working of Genetic Algorithms and other optimization techniques: (a) GAs work on a coding of the parameters, instead of the parameters themselves. (b) GAs function by maintaining a population of trial structures, - chromosomes, which repre­sents a set of control points being evaluated for usefulness to the system. Each trial structure has associated with it, a fitness value that de­termines the viability of the structure. (c) GAs use an objective function assessment, or feedback from an interacting environment, called payoff or reward, to guide the search. ( d} GAs use probabilistic rules to make deci­sions.

A simple Genetic Algorithm has three operators called, Reproduction, Crossover and Mutation. Reproduction is a process in which a new gen­eration of population is formed by randomly se­lecting strings from an existing population, ac­cording to their fitness. This process results in individuals with higher fitness values obtaining one or more copies in the next generation whilst lower fitness individuals may have none; a sur­vival of the fittest test. Crossover is the most dominant operator in the Genetic Algorithms, responsible for producing new trials. Under this recombination scheme, two strings are selected to produce new offspring by exchanging por­tions of their structures. The offspring will then replace weaker individuals in the population. Crossover serves two complementary functions. First, it provides new points for further testing within the existing 'subspaces' (represented by the parents) . Secondly, it introduces representa­tive members of 'subspaces' not already existing (through offsprings) . Mutation is a secondary operator, and is applied with a very low prob­ability of occurrence, typically less than 0.01.

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Its operation is to alter the value of a random position on a string. When used in this way, together with reproduction and crossover oper­ators, mutation acts as an insurance against to­tal loss of any bit value in a particular position in the population.

3 A GENETIC ALGORITHM FOR FUZZY LOGIC CONTROL

There are two issues to be considered in apply­ing Genetic Algorithms to learn fuzzy control rules. First is the coding of the structures that represent the rules to be learnt and secondly the evaluation of these structures. Fuzzy con­trol rules are conditional statements with a pre­determined number of linguistic conditions and one action. Each linguistic value (condition) is a fuzzy set that is representable by a member­ship function in the universe of discourse. Con­sequently a genetic rule structure is a coding of the membership functions of the conditions and action of a rule. In this study the mem­bership functions have been allowed to have a triangular (isosceles) shape. Hence, the param­eters that need to be learned by the GA can be selected to be the position of the peak of the triangle and the width of its base.

The second consideration in designing the Ge­netic Algorithm is the process of evaluating the rule structures (classifiers) . Normally, the Ge­netic Algorithm evaluates the population struc­tures using an objective function that returns a measure of each classifier's performance. In the case where the interacting environment is a dy­namic process, the evaluation can only be based on the performance of the controller in driving the response of the process towards convergence on the desired state, which is made more diffi­cult when the characteristics of the controlled process are not known to the Genetic Algo­rithm. Two types of performance measure are in general available: A global criterion, for ex­ample Integral Square Error (ISE), indicates the overall performance of the controller over a re­sponse trajectory; A local criterion on the other hand measures the performance of the controller over a neighbourhood of a few process states. One problem with the global measure is the dif­ficulty in relating it to the actions which con­tributed to its achievement. For this reason a local performance measure has been preferred, which enables credit assignment to individual actions at each instant. Unfortunately, such lo­cal performance measures, in most cases can only provide a binary, 'good' or 'bad' , indica­tion.

Usually, a Genetic Algorithm is operated m

batch mode, submitting all structures in a pop­ulation to evaluation and then assigning new strengths using an objective function. In apply­ing the GA to the control of an unmodelled dy­namic process there are a number of constraints: (a) there is no objective function assessment available, but the system relies on the noisy per­formance feedback, from an unknown environ­ment; (b) there is a limitation on the amount of com­putation that can be done between sampling in­stants; (c) the GA must provide an appropriate control structure at each sample instant;

In such a case, an incremental genetic algo­rithm, in which only one classifier from a pop­ulation is evaluated in each time interval has been preferred. Thus, from each population, a classifier is selected if it matches ( 'fires') the cur­rent input conditions. Then during credit asign­ment, reward or punishment is spread over the neighbourhood of classifiers which fire the pre­vious condition, responsible for the current per­formance measure, regardless of whether they existed in the population or not. The amount of reward given to each classifier depends on its weight (- a matching factor), the 'value' of its action and the objective assessment received from the environment. Classifiers selected for evaluation are decoded into fuzzy rules, which are then composed into a deterministic action - a weighted mean of all fired rules - using the compositional rule of inference [Zadeh, 73].

4 THE TASK ENVIRONMENT

The interacting task environment has been modelled by a real time simulation of closed loop administration of an anaesthetic (muscle relax­ant) drug, whose characteristics are not known to the GA. Muscle relaxation is required to ob­tain a certain degree of paralysis in patients un­dergoing surgery. The published pharmacoki­netics and pharmacodynamics of the muscle re­laxant drug, Atracurium, are given by the trans­fer function,

K(l + 10.64s) (1)

(1 + 3.08s)(l + 4.81s)(l + 34.42s) together with a nonlinear effect component given by the Hill Equation

(2)

The transfer function was simulated using the Runge-Kutta 4th order numerical method.

5 PERFORMANCE EVALUATION

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The learning controller in order to improve its performance needs information as to how well it is performing at each instant. In the fol­lowing we present a performance evaluation for a GA interacting with the unknown process. The primary objective of the controller is to achieve rapid transient response with minimal overshoots and small steady state errors. At the same time, we need to improve the system's be­haviour over the interval At leading to the next decision point. Such a task can be expressed in terms of minimization of an integral function:

(3)

A form of the integrand F which has been stud­ied is F = I e,. I , where e,. is a predicted error function, the purpose of prediction being to ap­ply corrective action before an undesirable con­sequence occurs. Accordingly, the minimization of the integral function requires that;

dN dtN I e,. I< 0. (4)

where N is the order of the highest derivative obtainable. A binary performance value, sign V can be derived from the above expression as;

dN signV = NOT(sign dtN I e,. I ) (5)

where signV = logical 1 is a 'good' performance and positive sign of error signals is also 1 .

The equivalent boolean formulation (for N=2) which has been used as the objective perfor­mance measure can be stated as:

sign V = sign( e,. ) sign( ej, ) sign( e;; ) +

sign( e,. ) sign( e� ) sign( e; ) ( 6)

6 ACQUISITION OF RULES

The problem of real time acquisition of rules for a fuzzy controller is the principal task addressed in this study. The approach followed is based upon a form of rule-based production systems, called Classifier Systems [Holland, 86] . These are systems in which many rules (classifiers) compete against each other and evolve under a Genetic Algorithm as possible solutions to a problem. All classifiers are in Condition/ Action form, representing codings of fuzzy conditional statements. A message list is maintained which in a simple form contains the existing heuristic rules, and against which incoming process sta­tus messages are matched, in order to determine whether a rule exists to deal with the present conditions. If no adequate rule exists then one

is created by generating a population of trial structures, and adding the corresponding mes­sage onto the list. The list is also used to match past conditions during the process of credit as­signment to determine which rules should be re­warded.

There are two functions to be performed by the learning algorithm in such a system: the rating of the competing rules and discovery of new plausible rules. In the classifier system, each rule has an associated strength that is a measure of the rule's usefulness in achieving system goals. The rating of a rule's useful­ness is performed by a Reward-Penalty algo­rithm that uses the external feedback to as­sign new strengths to competing rules. Because the classifiers play a direct role in influencing the environment's response, credit assignment is simpler (than the usual Bucket Brigade) ; thus, classifiers which result in a positive payoff are rewarded by increasing their strengths, while those leading to negative payoff are punished by decreasing their strengths. The amount of reward (or punishment) depends also on the degree to which each classifier matches the in­put conditions. The task of discovering bet­ter rules is performed by the Genetic Algorithm which also uses high strength classifiers as par­ents for new classifiers, using the genetic opera­tors reproduction, crossover and mutation. The strength is also used to make a probabilistic choice of which classifiers will be selected for evaluation.

7 SIMULATION RESULTS

The Genetic Algorithm uses population sizes of 100 classifiers, each 32 bits long. The main op­erators were a multiple-crossover and mutation. Simulation results are presented in the form of the response of the controlled dynamic process. Figure 1 shows the learning controller on a lin­ear 1 •t order process - control of mean arterial pressure (MAP). It is observed that convergence to a suitable control action is achieved fairly rapidly, and the response of the controlled pro­cess is good. When applied to the 3rd order nonlinear process - control of muscle relaxation (Figure 2) , this is more difficult, but the perfor­mance is comparable to that obtained using the established self-organizing technique (SOFLC), proposed by Procyk and Mamdani [Procyk, 79] (Figure 3) .

8 CONCLUSION

The paper has outlined a new approach to real­time learning, applied to fuzzy logic control. The Genetic Algorithm is being applied to the

338

task of accumulating fuzzy control rules, with­out any knowledge of the process. This is a nontrivial task. It has been demonstrated that performance comparable to established self­organizing techniques can be obtained, with­out the burden of designing a detailed control strategy. A number of issues are evident that need further consideration. The genetic opera­tors, notably crossover and mutation have been designed to work on arbitrary binary patterns, which may not take advantage of available do­main knowledge and may possibly be inappro­priate when dealing with rules for a dynamic situation. We are motivated to consider alter­native forms for the operators. If Genetic learn­ing can work for the tasks of rule acquisition and the tuning of fuzzy membership functions, it ought to be extended to the other problem­atic area of fuzzy design; the selection of scaling factors. The study proposes to incorporate Ge­netic Learning into fuzzy controller design for the multi variable Anaesthesia environment - the simultaneous control of muscle relaxation and the depth of unconciousness in surgical patients.

References [Holland, 75] Holland, J .H.(1975). Adaptation

in Natural and Artificial Systems, Univer­sity of Michigan Press, Ann Arbor Ml.

[Holland, 86] Holland, J .H.(1986). Escaping Brittleness, In R.S. Michalski, J .G. Car­bonell and T.M. Mitchell (Eds.) , Machine Learning Vol II, Morgan-Kauffman Los Al­tos, pp593-623.

[Karr, 89] Karr, C.L . , L .M. , Freeman, and D.L. , Meredith, (1989). Improved Fuzzy process control of spacecraft autonomous rendezvous using a Genetic Algorithm. SPIE Intelligent Control and Adaptive Sys­tems Vol. 1 196, pp 274-288.

[Procyk, 79] Procyk, T.J . , and E.H. Mamdani { 1979). A linguistic self-organizing process controller. Automatica, 15, 15-30.

[Zadeh, 73] Zadeh, L.A. ( 1973) . An outline of a new approach to the analysis of com­plex systems and decision processes. IEEE 1Tans. Syst. Man Cyber. , SMC-3, 29-44.

140

120

100 Ii. ; � \------------------------40

20

2000 Fla· l: mean arterial preaaure

2000 f'I&. 2: ilu8Cle relaxation

100 ' n ' \

4000

4000

8000 Seconda

8000 Seconds

I- - -- - OperaUna point MAP reaponae

- -- Iaofiurane

8000 10000

- - - - - Operating point 1 ----- Paral)'1118 reaponae - -- Atracurlum

8000 10000

80 I \_ I'\ I I '-- I �---------------------� 80

40

2000 4000 f'I&. 3: SOFLC technique

8000 8000 10000 Seconds

339

'--- -----12000 14000

Operating point Paral)'111• reaponae Atracurlum

18000 18000

Copyright © IF AC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

AUTOMATED SYNTHESIS OF CONTROL FOR NONLINEAR DYNAMIC SYSTEMS

T. Urban�i(I•, D. Juri�ic*, B. Filipi�* and I. Bratko*•**

* Jo!ef Stefan Institute, Jamova 39, 61000 Ljubljana, Slovenia **Faculty of Electrical Engineering and Computer Science, Tr!aJka 25. 61000 Ljubljana, Slovenia

Abstract . Artificial intelligence methods appear to be particularly well suited for control design when only inexact prior knowledge about the system to be controlled is available. Design tasks that can be solved include learning control from scratch, improving partial control knowledge, and controller tuning. The paper enlightens these approaches in two case studies, both dealing with nonlinear unstable systems: inverted pendulum control, and position control of a floating object. Comparison to the classical model-based control design approaches is also provided.

Keywords. Control system design; nonlinear systems; artificial intelligence; know­ledge acquisition; learning systems; qualitative modelling; genetic algorithms.

INTRODUCTION

By some estimations, the dissatisfaction with con­troller performance among plant operators is so high that over 50% of process control loops in in­dustrial applications run in manual mode (Litt, 1991). There are several reasons for the gap be­tween theory and applications in the field of auto­matic control. Unfortunately, some of the reasons are closely related to the very starting point of classical control design, that usually starts from an analytic model of the process to be controlled. First, in some cases it is very difficult to ob­tain an appropriate mathematical model. Sec­ond, an exact model is usually limited to the specific circumstances which might change in the future; this could result in discrepancy between the model and the real process. Finally, sophis­ticated mathematical methods are usually read­able only by highly qualified specialists, while process operators normally operate with quali­tative terms like "high", " low", " increase", "de­crease", etc. Their knowledge is experience-based and intuitive rather than precisely mathemati­cally formulated. Being able to process this kind of knowledge, artificial intelligence methods of­fer significant potentials especially in supervi­sion of the control loop along with tuning and adaptation. Also, in case of processes that are very unpleasant for any kind of analytical mod­elling (e.g. chemical processes) , artificial intelli­gence approaches can be applied to realise in-loop (feedback) controllers. For survey of principles,

341

achievements and perspectives of Al-based con­trol see e.g. (Astrom, 1991) .

The most critical step in non-classical control is knowledge acquisition. Expert controllers can be based on human operator's knowledge and men­tal skills (e.g. Schmidt and Bieker, 1987). Un­fortunately, operator's information processing is often unconscious, and therefore can not be sim­ply transplanted into a computer program. To bridge this serious problem, well-known also in other problem domains, automated synthesis of knowledge by means of machine learning and qualitative modelling emerged. Some substantial achievements have been reported, e.g. (Bratko et al. 1989). In the context of control design, es­

pecially machine learning has been explored, but the stage of greater practical applicability has not been reached yet.

The aim of this paper is to present some alterna­tive approaches to the control synthesis both at the level of direct feedback control as well as at the level of controller tuning. For this purpose, two case studies were chosen: inverted pendulum con­trol, and position control of a floating object. In both cases, the system to be controlled is highly nonlinear and unstable. For the first problem, some solutions are surveyed to show different pos­sibilities with respect to the different amount of available prior knowledge. For the second prob­lem, after experiencing a time-consuming clas­sical control design, we solved the problem by

an approach in which two difficult tasks can be avoided: development of an exact mathematical model, and laborious interactive controller tun­ing.

CASE STUDY 1 CONTROLLING INVERTED PENDULUM

Problem of the inverted pendulum control was often used to demonstrate both classical (e.g. Kwakernaak and Sivan, 1972) and nonconven­tional control techniques (e.g. Michie and Cham­bers, 1968; Barto et al. 1983, Connell and Utgoff, 1987; Anderson, 1987; Makarovic, 1988). Being an attractive benchmark problem, it bears simi­larities with tasks of significant practical impor­tance such as two-legged walking, and satellite attitude control (Sammut and Michie, 1991).

The goal is to achieve control of the inverted pen­dulum which is realised as a pole on a cart. Con­trol force is to be applied to the system to prevent the pole from falling and to keep the cart posi­tion within the specified limits. The system is presented in Figure 1 . For the dynamic equations see e.g. Anderson, 1987.

� x

Figure 1 : The inverted pendulum system

As usual in the artificial intelligence literature, the control regime is that of bang-bang. The con­trol force has a fixed magnitude and all the con­troller can do is to change the force direction in regular time intervals.

STARTING WITH THE MATHEMATICAL MODEL

To design a classical on-off controller with op­timal performance it is necessary to analyse the system behaviour in the state space. In other words, some performance index of the control sys­tem behaviour, J(�, u(t)) , could be achieved by minimization

F(�(t)) = arg ��) J(�, u(t)) E {Fmin , Fma%} (*) where � is the vector of state variables and u(t) is control input. In general, optimization ( *) could be very complicated (see e.g. Sage, 1968). There­fore we simplified the controller design by using the sign of output of the pole-placement controller (Dzeroski, 1989). The control law is then

F(�) = -8ign(A1z + A2z + A3<,o + A4<,?) If a model of the system is available, and if the model is linear, in matrix form y = Ay + BF,

342

then the parameters A1 , A2 , A3 and A4 can be computed from

det(A - BA - 81) = (8 - 81 )(8- 82)(8- 83)(8- 84) after choosing the poles 81 , 82 , 83 and 84 of the system such that they are all negative (for the real zeros) or have negative real parts (for the complex zeros).

Although optimality was sacrified for simplicity, the obtained control rule successfuly stabilises the system and keeps the quadratic error small. Fig­ure 2 shows the performance of the controller ob­tained when all the poles were set to -2 (Dzeroski, 1989).

0.8 0.8� 0.4

! 0.2 Q.jc 0 g -0.2 -0.4 -0.8 -0.8

·1+---..--..----..--..----..--..---.--..---.---' 0 2 4 8 8 10 12 14 18 18 20 Time (s)

Figure 2: Performance of the inverted pendu­lum "bang-bang" control obtained by the adapted pole placement method.

However, it should be noticed that some assump­tions must hold for this method to be applicable. Above all, an appropriate linearised mathematical model of the system must be available. Some fur­ther assumptions include availability of accurate numerical values of state variables, and invariant parameters of the system.

STARTING FROM A QUALITATIVE MODEL

Let us now assume that the system to be con­trolled is known only "qualitatively", i.e. de­scribed with relations instead of exact mathemat­ical functions. In the case of inverted pendulum, the qualitative description can be as follows:

Cart acceleration is a monotonically increasing function of the control force. When no force is applied, acceleration is also zero. The angular ac­celeration is due to two effects, gravity and force. The effect of gravity increases with the angle of the pole, and the effect of control force nega­tively increases with force and also depends on the angle as a piece-wise monotonic constraint A (monotonically increasing for negative angles, and monotonically decreasing for the positive ones).

Qualitative models can be defined using various formalisms, as for example qualitative differen­tial equations, qualitative physics theory or QSIM (Kuipers, 1986). In the formalism very similar to

that in QSIM, this the description above can be written as:

x Md°(F) t.p Md°(t.p) - Md°(F)A(t.p)

where Md° denotes a monotonically increasing function going through the point (0,0) . Bratko has shown (1991) that the structure of control rule for inverted pendulum can be derived from this model by qualitative reasoning, taking into account some basic control principles, such as con­trolling a variable indirectly through a monotonic constraint, or an integrator, or a chain of integra­tors. He obtained the control rule stated with the following relations:

Xgoal t.pgoa/ <Pgoa/ F

k2 * (k1 * (xgoal - x) - x) 1 .. g * Xgoal k4 * (ka * (t.pgoal - t.p) - cp) -Mt(<Pgoa/ )

When the system is controlled under the bang­bang regime, control action is determined by the sign of F. Taking into account Xgoal = 0 and k4 > 0, the rule can be simplified and normalised, resulting in the control rule

F(�) = sign( ax + bx + ct.p + cp)

which is up to the numerical parameter values equivalent to the rule obtained before from the mathematical model.

Of course, to apply any control rule in prac­tice, numerical parameters have to be determined. This problem is in qualitative approaches often solved ad hoc, by experimentation. As we have shown in (Varsek et al. 1992), the process of pa­rameter setting can be automatised in such a way that yields the "optimal" system response. Pa­rameter settlings that resulted in the same re­sponse as the one in Figure 2 were obtained. Es­sentially the same automatic tuning process can be applied also to the classical controllers, as will be shown and described in more detail in Case study 2.

STARTING " FROM SCRATCH "

Dynamic system control can be automatically synthesised even when nothing is known about the dynamics of the system. In this case, the sys­tem is treated as a black box and a program learns to control it by trials. Due to the black box as­sumption, initial control decisions are practically random, resulting in very bad performance in the first experiments. On the basis of experimental evidence, control decisions are evaluated and pos­sibly changed. Learning takes place until a cer­tain success criterion, usually a prescribed time of control, is met.

343

Inverted pendulum has been solved by many learning methods of this type, e.g. by (Michie and Chambers, 1968; Barto et al. 1983; Connell and Utgoff, 1987; Anderson, 1987) . Although the early work by Michie and Chambers (1968) has been recently improved in many respects, e.g. in (Bain, 1990), it provided some basic ideas for later approaches and was therefore chosen to be briefly sketched here to give an idea about this kind of approaches. In the description and analysis of their BOXES algorithm, we follow (Urbancic and Bratko, 1992).

BOXES learns to obtain a reasonable state-action table, i.e. a set of rules that specify action to be applied to the system in a given state. To make the problem tractable, the original, infinite state­space is divided into " boxes". A box is defined as a Cartesian product of qualitative values of the system variables, each qualitative value being an interval from a predifined partition. (In later ap­proaches, e.g. in Varsek et al. 1992, the borders of qualitative states are also learned automatically.) All the points within a box are mapped to the same control decision. During one trial, the state­action table is fixed. (Again, note that learning during a trial is also possible, e.g. in (Barto et al. 1983).) After a failure detection, decisions are evaluated with respect to the accumulated numer­ical information about the trial course.

BOXES is successful in achieving control. After 427 trials (average from 20 experiments) , a table that succeeded to control the simulated inverted pendulum for 10000 steps (being equal to 200 sec­onds simulation) was obtained. However, some weaknesses can be observed, such as unreliable repeated use of the obtained state-action tables, important role of ad hoc determined numerical parameters, which make the method nontranspar­ent and limit its generality and poor explanation capabilities.

To see how adding domain knowledge affects speed and results of learning, we carried out ex­periments in which state-action table was ini­tialised by a partial control rule:

if cp > tp1 then action + else if cp < -cp1 then action -

Decisions for the states covered by the rule stayed unchanged during the learning process. Although the rule alone is not effective at all (average sur­vival was 30 steps) , it considerably descreased the number of trials needed for achieving 10000 step control to 197 (average from 20 experiments). At the same time, the reliability (i.e. the percent­age of repeated state-action uses that resulted in 10000 step simulation) increased from 16.5% to 50%. More detailed description of the experi­ments is available in (UrbanCic and Bratko, 1992).

The problem of state-action incomprehensibility was overcome in (Sammut and Michie, 1991) by applying inductive learning. In the same work it is also shown that the method can be extended to solve more difficult problems.

CASE STUDY 2 POSITION CONTROL OF A FLOATING OBJECT

This study involves a laboratory device whose es­

sential part is an object, floating on an air bubble in a water tank. Depending on the size of the bubble, the object moves up and down. The con­trol problem is to keep the object at a desired position by properly influencing the size of the bubble through changes of pressure. The device is schematically presented in Figure 3, along with the dynamic equations.

x

h H

AH = au2 + {Ju + r AH; = �(-�H, + AH)

Pc = Pz H,':IJ;H, x = g(l + ;t(V, - s(l - h)))

me

+u-

h = � [ P•:,P· + % + l - �(-P·-:,-P·_+_z_+_l_)-::-2---4-(-�-.-+-z_l.....,) z : object position h : water level inside the object a, /3, "'f, r: constants p : water density Pz : initial air pressure at the top of the

reservoir (at u=O) Hz : initial water level in the reservoir (at u=O) tl.H, fl.Hi: relative change of the water level me , Vr , /: object mass, volume and length S : area of the object's profile Pc : pump pressure g : acceleration due to gravity

Figure 3: The laboratory device

As usual in classical control design, exhaustive mathematical modelling of the process was first undertaken. The entire model relating voltage on the pump u(t) (process input) and position z(t) (output) is a nonlinear third order system. Later,

344

it was found out that the floating object dynamics can be described sufficiently well by the linearised model of the form

z(s) k u(s) - s3 + l .96s2 - 0.51s - 1

where k is a gain dependent on the working point.

We used the model ( * *) to calculate the system impulse response. Notice that the latter could be determined also experimentally, e.g. from the step response of the stabilised system. Finally, having the impulse response, all we have to do in order to calculate the response of the controlled system is to solve a simple convolution integral. That means, in fact, that we can approach the controller design without prior modelling. This is very important since the model building phase can be very time consuming. In our case, for ex­ample, some weeks of graduate student work were spent to develop the model (Pavlinic, 1991) .

TUNING PID CONTROLLER

WITH A G ENETIC ALGORITHM

Classical PID controllers are widely used due to their simplicity (if compared, for example, to state controllers) and generality. Instead of com­plete state information only error, i.e. the differ­ence between the reference and actual output val­ues, is to be observed. Further advantage is also the fact that only three parameters are to be de­termined. Having at disposal the mathematical model or at least the impulse response, it is pos­sible to determine appropriate controller parame­ters by means of optimisation.

Standard optimization approach is based on min­imisation of some quadratic criterion. However, in practice it is desirable to state the optimisa­tion criterion in terms close to human understand­ing of the processes, like permitted overshoot, de­sired settling time, and similar. Namely, oper­ators in industry primarily check the qualitative characteristics of the system. Therefore, to meet their requirements, optimization by other crite­ria is often to be repeated several times. This may be quite laborious task because usually there is no engineering evidence about how to change weighting parameters to get a desired solution. To bridge this problem we tuned the PID controller automatically with a genetic algorithm that min­imizes overshoot at the prescribed settling time.

Genetic algorithms (GAs) are loosely based on Darwinian principles of evolution: reproduction, genetic recombination, and " the survival of the fittest" (Holland, 1975; Goldberg, 1989). Genetic algorithms maintain a set of candidate solutions called a population. (In our case, a candidate so­lution is a triple of numbers, representing numer­ical values of PID controller parameters.) Candi-

date solutions are usually represented as binary coded strings of fixed length. Initial population is generated at random. What happens during cy­cles called generations is as follows. Each mem­ber of the population is evaluated using a fitness function. After that, the population undergoes reproduction. Parents are chosen stochastically, but strings with a higher value of fitness func­tion have higher probability of contributing an offspring. Genetic operators, such as crossover and mutation, are applied to parents to produce offspring. A subset of the population is replaced by the offspring, and the process continues on this new generation. Through recombination and se­lection, the evolution converges to highly fit pop­ulation members representing near-optimal solu­tions to the considered problem.

In our case, the optimization problem was to de­termine such parameters kp, k1 and kv that over­shoot at the prescribed settling time is minimised. The controller used is as follows:

u(t) = kpe(t) + k1 1' e(r)dr + kve(t)

A genetic algorithm designed to tune PID con­troller parameters employed binary coding of can­didate solutions. Binary strings, representing triples of controller parameter values, consisted of three subsections that corresponded to the pa­rameters kp, k1 and kv , respectively. The string length was 3 x 8 = 24 bits, where each of the three 8-bit sections represented an integer from the in­terval [O, 255] . A real-valued controller parame­ter ki was derived from a related integer value Ni through the linear transformation

where km is the lower bound of the search in­terval for parameter ki and Llki is its discretiza­tion step. Some different search intervals and dis­cretization steps were applied initially to explore the parameter space, but for a detailed experi­ment km was set to 0 and Llki to 0.2 for all con­troller parameters. In other words, parameter val­ues were searched in the interval from 0.0 to 51 .0 with the resolution of 0.2.

The candidate solutions were assigned fitness val­ues according to the behaviour of the controlled system. For each triple ( k p , k 1 , k D), the system response to PID control action was calculated and evaluated with respect to the minimum overshoot criterion. In our experiment, the allowed settling time was 8 seconds, and the overshoot was to be reduced as much as possible.

To introduce the fitness function for this com­pound optimization criterion, let x denote a triple of controller parameter values, ta et( x) the settling time of a system controlled by the controller using

345

parameter setting x and Ymax (x) its overshoot. Furthermore, let toba be the observation time, i.e. the time period for which the response of the sys­tem is calculated, and Yref the desired system re­sponse. Then the fitness of the candidate solution x is defined as follows:

f(x) =

where fmin and !max represent fitness function upper and lower bounds, and f,ei is a thresh­old fitness value to distinguish between parame­ter settings satisfying the settling time constraint and the ones violating this requirement. Through f(x), the optimization criterion was implemented in the following manner. Parameter settings not stabilising the controlled system within the obser­vation time were all assigned the minimum fitness value fmin · Settings stabilising the system at or after tdea , but before toba were assigned fitness from the interval Umin , f,ei] so that decreasing settling time towards tdea resulted in increasing fitness values towards fa et · Finally, if the settling time criterion was satisfied, solutions were evalu­ated according to overshoot in a similar way.

The operators applied in the algorithm were se­lection, simple (i.e. single-point) crossover, and guaranteed mutation. The GA parameters used in the experiment were the following: population size 20, number of generations 30, crossover prob­ability 0.6, and mutation probability 0 .05.

The GA was run 10 times. In all the runs, the cal­culated parameter settings were found that pro­vided stabilization of the controlled system within the prescribed settling time. Among the obtained solutions, the setting kp = 12.4, k1 = 4.8, kv =

48.2 yielded controller performance with mini­mum overshoot. The system response to the PID controller with the obtained parameters is shown in Figure 4.

0.6

0.5

'.[ � 0.4 c: 0 � 0.3

0.2

0.1 T---r-....---..-�--r-�--.--.---.--i 0 10 20 30 40 50 60 70 60 90 100

Time (s)

Figure 4: Performance of the GA tuned PID controller in the floating object position control

It is worth mentioning that results obtained by GAs are similar to those .created by a model­based approach based on a sort of pole-placement (Pavlinic, 1991 ) .

CONCLUSION

The paper presents some possibilities that artifi­cial intelligence methods offer in obtaining control when little or even nothing is known about the syustem to be controlled. The cost for "know­ing nothing" is usually paid by time consuming experiments, so any kind of knowledge available should be taken into account. Considerable im­provements were noticed already when initializing learning with partial control rule. When structure of the system to be controlled is available in the form of a qualitative model, the controller struc­ture can be derived in advance, leaving only nu­merical parameters to be learned. Similarly, when the controller structure is determined, e.g. the one of classical PID, only the problem of choosing numerical parameters remains. All these situa­tions were considered and solved, but some se­rious problems still remain, indicating our fur­ther work directions. After all, it should be no­ticed that the described work is related just to a number of laboratory experiments. To tackle more realistic problems, the requirements inher­ent to real-world domains will become crucial. Among them, reliability, robustness, understand­ability and on-line adaptation of the synthesised control rules will have the highest priority in our investigations.

REFERENCES

Anderson, C.W. (1987) . Strategy Learning with Multilayer Connectionist Representations. In P. Langley (ed.) Proc. ,Ith Int. Workshop on Ma­chine Learning, Morgan Kaufmann.

Astrom, K.J. ( 1991). Intelligent Control. ECC 91 European Control Conf. , Grenoble, 2328-2339.

Bain, M. ( 1990). Machine-learned rule-based control. In M. Grimble, J . McGhee, P. Mow­forth (eds.) , Knowledge-Based Systems in Indus­trial Control, Stevenage: Peter Peregrinus, pp. 222-244.

Barto, A.G., Sutton, R.S. , Anderson, C.W. ( 1983). Neuronlike Adaptive Elements That Can Solve Difficult Learning Control Problems. IEEE Trans. on Systems, Man and Cybernetics, Vol . SMC-13, No.5, 834-846.

Bratko, I . , Mozetic, I . , Lavrac, N. (1989). KAR­DIO: A study in deep and qualitative knowledge for expert systems. Cambridge, MA: MIT Press.

Bratko, I. ( 1991) . Qualitative Modelling: Learn­ing and Control. 6th Czechoslovak Conf. on AI, Prague, June 1991 .

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Connel, M.E., Utgoff, P.E. ( 1987). Learning to Control a Dynamic Physical System. In Proc. 6th National Conf. AI, Morgan Kaufmann, 456-459.

Dzeroski, S. ( 1989) . Control of inverted pendu­lum. University of Ljubljana, Faculty of Electri­cal Engineering and Computer Science, BSc The­sis (in Slovenian).

Goldberg, D.E. ( 1989) . Genetic Algorithms in Search, Optimization and Ma chine Learning. Addison-Wesley.

Holland, J .H . ( 1975). Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, Ml.

Kuipers, B. ( 1986) . Qualitative Simulation. Ar­tificial Intelligence 29, 289-338.

Kwakernaak, H . , Sivan, R. ( 1972). Linear Opti­mal Control Systems. Wiley-Interscience, NY.

Litt, J . (1991) . An Expert System to Perform On-Line Controller Tuning. IEEE Control Sys­tems Magazine, Vol . 1 1 , No.3, 18-23.

Makarovic, A. ( 1988) . A qualitative way of solv­ing the pole balancing problem. Memorandum lnf-88-44, University of Twente. Also in: J . Hayes, D. Michie, E. Tyugu, (eds.) , Machine Intelligence 12, Oxford University Press, 1991 , pp.241-258.

Michie, D. , Chambers, R.A. ( 1968). BOXES: An experiment in adaptive control. In E. Dale, D. Michie (eds.) , Machine Intelligence 2, Edinburgh University Press, pp. 137-152.

Pavlinic, A. ( 1991) . Modelling and Computer Control of an unstable laboratory process. B.Sc. Thesis, Faculty of Electrical Engineering and Computer Science, University of Ljubljana (in Slovenian).

Sage, A.P. ( 1968). Optimum Systems Control. Prentice-Hall Inc. , Englewood Cliffs, N.J.

Sammut, C. , Michie, D. (1991) . Controlling a "Black Box" Simulation of a Space Craft. AI Magazine, Vol. 12, No. I , 56-63.

Smidt, G. K. , Bieker, B. ( 1987). Design and Test of an Expert Process Controller Based on Human Operator's Knowledge and Mental Skills. In: S. Tzafestas et al. (eds.) , System Fault Diag­nostics, Reliability and Related Knowledge-Based Approaches, Reidel Publishing Company, Vol. 2) pp. 183-197.

UrbanCic, T., Bratko, I. ( 1992). Knowledge Ac­quisition for Dynamic System Control. In B. Soucek (ed.) , Dynamic, Genetic and Chaotic Pro­gramming: The Sixth Generation. John Wiley, NY (in press).

Varsek, A. , UrbanCic, T., Filipic, B. ( 1992) . Ge­netic Algorithms in Controller Design and Tun­ing. Submitted for publication.

Copyright @ IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

ON REPRESENTATIONS FOR CONTINUOUS DYNAMIC SYSTEMS

E.A. Woods

SINTEF Aulomatic Control, The Norwegian lnsituJe of Technology, Division of Engineering Cybernetics, N-7034 Trondheim, Norway

Abstract. Through the use of a simple example involving a buffer tank, we illustrate the problems faced when attempting to formalize the dynamic aspects of a continuous process system. The problems are especially severe if we attempt to employ a purely qualitative representation. We show that the theoretical results obtained within qual­itative reasoning describing the limits of qualitative simulation can be extended to cover the rule based approach as well. We conclude that for those cases where it is necessary to make predictions from a model of a dynamic system, we need a model based on a quantitative mathematical representation. Since representations of this type will not support any kind of reasoning about the system, apart from the compu­tation of related values for variables, we need to employ some kind of hybrid approach to be able to make predictions about the evolution of variables while retaining the ability to reason about the behavior of the system at the same time.

Keywords: Artificial Intelligence, Inference processes, Modeling, Monitoring, State space methods, Knowledge Representation, Qualitative reasoning.

INTRODUCTION

One of the ultimate goals for the research on how to apply Artificial Intelligence systems to real time control must be to develop a theory describing which representation schemes are suitable for dif­ferent classes of problems. While no complete such theory is presently within reach, we are start­ing to accumulate insight on the limitations of some popular knowledge representation schemes. It is important to communicate this kind of in­sight as it may save the practitioners attempting real world applications the annoyance caused by discovering that the system cannot possibly work anyway.

This paper focuses on the issue of expressive ad­equacy for representational schemes to be used in programs intended for analysis of continuous dynamic process systems. These systems have certain characteristic features setting them apart from static systems or dynamic systems which can be described by a finite number of discrete states. These characteristic features affect which

347

tasks can be addressed by systems utilizing differ­ent knowledge representations as a basis for the models employed to reason about the system. The issues we are addressing are really epistemological, McCarthy (1977) .

In this paper we are not concerned with the good­ness of any particular model as such. Rather, our aim is to identify the limits of the representation scheme in which the model was expressed. All repres�ntations allow us to express some aspects of the system and situation being analyzed explic­itly. Anything which can be expressed explicitly is obviously within the expressive power of the repre­sentation. Moreover, other characteristic proper­ties of the system or its behavior will be implicitly described by the model. This means that given a proper reasoning scheme, the implicit properties or behavior can be derived and given an explicit description. But, for a given representati�n, some properties and behavioral aspects can neither be explicitly described nor derived from any model by any conceivable reasoning methodology. We shall characterize such information as being outside the scope of the representation.

1 I

Fig. 1: A buffer tank.

To identify the exact scope of a representation is difficult since it requires that we, implicitly, con­sider the most powerful possible inference mecha­nism and uses the most general semantical inter­pretation. In this paper, we discuss neither in­ference mechanisms, nor different semantical in­terpretations directly. Rather, we try to identify the limits of the scope of a representation by look­ing at examples illustrating when the scope of a representation is exceeded. From this, we can es­tablish certain boundaries for what can possibly be expressed using different forms of representa­tion. We will employ a buffer tank as an example to illustrate our points.

THE EXAMPLE SYSTEM

We shall consider a simple buffer tank as depicted in Fig. 1 . Buffer tanks are frequently used in the process industries to decouple the dynamics between process sections or to store utilities like cooling liquids. The task of monitoring that the tank will not overflow or run empty is often left to the operator. The operators will typically rely on some kind of alarm system to help them detect problems with buffer tanks like this one. In some plants the flow lines may be susceptible to clog­ging and similar malfunctions. We would like to implement a program which monitors the level in the tank and performs diagnosis. Since it n;iay be to late to take action when abnormal levels are ob­served, we would like the monitoring system to be able to predict future abnormal levels. Monitoring such a buffer tank seems to be a good example for a possible task for application of AI techniques in process control.

Note that the buffer tank of this example is an extremely simple system. The point in choosing it is that it incorporates the basic characteristic property of a continuous dynamic system, the re­lationship between the flows, q; and q0, and the level, l, is an integral relationship. The example thus covers the most basic dynamic interaction,

348

a single integrator. Any representational scheme intended for use with dynamic applications must at the very least be capable of capturing the char­acteristic features of the buffer tank.

A RULE BASED APPROACH

Production rules are widely used in AI as a means of formalizing knowledge and as a way of pro­gramming a solution. Commercial expert system shells rely on this technique which is convenient because it enables separation of knowledge, ex­pressed as productions by the implementor, and inference procedures, which comes as a part of the shell.

One typical way of employing a rule based ap­proach for analysis is to assume a hypothesis, use the available knowledge to predict the behavior of the observed system under this hypothesis, and then evaluate the hypothesis by comparing the predictions with available observations from the actual system. To make this approach work for the buffer tank, we would like to express the re­lation between the flows, q;(t) and q0(t) , and the level, l(t) , by means of a single rule or a set of rules. Some simple suggestions for how this could be done follows below.

Alternative 1 : (IF q; i s positive

THEN l is increasing) Alternative 2:

(IF q; is increasing THEN l is increasing)

Alternative 3: (IF q; is greater than q0

THEN l is increasing)

Alternative 1 is clearly wrong in those cases where the flow out of the tank is greater than the flow in. Alternative 2 is wrong as well since it does not matter whether the amount of liquid flowing into the tank is increasing or decreasing if the amount flowing out is greater. The third alternative is a correct description of the situation, but it does not say anything about the absolute level in the tank, only its rate of change.

The problem basically is that the absolute level l is a function of all previous values of q;(t) and q0(t). This means that the only way to derive the value for the level in the tank is to compute the sum of all previous contributions in terms of net in-flows over previous intervals of time. And treating the level in the tank as a state variable, this is just what is being done with any discrete

numerical integration algorithm. But this is ex­actly the point, to reason about the consequences on future levels from information on the amounts of the input and output flows requires numerical integration, nothing less.

Some rule based shells and programming lan­guages will easily accommodate a hack involving a numeric integration routine. For instance, Prolog will allow a seemingly elegant implementation of such a solution. Some rule languages which allow a numeric interpretation of the variables and the definition of computational predicates may also allow this, but note that the control part will in general be anything but nice and the efficiency compared to a traditional integration algorithm is bound to be lousy. But this is not the real problem. The point is that in this case, we are no longer attempting to formalize the relationship between flows and level. We have in effect aban­doned our original aim. We are merely using the rule based approach as a programming language to implement numeric integration, for which it is not very well suited.

Note however that this does not in principle af­fect our ability to apply rule based approaches to reason about the effects of dynamic interac­tions at a higher level of abstraction. We may for instance express a fact such as Integral­relationship( %1) and use this as one of the statements describing a larger section of the plant . Applying a knowledge based system with a know­ledge base describing how properties like oscilla­tions and instability depend on loops involving elements like integrators and hysteresis elements might conceivably allow us to reason about stabil­ity and oscillating behaviors in process plants.

But this does not alter the fact that the Integral­relationship relation is in itself useless when it comes to derive the value of the level from the flows. Also, we emphasize that we do not sug­gest that knowledge based stability analysis of this kind should be attempted. Since the numerical values of a number of parameters will be impor­tant in establishing the dynamic characteristics of a system, extensions to the approaches described by Sacks (1991) and Zhao (1991) may provide su­perior solutions.

A QUALITATIVE REASONING APPROACH

Within the field of Qualitative Reasoning (QR) , (Bobrow 1984; Weld 1990), several symbolic ap­proaches for reasoning about the behavior of con­tinuous dynamic systems were developed in the

349

late 70s and early 80s. The researchers in this field in effect developed a qualitative calculus where ev­ery variable would take on one of a finite set of symbolic qualitative values and the derivative of the variables would be either increasing, steady or decreasing. Knowledge on the physical system were expressed as constraints among variables and general reasoning procedures for deriving the be­havior of the systems were developed to operate on sets of such constraints.

Relating this to the buffer tank, we introduce a quantity space for the level in the tank consisting of the following symbols; {- ZERO +}. A quantity space defines the set of values which a variable may attain. The variable in this case is the level in the container. The symbols normally define a complete ordering. The intended interpretations of these symbols could be;

ZERO +

no liquid in container. between empty and full the tank is overflowing.

We could have introduced additional symbols in the quantity space above, hut the three values, which coincides with the notation used by (de Kleer 1984) is sufficient for our example. A quan­tity space spans a region on the real line which is partitioned into smaller regions, like ZERO, and points, like + and - in this case. Similarly, we introduce the quantity space of { + ZERO} for the two flows qi and q0 , for which the intended inter­pretations is "something is flowing" and "nothing is flowing" respectively.

A typical constraint between variables may look like;

deriv(l)

Although this looks like an equation, it is not. To see why, try to work out the value for deriv(/) when qi and q0 both equals +. Since the interpre­tation of + is that something is flowing, but we don't know how much, the result for deriv(/) can be anything. This is recognized by the qualitative calculus which in this case produces a "?" as the answer. This result would force the reasoner to investigate the consequences of all possible alter­natives, thus causing the analysis to branch.

Note that time is not explicitly defined in most QR schemes. The only points of time which is of inter­est is those where "something interesting is hap­pening" , this is generally taken to be those points of time where some variable changes its qualita­tive value.

Qualitative integration is performed by extrapo­lation. Assume that q; equals + and q0 equals ZERO. In this case, the qualitative calculus un­ambiguously identifies the value of deriv(l) as +. Assume the present value of the level is ZERO, then the next value is undecided, it could be either ZERO or +. This is due the lack of accuracy in the qualitative representation. In fact, the quali­tative representation will only allow us to express that if the situation where more is flowing into the tank than is flowing out persist for long enough, the tank will eventually become full. The implicit representation of time and the lack of quantitative values is essentially two aspects of this problem. The qualitative reasoners manage to live with this uncertainty by exploring all possible sequences of events, this means that the analysis branches.

The problems accumulate when there are more than one variable in the model . Assume that we were also interested in the temperature of the liq­uid in the buffer tank, and that the derivative of this temperature had been identified as positive and its value were below the boiling temperature. Since the reasoner is often unable to identify which variable will reach its new qualitative value first, it again has to take account of both possibilities thus creating another branching of the analysis. Some­times, the constraints constituting the model will impose limits on the order with which variables may change values, but the problem of branching is nevertheless very severe.

The researchers in the field of QR have taken these problems seriously. Two excellent papers pointing out the possibilities and limitations of the qualitative simulation approach are those by Kuipers ( 1986) and Struss ( 1990) . Kuipers related the qualitative models to underlying mathemati­cal models expressed as ordinary differential equa­tions (ODEs) and showed that there is a many to one mapping from ODEs to the Qualitative Differ­ential Equations ( QDEs) constituting the qualita­tive model . The qualitative analysis must there­fore predict all solutions which could be realized by any of the ODEs corresponding to the QDE, branching is therefore necessary. Struss, by relat­ing the qualitative calculus to interval arithmetic and group theory, showed that the conditions for certain mathematical properties, such as associa­tivity, was not in general satisfied. This is a source of so called spurious solutions, or solutions which would not appear for any of the ODES mapping onto the QDE in question.

These formal results confirms the conclusions we reached by considering the example with the buffer tank. Any rule based approach which do not support the use of quantitative calculus will

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have to implement a purely ad-hoc version of qual­itative integration if attempts are made to reason about the dynamic interactions in a continuous process plant. The ad-hoc procedures will not be able to circumvent the problems experienced in QR since it has been proved that the problems are due to low resolution in the qualitative representation. The QR approaches have in fact established theo­retical limits for what is possible with any qualita­tive approach in the realm of continuous dynamic systems.

These facts have eluded many researchers. Pa­pers reporting the use of qualitative simulation in architectures intended for real-life applications are not uncommon, see (Vina & Hayes-Roth 1991 ) for an example. We need to recognize that reasoning techniques which do not support the standard cal­culus can only be used to reason about physical process systems at a level of abstraction where dynamic interactions are not considered.

An example of an approach which adheres to this is the Multi Level Flow Modeling MFM techniques, (Lind, 1990) . This approach describes a plant in terms of abstract functions and goals, not in terms of physical interactions. However, one problem with this approach is that there is no obvious way to make full use of the available measurements from the plant when abstracting into the MFM de­scription.

A HYBRID APPROACH

This section provides a brief introduction to how the Hybrid Phenomena Theory, HPT, addresses these issues by tightly integrating both quantita­tive and qualitative representations. Spatial lim­itations prohibit an extensive description of the HPT, see (Woods 1991a; 1991b) for further details. At the quantitative level, the HPT employs state space models to describe the the interactions in the process in terms of changing numeric values for variables. At the qualitative level, a represen­tation describing physical components and inter­actions in terms of phenomena is used. The quali­tative part of the representation can be seen as an

extension of the Qualitative Process Theory, QPT (Forbus 1984; 1990) . The major difference is that the HPT does not attempt to make predictions by performing simulation with a qualitative model.

On top of the qualitative and quantitative lay­ers of the HPT there is another level, denoted the knowledge level. This level provides a vocabulary for describing the characteristic properties of dif­ferent kinds of physical interactions. These are formalized as a set of phenomena definitions. For

the example with the buffer tank, the most im­portant phenomenon is the FLUID-FLOW. In the HPT, a definition of FLUID-FLOW may be viewed as comprising three parts; topological conditions, operational conditions and effects.

The topological conditions govern instantiation. At the knowledge level, every phenomenon def­inition is given in an abstract manner which is not related to any particular occurrence of the phenomenon. The topological conditions for the FLUID-FLOW would specify that there would have to exist some fluid, there would have to exist a flow-path, and the position of the fluid relative to the flow-path would have to satisfy certain addi­tional criteria. Whenever these conditions were satisfied, an instance of the fluid flow would be created. For the example with the buffer tank, two instances, one for the flow into the tank and another for the flow out of it, would be created.

The operational conditions govern the applicabil­ity of each instance of a FLUID FLOW. These may include both conditions involving quantita­tive conditions, e.g. the difference in pressure over the flow-path must be positive, and predicates de­pending on user interaction, e.g. no valve must be closed. When all operational conditions are satis­fied, the phenomena-instance is said to be active.

The effects describe the impact of each active phe­nomenon. These may include both logical rela­tions and specifications of dynamic interactions in terms of how the values of certain variables is af­fecting the derivatives of others, such interactions are defined as influences. The semantical inter­pretation of the influences allows the HPT proce­dures to construct a state space model for every combination of active phenomena. An influence basically describes a term in a balance equation. Using the level in the tank, 1, as a state variable, each of the two fluid flow instances would specify how 1 was affected by the flow. The flow into the tank would provide a positive contribution to the level, the flow out would provide a negative con­tribution. The HPT combines these influences by summing them and so both would be accounted for in the resulting state space model.

The set of active phenomena provides a qualita­tive characterization of what is going on in the plant at a comparatively high level of abstraction. E.g. the fact that there is an active fluid flow leav­ing the buffer tank but there is no flow into the tank may be a relevant way to describe the situa­tion to an operator. The HPT supports simulation with an ordinary quantitative state space model, thus avoiding spurious solutions and branching. This simulation may also trigger changes in the set of active phenomena, thus allowing predictions to be presented at a high level of abstraction. These

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predictions may be used both for presentation to the operators and as input to a rule based system which may then operate on a level of abstraction where the qualitative techniques are well suited.

DISCUSSION AND CONCLUSION

It is important to distinguish between using a methodology to formalize the properties of a sys­tem, and using the methodology to program a so­lution. In this paper, we have been concerned with the possibilities for formalizing the dynam­ics of physical systems.

The representations worked out within QR were created to capture the properties of physical sys­tems to the fullest extent possible using purely qualitative models. The reasoning schemes em­ployed were tailor made to identify the best de­scription of the systems behavior which could pos­sibly be derived from a qualitative representation. The limitations which exist are due to the lack of accuracy in any qualitative representation. There­fore, no symbolic rule based approach can fare any better. We may use a rule based approach to cap­ture our heuristic expectations about what nor­mally happens in a specific plant, as exemplified below.

IF

AND

THEN

the amount of flow in exceeds 50 liters a minute

the amount of flow out is less than 5 liters a minute

conclude the tank will soon overflow

But it should be recognized that such rules is not capturing the dynamics of the physical system. It is merely relating a possible event to snap­shots of the values for two variables. Also, the use of numbers should not lead us to believe that this is a quantitative representation, the numbers have no value as numbers unless the reasoning mechanisms employed support extensive compu­tational mechanisms. A statement as the rule above should therefore not be confused with at­tempting to model the dynamic aspects of a phys­ical system. The rule above is also extremely in­flexible and difficult to combine with other infor­mation.

The HPT is an attempt to develop a framework which will allow us to formalize the effects of dy­namic interactions. This formalism makes use of a quantitative model to predict the effects of dy­namic interactions in the system. The basic idea is to apply knowledge about primitive physical

interactions to a description of a plant to iden­tify potential phenomena. The description of the phenomena contains the necessary conditions to establish whether the phenomenon can be instan­tiated. Next, every instance is tested to see if it contains a relevant contribution for the current state of the system. If these tests are all satisfied, the interactions prescribed by the definition is in­cluded in the quantitative description. The HPT in this manner allows us to combine reasoning about possible dynamic phenomena at an abstract sym­bolic level, and to make predictions by using a quantitative state space model. The approach is, like any numeric approach, vulnerable to missing or inaccurate values for parameters and variables.

If we really need to take account of the dynamic interactions in a process plant, we must rely on mathematical models to make predictions about the behavior of the plant. If we are content with a description capturing our experiences about what normally happen when certain patterns are ob­served, then a rule based approach will suffice. But we should not fool ourselves into believing that the latter approach may be used to describe the effects of dynamic interactions in continuous plants. It is in fact nothing more than a model of our conceptions about how the plant behaves, and it can only capture static relations of the plant.

ACKNOWLEDGMENT

The author would like to thank colleagues at SINTEF Automatic Control and The Norwegian Institute of Technology, Division of Engineering Cybernetics, for the many inspiring discussions. In particular, Professor Jens G. Balchen should be credited for being the first to use the exam­ple with the buffer tank to point out that no rule based formalism could capture the dynamic rela­tionship involved.

REFERENCES

Bobrow, D.G. (Ed) ( 1984). Qualitative Reasoning about Physical Systems. North Holland.

Forbus, K.D. ( 1984). A Qualitative Process The­ory. Artificial Intelligence, 24.

Forbus, K.D. ( 1990) . The Qualitative Process Engine. In D.S. Weld and J . de Kleer. (Eds.), Readings in Qualitative Reasoning about Physical Systems, Morgan Kaufmann.

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de Kleer, J . and J .S . Brown ( 1984). A Qualita­tive Physics Based on Confluences. Artificial Intelligence, 24.

Kuipers, B. ( 1986). Qualitative Simulation. Arti­ficial Intelligence, 29.

Lind, M. ( 1990). Representing Goals and Func­tions of Complex Systems, An Introduction to Multilevel Flow Modeling, Institute of Auto­matic Control Systems, Technical University of Denmark, 1990. 90-D-381 . .

McCarthy, J . ( 1977) . Epistemological Problems of Artificial Intelligence. . In B. L. Webber and N. J . Nilsson (Eds), Readings in arti­ficial intelligence, Morgan Kaufmann, 1985. Originally in PROC 5th Intl. Joint Conf. on Artificial Intelligence, 1977.

Sacks, E.P. ( 1991) . Automatic analysis of one­parameter planar ordinary differential equa­tions by intelligent numeric simulation. Arti­ficial Intelligence, 48.

Struss, P. ( 1990). Problems of Interval-Based Qualitative Reasoning. In D.S. Weld and J . de Kleer. (Eds.) , Readings in Qualitative Reasoning about Physical Systems, Morgan Kaufmann.

Vina, A. and B. Hayes-Roth ( 1991) . Knowledge based real-time Control. The Use of Abstrac­tions to Satisfy Deadlines., Paper presented at the IFAC workshop on Artificial Intelli­gence in Real Time Control, Rohnert Park, Sonoma County California, USA, 23 - 25 September, 1991 .

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Woods, E.A. and J .G . Balchen (1991b). Struc­tural Estimation with the Hybrid Phenomena Theory, Paper presented at the IFAC work­shop on Artificial Intelligence in Real Time Control, Rohnert Park, Sonoma County Cal­ifornia, USA, 23 - 25 September, 1991 .

Zhao, F. ( 1991) . Extracting and Representing Qualitative Behaviors of Complex Systems in Phase Spaces. In J . Mylopoulos and R. Reiter (Eds.) , Proceedings of the Jeth Inter­national Joint Conference of Artificial Intel­ligence, Morgan Kaufmann.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

PROCESS KNOWLEDGE ACQUISITION AND C ONTROL BY QUANTITATIVE AND

QUALITATIVE COMPLEMENTARITY

T. Nakagawa*, Y. Sawaragi** and Y. Yagihara*

*System Sougou Kaihatsu Co. Ltd. , 1-28-23 Hongou, Bunkyo-ku, Tokyo ll3, Japan **The Japan Institute of System Research, 4 Ushinomiya-cho, Yoshida, Sakyo-ku, Kyoto 606, Japan

Key words : A I , expert system, fuzzy system, model building , computer control , qualitative inference

Abstract

Even when an autoregressive model [ 1 , 2 ] is created and computer control is effected based on i t , the subsequent measured values are sometimes imperfect due to disturbances in the process and noise in the measurements . This paper proposes an approach for overcoming this drawback of tight control by an AR model when it is impossible to carry out computer online control based on an autoregressive model . This approach in the broad sense of the term involves robust control in which model -based deep knowledge based on an existing AR model or mathematical model is used and converted to fuzzy qualitative control . As an actual example we discuss a cement rotary kiln process, and we present an approach for process disturbances and incomplete measured values by transforming quantitative control into qualitative control and also making use of hidden information that cannot be abstracted without sensor fusion. As a feature of this method we d iscuss the effectiveness and purpose of the paradigm in which one does not quantify a qualitative model but rather goes in the opposite direction of qualitizing a quantitative model .

1 . Introduction

I t is no exaggeration to say that no one method can cover all the conditions in a complex process . That is , each method has its own advantages and disadvantages , so it is important to adopt a multi-approach in which the strengths of various methods [ 3 , 4 ] complement each other . In real-time control in particular , it is a well-known fact that we must deal w i th conditions in which various elements unavoidably occur together locally , including elements that a r e l i n e a r , n o n l i n e a r , q u a n t i t a t i v e , qual itat ive , objective , subjective , surface knowledge , deep knowledge , well-conditioned , and ill-conditioned . Thus a flexible environment must be created in which different techniques complement each other . In this paper we focus on a cement rotary kiln process with which we have long had experience and give our views on creating an environment in which the acquisition of surface knowledge , deep knowledge , and reasoning is done through mathematical model­based knowledge , time series AR model-based knowledge, fuzzy expert knowledge , measurable variables , observable knowledge , and other factors , and in which the strengths and weaknesses of the factors involved are put to use and complement each other .

2 . Model-based knowledge acquisition

The mathematical models [ 5 , 6 ] that we will deal with here are one for the cement-making process and an AR model that makes use of time series

353

analysis , and we will also take up a fuzzy inference model and a linguistic model . The rotary kiln process can be called a delay distributed counter-flow type heat exchange r , and thus it i s expressed by material balance and heat balance as a set of simultaneous tempo­spacial partial differential equations . The advantages of this mathematical model are that i t allows deep knowledge acquisition by a simulation solution using i t , that it can generally make use of variables that cannot be measured in real time , and activity values can be ascertained in many points such as knowledge acquisition of the nonlinear behavior between the rotation speed of the rotary kiln and the temperature of the raw materials, combustion behavior by long flame and short flame , and reasoning and behavior including transient changes in chemical composi t ion caused by d i f f i cul t - to -measure f i r i n g of the raw materials . On the other hand , the computation takes time , and it cannot be used for real-time control because the actual process noise is ignored and the parameter sensitivity is great, but various deep knowledge can be gained through computer simulation . [5 ] Figure 1 shows the indicial response of chemical composition of the exit clinker and mathematical equations are presented briefly in Appendices .

-

!; 60 s ... :::: 50 Ill 0 c. � CJ � 20 Q) ..:.s s::: ::::: 1 0 CJ .., ..... .. Czl

0 0

( Ca0) 3Si02

( Ca0) 2Si02

free lime "\

60 120 180 240 300 360 420 480 Minutes after step change

Fig . 1 . Exit clinker response , CaO/Sl02 ratio in feed step change decreased

Nex t , in AR model-based knowledge, various deep knowledge is given in the course of the model-building process . For example , the below­discussed noise contribution of the causal chain and the power spectra become very effective for reasoning and deep knowledge acquisition prior to control , such as selection of variables . [ 1 , 7 ]

I f the parameters of a multiple autoregressive ( AR ) model can be estimated , then the frequent response function

M A(f) = [I - L A(m) exp (- i2nfm)]

. . . . . . . ( 1 )

m = l

and cross power spectrum

P(f) = A(f) L A* ( f) . . . . . . . . . . . . . . . . . . . . <2 >

can b e calculated immediately . Here, I denotes the unit matrix and • the conjugate transpose . Figure 2-1 shows the power spectrum density of the wattage ( KW) of the driving motor determined from an AR model of a rotary kiln process . An arbitrary component of the coefficient matrix A(m) of the AR model in the formula ( 1 ) for computation of the frequency response function can be coercively set to zero ; for example , in this case , if a total of 7 variables are considered , then various types of simulation can be attempted by multiplying the 7 x 7 coefficient matrix A(m) by a masking matrix. Figure 2-2 shows the case where the noise component of the controlled variable has been set equal to zero , while Figure 2-3 shows the results of severing the path of the signal from the control input of the AR model to the controlled variables, and checking the efficacy of the previous control ; from these figures , one observes that the control operates effectively , but at the price of introducing fluctuations into the extreme low frequency domain .

Wattage

0.10 0.20 Freq.

Fig . 2-1 Model 1

N Wattage

0.05 0.10 0 . 1 5 0.20 Freq .

Fig . 2-2 Model 2

Also, its objectivity in the design of optimum control and in real-time control and the usefulness of a unified approach nowadays go without saying. But on the other hand , it has various problems that might more appropriately be called weaknesses rather than disadvantages . To list its main problems , there are the problem of the length of the running data, anxiety over the general difficulty of getting operators to understand multi-dimensional input and output and the unfamiliarity of operators with what must be done , and sometimes it occurs that a gap arises with the model and the continuation of computer control is interrupted because of incomplete measured values due to the occurrence of noise even if the data had been correctly taken at the time of identification . Here , if the measured values of the variables in computer control are inaccurate and unstable, as a method having weak covering power, the above­mentioned quantitative model is not useful but a qualitative model is useful . I t is familiar and friendly to construct a qual itative model inferred from this , and it is easy to transform it into a linguistic model . Thus this is expected to lead to further improvements in conventional expert systems that lack objective justification , and to the quite systematically effi c i ent construct ion of fuzzy control . [ 8 , 9 , 1 0 , 1 1 , 1 2 , 1 3 , 1 4 ]

Optimal control design can be achieved if a quantitative AR model is employed, but noise

354

problems arise in real-time measurement , and if problems of quantitative measurement exist , then qualitative control can be regarded as robust . Table 1 , 2 and Figures 3 , 4 show the AR modeling of the running data of an expert as well as the resulting relative contribution and the step response with feedback . In Figure 3, the contribution of manipulative variables to liter weight is comparatively great, while conversely , in Figure 4 , the contribution of liter weight to manipulative variables is comparatively slight .

This shows the fact that mutual temporal adaptation is poor , and can be regarded as reflecting "fuzzy" vagueness in manipulation .

Table 1 .

NO. HAVE VEIGHT 1 Liter weight . 3563E - 1 2 = Oxygen . 2358E - 1 3 = Fuel 1 4 . 84 4 = Damper position 2 . 570

Transition matrix LAG = 1 2

1 . 73 1 0E 0 - . 8484E - 1 2 . 5659E - 1 . 1 1 97E 1

LAG = 2 1 2 1 . 9 1 62E - 1 - . 1 253E 0 2 . 4979E - 1 - . 2902E 0

Driving matrix LAG 3 4

1 .2040E -2 - . 84 1 4E - 1 2 . 1 306E - 1 . 8756E - 1

LAG = 2 3 4 1 . 1 340E - 1 . 5201 E - 1 2 - . 1 95 1 E - 1 - . 6388E - 1

Gain matrix LAG = 1 2

3 - . 2479E . 24 1 7E 4 . 3978E - . 2228E

LAG = 2 1 2 3 - . 38 1 1 E . 3520E 1 4 .4955E - . 42 18E 0

Table 2 .

[ From % ] ( INPUT) 1 2 3 4

[To % ] 1 36 ( ) 1 5 ( - ) 3 8 (+) 1 0 (-) ( OUTPUT) 2 1 8 (+) 66 ( ) 7 ( - ) 9 (+)

3 1 ( - ) 1 7 (+) 80 ( ) 1 ( - ) 4 1 7 ( - ) 1 2 ( - ) 1 7 ( - ) 54 ( )

(SCORE) 36 44 62 20 ( ORDER) 3 2 1 4

� SIGN OF STEADY STATE GAIN�

[To] ( OUTPUT)

1 2 3 4

Fig . 3 .

[ From]

1 2

1 -

+ 1 - + - -

( INPUT)

3 4

+ -- + 1 -- 1

[SYSTEM OUTPUT ] 1 = Liter weight 2 = Oxygen

[ SYSTEM INPUT] 3 = Fuel 4 = Damper position

4 . Damper position 3 . Fuel 2 . Oxygen 1 . Liter weight

3.0 1.5 1.0 (T) hr

Relative contribution

4 . Damper position 2. Oxygen 1 . Liter weight 3 . Fuel

'-��-+-��--+���-r-� (T) 3.0 1.5 1.0 bl'

Fig . 4 . Relative contribution

This recognition is extremely effective for reasoning with respect to causal effects and knowledge acquisition . Moreover, as shown in Figures 5 , 6 , 7, simulation in accordance with opt imal control design by this AR model indicates the existence of control surpassing that of experts , hence , one may conclude that qualitative modeling of optimal control based upon quantitative objectivity is possible.

optimal control

- 15 L-�������������� O Fuel 60 hr

Fig. 5 .

- 10 L--�������������� O Damper 60 hr

Fig. 6 .

optimal control

CL Fig . 7 .

6 0 hr

355

3. Inference model building

As was mentioned above , provided the data is correctly acquired, then , once an AR model is constructed on the basis of this data , even in cases wher e subsequent run n i ng data is metrologically defective and becomes unreliable , if deep knowledge concerning causal effects , e tc . , can be acquired by s imulation in accordance with the previously constructed AR model , as shown in Tables 1 , 2 , then qualitative models can be constructed on the basis of this knowledge [ 1 5 ] .

Thus it can be said that reasoning about what the e xpert is see ing and doing is made convincing against a background of existing deep knowledge , and that this is a conversion of subjective operation data into something that is objective . Table 2 expresses qualitatively the relationships between the variables determined using the above AR model . It represents the acquisition of the expert's behavior and could be called a fuzzy quantification .

However , this in any case constitutes the ad hoc conversion into a qualitative inference model of a quantitative model created only with respect to a process such that the generation of subsequent process noise is unavoidable ; many such processes exist , such as rotary kilns , incinerators , etc.

The objectification of the subjective is what science tries to achieve, but is there ever any need for its opposite , the subjectification of the objective? This is one paradigm in the realm of process control , but as has been stated above , factors that can be cited include the problem of maintaining the correctness of measurements , coordination with human beings , fusion with the utilizat ion of observable variables in addition to measurable variables , and ease of coupling with a linguistic model .

4 . Preliminary study of qualitative control for the cement rotary kiln process

The unapplicability conditions for AR model building and online use for this process are as follows . 1 ) when the length of the running data cannot be ascertained under normal circumstances , 2 ) when the nonl inear factors exist in the process greatly , or 3) when the data is not stable and reliable in the long term, say several weeks, but stable and reliable in the short term, say one or two weeks .

In the cement rotary kiln process discussed in this paper we focus on case 3) and assume that an AR model has already been created with normal running data. That is , ( 1 ) when the rotary kiln process is in a normal state , running data is taken , identification is made , and an AR model is created ; ( 2 ) variables selection is done using power spectra and noise contribution ; and (3 ) an evaluation is made through simulation , and online use begins .

Here tight control such as an AR model will no longer suffice if conditions arise that make even part of the running data unstable or inaccurate . A consideration of such cases suggests that a fuzzy inference model be used . [ 8 , 9 , 1 2 , 1 5 ]

The process model illustrated in Table 1 and the matrix representation of optimal control for this model are as follows ,

( 1 ) Process Model [��Tu!J- = f:ii&l-ii�i}f i--lJ- [�,�;-�;)l la2(n) a21 (2) a22(2) : 0 0 ai(n-1 )

( 1)

(2) Optimum Control

Control gain

(F(n-1) ) (911( 1) D(n-1 ) = 921( 1 )

G _ (911(1 ) g12( 1) i g11(2) 912(2)) -Q21(1) 922( 1 ) I 92Pl 9,2(2)

g12(1 ) j g11(2) g12(2)) tV(n-1 ) l g,,(1 ) ! g,,(2) 9,,(2) - <?�'!:"�� -

a1(n-1) ai(n-1) (g ( 1) g12( 1 )J (V(n-1)J lg;:( 1) g22(1) O(n-1)

(911(2) g12(2)J [a1(n-1)l + lg21(2) 922(2) ai(n-1 )) (2)

Here, the state variables al and a2 are quantities which are calculated from the state equation , and serve to add predictive functions to the if- then rules . Thus , the attributes of the system under consideration are as follows .

( 1 ) State attributes : V ( n ) , O(n) ; (measurable ) a 1 (n ) , a2(n) ; ( observable )

( 2 ) Manipulation attributes : F(n ) , D (n) ; (measurable )

Since the objective consists i n the preparation of if-then rules , the manipulative quantity data are the manipulation quantities which should be adopted when the system is in the state [ V (n ) , O(n ) , a 1 (n ) , a2 (n) ] .

In the case of this example , if the values of the respective variables are classified into the three levels small , medium, and large , then the possible comb inations of these magn i tudes provide 81 state attributes ( 34 ) and 9 manipulation attributes ( 32 ) . As one example , Tables 3 , 4 show the classification by rough sets in accordance with the simulation data of the present AR model and the results so obtained . [ 15 ]

Figure 8 shows the process model as well as manual operation , opt imal control , fuzzy control , and a general block diagram of these functions . Figure 9 shows optimal control simulation when a stepwise disturbance is applied to clinker liter weight (CL) , while Figure 10 shows fuzzy if-then control and Figure 1 1 shows an example of manual control simulation . The fact that Figure 10, showing simulation by fuzzy inference , represents a mode intermediate between optimal control and manual operation is extremely interesting as a case of control in an environment characterized by the multiple sources of uncertainty contained in the knowledge referred to as "common sense" , and will be further studied hereafter . Four representative variables have been selected in the examples cited up until now , but the further exploitation of observable var iables is

desirable. For example as measurable variables, we l i s t the fol l owin g : burn ing zone temperature, power ( kW) of the kiln driving motor , secondary air temperature , oxygen content in the kiln end , temperature in the kiln end , hood draft, quenching cooler speed , and kiln rotation speed . As attributes of the observable variables we set

Obs = {C 1 , C2 , C3 , C4} , where

dark points in burning zone through image recognition ( under study ) rough estimate of clinker granulation by spectral analysis of load of quenching cooler recognition of flame length by spectra of hood draft through FFT recognition of situation around burning zone by sensor fusion of C 1 , C2 , and C3 in the neural network model .

Further details concerning these matters may be found in previously published references [ 2 , 3 , 1 5 , 1 6 ] . The aforesaid introduction of variables measurable under uncertainty and observable variables serves to extend their m e a s u r e m e n t a n d c o n t r o l fun c t i o n s to qual i ta t i ve ly nonl inear domains or fuzzy domains . The importance of diagnostic inference engines based upon deep knowledge grounded in system models and gestalt concepts is likely to become progressively more recognized in the future .

Table 4 . Classification of rules

CL 02 ai ai F D

1 1 2 2 2 2 1 1 2 3 2 1 2 2 2 1 2 3

1 2 2 2 1 2 2 2 2 2 2 2 3 2 3 2 1 2 3 2 2 3 2 2 2 3 3 2 1 1 1 1 3 3 1 1 2 1 2 1 2 1 3

2 1 2 2 2 1 2 2 3 1 3 1 2 2 3 1 1 2 3 1 2 2 1 3 2 1 3 2 1 3 3

3 2 2 3 2 3 1 3 2 3 2 3 1 3 2 3 2 3 3 3 1

4 2 2 1 2 3 2 2 2 1 3

s 3 2 2 1 2 3

Table 3 . Condition N= 1 26

CL 02 a1 a2 F D

3 0 . 7992 0 . 8500 0 . 291 1 69 0 . 1 76748 1 . 0734 4 . 7999 and up and up and up and up and up and up

2 -0 . 3944 -0. 8364 -0. 096331 -0. 308472 -3 . 746 - 1 . 39 13 to 0 . 9992 to o . 8500 to 0 . 29 1 169 to O. 1 76748 to 1 . 0734 to 4 . 7999

1 to 0 . 3944 to -0 .8364 to 0 . 096331 to -0 . 308472 to -3 . 746 to - 1 . 39 1 3

means 0 . 3024 0 . 0068 0 . 0974 1 9 -0 .065862 - 1 . 3363 1 . 7043 µ

a 0 . 6968 0 . 8432 o. 1 9375 0 . 2426 1 2 . 4097 3 . 0956

356

Relay flag MAN. OPT.

170 -1 1 65 1 1

F

I I : ------' I I I I L _ � ��·��".. 2���6_:i- --- __ --- _ _ -- - -i " "� �---..

Fuzzy D : parameter matrix 1 or-1

-1

Fig . 8.

F

P = -1 .5

x,

x,

Fuzzy Control

F

-lo '------------....,5:-,0,,....-,h�r

-10 '-------------.,,,,,..-,,......; to �-----------'5�0:;__:h.;;;;.,r

- 10 ..._ ____________ __, 50 hr 10 �------------=--� � ,....----------------.

D 1o f----------------i

D D

-10 '-------------=-..,-� F=Fuel 50 hr

-10 '-------------=-,......., 50 hr -20 '--------------,5"'0:--:h-'

r D=Damper Fig. 9 . Fig . 1 0 .

5 . Conclusion

It would be no exaggeration to say that most work in process identification has adopted this paradigm to incorporate qualitative factors in a quantitative model . Another paradigm is the opposite approach , that is, building qualitative models by converting quantitative models into qualitative ones . This opposite approach is followed because

357

Fig . 1 1 .

1 ) the problem is described both quantitatively and qualitatively ; 2 ) measuring variables are not always reliable ; and 3 ) there can be an qua l i tat ive algor i thm corresponding to quant itative part of the process such as time series analysis and optimum control . What is needed , therefore , is a qualitative approach and inference together w i th a

quantitative approach . This paper br iefly refers to a cement-making process with a mul t i p l e compl e x causal c h a i n , as an illustrative example . The mathematical model and autoregressive model for the kiln process are adopted for the acqu i s i t ion of deep knowledge, and the quantitative control based on this quantitative model is converted into qualitative control . In conventional fuzzy expert systems , because of the difficulty of creating a quantitative model , the usual approach is to learn from an expert . This makes knowledge acquisition difficult , and a number of rules are specified by transferring expertise from a human expert or experts. This paper has proposed a hybrid system for processes for which a quantitative model is available but in which the reliability of input signals during actual operation cannot be maintained . In this proposed hybrid system, a qualitative model is created on an objective basis, a linguistic model is built with a small number of rules and effective reasoning , and it is fused with the linguistic hidden information . This approach comb ines the advan tages of conven t ional quan t i tative online computer control and qualitative fuzzy expert control and compensates for their respective d isadvantages , thereby helping to create an environment for user­fr i endly man-machine systems having some objectivity .

APPENDIX

( a ) Relative contribution We define qij ( f) by qij ( f ) = lbij ( f) i2p(uj ) ( f) , where bij ( f) : p ( uj ) ( f) :

frequency response function power spectral density function of noise

This represents the contribution of p(uj ) ( f) to the power spectral density pu(f) at frequency f . Accordingly the relative power contribution is given by

and the cumulative relative power contribution is given by

j Rij(/) = I ril,(/)( j = l ,2, . . . ,k)

h=l (b) Mathematical model If we make the assumption that the velocities of the gas and the solids are constant during their residence time in an elemental axial section of the kiln , but not necessarily the same in each section , then the partial differential equations can be rewritten as follows .

The material balance equations for the solids can be represented by ( lb/lb clinker/hr )

axj a(V,x) - + -- = {. at at J

j = 1, . . . , 12

358

The material balance for the gas can be represented by the general equation ( lb/hr/hr )

( 1 )

( 2 )

( 3 )

( 4 )

( 5 ) ( 6 )

( 7 )

( 8 )

( 9 )

( 10 )

( 1 1 )

( 12 )

( 13 )

( 1 4 )

( 15 )

( 1 6 )

ayj _ a(V ,?) =

g at at j

REFERENCE

j = 13, . . . , 16

H. Akaike , T. Nakagawa ; Statistical Analysis and Control of Dynamic Systems , Kluwer Academic Publ ishers , 1 988 T. Nakagawa , Y . Yagihara ; The approach to the design of optimum Production Level and pursuit control in industrial process , Jour . of SICE ( Japan ) , Vol . 24 , No . 1 1 , 1 985 T . Nakagawa, H . Ogawa ; The Identification and control , partially added with the Artificial Intell igence approach , 4th IFAC/IFIP symp . , Graz , Austria , 1 986 Y . Sawarag i ; Towards I n teractive and Intelligent Decision Support Systems , VIIth I nternat ional Confe rence on Mul t i p l e Criteria Decision Making , Vol . 2 , Aug . , 1 986, Kyoto , Japan R . Stillman ; IBM Technical report , 1 964 T . Nakagawa , Y . Sawaragi et al ; The management through Cooperative multi-agent model in the plan t , 1 1 th I FAC World Congress , Tallinn , Estonia, Aug . 1 990 M. Ishiguro ; System Analysis by multi­variate AR model , Jour . of Operations Research , ( Japan) , No . 1 0 , 1 989 L . P . Holmblad , J . J . Ostergoard ; Control of A c emen t k i ln by Fuzzy Log i c , Fuzzy information and Decision process , M .M . Gupta E . Sanchez ( Eds ) Valerie L . et al ; A formal analysis of machine leaning systems for knowledge acqusition , Int. J. Han-machine Study , Vol . 29 , 1 988 Richard M. tong ; The construction of Fuzzy models , Eds . M . Gupta et al , Advances in Fuzzy set theory and application , North­Holland Pub . Co . 1 979 F. van der Rhee et al ; Knowledge based fuzzy model ing of systems , 1 1 th I FAC World Congress , Tallinn , Estonia, Aug . 1 990 Neville Moray et al ; Acqusi tion of process control skills , IEEE Trans . on System, Han and Cybernetics , Vol . SMC- 1 6 , No. 4 , 1 986 R . E . King ; Intelligent control in the cement industry , IFAC meeting , Varna , Bulgaria , 1 988 T . Takagi , M . Sugeno ; Fuzzy Identification of systems and its application to modeling and control , IEEE Trans . Vol . SMC- 1 5 , No . 1 , 1 985 A . Mrozek ; Rough sets and Dependency analysis among attr ibutes in computer implementat ions of expert ' s inference models, Int. J. Han-machine studies , Vol . 30, p457-473 , 1 989 K. Haruna et al ; Morphological Relaxation method and its application to control of Refuse Incinerator , Jour . of Electrical Engg . , Japan , Vol . 97 , No . 8, Hay , 1 977

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

MODEL-BASED DIAGNOSIS - STATE TRANSITION EVENTS AND CONSTRAINT EQUATIONS

A. Nilsson*, K.-E. Arzen* and T.F. Petti**

*Departm.enl of Automatic Control, Lund Institute of Technology, Box 118, S-221 00 Lund, Sweden ••Department of Chemical Engineering, University of Delaware, Newark, DE 19716, USA

Abstract: Two different approaches to model­based on-line diagnosis are compared. The DMP method is based on quantitative constraint equa­tions. MIDAS is based on signed directed graphs that are translated into an event graph consisting of the possible state transition events of the pro­cess and the failures that they are symptoms of. The methods, which both have been implemented in G2, have been applied to a real-time simulation model of a sterilization process.

1 . Introduction

Computer assisted on-line monitoring and diagno­sis is becoming an increasingly important part of modern process control systems.

Model-based diagnosis systems are based on a model of the process. During diagnosis the model's predicted process outputs are compared with the real measured outputs. Discrepancies indicate fail­ures. Model-based diagnosis is nothing new in the control community. For long, diagnosis meth­ods based on detailed process models, often on differential equation form, have been suggested and also in quite a few cases applied industri­ally. These include parity space approaches and observer-based approaches {Frank, 1990). How­ever, a problem with these "classical" methods is the detailed models that are needed.

During the 1980s model-based on-line appli­cations have received increased attention from the AI community. The difference from "classical" model-based methods is the nature of the mod­els. The AI community focus on coarse models that often only give a qualitative description of the process behaviour. Models of these types in-

clude signed directed graphs, qualitative physics models represented, e.g., as confluence equations, constraint equations, etc. The diversity of models used and differences in how the models are ac­tually used for on-line diagnosis, however, make

359

it extremely difficult to evaluate different ap­proaches against each other.

One part of the project "Knowledge-Based Real-Time Control Systems" {Arzen, 1990) has been to explore various approaches to model­based on-line diagnosis. This project is a joint industrial project between ABB and the De­partment of Automatic Control, Lund Institute of Technology. Within the project a common test process - Steritherm - is used. Steritherm is a food engineering process for sterilization of liquid food products. A real-time simulation model of Steritherm has been implemented in the real-time expert system environment G2 from Gensym Corp. Within the same environment a "knowledge-based" control system has been imple­mented that controls, monitors, and diagnoses the simulated Steritherm process. Within this control system various knowledge-based, as well as con­ventional, applications have been implemented. These include symptom-based monitoring, off-line troubleshooting based on fault trees, production scheduling, alarm analysis based on functional process models, and finally the topic of this pa­per, two different on-line model-based diagnosis schemes: the Diagnostic Model Processor {DMP) method and the MIDAS method.

2 . DMP

The Diagnostic Model Processor method (DMP) (Petti and Dhurjati, 1991) is based on quantitative constraint equations called model equations. By examining the direction and extent to which each model equation is violated and by considering the assumptions on which they depend, the most likely failed assumption {fault) can be deduced. Redundancy, sensor or analytic, which is available in the system leads to better performance because an assumption that is common to many violated equations is strongly suspect; whereas satisfaction

Assumptions:

Flow sensor is OK Diff. Pressure sensor is OK No burn-on No piping leaks

2 p * Frl e = DPl -c;

Tolerance:

HX I

Figure 1. Example of the formulation of a model equation with its associated assumptions.

of equations provides evidence that the associated assumptions are valid.

The process model consists of series of equa­tions on residual form. The equations may contain anything that can be calculated at run-time in­cluding past sensor values, mean values, etc. Usu­ally equations compare a sensor value to what it ideally should read, compare multiple sensors measuring the same physical value, compare a sen­sor reading a physical value with a calculation of of the physical value based on other indirect sen­sors, or express a general balance equation, e.g., a mass or energy balance.

Associated with each equation are tolerance limits which represent the expected (fault free) up­per and lower values of the residual for which the equation is considered satisfied. Also associated with each equation is a set of assumptions which if satisfied guarantee the satisfaction of the equa­tion. The j'th equation is denoted e; = c; (P; a) ,

where P denotes the process data and a indicates that each equation is dependent on the satisfac­tion of a vector of modeling assumptions.

A simple example of an equation and the as­

sociated assumptions is shown in Fig. 1. FTl and DPl are flow and differential pressure transmit­ters. The equation compares the measured and calculated pressure drops over the heat exchanger. Notice that some of the assumptions are explicit in the model equations, such as correct sensor read­ings, and some are implicit such as the fact that there are no piping leaks.

Since the residuals are not uniform in mag­nitude, they are transformed into a metric be­tween -1 and 1 which indicates the degree to which the model equation is satisfied: 0 for per­fectly satisfied, 1 for severely violated high, and -1 for severely violated low. These values consti­tute the satisfaction vector, sf, which is calculated using the model equation tolerances, r. For the jth model equation,

sf- = (e;/r; r 1 l + (e;/r; )n

(1) .

The value of sf; is given a positive value for a positive residual, e; , and a negative value for a negative residual. The curve is a general sigmoidal function with the steepness determined by the constant n. If the tolerances are not symmetric around the origin, the upper tolerance � is used for a positive residual and the lower tolerance 71 is used if the residual is negative.

A matrix of sensitivity values, S, which de­scribes the relationship between each model equa­tion and assumption is computed to weight the sf values as evidence. The ijth element of S, which represents the sensitivity of the jth model equa­tion to the ith assumption is calculated as:

IJc; S

811; ij = lr; I (2).

The larger the partial derivative of an equation with respect to an assumption, the more sensitive that equation is to deviations of the assumption. Many model equations are non-linear in some assumptions; these partials are estimated by linear approximations. Assumptions which are implicit with respect to an equation (i.e., pump operation) are arbitrarily given a partial derivative equal to 1 or -1 , unless experience suggests otherwise. Also, equations independent of an assumption have an associated sensitivity of zero. Explicit assumptions normally represent sensors which are used explicitly in the equations. In this case the sensitivity is expressed by the partial derivative of the equation with respect to the sensor according to Eq. 2. This expression is recalculated on-line. A sensor is assumed to either fail high or fail low, i.e., read either too high or too low.

Conclusions about the satisfaction of each assumption (fault state) is made by combining the evidence from the model equations, sf, with consideration to the sensitivity matrix S. This is done through the calculation of a vector of failure likelihoods, F, such that

(3)

where N is the number of model equations. It is evident that this method of combination allows the sf values of those equations which are most sensitive to deviations of assumption a; to be weighted the most heavily in the calculation of Fi. The failure likelihood is interpreted as indicating a likely condition of assumption a; failing high as the value of Fi approaches 1 , while an Fi tending toward -1 indicates a likely failure low.

DMP allows the detection of non-competing multiple faults. This often leads to several assump­tions' failure likelihood exceeding the likely limit that determines if they should be presented to the

360

operator or not also when a single failure has oc­curred. To limit the number of faults presented and to direct attention to the most probable condi­tions a procedure is used to check the casual rela­tionships between the assumptions. The procedure basically assumes a fault and checks the expected behaviour of the equations to see if other failure likelihoods should exceed the likely limit. If this is the case, the assumption is said to "explain" the appearance of the other assumptions. All likely as­sumptions are tested pair-wise and those assump­tions that are not "explained" by other assump­tions are considered top-level and get a special graphical indication.

G2 implementation

Equations and failure assumptions are represented as G2 objects. A dependency between an equa­tion and an assumption is represented by a graph­ical connection, a dependence connection object, between them. Equations have attributes repre­senting the residual, the tolerance limits, and the satisfaction value. The dependence objects have attributes characterizing the type of relationship (implicit or explicit) , a formula to calculate the partial derivative of the equation with respect to the assumption, and a sensitive attribute. The cal­culation of satisfaction values and failure likeli­hoods are performed by generic formulas referring to the connections between equations and assump­tions.

3. MIDAS

MIDAS (Model Integrated Diagnosis Analysis System) is an approach to model-based, on-line diagnosis developed at MIT by Kramer, Oyeleye, and Finch and described in (Oyeleye, 1989) and (Finch, 1989). MIDAS belongs to the diagnosis methodologies based on qualitative causal reason­ing about deviations from a nominal steady-state. During the diagnosis, events representing quali­tative state transformations, e.g., that a sensor changes from NORMAL to HIGH, are clustered together into groups that each could be explained by a certain fault.

MIDAS models

MIDAS is based on a chain of different qualitative models. The final model in this chain is what is used on-line during the actual diagnosis.

SDG model: The first model is the Signed Di­rected Graph (SDG) that is derived from the phys­ical equations of the process. A SDG describes the variables of the process as nodes and the qualita­tive relationships between the variables as arcs be­tween the nodes. Nodes have the qualitative states 0, +, or - depending on if the process variable Zi

361

L

L = C 1 F in - C 2 Fout

F out = f- ( R s ) VL Oulk:t BlockaF�

Tank leak + _-r Low Inflow

- � 1- + + --Fm o- - Fout

0

Figure ::a. A gravity flow tank with its equations and SDG

= 0, Zi > 0, or Zi < 0. An arc between two nodes n1 and n2 has the sign +( -) if an increase in n1 causes an increase (decrease) in n2• A zero-signed arc initiating and terminating at the same node indicates an integrator.

Included in the SDG is also the set of root causes that might affect the process. All the faults concerning the process that should be detectable must be incorporated in this set. For each fault there must exist a primary deviation variable, i.e., a variable included in the SDG which is first affected by the root cause, and a sign that tells in which direction this variable is deviated. An example of a SDG for a simple gravity flow tank is shown in Fig. 2 .

The construction of a SDG for a whole pro­cess consists of combining together sub-SDGs rep­resenting the process components of the process. The sub-SDGs can be seen as generic SDG models that describe the qualitative models for classes of process components.

A problem with the SDG process models is that they only describe local, direct causalities between variables. Non-local causalities due to, e.g., feedback effects cannot be handled. Consider the tank in Fig. 2 once again. Assume that the pipe resistance R. is somehow decreased. Following the arcs gives that Fout will increase, L decrease, Fout decrease, L increase, and so on. This leads to a chain of contradictions and the SDG does not tell whether the outflow and the level will ultimately be low or high, oscillate or return to their initial values.

ESDG model: To overcome the above problem MIDAS analyzes the loops in the SDG and insert additional non-physical arcs into the graphs. This leads to the Extended Signed Directed Graph (ESDG) , which can explain the behaviour of the process through feed-forward paths only. The interpretation of the non-physical arcs and the algorithms for analyzing the graphs are found in (Oyeleye, 1989).

Et1ent graph model: The model that MIDAS

!zvel Normal-Low

Higb lnllow

lzvel Sensor High Biu

:NOT lzvel Sensor Bi• OUllet BlockaF

:NOT !zvel Sensor Biu

I j Tank lzok i Low Inflow

Level Senior Low Bi•

Dowmtream !zok

Flow Semor High Bia

Flow Narmal-Hi&h

High Inflow 0 Flow High-Normal 0 Flow Low-Normal

I

:NOT Flow Senscr Bia

Low laflow

Tanklzok

Flow Nonnll-Low

! Oullet Blockap · Flow Senior Low Bia

Figure 3. The event graph of a gravity flow tank

uses on-line during diagnosis is an event graph model. It consists of events, i.e., qualitative state transitions, root causes, and links connecting events with other events and with the root causes. A qualitative state of a variable is either high, nor­mal or low, compared to the nominal steady-state value. That is, for every measured variable four events are possible: a transition from normal to high, from high to normal, from normal to low, and from low to normal.

The event graph model can be derived di­rectly from the ESDG. Briefly, the transformation of an ESDG into an event graph is done by re­moving all unmeasured nodes in the ESDG, but for each measured node create four nodes in the event graph, each representing one of the possible state changes. The arcs in the ESDG are trans­lated into arcs in the event graph. Each root cause is connected to the event that should be the first symptom of the fault. Further, there are links be­tween the events in order to express possible fault propagation. These links may have conditions at­tached to them telling when the arcs are valid and what diagnostic conclusions that may be drawn when two events are linked together.

It is also possible to include other types of events in the event graph, e.g., operator actions, off-line test results, changes in trend, and quanti­tative constraint equations. However, the MIDAS methodology does not contain any structured way of building a model containing relations between such events. These have to be added on a purely heuristic basis.

An event graph for the single gravity flow tank in Fig. 2 where the level and the outflow are measured is shown in Fig. 3. Compared to the SDG in Fig 2, the set of root causes is somewhat extended. In the event graph the circles represent

362

SDG Lllnry

Quentllatlv• Conlllrlllnl Equetlan•

SDG Model

1 ESDG Model ,J-__

Data From s.n.or•

Figure 4. MIDAS model generation and the structure of the diagnosis

events. When an event has been detected. e.g. , the flow gets low, either of the root causes pointing at this event has probably occurred, in this case outlet blockage or flow sensor low bias. The :NOT­conditions attached to most of the compiled links will be interpreted as follows: when the events at both ends of the link are detected, the root causes in the :NOT-conditions of the link are no longer likely. The :ONLY-IF-TRANSIENT means that the event at the termination of the link will not occur for any of the modeled root causes until the root cause has been corrected.

The model generation in MIDAS is summa­rized in the upper half of Fig. 4.

MIDAS diagnosis

The structure of the diagnostic function and the flow of information is shown inside the dashed line in Fig. 4.

Monitors: The diagnosis unit in MIDAS is linked to the process via monitor objects. Every sensor variable has an associated monitor which is re­sponsible for detecting state changes, i.e. events, concerning the variable. The monitors in the G2 implementation contain information about the threshold levels between the qualitative states of the measured variables. When a monitor samples a sensor value, this value is first smoothed by a first-order filter.

l!il W

� ln�11•J •.-....Utl',..1• '°"'""'"" __ , � f!bi!ut\ ........... I

�· '.Gel ..... ) ( .:z ) ·� � /-1-..... --'::::,,.,..,... ,,..,,.,,,.. I

_,..,,..,,..,,.. I

� / u"6 / --1.£·S _"OE 1

/ > LJ > LJ l ·l·N FH.-N LHf I _1£-) --Af·4 > LJ Ll'-IH �___y--0 J..Ftt;.t Fl#l �::::. ...... HR::-? . ""<) lt-81.AS-.O ;ltic-J 'v 0 PU#FAILl.ff

TN«-t£AK

Figure 5. An example of an inferred malfunc­tion

In Fig. 4 there is an arrow labeled "Interroga­tion" from the event interpreter to the monitors. This indicates that the event interpreter may ask a monitor to predict a future event before this has actually occurred. This is done with polynomial, in its simplest case linear, prediction. If the moni­tor predicts an event to happen in the near future, a new predicted event is created and treated like a true recorded event, only with less probability of accurate detection.

The hypothesis model: The hypothesis model consists of clusters of dynamically created and in­terconnected objects representing previously de­tected events along with the current fault hy­potheses. Each cluster, occasionally called inferred malfunction (IM), contains recorded events (REs) that are causally linked in the event graph, �nd hypothesized root causes (HRCs) that may have caused the events. An IM can be seen as a sub­graph of the event graph, since the recorded events and hypothesized root causes are copies of the cor­responding components in the event graph. MI­DAS assumes that exactly one HRC is the true fault in each IM. !Ms are created and altered as new events are detected and the diagnosis evolve.

Fig. 5 shows a hardcopy in G2 of an IM. The icon of the IM can be seen on the small workspace at the upper left corner of the figure. The rest of the G2 window displays the REs and HRCs that are members of the IM. This IM has been created when MIDAS worked against a simulated tank process and a tank leak was simulated.

The e11ent interpreter: When a monitor has detected a new event, this will be handled by the event interpreter, which is a set of procedures and algorithms used to link new events with old ones and to make a diagnosis from the observations.

The event interpretation consists of a proce­dure that is run for every recorded event. When a new event occurs a RE is created and cata-

363

Figure 8. Steritherm DMP network

logued in the hypothesis model. The interpreter tries to link the new RE together with clusters of old events. If the search for such a cluster, or IM, is successful, the RE will be incorporated in this cluster, otherwise the event interpreter creates a new IM containing the RE. The cluster containing the new event is examined to see which events in the cluster may be source events, i.e. events that can explain all other events in the cluster. Finally, the existing hypotheses are revised to include the information provided by the new event.

The basic strategy is to group related events together. Since the source events explain all other events in the cluster, all root causes in the event graph pointing at one of these events are incorpo­rated in the IM. These HRCs are finally ranked, based both on a priori probabilities for the faults and the conditions associated with the links in the IM. Details about the event interpretation can be found in (Finch, 1989) and (Nilsson, 1991).

4. Steritherm diagnosis

Steritherm is a process for indirect UHT treatment of liquid food products. The product is heated up to the sterilization temperature and cooled down again in plate heat-exchangers. A water system with steam injection is used for heating and cooling. The process consists of six heat exchanger sections, three pumps, two PID controllers, one product balance tank, one water balance tank, one steam injector, eight temperature sensors, one flow sensor, two level sensors, and one differential pressure sensors.

A total of 18 model equations are used in the DMP model with connections to 17 assumptions. Additionally, 7 model equations which are activat­able with supplied values coming from indicators that the operator manually has to read and enter are available. The DMP network is shown in Fig. 6 with most of the dependencies hidden.

Figure T. Steritherm event graph

In the MIDAS application only about two thirds of the Steritherm was modeled. The SDG consists of 68 nodes and 1 1 root causes. The corresponding event graph is shown in Fig. 7.

Both DMP and MIDAS were quite capable of identifying the correct fault condition. In some cases also other failures than the ones actually simulated were indicated. However, the actual fault was never omitted.

The DMP diagnosis was presented to the operator by highlighting the process components associated with the fault assumption. The MIDAS results were presented as text messages. In the process engineer interface both the DMP network and the dynamically created IMs were presented.

5. Conclusions

MIDAS and DMP are two quite different methods aimed at the same problem. DMP is simple from a computational point of view. The real expertise in DMP lies in the formulation of the equations something which the engineer must do manually. DMP is also memoryless. It is entirely based on snapshots of sensor values. A strong advantage of DMP is that it is not based on crisp threshold values. Both the satisfaction values and failure likelihoods are real-valued numbers between -1 and 1 . Due to this DMP is not particularly sensitive to the choice of tolerance limits.

364

The implementation of MIDAS described here only makes use of the qualitative SDG mod­els. As pointed out by Kramer (1990) the diagnosis accuracy of MIDAS is greatly enhanced if quan­titative constraint equations also are used. From a computational point of view MIDAS is quite complex. The process knowledge behind MIDAS is the qualitative SDG models. The semi-automatic generation of an event graph from the SDGs is very attractive. However, somewhere in a diag­nosis scheme the quantitative information must be used. In MIDAS the quantitative information shows up in the selection of threshold values. Since MIDAS is based on events the threshold levels are crisp. It was quite difficult to tune the threshold levels appropriately. MIDAS records past events. This memory type of function has both advantages and disadvantages. While it enhances the diagno­sis it also gives problems with which information to discard and when to discard it. On purpose MI­DAS does not take the order of events or time be­tween events into account during diagnosis. The reason for this is the uncertainty about whether events arrive to the diagnosis system in the order they really occurred. However, in many types of processes the order and time of events can give useful information.

References

Arzen, K-E. ( 1990): "Knowledge-based control Sys­tems," Proc. of the American Control Conference,

ACC 90, San Diego, CA.

Finch, F.E. ( 1989): "Automated Fault Diagnosis of Chemical Process Plants using Model-Based Rea­soning," Sc.D. Thesis, Massachusetts Institute of Technology.

Frank, P.M. ( 1990): "Fault Diagnosis in Dynamic Systems Using Analytical and Knowledge-based Redundancy - A Survey and some new results," Automatica, 26, 3, 459-475.

Kramer, M.A. (1990): "Process System Diagnosis: Theory and Practice," Proc. of the 1 990 Interna­

tional Workshop on Principles of Diagnosis, Stan­

ford, July 23-25. Nilsson, A. ( 1991): "Qualitative Model-Based Diag­

nosis - MIDAS in G2," TFRT-5443, Department of Automatic Control, Lund Institute of Technology, Lund, Sweden.

Oyeleye, 0.0. (1989): "Qualitative Modeling of Con­tinuous Chemical Processes and Applications to Fault Diagnosis," Sc.D. Thesis, Massachusetts In­stitute of Technology.

Oyeleye, 0.0. and M.A. Kramer (1988): "Qualita­tive Simulation of Chemical Process Systems: Steady-State Analysis," AIChE J., 34, 9, 1441.

Petti, T.F. and P.S. Dhurjati (1991): "Object-based automated fault diagnosis," Chem. Eng. Comm., 102, 107-126.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

MULTIPLE MODELS BASED ON FUZZY QUALITATIVE MODELLING

Q. Shen and R.R. Leitch

/nJel/igefll Automation Laboratory, Departmefll of Electrical and Electronic Engineering, Heriot-Wall University, &iinburgh EHJ 2Hf, UK

Abstract. This paper presents a systematic investigation of developing multiple models of a physi­cal system through the use of Fuzzy Qualitative Modelling (FuSim) technique, essentially along with four basic modelling dimensions identified: abstraction, commitment, model resolution, and relation strength. Implications of multiple models for Model-Based Reasoning in general and Model-Based Diagnosis in particular are discussed. Examples for building up multiple models against different modelling dimensions are provided with respect to a simple physical system and experimental simulation results shown.

Keywords. Multiple models, modelling, modelling dimensions, simulation, model-based reasoning

INTRODUCTION

The ability to qualitatively represent and reason about the behaviour of physical systems is important to under­standing and interacting with the real world for both human beings and intelligent machines (Weld and de Kleer, 1990). However, at which level of detail a quali­tative representation becomes the most suitable one for a particular application task is very dependent upon the nature of the application system. A focusing point of research on Qualitative Reasoning is, therefore, to estab­lish techniques that are able to represent knowledge about the behaviour of physical systems at an appropri­ate and intuitive level of detail. An exciting theme in the utilisation of such techniques is in the development of multiple models of a physical system that can be used for a variety of purposes (Leitch, 1992; Shen and Leitch, 1992b). For instance, such models can be used to improve the efficiency of the computation within a given task by first searching on a simpler model and to improve that of an application system by utilising less complex models in preference to more detailed ones. Tasks like Model-Based Reasoning (MBR) in general and Model-Based Diagnosis (MBD) in particular can benefit from the use of multiple models (Leitch and Shen, 1991; Struss, 1991). Also, they can be used to provide further constraints to reduce qualitative ambi­guity or spurious behaviours on that resulting from another, less detailed, model.

The development of multiple models, however, requires a clear understanding of the process by which models can be built up from one another and the consequent relationship between them. Thus, important modelling dimensions must be characterised to set up the common bases upon which these models can be described. Within Fuzzy Qualitative Simulation (FuSim) (Shen and Leitch, 1991), four basic dimensions have been identified, namely, abstraction, commitment, model

365

resolution, and relation strength (Shen and Leitch, 1992b). Upon such a basis this paper presents a sys­tematic investigation of developing multiple models of a physical system through the use of a fuzzy qualitative modelling technique. Although the present discussion focuses on the utilisation of the FuSim algorithm, we believe, the analysis of multiple models based on funda­mental modelling dimensions or model variation direc­tions applies to all approaches to Qualitative Modelling (Leitch, 1992).

To be self-contained, the FuSim algorithm is briefly reviewed first. Next, the way to develop a set (hereafter called a sub-space) of models based on each particular modelling dimension is investigated. Implications of multiple models for model-based applications tasks are then discussed. Finally, examples for building up multi­ple models against different modelling dimensions are provided with respect to a common physical system and experimental results of performing fuzzy qualitative simulation by the use of these models are presented.

AN OVERVIEW OF FUZZY QUALITATIVE SIMULATION

The choice of representation of physical quantities plays a critical role in qualitative simulation (Shen and Leitch, 1992a; Weld and de Kleer, 1990). All qualitative modelling techniques describe quantities with a small set of symbols, called qualitative values, which are abstracted from the underlying field that the variables of a physical system take values from. In FuSim a qualita­tive value of a system variable is a fuzzy number chosen from a subset of normal convex fuzzy numbers (Dubois and Prade, 1980). This subset, called the fuzzy quantity space, is generated by an arbitrary but finite discretisation of the underlying numeric range of the variable. For computational efficiency, such qualitative

values are characterised by the 4-tuple parametric representation of their membership functions within the implementation of the algorithm (Shen and Leitch, 1991).

FuSim adopts a constraint-centred ontology (Weld and de Kleer, 1990) in system-modelling. A model is derived from an underlying differential equation representation or from direct application of first order energy storage mechanisms. The sets of possible values which system variables can take are thus restricted by either algebraic, derivative or function relational con­straints amongst the variables. More specifically, the algebraic operations performed within a fuzzy quantity space are those in the set of fuzzy numbers. A deriva­tive constraint simply reflects that the qualitative value of a variable's magnitude must be the same as that of another variable's rate of change. Functional relation­ships within FuSim are represented by fuzzy relations (Dubois and Prade, 1980), thereby allowing imprecise and/or partial numerical information on functional dependencies between variables to be exploited if indeed such information is available.

Based on such a qualitative representation of values and constraints, FuSim takes as input a set of system vari­ables, a set of constraints relating the variables (as the system model), and a set of initial values for the vari­ables, and produces a tree of states with each path representing a possible behaviour of the system as out­put. In fact, FuSim first generates a set of transitions from one qualitative state description to its possible suc­cessor states by exploiting the continuity of the system variables. Further restrictions on these possible succes­sor states are then imposed by checking for consistency with the definition of the constraints and the consistency between constraints which share an argument -- called constraint filtering, and information on the rates of change of the system variables held as part of the fuzzy qualitative state -- called temporal filtering. In addition. other knowledge about the system such as energy con­servation may be used to produce so-called global filters (Weld and de Kleer, 1990). Importantly, associated with each sequence of states, i.e., each path of the out­put tree, FuSim also generates a sequence of temporal intervals to indicate how long the system will persist within a particular state. This is a distinct advantage of FuSim over other qualitative simulation techniques. Especially, when used for diagnosing dynamic systems, FuSim is thus able to show which particular portion of the predicated behaviour should be matched by an observation at a particular time point or during a partic­ular ti.me interval (Leitch and Shen, 1991).

MULTIPLE MODELS BASED ON MODELLING DIMENSIONS

A modelling dimension is defined as a direction of pos­sible variations of a given system model such that the variated or modified models share some common pro­perties amongst themselves and also with the given model (Shen and Leitch, 1992b). It is such common properties that enable the construction of a sub-space of system models and the classification of multiple models. Four sub-spaces of models have been developed in the following in response to their corresponding basic but

common properties used to characterise each of the four modelling dimensions used within FuSim.

Multiple Models via Abstraction

As stated earlier, the critical task in Qualitative Model­ling is to decide on the form of the abstract representa­tion of system variables and the relationships amongst those variables. Actually, developing abstract models, with respect to a reference model, has been a major pre-occupation of Qualitative Reasoning. In FuSim, the variables within a model take values from a fuzzy quan­tity space. The cardinality, with associated underlying semantics, of the quantity space is called the level of abstraction of the model (Shen and Leitch, 1992b). Thus, a sub-space of system models can be obtained by varying the level of abstraction utilised to represent the physical quantities. The common property shared by such multiple models is that they are all able to elim­inate distinctions in the simulated system behaviour that are not essential with respect to certain specific applica­tion purposes. Within this model sub-space more abstract models are those with weaker quantity space (or smaller cardinality) that support less distinctions between the values and hence states of the system vari­ables. In fact, the term abstraction is herein so used to reflect the change in the quantity space in the sense that as the number of qualitative values which a variable may take decreases a more abstract description of this variable results. Or, as the cardinality of a quantity space employed decreases the number of distinctions in representing the variables also decreases.

Multiple Models via Commitment

366

Commitment dimension is related to uncertainty in the description of system model and behaviour. Within a qualitative modelling and simulation process uncertainty can occur in (at least) three different ways, namely, in the representation of relationships between system vari­ables, in the representation of quantity space, and in the determination of which simulated behaviour reflects the actual behaviour of the physical system. Although, in general, the first of these is an important class of uncer­tainty in system modelling, there does not exit a general method for assigning and reasoning about information on the certainty degrees regarding operational relation­ships within Qualitative Modelling. Thus, the following discussions will focus on the other two kinds of uncer­tainty only.

For a given physical system, when the level of abstrac­tion of its model is chosen the description of the under­lying range of the system variables on the quantity space may require the degree of certainty about such a description to be explicitly reflected. With respect to a presented quantity space, in FuSim, the particular form of the membership functions of the fuzzy qualitative values within this space is called the commitment to the quantity space (Shen and Leitch, 1992b). Clearly, a different assignment of the membership functions for each qualitative value that a variable can take reflects the different possibility that the variable should take the underlying real values. In other words, it indicates a different credibility on the discretisation of the underly-

ing real values. Based on this property, modifying the form of such commitment associated with a given sys­

tem model will then result in a sub-space of models such that variables within a particular model take their qualitative values with different degrees of certainty from those within other models.

The third type of uncertainty arises when a qualitative simulation algorithm generates spurious behaviours, due to the inherent ambiguity of the qualitative calculi (Struss, 1988). In present approaches to qualitative simulation, except for FuSim, the worst case solution is always assumed. That is, in spite of physical impossi­bility, all theoretically possible conditions regarding the transitions between system states are considered and maintained with equal status. This usually leads to multiple behaviour predictions from a single system model that are at variance with the uniqueness of the behaviour of the physical world. Fortunately, a tech­nique for uncertainty measurement to those potentially true state transitions has recently been developed and, hence, a commitment to each simulated behaviour can be assigned (Leitch and Shen, 1992). Adjusting the degree of the commitment associated with a behaviour equivalently increases or decreases the priority of that behaviour within a behaviour space determined by the currently used model and the other given models. In this sense, varying the level of the commitment leads to a model sub-space within which different models will produce qualitatively distinct behaviours but with the same priority.

Multiple Models via Model Resolution

Both abstraction and commitment are defined based on the assumption that the set of system variables that is of interest is fixed. However, in modelling a real physical system for specified purposes, it must be decided that which of those variables to represent within a model and consequently which to ignore. The number of vari­ables incorporated within a particular model is called the resolution of the model or, simply, the model reso­lution (Shen and Leitch, 1992b). In fact, moving from higher model resolution to lower one against this dimension aggregates system variables (to generate less detailed models) and, usually, results in the reduction of the corresponding system order. Reflecting this charac­teristics, lower resolution models, with respect to a reference model, can be obtained by neglecting some of the internal variables of the reference model. For instance, the dynamics, or speed of response of certain variables may be assumed to be instantaneous when comparing with other variables and hence can be replaced by their steady state values. A sub-space of models can, therefore, be attained by varying the resolu­tion of the system model, i.e., by changing the represen­tation of the given scope of the physical system with greater or less detail.

Multiple Models via Relation Strength

As reviewed previously, within FuSim, relationships between system variables are represented by either alge­braic or derivative or functional constraints. In particu­lar, functional dependencies are described by fuzzy rela-

tions holding against two or three variables, allowing both strength and sign information to be represented.

Varying the level of the relational strength implies the modification of the 'gain' between the related variables. Such a model variation direction is called the relation strength dimension (Shen and Leitch, 1992b). This results in a commonly used sub-space of models within which each model contains at least one fuzzy relation between certain variables such that similar relations between these variables (in terms of the same represen­tational form) exist within other models but the depen­dency strengths are different from each other. For example, a fuzzy relation describing the relationship between pressure and flow in an orifice can normally be represented by a relational matrix with multiple corresponding entries (such that a single pressure value may be associated with more than one flow rates and vice versa) to reflect the underlying quadratic charac­teristics of the orifice. To simplify the reasoning pro­cess involved in a particular application task, such a matrix may be required to be substituted by a diagonal matrix to express the piecewise 'linear' approximation of the non-linear characteristics. Of course, whilst the simplified model reduces computational complexity that would otherwise be encountered, the qualitative behaviour(s) resulting from simulating such a model may miss the underlying 'real' behaviour.

It is important to notice that the limitation of possibly missing actual behaviour in exploiting multiple models along the relation strength modelling dimension also exists when dealing with models obtained from modify­ing model resolution. In fact, a simplified model result­ing from weakening the functional dependency or from reducing the number of variables represented only dep­icts the behavioural approximation of the original model. This is because the reduction in information on either the model resolution or the relation strength, with respect to a fixed reference model, will change the model accuracy and hence not guarantee the soundness property of the simulation. Viewing this, a synthesised model sub-space can be developed by merging the two sub-spaces of models determined by the relation strength dimension and model resolution dimension. As a matter of fact, these two dimensions are sometimes combined within a single, synthesised modelling dimen­sion termed approximation (Struss, 199 1 ).

In summary, the conjunction of the model sub-spaces determined by the variations in each modelling dimen­sion defines a space of multiple models with a particular model being a point within this space. The location of a model within the space is dependent upon the current choice on each modelling dimension This visualisation of the model variations is very important in determining appropriate strategies in the potential applications of the multiple models.

367

IMPLICATIONS OF MULTIPLE MODELS FOR MODEL-BASED REASONING

The basic goal in the utilisation of multiple models is to start with a model with the most abstract, least commit­ment, lowest model resolution, and weakest relation strength and then to 'pilot' within this space until a par-

ticular MBR task is satisfactorily achieved. Although this approach is just beginning, a comprehensive inves­tigation of multiple models appears to have significant implications for MBR and, especially, for MBD (Leitch and Shen, 1991; Struss, 1991).

The establishment of multiple models based on the abstraction dimension, for example, immediately results in two important impacts on MBD systems. On the one hand, to reduce the complexity of system modelling, and thus that of the entire diagnostic process, the most abstract model available is desirable to initiate the diag­nostic search. On the other hand, too abstracted model may collapse behaviour distinctions necessary for distin­guishing between normal and faulty behaviours. A trade-off between the generation of correct diagnoses and the efficiency of the diagnostic process is, therefore, required. This inspires the significant idea of utilising hierarchical models within MBD systems so that different abstracted models can be used for finding faults with different levels of detail (Struss, 1991).

Clearly, commitment to a quantity space can be very useful within those model-based systems that have to cope with unreliable observations and/or ill-defined models. In particular, FuSim's capability to subjectively assign the commitment to a fuzzy quantity space within an application simulation greatly eases the interpretation problem often incurred when mapping a real-valued observation to a qualitative value (Shen and Leitch, 1992a). Further, commitment to simulated behaviours permits a progressive approach to qualitative simulation that first generates or utilises the 'most likely' behaviour and only progresses to other less committed behaviours if the behaviours considered fail to meet the purpose of an application task. Thus, ultimately, the important pro­perty of a simulation algorithm that guarantees the gen­eration of the correct behaviour along with, perhaps, other spurious behaviours is still retained, however, a significant improvement in efficiency is possible by exploring the highly committed behaviours first. This forms a firm basis for the use of qualitative simulation within any MBR tasks for which efficiency is important such as real-time model-based diagnosis of dynamic systems and real-time critical-event simulation (Leitch and Shen, 1992).

The choice for changing the level of detail in the representation of system model against model resolution dimension, i.e., the selection of a model with either more or less variables represented from the model space, is, of course, very dependent upon the task and the precision to which the specification of that task is expressed. When coping with the diagnosis of a com­plex dynamic system, a useful strategy to perform the reasoning process in an effective and efficient way is to utilise models with low resolution first. At such low levels, the physical system may be described by a static model within which, say, a real sub-system or an origi­nal internal feedback loop can be treated as a single 'component' and, therefore, techniques particularly efficient for diagnosing static systems can be directly applicable. As a result, one or a few such 'components' may be produced as faulty ones. Then, a diagnostic method capable of finding faults with dynamic models is applied to pinpoint detailed failures within the system by focusing on those sub-systems that reflect system dynamics with higher model resolution.

368

Considering model-based diagnosis of continuous sys­tems and, in particular, when suspicion is focused on parameter shifting, it is natural to generate predictions from those models returned by modifying the 'gain' between related variables and to compare such predic­tions against observations first in order to determine a fault. This is a major reason that, as indicated before, the model sub-space resulting from adjusting the rela­tion strength dimension (with respect to a reference model) presents multiple models that are commonly used for MBR. In addition, simpler models so obtained can be used, as the low resolution models, to increase efficiency in the applications of MBR, although the assumed correctness of the reference model may not be entirely preserved (Struss, 1991). In fact, within an application of such models, some detail of the reference model is intentionally omitted, thereby reducing the accuracy of the behaviour simulation required and hence simplifying the reasoning process. Further, these multi­ple models are often empirically derived and, therefore, are necessarily restricted to the operating range of the system experienced a priori and fundamentally the approximations of the reference model.

EXAMPLE

A simple example, of "a mass on a spring", as depicted in Fig. 1 , is used to demonstrate how multiple models of a single physical system are developed based on the four modelling dimensions within FuSim and what differences exist amongst the simulated behaviours resulting from the fuzzy qualitative simulation of these models.

Modelling

It is assumed that the reference model of the physical system consists of three variables: the displacement of the mass from the rest point of the spring, x, the velo­city of the mass, v, and the acceleration of the mass, a. It reflects frictionless motion and, therefore, can be described by the following derivative and functional constraints:

deriv x = v , deriv v = a ,

a - x -b --0.6 -s 0 s 0.6 b

-b 0 0 0 0 0 0 1

-0.6 0

-s 0

0 0 s 0 0.6 0

b 1

0 0 0 0 1 0

0 0 0 1 0 0

o o 1 o o o · 0 1 0 0 0 0

1 0 0 0 0 0

0 0 0 0 0 0

where the first two constraints establish the ordinary derivative relationships holding amongst the distance, velocity, and acceleration of the mass respectively and the third one is a weak, but stronger than monotonic operator, form of Hooke's law represented as a degen­erated fuzzy relation (Shen and Leitch, 1991). The fol­lowing quantity space, as shown in Fig. 2, is used to

describe its level of abstraction:

{-b . --0.6, -s . 0, s . 0.6, b } ,

with each value corresponding to a perceived meaning, e.g., -b denoting negative big and s indicating positive small. The commitment to the quantity space of this reference model is also defined within Fig. 2.

0

0.6

x

Fig. 1. A Mass on a Spring

µ(u)

.,

_ _L __ _1_ ___ __JL-----�:-;:-.:-�- u, u=:.;.v,a - l - 0 . 8 -0 . 6 - 0 . 4 -0 . 2 O 0 . 2 0 . 4 0 . 6 0 . 8 I

Fig. 2. Abstraction and Commitment of Reference Model

Varying the abstraction dimension, say, changing the above-given quantity space to another with a denser car­dinality as follows:

{-b , --0.6, -m , -s , 0, s , m , 0.6, b } ,

a new model results. Within which, two derivative con­straints are, of course, remain the same as their origi­nals. However, the relational constraint between x and a is modified with more detailed corresponding values between the two variables being represented such that,

a - x -b --0.6 -m -s 0 s m 0.6 b -b 0 0 0 0 0 0 0 0 1 -0.6 0 0 0 0 0 0 0 0 -m 0 0 0 0 0 1 0 0 -s 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 s 0 0 0 0 0 0 0 m 0 0 0 0 0 0 0 0.6 0 1 0 0 0 0 0 0 0 b 0 0 0 0 0 0 0 0

Figure 3 presents the outcome quantity space of adjust­ing the commitment to the reference space. In response to the modification against this modelling dimension, the symbolic representation of the reference model is unchanged.

µ(u)

_ __J._ __ _i_ ____ .._ ___ �--�- U, U=A,V,3. - 1 -0 . 8 -0 . 6 - 0 . 4 -0 . 2 0 0 . 2 0 . 4 0 . 6 0 . 8 l

Fig. 3. Modifying Commitment of Reference Model

With respect to the model resolution dimension, the fol­lowing model is obtained when the variables v and a vanishing, indicating a mass-stuck (at x0) condition:

X = Xo. v = a = 0.

Based on the modification of the relation strength, com­monly used multiple models of this system can be developed. For instance, when considering a medium friction condition, the system can be modelled by five fuzzy constraints, namely,

369

deriv x = v , deriv v = a ,

x , v · .

where additional parameters a1 and a2 are introduced to include the effectiveness of the friction. Two fuzzy relations, a 1 - x and a2 - v , are represented in a very similar way to the weak form of Hooke's law shown earlier and hence are omitted herein due to lack of space. If an infinite friction condition is concerned this model is then required to be further modified along the same dimension. Interestingly, this leads to the mass­stuck model that happens to be the same as the model obtained from reducing model resolution. This shows that a model sub-space resulting from modifying a par­ticular modelling dimension may often share certain models that also belong to other model sub-spaces attained via adjusting other dimensions.

Simulation Results

Suppose that the initial state indicates that the mass is moved away from the equilibrium point, x = 0, to x = 0.6 > 0, and then let go. FuSim produces a unique but different behaviour in response to each different model presented above. It is because of this that models dependent upon commitment to behaviours are not necessarily to be developed and hence omitted herein.

First of all, resulting from applying FuSim to the refer­ence model, Fig. 4.a presents one cycle of the system behaviour with the time points, associated with the fuzzy qualitative states, falling within the following intervals (Shen and Leitch, 1991) (notice that, these time ranges are also presented in other sub-figures of Fig. 4 to compare the results):

t0 = 0, t 1 e [ l , 1 1] , t2 e [ 1 .09, 12],

t3 e [2.09, 23], t4 e [2.18, 24],

ts e [3. 18, 35], t6 e [3.27, 36], t1 e [4.27, 47].

With each of the four modified models, resulting from the adjustment of the reference model against either of the following modelling dimensions: abstraction, com­mitment, model resolution, and relation strength, their corresponding behaviour variations are shown in figures 4.b, 4.c, 4.d, and 4.e respectively. Within Fig. 4.c, it is necessary to notice the changes of particular time inter­vals while the period keeps unchanged. Also, it should be noticed that the behaviour shown in Fig. 4.d describes the situation where the mass is stuck at its ini­tial state, i.e., x = 0.6.

b 0 . s

0 - s

- 0 . 6 - b

b 0 .

x

0

x

t m - 0 B

- s

- m - o . 6 - b

b 0 . s

0 - s

- o . 6 - b

b o . s

0 - s

- 0 . 6 - b

b 0 . s

0 - s

- 0 . 6 - b

x

x

x

0

0

0

0

(4.a)

(4.b)

(4.c)

t � 0

0 0 0

(4.d)

(4.e)

0

Fig. 4. Simulation Results

0 t

0 0

0 t

0

t

0 t

CONCLUSION

This paper presents a systematic investigation of developing multiple models of a physical system through the use of Fuzzy Qualitative Modelling (FuSim) technique. Basically, multiple models are developed against four crucial modelling dimensions within FuSim, namely, abstraction, commitment, model resolution, and relation strength. Implications of such an approach to multiple modelling for model-based application tasks are discussed. Examples for building different models by modifying a reference model along with the four dimensions are shown and the results of the experimen­tal simulations of these models are presented. This investigation provides a finn and formal basis for creat­ing useful strategies for the utilisation of Qualitative Modelling techniques in Model-Based Reasoning in general and Model-Based Diagnosis in particular.

REFERENCES

Dubois, D. and H. Prade (1980). Fuzzy Sets and Sys­tons: Theory and Applications, Academic Press.

Leitch, R. R. (1992). Knowledge-based control: select­ing the right tool for the job. Invited Plenary Talk, AIRTC-92.

Leitch, R. R. and Q. Shen (1991). Finding faults with model based diagnosis. Proc. 2nd Int. Workshop on Principles of Diagnosis, 121-134.

Leitch, R. R. and Q. Shen (1992). Being committed to qualitative simulation. Proc. 6th Int. Workshop on Qual­itative Reasoning.

370

Shen, Q. and R. R. Leitch (1991). Combining qualita­tive simulation and fuzzy sets. In B. Faltings and P. Struss (Eds.). Recent Advances in Qualitative Physics, MIT Press.

Shen, Q. and R. R. Leitch (1992a). On extending the quantity space in qualitative reasoning. J. Al in Eng., Computational Mechanics.

Shen, Q. and R. R. Leitch (1992b). Application studies of fuzzy qualitative simulation. In P. Borne and S. G. Tzafestas (Eds.). Mathematics of the Analysis and Design of Process Control, Elsevier.

Struss, P. (1988). Mathematical aspects of qualitative reasoning. J. Al in Eng., Computational Mechanics, 156-169.

Struss, P. (1991). A theory of model simplification and abstraction for diagnosis. Proc. 5th Int. Workshop on Qualitative Reasoning, 25-51.

Weld, D. and J. de Kleer (1990). Readings in Qualita­tive Reasoning about Physical Systems, Morgan Kauf­mann.

Copyright © IF AC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

APPLICATION OF ARTIFICIAL INTELLIGENCE TECHNIQUES

ARCHITECTURES AND TECHNIQUES OF ARTIFICIAL INTELLIGENCE IN PROCESS CONTROL

J. Efstathiou

Department of Engineering Science, Oxford University, Parks Road, Oxford, UK

Artificial Intelligence has been applied in process control, using a range of AI techniques, such as rules, fuzzy logic and neural nets, and architectures, including blackboards, lay­ered architectures and, most recently, distributed and multi-agent architectures. In the early days, expert systems in process control were seen as a way of possibly removing the operator from the control loop. But as applications have become more complex and the processes are becoming managed rather than merely controlled, the role of the operator has changed. It was never possible to define permanently the operator's role when sup­ported by an intelligent machine, so now are we are seeing the emergence of negotiation and dialogue between operator and machine for dynamic allocation of control tasks?

keywords: Process control, artificial intelligence, blackboard architecture, user interface, multiagent systems.

INTRODUCTION

Artificial Intelligence has been applied in process control for several years, with some notable suc­cesses. Different architectural styles have been em­ployed, such as rule-based expert systems, black­boards, distributed architectures and, recently, multi-agent architectures. Similarly, several AI techniques are being used, such as rules, fuzzy rules, model-based reasoning and neural nets.

Real-time applications of AI have evolved diver­gently from their origins with medical expert sys­tems and are now becoming a separate genus, with several features which make them distinct from the other genera of medicine and financial applications, for example. By definition, coping with time is a major distinguishing feature of real-time applica­tions and in this paper we shall argue that the fea­tures which have been adopted so far are only a partial solution of how to meet deadlines, optimise performance and cope with interruptions.

Turning to the other pillar of this symposium, one should examine these developments from the point of view of the live intelligence within the complete control system. The operator was originally seen as an expensive and unreliable component in the control system, leading to sub-optimality and ex­cessive expense. By contrast, AI supports the op-

erator by providing tools to help in controlling and managing complex tasks to a higher degree of per­formance. On the one hand, the operator may be perceived as a necessary evil, a sub-optimal con­trol component in well-understood conditions, but on the other hand, the operator is still required to cope with anomalous or unusual situations. This leads to an uneasy allocation of tasks and discre­tion between the operator and control system, with the operator unwilling to hand over control to the computer, and the computer unwilling to submit responsibility to the fallible human. In this way, the operator may be perceived as being too greedy in intervening to take tasks away from the opera­tor. If the operator is there to take responsibility for the operation of the plant, the operator must be assured that the computer will be co-operative on the operator's terms.

The paper is organized as follows. The next section looks at the evolution of architectures in applying Al to process control, with the third section review­ing the techniques that have been used. The fourth section examines the changing role of the operator and considers how multi-agent architectures could extend the role of the operator. The fifth section how these must be accommodated within the con­trol requirements for speed of response and coping with disturbances and faults.

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AI ARCHITECTURES IN PROCESS CONTROL

The earliest applications of AI in process control used notions from medical expert systems, using a knowledge-base and a forward chaining inference engine which applied control actions directly to the plant (Efstathiou, 1990) . The Linkman system (Haspel and Taunton, 1986; Efstathiou, 1990) was based on such an architecture, with the knowledge base consisting of groups of rules, and the group selected according to the operating conditions de­tected by the plant's sensors. Forward chaining systems were useful where knowledge of the oper­ation of the plant was too scant to support tradi­tional mathematical control techniques, but opera­tors knew how to control the plant.

At first, separate systems were constructed for fault diagnosis and control, but links between con­trol, fault detection and diagnosis were quickly es­tablished, since they depended on the same sen­sor data, although quite distinct knowledge bases, inference techniques and time-scales. Compared to forward chaining control, fault diagnosis was a very knowledge-intensive activity, with the heuris­tic knowledge of operators being relevant as well as the "textbook" knowledge derived from an under­standing of the underlying structure and behaviour of the plant .

With the linking of fault diagnosis and control, two things happened. First, this marked a shift away from the original paradigm of a knowledge base and inference engine as the only two constituent parts of the expert system. The operator alone was no longer seen as the only reliable source of knowl­edge about the plant, and the knowledge the ex­pert supplied needed to be extended with knowl­edge that could be obtained in other ways. The second effect was the appearance of some diagnos­tic systems which combined forward chaining with a component which was model-based, as opposed to rule-based. This enabled the system to reason about some states which could possibly occur, but which were not part of the heuristic knowledge base because the operators had never encountered these conditions before, or had overlooked entering them into the knowledge base (e.g. Dvorak and Kuipers, 1991).

So, it is at this point that an architecture must be defined, so that the different components of the con­trol system may be coordinated. Data may then be allocated to the relevant components and con­tention between components of the architecture for on-line computing resources could be handled cor­rectly. Two main approaches may be identified to solving this problem, although they are lately show­ing convergence. These are the blackboard and lay­ered architectures.

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Blackboard and Layered Architectures

The blackboard architecture permits the several components within a knowledge-based system to communicate by means of a shared space in mem­ory known as the blackboard (Engelmore and Mor­gan, 1988). The separate components, or knowl­edge sources, may write conclusions to the black­board and read information as it appears, which may then be used to generate further conclusions. The contributing expert systems may have different rights to access the b \ckboard, but data was made available to all.

The blackboard architecture is extended by the ad­dition of a manager which controls the data writ­ten to the blackboard and the order in which ex­pert modules use scarce resources to perform their tasks. Recent papers have reported on blackboard implementations enhanced with a "scheduler" ( Cre­spo and co-workers, 1991) , "server" (Krijgsman and co-workers, 1991) and "top level controller" (D'Ambrosio and co-workers, 1987) The role of these blackboard managers was to cope with timing constraints, by setting deadlines and using schedul­ing algorithms. Some of them showed some adap­tive behaviour (Krijgsman and co-workers, 1991) by amending the ordering of the rules, for exam­ple. Others used off-line computation to give suffi­cient abstraction to meet some deadlines (Vina and Hayes-Roth, 1991) .

The layered architecture designs the expert systems so that their tasks may be layered according to the time-scale at which events occur. The low-level con­trol system takes data from the sensors and applies actions to the plant. The supervisory system may also observe the sensor data and control actions from the level below, but takes longer to formulate fault hypotheses and assess their validity. Such a system would be expected to recommend actions to avoid or control faulty behaviour at a longer time­scale than the low-level controller. Hence, the lay­ered architecture may consist of several layers of expert systems, building up from low level control to upper layers of monitoring, supervision and plan­ning. The separate expert systems receive and may request data from systems below them in the hierar­chy, but are more likely to receive and transmit data according to a pre-specified protocol established at design.

Both the blackboard and layered architectures, have several component modules, each with specialised expertise and data requirements. Communication between the expert modules is performed either by granting total access to all data, or managing the flow of data only along selected pathways within the layers. By dividing up the IKBS into several expert modules, the possibility is immediately created of locating the modules on separate items of hardware

which may then be physically distributed around the plant. But now, communication between the expert modules must be carefully managed.

The layered architectures distinguish between the separate tasks according to the time-scale at which conclusions are reached. For example, Krijgsman and co-workers (1991) define the difference between in-line and on-line actions, with in-line actions tak­ing place within a sampling interval and on-line ac­tions based on reasoning which require data gath­ered from several intervals. Many of the blackboard architectures have designed the knowledge sources along this pattern, in order to cope with timing con­straints, leading to a convergence in the blackboard and layered architectures. Vina and Hayes-Roth (1991) and Krijgsman and co-workers (1991) show this feature.

Coping with Real-Time Interruptions

This convergence has been driven by the need to cope with the demands of operating in real-time. The strategies adopted so far include:

• sorting the rules by antecedent or operating con­dition to speed up search,

• sorting the rules by frequency of use to find often used rules quickly,

• performing immediate control actions at once, so that hypothesis formation can be done in non­critical remainder of interval,

• abstracting the plant model off-line so that search can be rapidly focussed on the target area,

• using an intelligent blackboard manager to en­sure that knowledge sources are allocated suf­ficient processing time to produce an adequate answer which can be accommodated within the reasoning schedule,

• improving the hardware processor performance.

Although all of these strategies can improve on real­time performance, none can guarantee adequate real-time performance. The levels of real-time per­formance achieved so far are even more questionable when one considers how little provision has been made for coping with interruptions, when the rea­soning process of a knowledge source may not be given its full pre-assigned processing time.

In order to guarantee real-time performance, close study must be made of the performance profiles of the reasoning processes, to understand how much the results of the reasoning improve with the expen­diture of more processing time (Boddy and Dean,

1989). So-called 'anytime' algorithms can be de­vised, which return an answer after the expendi­ture of any amount of time, with a better answer returned the more time is available. Many real-time applications require a sequence of reasoning opera­tions to be carried out, each of which may be turned into an anytime operation.

The next problem is coping with interruptions. D'Ambrosia and co-workers (1987) are amongst the few to mention the need for this facility, but admit that their implementation does not exhibit any of these properties, especially since it was not operat­ing in a "time-stressed environment" .

This problem has been addressed by Russell and Zilberstein (1991) who have written an optimising compiler which can schedule time between a se­quence of anytime operations so that the overall system is guaranteed to return an answer, even if interrupted, with the answer improving the more time is spent. The compiler uses tables represent­ing t.he performance profiles of the separate anytime operations in the sequence. Like Dean and Boddy (1989), the performance profiles of Russell and Zil­berstein (1991) are based on empirical studies of the component operations. Not all the available com­putation time is spent generating an answer, but an answer is always guaranteed, even allowing for interruptions.

Distributed Architectures

Apart from coping with interruptions, the process control system will also need to be robust to faults in the hardware. With distinct knowledge sources, a distributed hardware architecture suggests itself, so that the processing associated with each knowledge source may be placed on a separate processor.

Under a distributed hardware architecture, to re­quire each expert module to write all conclusions to a central blackboard while monitoring that black­board for any information likely to be of interest would place an impractical burden on the commu­nication bandwidth. Hence, the blackboard solu­tion is not likely to be feasible under a physically distributed system. However, a blackboard system managed by a central manager would seem more likely, although the central manager would mean that the whole system would be vulnerable should the manager fail.

A derivation of the layered system is more practical, since the amount of data interchange is limited be­tween those layers or components which have an in­terest in exchanging data. A physically distributed hardware configuration has other possible advan­tages to do with robustness should one processor in the network fail. If the others are smart enough,

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they should still be able to carry on, although with less than ideal performance. So, the attractive way to achieve maintained levels of performance is to grant each expert module some more intelligence , so that it can recognise faults in the network and its data input and cope accordingly. Indeed, it might even go so far as to decide when to request and grant data. Knowledge sources showing these fea­tures could be considered intelligent agents.

Hence , under a distributed architecture , the black­board or layered architectures would suggest the distribution of knowledge sources around separate processors, with each one capable of managing its own data exchange. This is the essence of the multi-agent architecture , with several expert modules, possibly physically distributed, and capa­ble of some control over their communication and decision-making.

In a process control system, it would be reasonable to expect that these agents all had the same goal, namely the safe and efficient production of product, but at a lower level there could be the potential for conflict, as when an agent is requested to transfer data, but is too busy on another task or short of resources to comply in the time expected. Strate­gies for resolving such conflicts would need to be addressed before putting such a system in control of a safety critical plant. We shall return to possible strategies later in this paper.

Al TECHNIQUES IN PROCESS CON­TROL

Let's go back to the beginning again and open up the boxes inside each IKBS to find out what tech­niques were being used. One of the earliest suc­cesses in the application of AI to process control involved the use of a fuzzy rule-based expert sys­tem (Efstathiou, 1989; Haspel and Taunton, 1986) , with the original laboratory demonstrations occur­ring in 1974 (Mamdani, 1974). This system took advantage of the simplifications possible under for­ward changing to produce a simple and effective system, capable of achieving standards of control, effective utilisation of plant and energy and consis­tency of product well beyond those that had been previously achieved under the only control option previously available - manual control.

Many knowledge-based systems for process control use rule-based inference or fuzzy logic to cope with at least part of their control strategy. For ex­amples see Sugeno ( 1985) , Crespo and co-workers (1991) , Krijgsman and co-workers ( 1991) . Fuzzy techniques are incorporated in commercially avail­able tools such as G2 and Linkman.

As well as the rule-based methods for knowledge

374

representation, we have recently seen the emergence of neural network methods for control of processes. Although there have been problems with under­standing how to construct a neural net and un­derstanding why it should reach a particular final state, these difficulties are now being addressed. It was not satisfactory to the control community that the neural network experts did not have a well­established, general procedure for designing neural network controllers, but it was too bad altogether if they could not even explain why it adopted a par­ticular final configuration.

Current work in Japan and the US is seeking to combine fuzzy control with neural nets. Fuzzy logic and neural nets are being combined in a number of ways (Takagi, 1990) :

• to give fuzzy logic systems a learning function,

• to process data with neural nets before applying the fuzzy methods,

• to incorporate logics in the structure of neural nets.

Combined techniques are being used to identify fuzzy rules and membership functions from data, which are then being incorporated into a self­organizing fuzzy controller. Similar methods are used for plant control, air conditioner control and others, although most of the publications so far are in Japanese.

THE ROLE OF THE OPERATOR

The previous sections on architectures and tech­niques show contrasting attitudes to the operator. Recent techniques, such as neural nets and neural­fuzzy fusions, have little role for the operator, since they are designed to remove the operator from the control loop and are not expected to provide oper­ator support. Fuzzy and rule-based controllers at least involved the operator as a source of expertise which could then be programmed into an automatic controller. So, AI techniques provide tools to mimic the operator, either by capturing his knowledge or by detecting new patterns in the data altogether. Hence, AI techniques tend to leave the operator on the sidelines.

Al architectures are still able to accommodate the operator, as one of the possible knowledge sources or as a supervisory controller who receives the infor­mation presented by the complete KBS. But in this role, the operator and control system play an un­easy game, concerning which of the two retains over­all control of the plant. Under what circumstances may one override the judgement of the other? What games of mutual deceit may be played so that one

player is lulled into believing the plant is in a dif­ferent state than the other supposes? And how do these games affect the optimality and safety of the plant?

The problem of allocating autonomy between the operator and control system comes back to the pur­pose of the operator's presence. As systems become more complex and have to cope with many changes to the plant's structure and behaviour, the opera­tor can keep the plant working effectively by coping with the defects in the control system as originally designed. Hence, the operator is kept in the control loop so as to be aware of the changing state of the plant and to cope with unforeseen changes to the operating conditions of the plant.

The operator's continued presence shows that it is not possible to predict all the states of the plant in the future. Hence, it is problematical to pre­dict all the unsafe conditions which might occur and lay down ahead of time exactly how they should be detected and managed. Strategies for coping with unforeseen conditions need to be kept under contin­uous review, with the control system and operator reassessing how each should respond in an emer­gency.

It can be seen that all the ingredients are in place for a multi-agent architecture, with complex dialogue between the agents. Galliers ( 1983) has examined the dialogue between intelligent agents, including circumstances where intention to mislead is part of the agents' repertoire of speech acts. Although this might seem fanciful in the domain of process con­trol, it is exactly what may happen as the plant and control system evolve away from the original speci­fication. Not only may the operator seek to deceive the control system about the state of the plant, the control system may also seek to simplify or other­wise present information about the plant in such a way as to make the operator believe the plant oper­ates in a fashion different from actuality. This may be done in the belief that the operator will be able to cope better cognitively with an incomplete model, thereby improving his performance under adverse circumstances.

Beck and Gomes ( 1992) have compared multi­agent and distributed architectures with sequen­tial problem-solving architectures for the job-shop scheduling problem. They identify several possible advantages which apply to process control:

• speed Several processors operating concurrently can improve the overall speed of computation.

• opportunism A variety of agents with different problem-solving capacities offers the possibility of solving multiple co-occurring problems in a novel way.

375

• specialisation Agents and their processors may be specialised to specific tasks.

• cost Implemented on low-cost computers, a dis­tributed system may be cheaper to implement than one based on a centralised computer.

They point out that once data, knowledge and con­trol are distributed, it becomes more difficult to en­sure coherent and cooperative behaviour between agents.

Beck and Gomes (1992) do not mention the role of the operator in their discussion, although the oper­ator must be one of the agents involved in the over­all control. Hence, the analysis of communication between the agents must include how the operator interacts with the agents, whether as a supervisor looking down on the agents active on a lower plane, or as just another agent with specialised skills and known weaknesses.

Multi-agent architectures must focus on the com­munication and negotiation which occurs between agents as they cooperate to solve problems. The procedures for agreeing how to solve problems can be changed as circumstances change. Compare this with current approaches which attempt to lay down rules defining the actions which ought to take place in the foreseen situations. Instead of working with, around or against the regulations written into the control system, the multi-agent system specifies the manner in which those procedures are implemented or changed. This would imply a radical change in the approach to operator involvement in control, but offers a possible solution on how to maintain the operator's situational awareness and control skills, since negotiation and revision would become a con­stant part of the supervisory control task.

CONCLUDING REMARKS

Artificial Intelligence offers many tools to support the operator, or replace him altogether. Architec­tures and techniques of AI are discussed to demon­strate the variety of support that may be offered to the operator of the process control plant.

For the control system designer, decision-making autonomy has to be allocated between operator and computer, so that the plant may be operated safely and efficiently. The operators must not be placed under undue stress, nor must they be given such a routine job that they do not have the opportunity to practise their control skills and maintain situational awareness. Placing the boundary on autonomy be­tween operators and computers has been a difficult problem, with no obvious solution, since it is likely to change dynamically and as a function of the in­dividual operator, his level of stress and workload.

This paper suggests that these problems may be ad­dressed under a multi-agent architecture, with the operator as one of the agents negotiating tasks with the other computer-based agents. Many practi­cal problems on managing communication between agents, establishing rules of negotiation and cop­ing with emergencies would need to be investigated. However, the possibilities are worthy of considera­tion.

REFERENCES

Beck, H. and C.P. Gomes { 1992) . Princi-ples underlying the decomposition of job-shop scheduling problems. To be presented at Intel­ligent Systems Engineering Conference, Heriot­Watt University, August 1992. Peter Peregri­nus, London.

Boddy, M. and T. Dean ( 1989). Solving Time­Dependent Planning Problems. Technical Re­port CS-89-03 , Brown University Department of Computer Science, Providence, RI 02912, USA.

Crespo, A. , J .L. Navarro, R. Vivo, A. Garcia and A. Espinosa (1991). A real time expert system environment for process control. In Proceed­ings of 3rd IFAC Workshop on AI in real-time control. Pergamon.

D'Ambrosio, B. , M.R. Fehling, S. Forrest, P. Raulefs and B.M. Wilber, (1987). Real-time process management for materials composition in chemical manufacturing. IEEE Expert, .2,, part 2 , 80-93.

Dvorak, D. and B. Kuipers ( 1991). Process Mon­itoring and Diagnosis. IEEE Expert, .§, part 3 , 67-74.

Efstathiou, H.J. (1989). Expert Systems for Pro­

cess Control. Longmans, UK.

Efstathiou, H.J. ( 1990). Introduction to Knowledge-based systems for process control. In J .McGhee, M .J .Grimble and P.Mowforth (Eds.) . Knowledge-Based Systems for Indus­trial Control. Peter Peregrinus, London, UK. pp. 16-33.

Engelmore, R. and A. Morgan (1988). Blackboard

Systems. Addison-Wesley, London.

Galliers, J .R. ( 1983) A theoretical framewok for computer models of cooperative dialogue, ac­knowledging multi-agent conflict. University of Cambridge Technical Report 172, Cambridge, UK.

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Haspel, D.W. and C.J . Taunton ( 1986) . Apply­ing linguistic control to process optimisation: a case study. In KBS '86, Online Publications, UK. pp. 133-140.

Krijgsman, A.J ., R. Jager, H.B. Verbruggen and P.M. Bruijn, { 1991). DICE: A framework for intelligent real-time control. In Proceedings of 3rd IF AC Workshop on AI in real-time control. Pergamon.

Mamdani, E.H. ( 1974). Application of Fuzzy Al­gorithms for the control of simple dynamic plant. Proceedings IEE, 121 , part 12, 1585-1588.

Russell, S. and Zilberstein ( 1991). Composing real time systems. IJCAI-91.

Sugeno, M . { 1985) . Industrial Applications of Fuzzy Control. North-Holland, Amsterdam.

Takagi, H. ( 1990). Fusion Technology of Fuzzy Theory and Neural Networks - Survey and Fu­ture Directions. Proceedings of the Interna­tional Conference on Fuzzy Logic and Neural Networks, July 20-24, pp. 13-26.

Vina, A. and B. Hayes-Roth ( 1991). Knowledge­based real time control: the use of abstrac­tion to satisfy deadlines. In Proceedings of 3rd IF AC Workshop on AI in real-time control. Pergamon.

Copyright © IFAC Anificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

REAL-TIME SUPERVISORY CONTROL FOR INDUSTRIAL PROCESSES

D.A. Linkens and M.F. Abbod

Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK

Abstract . Supervisory control has been applied to many cases in control industry. It consists of monitoring the process and the controller for maintaining the system in the best operating conditions. In this paper a knowledge-based supervisory control system is built as a multi-level structure which is used for controlling and monitor­ing industrial processes. The system is applied to a real-time liquid level rig which highlights the system specifications as a supervisory controller.

Keywords. computer control; fuzzy control ; fuzzy set theory; industrial control; paral­lel processing; real-time computer system; self-organising control; supervisory control.

INTRODUCTION

The control of complex plants such as chemical plants or cement kilns usually requires the oper­ation of the plant under its optimal conditions to meet the required efficiency or to prevent a shut down of the plant in case of any compo­nent failure. The supervisory control consists of monitoring the plant operation including the controller, sensors, actuators, and the process behaviour itself. It should be able to distinguish between the different types of the system be­haviour, e.g. normal operating behaviour, un­stable behaviour, and faulty behaviour in the system's various components. Most of the sys­tems with a supervision facility use alarm sig­nals indicated to the operator so that depending on his knowledge of the system he can distin­guish the faulty part of the system.

The supervisory structure presented in this pa­per is constructed in a multi-level manner, where the lower level consists of a rule-based fuzzy logic controller to control the process lo­cally {Linkens and Abbod, 199la) . In the next level a monitoring system monitors the system variables, while in the upper level different lay­ers exist such as the rule-base self-organising layer, the controller parameters tuning layer, the fuzzy fault detection layer, gain schedul-

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ing layer, alarm system layer. On top of this is the supervisory manager level with embedded knowledge-base. The same system structure has been implemented on medical systems {Linkens and Abbod, 1992).

The system has been implemented on a labo­ratory scale liquid level rig, while the real-time computing burden has been tackled using paral­lel processing techniques. The presentation will illustrate the supervisory control structure and its advantages via experimental results on the liquid level rig under different fault conditions

KNOWLEDGE-BASED CONTROL

Decision making in human behaviour is usually related to a set of information supplied from the environment and based on a set of rules relating to that specific condition in the environment. Accordingly, three levels of human behaviour can be distinguished: skill, rule, and knowledge­based behaviour (Stassen, 1987). Verbalising the human operator control actions is useful for skill-based behaviour, and can be extended to a rule-based behaviour. Knowledge-based be­haviour would require global information of the environment to be controlled. This consists of involving all the parameters which have an ef-

feet on the environment and scheduling a plant for achieving the required task.

Control of a process may be done by using a simple rule-based controller which would be ef­ficient enough to track the set-point by reduc­ing the error between the required value and the process output using a closed-loop feedback technique. This type of control is valid un­der normal operating conditions, but if a fault occurs in the process the rule-based controller would not cope with the new environment . A supervisory level on top is required which con­sists of a knowledge base describing the process normal operating conditions and the relation­ship between the process variables.

Fuzzy Logic Rule-Based Control

Fuzzy logic introduced by Zadeh ( 1965) is used to describe systems that are too complex or ill defined to obtain a mathematical model. It is described as linguistic rather then numeric and uses conditional statements to characterise the relation between variables. Zadeh has applied it in the field of economics, management and medicine. Assilian and Mamdani ( 1978) ex­tended the concept to deal with industrial pro­cess control, since it can be applied to systems for which precise measurements of the state variables cannot be obtained. Fuzzy logic rule­based control is a means of dealing with impre­cision and a method of modelling the human behaviour in controlling a system which cannot be modeled rigorously. The rule base describes linguistically the action of the human operator supported by information from the sensors.

The control action in the rule-based system is derived first by measuring the relevant variables and then converting them into fuzzy sets de­scribing their membership function. Then the intersection of the associated fuzzy set with the given rules is used to obtain the effect of each rule (membership function) on the output con­trol signal. Finally, the control action is formed by combining the actions specified by each rule and defuzzifying the final fuzzy set to a numer­ical value.

In the case of this work, the controller is de­signed to rely on the error between the set-point and the process output and the change in error which gives a fuzzy PD controller, as well as including fuzzy I term control rules to form a fuzzy PID controller.

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Supervisory Expert Control

Industrial controllers are often supported by a considerable amount of heuristics for dealing with conditions where the controller may not perform well. Such heuristics include precau­tion procedures in the case of process malfunc­tioning such as alarm conditions, switching the controller parameters tuning on-off, and switch­ing the controller between manual and auto­matic control. Such features are well defined in the expert control of Astrom et. al. ( 1986) which is useful for tracking the set-point and making the system more stable. However, such features may fail if there is a fault event occur­ring in the plant such as a failure in the sensors, actuators, and even in the physical structure of the plant. This would lead to a shut-down in the plant for maintenance which will reduce the productivity. A better approach is to use the supervisory control structure which keeps track of all the system conditions and keeps the plant on-line if a fault occurs as long as possible de­pending on the severity of the failure.

The supervisory architecture for the proposed system as shown in Fig. 1 consists of dif­ferent layers which involve the rule-base self­organising technique, a performance monitor, fault detector and diagnosis procedure, gain­scheduling procedure, alarm and warning sys­tem, and a manager for the supervisory level which will schedule the system operation. A de­scription of each procedure is given as follows:

Self-organising rule base. The self-organising facility provides for rule-base modification which allows a dynamic change to the rule-base according to the environment dynamics. It was first introduced by Procyk and Mamdani (1979) as part of a self-organising controller. It evalu­ates the effect of the rule in the past that con­tributed the present performance, then a modi­fication procedure is applied. Several techniques are used for the rules modifications which in­cludes l . adjusting the membership function. 2 . changing the range set of values describing the fuzzy set. 3. and reformulating the set of rules in the rule base. The self-organising tech­nique involved here uses the first and last choice together.

Gain-Scheduling. A gain-scheduling procedure is used to estimate the process gain in order to classify the process into one of the classified cat­egories in the supervisory manager. Depending on the process category specified by the gain scheduler, the supervisory level selects an ini­tial rule-base for the controller and an initial set

of controller parameters. This procedure is acti­vated during the starting up of the process. The estimation of the process gain depends on the input signal supplied and the initial response when compared to a set of responses in the knowledge base to select the process categori­sation.

Performance monitor. The performance moni­tor procedure acts as a tuner for the controller parameters. It uses simple pattern recognition techniques using the error versus time which is represented in peaks. The controller scal­ing factors are tuned if an oscillation, under­shoot , over-shoot, or steady-state error is de­tected. This procedure is activated by the su­pervisory level manager when starting the con­trol loop , changing the set-point, or when a fault is detected.

Fault detection and diagnosis. The fault detec­tion procedure is for the purpose of detecting any physical faults occurred in the process, such as sensors or actuators failure, or even physical structure in the process. Faults are detected us­ing alarm signals indicated to the operator such that depending on his knowledge of the system he can distinguish the faulty part of the sys­tem. Traditional methods such as fault trees are time consuming and require specific infor­mation about the process. When the process is complicated and has an ill-defined mathe­matical model such methods will be hard to implement. An alternative approach uses the fault detection and diagnosis with a knowledge­base derived from the operator's knowledge of the system. In this paper, a fuzzy approach is considered, based on the relationship between symptoms and failure in the process variables given by a set of conditional statments of the following general form:

IF S1j AND S2j . . . . THEN Li

where Si; is the value of the jth symptom in the ith statement . A linguistic statement would be as follows:

IF Fluid Pumping IS Normal AND Fluid Level IS Dropping THEN There is a Leakage in the Process.

The fuzzy sets defined for the process variables are considered to have a piecewise grade of membership giving for the process variables a wide range to be defined as the normal opera­tion condition.

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Alarm and warning system. This is a simple procedure which is gives an alarm or warning signal via the screen or in an oral form . The faults usually set a warning signal in the system. If the fault is not manageable when certain val­ues exceed threshold limits, the alarm system would be activated then a recovery procedure should be scheduled and implemented. If the failure is not recoverable then a shut-down rec­ommendation is issued.

Supervisory level manager. The supervisory level manager is the part which controls all the other blocks in the supervisory level. With its embedded knowledge-base it can schedule the operating procedure by assigning tasks to the different blocks according to the operating con­ditions. It also manipulates the rule-base mod­ification procedure and its size (the smaller the better) by switching the rules modification on­off and disabling the rules which do not con­tribute to the output (depending on a forgetting factor). It enables the rules in the case of any event occurring such as a change in the reference point or a detection of a fault in the system.

AN EXAMPLE: LIQUID LEVEL RIG

Consider a liquid level rig as a supervised pro­cess. The rig, as shown in Fig. 2 , consists of pumping the fluid in tank 1 then to tank 2 then out of tank 2. The control task involves main­taining the level in tank 2 to a reference value by controlling the pumping rate of the fluid. The information available from the process is via the two level detectors mounted in tank 1 and 2 respectively. Different types of fault to be considered are as follows: 1 . a block in the inter-connection hole. 2. a block in the outlet discharging tap. 3. leakage in tank 1 . 4. leak­age in tank 2. 5. sensor 1 failure. 6. sensor 2 failure. The different types of faults will be evaluated on the rig in the experimental results section.

SYSTEM IMPLEMENTATION

The system was implemented using parallel pro­cessing techniques because of the computation burden due to the fuzzy logic implementation which demands heavy computational power. A transputer platform has been developed based on previous work (Linkens and Abbod, 1991b). The system includes a human-machine interface via the keyboard and the screen, and a machine-

machine interface via the ADC and DAC. A sampling time of 10 sample/sec was chosen and 1 sample/sec for the control signal. This ap­proach was used because of the need for a spe­cial type of filter for filtering out the noise em­bedded with the incoming signals from the pro­cess. This type of filtering technique is known as a median filter which uses a moving window over the data. A special type used here is the non-recursive linear median filter.

EXPERIMENTAL RESULTS

This section demonstrates the experimental re­sults obtained from the process using the super­visory control algorithm with the different types of fault stated in the previous section. First , a normal operating condition is considered when there are no faults. The control algorithm starts by feeding a step input to the process and moni­toring the rise of the process variables e.g. levels of liquid in the tanks. According to the initial response and the input step signal, a compari­son with a set of template responses is done by the supervisory level to select the process cate­gory. According to the process category, a set of initial rules is selected for the rule-based con­troller as well as setting the controller parame­ters with initial values, such parameters involv­ing the scaling factors and the delay-in-reward parameter. The next step is switching the rule­based controller on-line and starting the perfor­mance monitor which according to the response adapts the controller parameters. Fig. 3 shows the time response under normal operating con­ditions.

If there is a fault in the process, the perfor­mance monitor block will report to the super­visory level manager such an event , which in turn activates the fault detection and diagnosis block. According to the set of fault detection and diagnosis rules in the knowledge-base, the process behaviour will be analysed and if there is a real fault it will be detected and diagnosed. A recovery procedure will take place depending on the fault severity. It starts by stopping the controller rule-base modification, reinitialising the performance monitor block, and activating the alarm and warning system. All the faults are considered to occur at time 150 second.

If the fault occurs in the physical structure of the process and is manageable then the con­trol system carries on controlling the process with the new faulty parameters by retuning the controller parameters and starting the rule-base

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modification after the process has settled down. Fig. 4 shows fault type 1 when a block in the inter-connection hole between the two tanks oc­curred. This leads to less fluid passing from tank 1 to tank 2, which results in a higher level in tank 1 and maintaining the same level in tank 2. Fig. 5 shows a fault of type 2 when a block occurred in tank 2 which results in keeping the same levels but increasing the gain i.e. lower fluid pumping rate.

In the previous cases a blockage was considered, whereas another common fault in such systems is leakage. Two cases were considered, the first is a leakage in tank 1 , which results in a higher pumping rate and keeping the same levels in the tanks as shown in Fig. 6. A leakage fault in tank 2 will result in an increase in the pumping rate and an increase in the level of tank 1 as shown in Fig. 7.

In the case of physical faults in the process, the fault detector and diagnosis system gives an in­dication of the fault type where the process is controlled under the new faulty environment. In the four physical faults cases considered, an un­stable behavoiur was occurred due to the fault, then the fault was detected, diagnosed and a correction procedure was implemented by acti­vating the gain scheduler to estimate the new gain of the process and the performance moni­tor to re-tune the controller parameters. After a while the system went stable proving good per­formance for the different cases.

If a fault of a different kind occurs, such as a faulty instrument the supervisory level manager selects the non-faulty instrumentation, and con­trols the process according to the data coming from such sensors. Fig. 8 shows a fault in sensor 1 where no data were received from the sensor. In this case the process was controlled using the data from sensor 2 for which the fault detection procedure would be disabled. Fig. 9 shows a fault in sensor 2 where no data were received from the sensor. In this case the process was controlled using the data from sensor 1 with a new set-point relative to the original set-point and the level difference in the tanks under nor­mal operating conditions. Thus, faults in the sensors can be managed while keeping the pro­cess on-line. In the first case the system was controlled with good performance, while in the second case a steady-state error occurred due to controlling the system via the unfaulty sen­sor. This can be considered an acceptable per­formance for keeping the process running with­out resorting to a full shut-down of the system.

CONCLUSIONS

The supervisory knowledge-based controller de­scribed combines aspects of rule-based con­trollers working in a multi-level structure to achieve the best performance for a real-time rule-based system. It consists of the algorithm running on a transputer platform using paral­lel processing techniques in order to cope with the real-time computing burden. The use of the supervisory level makes the system look more like a manager of a plant who gives orders to the operators who in turn act as controllers for certain processes in the plant. The plant man­ager is responsible for keeping the plant on-line, and making the correct decision in case of any abnormal behaviour in the plant. The super­visory controller has been successfully demon­strated on an experimental liquid level rig with different faults.

REFERENCES

Astrom K. J . , Anton J. J . , Arzen K. E. { 1986). Expert Control. Automatica, 21 , 539-545.

Linkens, D. A. , Abbod, M. F. {199la) . Self­Organising Fuzzy Logic Control for Real­Time Processes. IEE International Con­ference "Control 91 ", Edinburgh, March 1991. 971-976.

Linkens, D. A., Abbod, M. F. {1991b) . Fast, Self-Organising Control for Industrial Processes. IFAC Workshop on Algo­rithms and Architectures for Real-Time Control, Bangor, 11-13 September 1991.

Linkens, D. A. , Abbod, M. F . {1992) . Su­pervisory Hierarchical Intelligent Control for Industrial and Medical Systems. ISA Conference and Exhibition on Industrial Automation, Montreal, Canada, 1-S June 199�.

Procyk, T.J . Mamdani, E.H. { 1979). A Linguistic Self-Organising Process Con­troller. Automatica, 15, 15-30.

Stassen H. G. (1987) . Human Supervisor Mod­eling: Some New Development. Int. J. Man-Machine Studies, 27, 613-618.

Zadeh, L. A. { 1965) . Fuzzy Set . Information and Control, 8, 338-353.

SUPERVISORY LEVEL

USER INT!RFACE

BASIC CONTROL

LEVEL PROCESS

Fig. l . Schematic diagram of the control algorithm

Q . � · !f'i1 tank 1 tank 2

pump

Fig. 2 . The coupled tank apparatus

381

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50 100 150 200 T1me(aec)

250

Fig. 3 . Normal operating condition

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.

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300

300

120 .....-...._ __ , _ _ _ _ _ _ _ _ _ __ _ _ _ _ e 100·+--�_,.....:==--��� ...... --��---=--�--..... e / '·. I � 80 " '/ ·. . � 80 l •o '\ ...... , .. t!·•·1' '·- ·�· ., .. ............ � \ ...... -,·' .. , ... � ' ' , ·)�'"ti • • ,.1 ' "' '

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- - -- - - Levell ----- Leve12 ----- s.t-polnl - - - - - - - - - - - Pwnp Drive -------- raulh" Senaor

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

THE DEVELOPMENT OF AN INTELLIGENT MONITORING AND CONTROL SYSTEM FOR A SOLVENT

EXTRACTION PROCESS

G. Robinson, S. Pallett, R. Fripp, J. Mullhi and A. Spence

lnlelligenl AUlomation Division, Salford University Business Services Ltd., Technology House, Lissa/kl Street, Salford, UK

Abstract The requirements of an intelligent real-time system have been described by many authors. These requirements are briefly outlined and discussed in light of our own practical experiences in developing this and other applications. The application of the real-time expert system shell G2 to a solvent extraction process is presented, covering topics throughout the development cycle from conceptual design and development to implementation. Attention is paid to issues surrounding modular development within the G2 environment. Control of the solvent extraction process is effected through traditional three term controllers. However, the process poses a number of problems that are beyond the capabilities of conventional control strategies. The application serves to illustrate the potential for complementing conventional real-time control strategies with intelligent rule­based control and statistical process control techniques. The need for such a hybrid control strategy is illustrated and discussed. Finally, a brief discussion on the future of intelligent monitoring and control systems is presented.

Keywords Conventional Control, Knowledge Based Systems, G2

INTRODUCTION

The ability to produce quality products, quickly, economically and in response to rapidly changing market demands is the objective of all manufacturing and process-oriented organisations. In order to achieve this goal, many industrial organisations have made significant investments in automation, instrumentation and new manufacturing technologies. Process operations are becoming more complicated as older plant components are replaced with modern autonomous machines. As more automation is introduced, the reliance upon human operators expertise diminishes and the need for intelligent systems increases.

The sophistication of plant components has resulted in an increase in the information that an operator has to monitor and interpret. If a problem occurs, often the operator is presented with a bewildering array of raw information in the form of mimic diagrams, raw sensor readings and process trends. Of the information presented, only a fraction may be of any

383

significance . In addition, the operator usually has a finite time interval within which to identify the cause of a problem and instigate corrective action. In many instances this is beyond the capabilities of human reasoning. The need for intelligent operator support tools to help alleviate some of these problems has never been greater.

In order to implement robust systems that can exercise more autonomy requires the introduction of some form of intelligence to augment conventional data processing and control systems. Many organisations are investigating the potential of AI techniques to incorporate additional intelligence within such systems. In particular real-time Knowledge Based Systems (KBS) have been widely used in this capacity to enhance the decision making capabilities of operations personnel (Nilsen,1990; Rowan,1989; Williams,1990).

This paper describes how conventional control systems technology can be used in conjunction with the real-time expert systems shell G2, to develop an

intelligent monitoring and control system on a pilot­scale solvent extraction process. The efficient operation of the process requires numerous control and operational problems to be resolved. The complexity of the process, and the need for consistent and efficient operation, makes this process an ideal application for knowledge based systems technology.

The application serves to illustrate the potential for complementing conventional real-time control strategies with intelligent rule-based control and statistical process control techniques. In addition, the solvent extraction process requires a number of disparate tasks to be performed. The architecture of the intelligent monitoring and control system required to perform these tasks in real-time is described. The resulting intelligent control system can be deployed in a number of different operating modes, to provide the operator with increasing levels of support.

REAL-TIME ATTRIBUTES

For a real-time KBS to support the monitoring and control capabilities of existing Distributed Control and Supervisory Control And Data Acquisition systems, it must possess a number of fundamental attributes. These attributes are outlined below and have been discussed at length by many authors, (Efstathiou,1989; Kaufmann, 1989).

Speed

The speed at which processing tasks are performed is a fundamental factor in achieving a real-time response. However, a fast response by itself does not constitute a real-time system.

Connectivity

A real-time system must support on-line access to information from data acquisition and process control equipment. Interfacing to industrial control systems is a prerequisite for any real-time application. The enhanced monitoring capabilities of real-time KBS enable wide scale process surveillance to be performed that could not be undertaken by the operator.

Time-constrained Reasoning

The ability to reason with incoming data and reach valid conclusions, within timescales relative to the validity of the data, is a principal feature of a real­time system. The accuracy of the conclusions and the advice generated within this timeframe should provide an acceptable response time for the operator.

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Temooral Reasoning

The representation of temporal knowledge is at the heart of any real-time system. A real-time system must be able to represent and reason about past, present, and future events. This should include the sequence in which events occur, which in many instances is just as important as the events themselves.

Truth Maintenance

A real-time KBS must be able to maintain a consistent view of the outside world. If the validity of incoming data changes, the system must be able to update or even retract, conclusions that have been reached as a consequence of the data.

Continuous Operation

The reasoning capabilities of the real-time system must not be interrupted by routine processing e.g. for data acquisition, updating displays or memory management.

Asynchronous Events

The majority of real-time systems are driven by external events, therefore the system must be able to dynamically adapt to changes in work load. If a significant external event occurs, the system must be able to modify the focus of inference in accordance with the perceived importance of the event.

Real-Time KBS Products

KBS products have increased in sophistication over the last decade. Selecting the most appropriate KBS shell is an application specific task that is made all the more difficult if the problem requires a real-time response.

There are a number of commercially available real­time KBS products that claim to offer all, or some, of the real-time attributes outlined above. The Intelligent Automation Division has developed applications using a number of the leading real-time KBS products. These applications have allowed the strengths and weaknesses of each product to be identified.

The majority of real-time KBS products contain most of the attributes required for a real-time response. However, there are very few products that provide explicit truth maintenance or temporal reasoning schemes and usually only a point-based temporal representation is provided.

Most real-time KBS products provide facilities for polling data or receiving data on an event driven basis. In G2, this is achieved via the G2 Standard Interface (GSI). The GSI is an external communication driver written in C. Gensym provide bridge code for a number of well known process control systems. The GSI is responsible for all on-line communication between the control system and G2.

There is an increasing trend towards the integration of KBS and conventional control systems. An increasing number of DCS and SCADA vendors are beginning to support links to commercially available KBS products. This is a trend that will continue over the next decade.

Most KBS products handle asynchronous events on a priority basis. Generally, significant events have to be identified during development and assigned a priority that is high enough to dominant the current line of inference. However, in many instances, the priority of an event is context sensitive and can only be assigned dynamically. Very few commercial products allow dynamic priority assignments.

Generally, the real-time capabilities of most KBS products are adequate for the majority of applications. Speed is currently a problem with some products, but is very much application specific; depending upon the application, the dynamics of the process and the hardware platform adopted.

PROCESS OVERVIEW

A schematic representation of the process is given in Fig. I . The process is based on sol vent extraction technology typically employed for liquid-liquid extraction within the process industries. The main process unit is the pulsed column, in which aqueous and solvent feeds are contacted counter-currently. Pulsing is provided by compressed air. The solvent product flows to the top settler and the aqueous product to the bottom settler.

The key to stable operation is the control of the aqueous/solvent and the solvent/air interfaces at the top of the column. The interfaces are detected through the use of pneumercators. The solvent/air interface is controlled by removing solvent from the top settler and the aqueous/solvent interface is controlled by removing aqueous product from the bottom settler. The interface control problem is compounded by both natural noise on the signal and noise from pulsing. Accurate control is required to keep the aqueous/solvent interface within the measurement range of the pneumercators.

385

As shown in Fig. l , the operation of the pulsed column is supported by ancillary equipment including feed tanks, product tanks, a dump/ recovery tank, and compressed air equipment for pulsing. Although the process is based around solvent extraction technology, the operational problems encountered are generic to most process plants. These include: • instrument failures relating to both sensors and

alarms • process item problems such as pumps failing or

valves sticking etc. • inadequate control from conventional PID

controllers requiring periodic manual intervention

• insufficient information processing, for example display of consequential alarms

• inadequate feedback and diagnostics when automated procedures and sequences encounter unexpected conditions

• requirement for continual operator vigilance to recover from process failures

A level of sophistication beyond that of conventional control systems technology is required in order to accommodate these situations and process maloperations within the normal operating regime of the pulsed column. The intelligent monitoring and control system can be utilised to maintain plant availability in the event of various failure scenarios.

IMPLEMENTATION

The implementation of the monitoring and control system on the pilot-scale process is shown in Fig. 2. A Programmable Logic Controller (PLC) is responsible for all low level data acquisition on the process. In-house bridge code has been developed to allow serial communication between the PLC and CONIX, a data acquisition system providing a level of functionality equivalent to that of a traditional SCADA system. The SCADA system (CONIX) and G2 run concurrently on a SPARCstation 1 + and SPARCstation IPC respectively. The GSI tool-kit has been used to implement remote communications between G2 and CONIX.

G2 receives scanned analogue signals from the process, typically every 12 seconds. Some key signals are scanned more frequently. The digital signals from the process are received on an event driven basis using the unsolicited input facilities of the GSI. The controller parameters, for example

set-points and controller outputs, are also visible to G2. Digital control signals can be sent from G2 to open/close valves on an as needed basis.

Process control is effected through the use of conventional three tenn controllers. However, to run the process at maximum efficiency requires a level of sophistication beyond that offered by conventional control regimes. The implementation architecture provides a means of investigating advanced intelligent control using a hybrid of rule­based and conventional control strategies.

The real-time expert system is implemented as a intelligent supervisor with specific tasks under the dedicated control of the SCADA system. The configuration of the intelligent control system can be altered interactively with the appropriate use of operator privileges. This enables the system to exercise a greater degree of autonomy.

The intelligent monitoring and control system provides capabilities to:

• exploit the advanced monitoring and diagnostic capabilities of knowledge based systems technology to improve the overall operation of the process

• gain a greater insight into the complexities of the process

• implement alternative control strategies for operating the process at maximum throughput

• dynamically reconfigure control strategies to recover from plant maloperations

APPLICATION ARCHITECTURE

The solvent extraction application requires a number of disparate tasks to be perfonned. These tasks include the implementation of a number of self-contained modules. A decomposition of the overall monitoring and control problem into manageable sub-tasks has resulted in a modular design as delineated in Fig. 3.

The design resembles a classic blackboard architecture. The blackboard holds all data and conclusions, providing the only means by which modules can communicate. This enables the overall design to be controlled by identifying key data structures and data flows. Modules are triggered in response to changes on the blackboard. Once the module has finished its processing, any conclusions that have been made are posted onto the blackboard. This new infonnation is thus available to all the other modules.

386

The blackboard architecture has enabled some of the opportunistic strategies of the operator to be implemented. The sequence in which events occur can be monitored independently of the events themselves. This has been used to identify scenarios where emergency shutdown procedures have to be invoked quickly to avoid catastrophic failures.

The user interlace control module coordinates operator access to supervisory system. The intelligent control system supports a range of functions that can be invoked interactively from the user interface or directly by the intelligent supervisor. These activities include:

• Plant procedures

• Interface control

• Message displays

• Mimic displays

A number of dedicated modules are provided by the supervisory system to ensure plant availability which include:

• Diagnostics/Prognostics

• Alann Analysis

• Sensor validation

• Statistical Process Control

INTELLIGENT CONfROL

Control of the solvent extraction process poses a number of problems that are beyond the capabilities of conventional control strategies. The intelligent control system employs the functionality provided by two basic modules within the real-time KBS. A hybrid control strategy combining rule-based control and statistical process control techniques is utilised to tackle the control problem outlined below.

Control Problem

The pneumercators in the top settler can be used to estimate the position of the solvent/aqueous interface, provided that the solvent/aqueous interface is between the two pneumercators and the solvent/air interface is above the top pneumercator.

Given that these conditions are satisfied, then the top pneumercator can be used as an indication of the solvent level in the top settler. Furthennore, an empirical fonnula can be applied to the difference between the pneumercators to infer the position of the aqueous/solvent interface.

If the region between the two pneumercators is all aqueous, then a constant value will be inferred equivalent to the head of aqueous; if the region between the pneumercators is all solvent, then a constant value will be inferred equivalent to the head of solvent. A mixture will generate an intermediate signal. The interface control problem is compounded by both natural noise on the signal and noise from pulsing. Accurate control is required to keep the aqueous/solvent interface within the measurement range of the pneumercators.

Rule-based control

The rule-based controller infers the position of the aqueous/solvent interface and then adjusts the aqueous product flow, to keep the interface within the bounds of the pneumercators. Additionally, if the interface should go out-of-bounds, for example due to fast transient changes, then the rule-based controller is capable of adjusting the aqueous product take-off in real-time to bring the interface back within bounds.

The main advantages of the rule-based controller combined with conventional three term control are:

• explicit display of the controller action facilitates the understanding of a difficult control problem

• controller action can be programmed in terms of simple heuristics, which can be easily modified in line with an increased understanding of the control problem

• controller action can be easily re-configured dependent upon the prevailing process conditions.

Statistical Process Control

The primary objective of the statistical process control (SPC) module is to identify abnormal process behaviour. A combination of interpretation rules and techniques based on Shewhart charts have been developed to identify the state of the value, for example high, low, normal etc. A generic architecture has been adopted to control the level of SPC processing to be applied to each sensor, and to enable the SPC parameters and action limits to be specified off-line and/or be dynamically reconfigured on-line.

The SPC module provides an early warning of process parameters beginning to drift. Significant drifts on key process parameters are used to trigger the diagnostic capabilities of the KBS which in turn, control the conventional three term controllers. This hybrid control strategy provides an effective monitoring and correction facility that is beyond the

387

capability of each of its constituent parts. Figure 4 depicts the raw sensor values from one of the pneumercators, along with the SPC charts showing processed values in relation to the action limits.

SUMMARY

The ability to reason with and analyse the large volumes of data associated with industrial applications and present meaningful advice is a natural application for real-time KBS. However, real-time KBS are a complementary technology to conventional data processing systems. The intelligent monitoring and control system outlined in this paper has been developed to demonstrate the integration of control systems with real-time KBS. Industrial KBS applications should be regarded as an extension of conventional data processing rather than a replacement.

REFERENCES

Nilsen, S (1990). Experiences made using the expert system shell G2. IEEE Conf. Tools for artifical intelligence

Rowan. D (1989). On-Line expert systems in process control. AI Expert, August

Williams T. Application of COGSYS to a small gas-processing plant, Knowledge-based systems for industrial control, J McGhee (Ed.). pp 297-296

Efstathiou J. ( 1989) Expert systems in process control. Longman

Kaufmann, M. ( 1989). Real-time AI systems: A definition and an architecture. Int. Jnt. Conf. on AI, Vol. 2. pp. 256-261

till

KEV' A: TOP SETTLER B: BOTTOM SETTLER C: AQUEOUS IN O: AQUEOUS OUT E: SOL VENT IN F: SOL VENT OUT G: SOI.VENT/AIR INTERFACE H: AQUEOUS/SOL VENT INTEAF ACE I: COMPRESSED AIR PULSE J: VENT

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Copyright © IF AC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

KNOWLEDGE-BASED SYSTEMS FOR REAL-TIME PROCESS CONTROL: THE MIP PROJECT

X. Alaman, S. Romero, C. Aguirre, P. Serrablma, R. Munoz, V. L6pez, J. Dorronsoro and E. de Pablo

lnstituto de lngenieria de/ Conocimiento, UAM Cantoblanco, Modulo C-XVl, planta 4, 28049 Madrid, Spain

Abstract. In this paper a detailed description of the MIP project is presented. M I P (Intelligent Process Monitoring) is a Real-Time Expert System that monitors, diagnoses, and generates suggestions in real time about optimization and stability concerning the oper­ation of a petrochemical plant. MIP software architecture is based on the concept of Blackboard. The Blackboard is the central mechanism for information exchange between the modules of the system, being also the only centralized knowledge representation scheme within the system. MIP uses a hierarchical knowledge representation with four levels of abstraction, different knowledge sources being responsible of maintaining each of these levels. MIP is deployed and in current use since March 1 991 in an acrylonitrile plant of REPSOL QUIMICA, S.A. at Tarragona (Spain), with a reported success both from the technical and the economical point of view.

Keywords. Expert systems; monitoring; supervisory control; chemical industry; real-time computer systems; blackboard architecture.

INTRODUCTION

In this paper a detailed description of the MIP project is presented. MIP is a Real Time Expert System developed at the Knowledge Engineering Institute at Madrid (IIC). The system monitors, diagnoses, and generates suggestions in real time about optimization and stability issues concerning the operation of a petrochemical plant. MIP is deployed and in current use since March 1991 in an acrylonitrile plant of REPSOL QUIMICA, S.A. at Tarragona (Spain), with a reported success both from the technical and the economical point of view.

The UC (lnstituto de lngenieria del Conocimiento -Knowledge Engineering Institute) is the result of an original idea from IBM Spain and the Autonomous University of Madrid. Eight leading Spanish compa­nies endorsed the idea, the IIC being founded in December 1 989. Around 70 persons work in Artifi­cial Intelligence R&D in this university institution, which specially promotes the transfer of technology to industry. Both the Spanish University & Educa­tion and the Industry Ministries are also involved in funding the II C.

The paper is structured as follows: the second section describes the problem to be solved and the reasons to use an expert system. The following sections describe the hardware architecture, know­ledge architecture, software architecture and meth· odology used in the MIP project. The last section discusses the results obtained both from technical and economical points of view.

391

STATEMENT OF THE PROBLEM

The main goal of the MIP expert system is to assist in controlling a petrochemical reactor in a refinery plant belonging to the REPSOL group. It supplies information and recommendations in real time that help to diagnose and to take decisions concerning the control of the plant. These recommendations mainly address two issues: efficiency supervisory control, that consists in optimizing parameters with the aim of improving the overall productivity of the process, and stability supervisory control, that deals with diagnosing would-be problems before they actually occur, describing their causes and indi­cating possible actions to be taken.

The petrochemical process considered is the pro­duction of acrylonitrile from propylene, ammonia and oxygen, by means of a catalytic reaction. The project takes into account the first section of the plant, that includes the preparation of reactives and the reaction in itself. This involves around 500 vari­ables. It is a continuous process, fully automated, but with no global analytical model available. This is due to the presence of catalytical processes. The lack of such a model plus the variability of the cata­lyst behavior causes difficulties to classical auto­mated control. Manual expert adjustments are needed to assure continuous productivity optimiza· lion.

Originally the control of the reaction was performed both by the automated control system for routine operations and by human expert actuation for supervisory control. However some requlrementa were identified that were not meet by the existent

Senaora, actuator•

TDC- 3000 console

Fig. 1. Hardware architecture.

control procedures and recommended the incorpo­ration of expert system technology:

• Augmentation of the capabilities of the operator: when dealing with abnormal situations, the process engineer has a set of techniques and knowledge that, if permanently accessible to operators, would allow their effectiveness to be substantially increased.

• Unification of problem solving criteria: different operators respond in different ways to the same problem, depending on their education and previous experience. This may cause problems with process stability and equipment mainte­nance.

• Cognitive overload: both the impossibility of tracking continuously the evolution of each var­iable and the huge number of variables involved, prevent some decisions from being made in a timely fashion.

• Information integration: Several sources of information are usually available to operators. An information integration facility is a real need in such an environment.

As Laffey and others (1988) discuss, the above stated requirements are clear indicators of the need to include an expert system in the existent control environment. Such an application would contin­uously offer to operators some of the expertise of the process engineer, would favor the development of common knowledge and common problem solving strategies among operators, and would dis­charge their cognitive overload, providing addi­tionally a highly integrated view of the process. The MIP project is the response to these needs.

In the following sections the MIP project is described in detail from four points of view: the hardware architecture, the knowledge architecture, the software architecture and the software method­ology.

HARDWARE ARCHITECTURE

The control computer installed in the plant is a Honeywell TDC-3000. Additionally, a mass spectrometer is controlled by means of two personal computers, that communicate via RS232 serial

Masa spectrometer

HYWAY bua

PCSI Interlace

RS-232

RS-232

IBM PS/2 Mod.00

392

lines. These are operated off-line from the rest of the control equipment, in spite of managing some essential data. We added a IBM PS/2 to the system, as shown in Fig. I , providing data integration capa­bilities.

The installed equipment is an IBM PS/2 model 80, 1 6MB RAM, 300 MB hard disk, math coprocessor, one additional RS232 communication card, and 8514A monitor (768 • 1 024 pixel, 256 colors). The PS/2 was connected to the control computer via a RS232 communication port, using a dedicated inter­face from Honeywell (PCSI). The other RS232 port was used to monitor the communication line in the mass spectrometer subsystem.

KNOWLEDGE ARCHITECTURE

One of the most important steps in the design of an expert system is the selection of an appropriate knowledge representation scheme. In process control applications this problem is further compli­cated because of the existence of various types of knowledge that require different knowledge repres­entations each, as is better argued by Stock (1989).

More specifically, part of the knowledge about process control is in form of analytical models: this knowledge may be directly encoded as a simulator. Part of the knowledge is expressed in form of heuristics and *rules of the thumb*: this knowledge is better encoded by means of a rule based scheme. Finally, part of the knowledge is concerned with the physical and logical structure of the plant, n�rmally expressed in form of diagrams and charts: this knowledge could be encoded using a frame I relationships representation.

Two criteria were considered while designing the knowledge architecture: it had to be close to the knowledge representation mechanisms of the human expert and it had to be modular. The first requirement assures better communication at know­ledge acquisition meetings, easier validation of the system, better acceptance of the final product, and easier maintenance in the future. The second requirement enables teamwork, by specializing developers in different aspects of the problem (i.e. numerical procedures vs heuristic rules), as well as

Qlobol Hel.lrl stlc

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facilitates modular implementation, validation and maintenance of the system, keeping the complexity of each module within reasonable bounds.

The final design is a hierarchical architecture, as shown in Fig. 2. The measurements from the plant form the base of the architecture. It is the Direct Quantitative Model. Each measurement is comple­mented with other information, such as a time stamp, the validity period, pointers to related vari­ables, alternative sources in case of sensor fault, etc. It is implemented in form of a frame based scheme, where relations represent the physical and logical structure of the plant.

The next level is the Elaborated Quantitative Model. A large part of the knowledge about petrochemical processes is numerical and algorithmic in its nature. The most rational implementation of this knowledge is a simulator. In our case, we had available many accurate analytical models of parts of the plant, but no global model. The unavailability of a global model was intrinsic to the presence of catalyst in the core of the process. The final result is a set of very accurate simulators of parts of the plant loosely coupled to each other. This set as a whole repres­ents all the numerical relations of interest among variables of the process.

The third knowledge level is formalized as a rule based system: it is the Local Heuristic Model. The knowledge enclosed in this level is related with the local diagnosis of parts of the plant. With .. local diagnosis' we mean the diagnosis of a subsystem of the plant that is made taking into account just local variables. The source of the knowledge at this level is the set of logical and heuristic rules that human experts have developed during their professional career and that expresses those local aspects of the process that cannot be easily included in an analyt­ical model, but nevertheless human experts are able to cope with.

The fourth level is the Global Heuristic Model. It complements the previous level by performing global diagnosis of the plant from the local diag­nosis produced there. This global diagnosis is imple­mented as an evidential reasoning scheme that uses the local diagnostic assessments as symptoms and obtains the possible set of problems that best explains such symptoms. This mechanism will be described in detail in a forthcoming paper.

393

This architecture follows closely the knowledge rep­resentation of the human expert, that starts with the knowledge of measurements and their underlying structure, then calculates and estimates intermediate variables, obtaining the complete description of the plant, then studies the situation locally, trying to find anomalies in individual subsystems, and then relates the existent anomalies in a bigger picture, producing a final global diagnosis.

One interesting feature of this hierarchical scheme is that each level has access only to data and know­ledge in lower levels. With this protocol, interaction between knowledge representations is simplified while modularity is highly incremented.

SOFTWARE ARCHITECTURE

The software architecture that implements the knowledge architecture described in the previous section is shown in Fig. 3.

The architecture is based on the concept of black­board (see Erman and others, 1 980; Engelmore and Morgan, 1 988). The main characteristic of the Blackboard is that any module in the system uses this data structure to communicate with any other module. The Blackboard has its own mechanisms to certify the consistency and validity of the data it contains, being the only centralized knowledge rep­resentation in the system. The Blackboard is also used for collaborative problem solving. The other modules in the system are described below.

The Blackboard Manager is the program that manages the refreshing of variables, keeps the con­sistency, and in general maintains the Blackboard data. It is implemented as a C language program.

The Communications Module contains all the rou­tines that allow communication with external vari­ables. In particular it contains routines to communicate with the TDC-3000 control computer and routines to communicate with the mass spectrometer. It is implemented as a library of C language functions.

The Simulator is the module that is continuously performing the calculations of new variables from other variables and measurements. It takes the values it needs from the Blackboard, performs the calculations, and return the reaulta to the Black.­board. It is implemented as a C language program.

0[�J-�- 1 l _ _I I Reasoning Modules -

I l -- I .s Blackboard

� t B ---J Blackboard

Manager

Fig. 3. Software architecture.

The User Interface is the program that drives the interaction of the operator with the system. It has been carefully designed, taking into account ergonomic principles as well as user requirements and comments. It is a high quality graphical inter­face, with information integration capabilities (See Fig. 4). The user interface was developed using A VC (a hypermedia tool from IBM), that allowed easy modifications and fruitful user feedback. Once the final design was reached, the user interface was reprogrammed in C language, for efficiency reasons. A complete description of the MIP User Interface design and implementation may be found in (Aguirre and others, 1 992).

The Reasoning Modules have been developed using The Integrated Reasoning Shell (TIRS), an expert system shell from IBM, frame and rule based and with forward and backward reasoning capabilities. We essentially use the forward chaining paradigm, therefore optimizing the RETE network updating scheme is fundamental in terms of efficiency. We designed an interface to the Blackboard specially tuned to that achievement. The idea is that TIRS receives new data when and only when the data has changed appreciably from the last time the same data was communicated to TIRS. Using this pro­tocol, an average of only 20 variables out of 482 are communicated to TIRS in each cycle, improving impressively the efficiency of the infer­ence engine.

M ETHODOLOGY ISS UES

Many results in this aspect have been obtained, that are described in detail elsewhere (see Alaman and others 1991). Here we present a summary of them, including the most important aspects that, in our opinion, contributed to the success of the project.

Integration: A real time expert system that is not able to get the data on-line and without intervention of the operator is almost useless. In the MIP project one of the initial tasks was to build the communi­cations interface with the existing hardware and software in the plant. In real life, solutions tend to be effective, not necessarily elegant, and therefore many times ad-hoc equipment is installed in the plant, sometimes off-line from the control computer.

394

This was the case of the mass spectrometer in our plant. Imaginative solutions are needed to deal with such contingencies, because solving these initial problems is a prerequisite to any further develop­ment.

Several advantages have been obtained from the early connection to the plant. Firstly, users, experts and management were encouraged at seeing an early success in the project. Second, the communi­cations module in.itself, with the addition of a first version of the user interface, was already helpful for the operators: they could access the data in the plant in an easier way than with their older proce­dures. This favored fruitful interaction with users right from the beginning. Third, it was compiled a data log of values of selected variables at specific situations that we used subsequently for off-line vali­dation of the expert system. Fourth, The final struc­ture of the communications module had some impacts in the design of the whole system that could have caused problems if not have been known in advance.

Modular development vs incremental development: We did not use the classical approach of incre­mental development of expert systems. This approach has the advantage of encouraging user feedback, and allowing to incrementally educate the experts in what is expected from them, and what they can expect from the expert system. The draw­back is the ad-hoc, handy craft nature of the process. Instead, we used a strict software engineer approach, with a classical life cycle composed of analysis, design, implementation, validation, and deployment tasks, but applying it to individual modules, not to the total system. With this strategy, we did really grow incrementally, module after module, but each module being involved in a strict software engineering process. The first module deployed was the communications subsystem, with a initial release of the user interface. It was not a prototype, but the real, final version of the commu­nications module. When deployed, users had a first release of the MIP system, just with the data gath­ering functionalities. This in itself was already useful for operators, so they began to use the system regu­larly, and we obtained frequent feedback from them. The second step was the deployment of the

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Fig. 4. User interface main screen (for confidentiality reasons this figure has been edited).

simulator. This module added a new, and useful, functionality as well as further comments from operators and experts. The third step was the deployment of the reasoning modules, and finally the last step was the deployment of the global version of the user interface.

Many advantages have been obtained from this modular approach. Software engineering tech­niques have been rigorously applied, with a substan­tial impact in credibility, maintainability and documentation. As useful results were shown right from the beginning, users, experts and management were encouraged and became involved in the project. Additionally, while some low-level modules were being deployed, other modules were in design or implementation phases. In this way we could use the interesting user feedback already available, keeping most of the advantages of incremental development without suffering its drawbacks. Finally, having an individual life cycle, each module was easily modified, validated and installed in case of updating.

Development team: To implement such a complex application, a well balanced, interdisciplinary devel­opment group is a must. In our case the group was led by a person from the user company (INH-REPSOL). This contributed significantly to ease the relations with management, experts and users in the plant, apart from furnishing substantial knowledge about technical and human consider­ations about the process. The rest of the team was composed of two computer scientists specialized in A.I., two university professors (one mathematician, one chemist), and two programmers.

Experts: We worked with three experts, one of them leading. Factors that contributed positively were that they had real hands-on experience on the process (as opposed to book experience or to strict management experience), they had some prior knowledge about computers, they were well moti­vated (and we took care to encourage this moti­vation as much as we could, sometimes abandoning better technical solutions to meet "special" user requirements), and they were provided with funda·

395

mentals of Experts Systems and Artificial Intelli­gence, easing the communication in knowledge acquisition meetings.

Documentation: A careful documentation was written during the knowledge acquisition process. This was enforced in our case, because three experts and three developers were involved, and usually only one expert and two developers attended each meeting. To assure coherency a very complete documentation was written, with the underlying idea that "nothing was to be supposed". That had a very positive influence in the project, as was demonstrated by the substitution of one of the three persons in the development team with no dis­continuity in the works.

CONCLUSIONS

In summer 1990 the first connection with the plant was installed. First quarter 1991 the complete application was validated and deployed. The system is fully operational since then.

The expert system takes into consideration 482 vari­ables, 328 of them are measurements, the other 1 54 calculations in the simulator. The simulator has IO levels of nesting in variables, and includes 1 84 user defined parameters. A total of 70 different problems can be diagnosed, each diagnostic message con­taining full information about possible ways to solve the problem. The average reasoning time is 600 msecs., using the data acquisition protocol between TIRS and the Blackboard described above. The average communication time is 3.5 seconds, and the total refresh cycle installed is 20 seconds, including reasoning, communications, simulation and user interface.

Real-Time performance is achieved by means of the blackboard architecture above described: the sepa­ration of the problem solving strategy in several modules allows to allocate different priorities to each task, depending on the relative urgency. For example, the local reasoning module works with a higher priority than the global reasonln& one. It is a11ured the achievement of local dla1no1l1 within

the 20 seconds bound, while global diagnosis is achieved in a background (not bounded) fashion. This meets the plant operation requirements: local problems may be (and must be) quickly spotted and solved on the fly, while global problems tend to be more tricky: some caution is advisable before trying any solution, just lo avoid irreversible mistakes. The communication protocol between the Blackboard and the RETE network also contributes signif­icantly to improve the efficiency of the reasoning, essentially by avoiding the reasoning on variables that have not changed appreciably. The rational is that in steady operation (that is what the MIP system i s design for), most of the variables do not change abruptly: only the variables that have some kind of problem will originate reasoning.

Some temporal reasoning capabilities are available to the system. Variables and diagnostic messages are time stamped, and it is possible to reason about things that happened HbeforeH or Hafter# 0U1er things. Additionally, some support to temporal data analysis is included, such as derivatives, inte­grals and trend analysis.

The system has been enthusiastically received by the operators and the process engineer. This acceptance is due to the careful treatment that every suggestion from them has received, as well as to their early involvement in the design of U1e user interface.

From an economical point of view it is being obtained a high revenue, in estimation of U1e experts. Given the kind of process involved, small improvements in the productivity usually have a large economical impact. An estimate of al least 1 % improvement in productivity is being obtained, caused by means of a better control of some impor­tant parameters. As an example, the system has already helped to avoid a plant shutdown, and this has been quantified in more than US$400,000 in savings.

In conclusion, we have presented in this paper a Real Time Expert System to assist in the operation of continuous processes developed around The Inte­grated Reasoning Shell. The application is deployed, and runs efficiently, being considered as very helpful by the users. We are currently plan­ning to port the application to other plants of the INH-REPSOL group, as well as adding new functionalities lo ilie tool. Fundamentally we are working in adding one module to help with sensor validation, based in fuzzy logic techniques (see Aguilar, Alaman and de Pablo 1 992), and adding anoilier module to achieve forecasting capabilities, based iri neural network techniques (see Lopez and Dorronsoro 1 99 1 ). The llC is currently the prime contractor of ilie ESPRIT project HINT iliat is aimed to develop and combine iliese other Artificial Intelligence techniques in ilie framework of an hetereogeneous integration architecture. This project will build on the MIP experience.

396

ACKNOWLEDGEM ENTS

We would like to iliank Isabel Zapata, Guillermo Fernandez, and Juan Alberto Siguenza for ilieir early involvement in the design of the system, as well as Jose Luis Zaccagnini for his collaboration in ilie design of the User Interface and Sesh Murthy for his useful comments and insights about ilie global reasoning module. We want to iliank also ilie experts, Ramon Nieto, Juan Romero and Graciano Ruiz, as well as ilie process manager Guzman Garcia. This project would not have suc­ceeded wiiliout ilieir interest and help. Finally we want to thank ilie I IC for all kinds of support we received during ilie project. This project has been partially supported by ilie PEIN I I program of ilie Spanish Ministry of Industry

REFERENCES

Aguilar, J.A., X. Alaman, and E. de Pablo (1 992). A fuzzy logic approach for sensor validation in real-time expert systems. Proceedings of the International Conference on Information Proc­essing and Management of Uncertainty in Knowledge-Based Systems IPMU'92, Palma de Mallorca, Spain, July 1 992.

Aguirre, C., E. de Pablo, J.L. Zaccagnini, and X. Alaman (1 992). The user interface in expert systems for real-time process control: The MIP system experience. In Proceedings of the I FI P 1 2th World Computer Congress, North Holland, Amsterdam.

Alaman, X., J. Alarcon, E. de Pablo, and J.L. Zaccagnini (1991 ). A proven methodology for developing real-time knowledge-based systems for process control assistance. ITC tech. report 802/91. (For copies of this paper, please contact the author).

Engelmore, R., and T. Morgan (1988). Blackboard Systems. Addison-Wesley, New-York.

Erman, L.D., F. Hayes-Roth, V.R. Lesser, and D.R. Reddy (1980). The H EARSA Y-11 speach understanding system: integrating knowledge to resolve uncertainty. Computing Surveys, Vol. 1 2, No. 2, 2 1 3-253.

Laffey, T.J., P.A. Cox, J.L. Schmidt, S.M. Kao, and J.Y. Read (1 988). Real-time knowledge­based systems. AI Magazine, Spring 1988, 27-45.

Lopez, V., and J.R. Dorronsoro (1991). Neural Network Learning of Polynomial Formats for Coupled Time Series, in T. Kohonen, K. Makisara, 0. Simula and J. Kangas (editors), Artificial Neural Networks, North-Holland, Amsterdam.

Stock, M. (1989). Al in Process Control. McGraw-Hill, New York.

PS/2, OS/2, The Integrated Reasoning Shell, and A VC are trade marks of IBM Corporation.

TDC-2000, HYWAY, and PCSI are trade marks of Honeywell Inc.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

USING GRATE TO BUILD COOPERATING AGENTS FOR INDUSTRIAL CONTROL

N.R. Jennings

Department Electronic Engineering, Queen Mary and Westfield College, Mile End Road, London El 4NS, UK

Abstract. Communities of cooperating problem solvers have recently begun to emerge as a paradigm for overcoming the complexity of building large software systems in the area of process control. Each agent is capable of solving some problems by itself, but its power can be extended by sharing information and tasks with others. Also, more importantly, the community as a whole exhibits some desirable problem solving characteristics (eg graceful degradation of performance, robustness, etc.) as well as offering the opportunity of connecting and integrating existing problem solvers. GRATE is a general purpose cooperation environment which enables groups of interacting problem solvers to be built for the domain of industrial control. It has been applied to two real-world problems in this area: electricity transport management and diagnosis in a particle accelerator beam controller. We reflect upon GRATE's functional architecture, its underlying principles and the insights gained during this process.

Keywords. Artificial Intelligence; Distributed Control; Multi-Agent Systems; Electricity Transport Management.

INTRODUCTION

As computing systems are being applied to ever more demanding and complex domains, so the infea­sibility of constructing a single monolithic problem solver becomes more apparent. To combat this com­plexity barrier, system engineers are starting to investigate the possibility of using multiple, cooper­ating problem solvers in which both control and data is distributed. Each agent has its own problem solv­ing competence; however it needs to interact with others in order to solve problems which lie outside its domain of expertise, to avoid conflicts and to enhance its problem solving.

To date, two types of multi-agent system have been built: those which solve particular problems (eg air traffic control (Cammarata et al., 1983), vehicle monitoring (Lesser & Corkill, 1983) and acting as a pilot's aid (Smith & Broadwell, 1988)) and those which are general (eg MACE (Gasser et al., 1988) and ABE (Hayes-Roth et al., 1988)).

The general systems either provide a language with which a system can be constructed or a "shell" which the application developer is able to instantiate with the appropriate cooperation and control knowledge.

397

In the former case, the application designer has com­plete flexibility over the system to be built, but expends a substantial amount of effort imposing the desired structure, because each application must be constructed from scratch. In the latter case, the struc­ture and the mechanisms available are determined by the shell and the designer has to use the languages and tools provided to build the working system.

However, as yet, there have been few attempts to construct multi-agent systems for real-world or com­plex domains (Jennings & Wittig, 1 992). One of the reasons for this lack of progress is the nature of the development environments. They fail to provide the support to cope with the complexities of real-size problems (Bond & Gasser, 1988). The research described here sought to address this fundamental issue by constructing a multi-agent development environment in which some of the knowledge required to build a working system is already embed­ded. For reasons of comprehensibility, it was decided to encode the inbuilt knowledge in a declarative manner using generic rules. The rules aim to repre­sent high level knowledge and reasoning which is applicable for most multi-agent systems, but is often only represented implicitly. Thus the developer can utilise it directly, rather than constructing the system

from scratch and coding this knowledge himself. This is a step forward because a large corpus of the knowledge which must be brought to bear is already coded, thus the application designer can build upon this and concentrate on defining knowledge and structures specific to the application at hand.

This general description of cooperative agent behav­iour, represented by GRATE's built in knowledge, is possible because all the domain-dependent informa­tion, which is obviously necessary to define individ­ual behaviour, is stored in specific data structures called agent models. These models provide an explicit representation of other agents in the commu­nity (Gasser et al., 1988) - including knowledge about the state of the system, the capabilities and aims of the individual agents and evaluative knowl­edge which enables alternatives to be distinguished between (Jennings et al., 1992). The information which may be maintained in the models (i.e. their structure) is consistent across all applications. How­ever some parts may be left unfilled in particular cases (eg the goals of a database system may not be represented, whereas for an expert system they may be an integral component). Obviously the particular instantiation of an agent model is highly domain dependent and must be carried out by the application builder. The generic knowledge built into the system, however, is able to operate on the homogeneous structure of the agent models rather than the idiosyn­cracies and domain dependent level of their specific contents. This approach is an extension of the notion from conventional AI that generic structure can be utilised when building specialised systems (Chan­drasekaran, 1986; Steels, 1990).

A further innovation of GRATE is in the type of problem which is being tackled. Early Distributed AI (DAI) systems concentrated on communities which were purpose built for cooperation and typically had one overall problem to achieve. In such systems (often called distributed problem solving systems) the main emphasis was on techniques for problem decomposition and assigning agents to tasks (Smith & Davis, 1981). Within the domain of industrial pro­cess control, such an approach is infeasible because of the large number of systems which are already in existence and the complexity of the problem being tackled (Jennings, 1991). To address this problem the ARCHON project (Jennings & Wittig, 1992), in which some of the work described here took place, focussed on getting possibly preexisting. and inde­pendent intelligent systems (eg knowledge/data bases, numerical systems, etc.) to cooperate with each other on a variety of goals. The fact that there is no longer just one aim for the whole system, requires explicit reasoning about the process of coordination and means that multiple, unrelated social activities may be taking place concurrently.

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GRATE ARCHITECTURE

GRATE agents have two clearly identifiable compo­nents: a cooperation and control layer and a domain level system (see fig. 1). The domain level system may be preexisting or purpose built and solves prob­lems such as detecting disturbances in electricity net­works, locating faults and proposing remedial actions. The cooperation and control layer is a meta­controller which operates on the domain level system in order to ensure that its activities are coordinated with those of others within the community. Commu­nication between agents is by the passing of mes­sages.

The diagonal shading indicates those components which are inbuilt (i.e. require the builder to do noth­ing with them), the lightly dotted boxes those struc­tures which the developer must instantiate and the domain level system which the developer must build. The thinner arrows represent control and the thicker ones data flow.

Inter-Agent Communication

Communication Manager

Fig 1 : GRATE Agent Architecture

The information store provides a repository for all domain information which the underlying system has generated or which has been received as a result of interaction with other agents in the community. Each agent has two types of agent model: acquaintance models represent other agents in the community while self models represent an abstracted view of the local domain level system.

GRATE communities have a "flat" organizational structure - there is no centralized or hierarchical

structure and also there is no predefined authority . structure. A global controller was not considered because interagent communication has a limited bandwidth, meaning that each agent could only maintain a restricted view of the overall problem solving process. Secondly a global controller may be a severe communication and computational bottle­neck. Finally reliability criteria require that commu­nity performance degrades gracefully if one or more agents fail - which would certainly not be the case if the global controller failed.

By having control distributed within the community, an individual agent plays two distinct roles. Firstly it has to play the role of a team member acting in a community of cooperating agents and secondly the role of an individual. It also means that there may be more than one goal being pursued by the community - for example there may be agents which are trying to detect faults, agents locating faults and agents pro­posing remedial actions. Much of the early work on DAI concentrated almost exclusively on the former view and paid scant regard to the latter. However contemporary DAI, with its greater emphasis on autonomous agents, also highlights the role of the individual. Therefore when designing a cooperation framework both aspects should be accounted for. Such a system must:

• Direct local problem solving

decide which tasks to launch, when they should be launched, their relative priorities and how best to interleave their execution

• Coordinate local activity with that of others within the community.

when and how to initiate cooperative activity, how to respond to cooperative initiations and which activities require interagent synchroniza­tion.

When defining GRATE 's modular architecture, it was initially appealing to try and reflect this binary distinction directly. However because of the multiple cooperation contexts within the community, caused by the lack of a single unifying goal, there is a signif­icant class of activities which fall into a grey area between the two. These activities are concerned with situation assessment; for example deciding: which activities should be carried out locally and which should be solved with aid of others, what cooperation requests should be honoured and which should not, the relative priority of activities which have to be performed and so on. Therefore to promote a clean separation of concerns, GRATE has three main mod­ules in which the situation assessment module acts as an interface between the local and social control mechanisms. The control module is informed by the

399

situation assessment module of the tasks which should be performed and their relative priorities; it is then the control module's responsibility to ensure that this is carried out. Similarly the need to initiate social activity is detected by the situation assessment module and then the responsibility for realising this activity is left to the cooperation module.

So, for example, the agent's control module may require information i in order to execute a particular task. If this information is not available in its infor­mation store then it would send the request "provide i" to the situation assessment module. This module would, in tum, identify whether i could be provided locally and also whether another community member could provide it. If both options are viable, the mod­ule decides whether to generate i by launching a local task or by asking an acquaintance. If the latter option is chosen, the request will be passed to the coopera­tion module which will use its acquaintance models to make the request to an agent which it believes is capable of supplying i.

Each of the three main modules is implemented as a separate forward-chaining, production system with its own inference engine and local working memory. The generic rules are written in a standard if-then format. The following rule taken from the situation assessment module expresses the condition that if the agent is unable to produce a piece of information locally, then it should try and determine whether an acquaintance is capable of supplying it. Thus the need for social interaction is detected by the situation assessment module and passed onto the cooperation module to enact.

(rule situation-assessment-5

(IF ( INFO-NEEDED ?INFO ?TASK)

(CANNOT-PRODUCE-LOCALLY ?INFO))

(THEN (TELL-MODULE COOP-MODULE INFO-REQUIRED ?INFO ?TASK)))

As the TELL-MODULE statement indicates, com­munication between modules is by message passing, there is no shared memory. At present all three infer­ence engines are identical. However to meet the requirements of future applications, one or maybe all of the inference engines might need to be custom­ised. For example, the control module may need to respond rapidly to certain key events and hence need to be more sophisticated than that of the cooperation module in which events can be handled on a first come first served basis in most circumstances.

BUILDING GRATE APPLICATIONS

At present, GRATE applications embody only com­pletely generic knowledge and knowledge required to control activity in a particular application. The generic rules define an agent's default behaviour (i.e.

given no infonnation to the contrary an agent's activ­ity will be governed by generic rules). However in certain well defined instances this default behaviour is overridden by behaviour tailored to the specific sit­uation at hand. These two types of knowledge can be viewed as opposite ends of a spectrum which could be brought to bear in the problem of ensuring coher­ent behaviour between cooperating agents. The fonner being applicable to all cooperative scenarios and the latter to one specific problem. In between, however, are several others layers which represent varying levels of generality (see fig. 2). Ideally a cooperation shell would provide built-in knowledge for all levels but the individual problem, which must obviously be provided by the application developer.

General (eg GRATE knowledge)

Application Area (eg Process ControVFinance)

Area Subfield (eg Diagnosis, Planning, Supervision)

•

•

• Individual Problem

Fig 2: Spectrum of Cooperation Knowledge

For such an approach to succeed, it must firstly be possible to identify and characterise general areas of problem solving. The feasibility of constructing generic tasks models has been demonstrated by Chandrasekaran ( 1 986) and libraries of such tasks have been constructed in the KADS project as a means of simplifying the domain modelling process (Hickman et al., 1 989). Similar approaches in con­ventional AI have been championed as a mechanism for making software development easier (by supply­ing programs which solve classes of problems (McDermott, 1990)) and fonn the basis of the knowl­edge sharing vision of building conventional expert systems (Neches et al., 1991).

As such models appear feasible for conventional AI, there is no reason to doubt that it is possible to con­struct similar descriptions of generic social interac­tions. In the above hierarchical knowledge model the application area knowledge for control would define typical cooperative scenarios for process control sys­tems and the area subfield diagnosis would provide general models of cooperation between systems working on diagnosis, and so on.

400

As an example of such a general model of interac­tion, consider the problem of diagnosis. In this appli­cation the following are illustrations of high level interactions, agents may:

• divide the problem domain into non-overlap­ping parts and each work separately

• both perform the same diagnosis using different data or problem perspectives

• cross-check diagnoses of the same problem

• focus each others problem solving by exchang­ing highly rated hypotheses

If such knowledge could be assimilated (and the suc­cess of GRATE in defining some generic knowledge is an initial step in this direction) then a new para­digm is required for building multi-agent systems. Rather than constructing the system afresh for each new application, the developer starts from a state in which much of the knowledge required for building multi-agent systems is available in various "knowl­edge libraries". Thus he has to select the required knowledge, configure it for his particular system and then augment it with any necessary application spe­cific knowledge (as shown below). Such reasoning may be necessary to provide a shortcut in the general reasoning process in order to meet the desired perfor­mance characteristics or to reflect truly domain dependent reasoning

General

Problem specific

knowledge

Process Control

Finance

Scheduling

Diagnosis

Planning

Working Multi-Agent System

Fig 3: Building Multi-Agent Systems Using Levels of General Knowledge

The process of configuration, in this instance, involves two steps. Firstly selecting a subset of the available knowledge, for the problem at hand. For example the application builder may never want to use a contract net (Smith & Davis, 1981), in which case he would remove the general knowledge associ­ated with this protocol. Also he may be building an application for process control, in which case knowl­edge from the finance domain is not appropriate. Sec­ondly the control strategies of the problem solving modules may need to be fine tuned to meet the desired performance characteristics. For instance in the present implementation of GRATE equal weight is given to each of the three modules; however in applications which require more sophisticated local control and less interagent interaction the control and situation assessment modules may need to be given more resources than the cooperation module.

This paradigm has significant advantages over con­ventional means of constructing multi-agent systems - including the reuse of problem solving components (increasing reliability, decreasing risks and develop­ment time and making effective use of specialists (Horowitz and Munsen, 1984)) and provides the abil­ity to fall back on increasingly general knowledge (Lenat and Feigenbaum, 1991). It also follows the lead of other disciplines which engineer complex artifacts (eg planes, cars), in that product develop­ment would consist predominantly of assembling components (Stefik, 1986).

GRATE IN INDUSTRIAL CONTROL

GRATE has been applied to two distinct domains: electricity transport management (Jennings et al., 1992) and diagnosis in a particle accelerator beam controller (Fuchs et al., 1992). In both cases the applications have been constructed rapidly and with­out the need to significantly augment GRATE's inbuilt knowledge. In both instances the designer has merely filled in the agent models and provided the appropriate interface functions to the underlying domain level system. The number of agents in the community has been three to five agents, the domain level systems have been mainly expert systems and in the latter application they were running on differ­ent machines and in different languages.

The types of cooperation encountered in these two applications were fairly simplistic in nature. Two main forms were observed: firstly agents would spontaneously send information to other agents that they believed (based on their acquaintance models) would benefit from receiving it (result sharing). Sec­ondly, agents were able to make requests of each other - asking for tasks to be performed or informa­tion to be supplied (task sharing).

The generic knowledge embodied in GRATE's con-

401

trol module was sufficient for these two applications because the control exerted over the domain level systems is fairly rudimentary in nature - consisting of stopping, starting, suspending and aborting tasks -and the performance criteria demands have not been too high. Also the types of domain level system were limited to expert systems - not the full range of sys­tems (eg databases, numerical systems, etc.) which would be expected in a full industrial control envi­ronment For the reasons of performance, domain dependence and heterogeneity of the underlying domain level system, we doubt whether it is possible to continue to use such generic control knowledge in all future applications. Due to these reservations, within the ARCHON project it was decided that the component responsible for controlling the domain level system should predominantly consist of generic mechanisms not generic knowledge.

In contrast with the control level, functions associ­ated with social activity are more or less independent of the application domain and are relatively few in number. Therefore the approach advocated by this work is kept for these functions.

CONCLUSIONS

We have outlined a general purpose development environment for the domain of industrial process control. This environment was designed to speed up the process of building multi-agent systems by pro­viding a shell which has a significant amount of inbuilt knowledge related to cooperation and control. This approach, and its logical extension to general classes of cooperative problem solving, requires a paradigm shift for application builders. Rather than constructing a system from scratch and continually re-coding the same basic knowledge - the designer is faced with pre-built libraries of knowledge. The pro­cess of building applications then becomes one of configuring this knowledge and augmenting it with any application specific knowledge which is required.

At present, the general knowledge embodied in GRATE has no formal theoretical grounding. That is, there is no deeper model of coordination or coopera­tion represented by the generic rules. However, as a result of the generality and explicit representation of the knowledge embodied in GRATE, it was possible to devise such a theory (Jennings, 1991 ; Jennings & Mamdani, 1992). This theory (called joint responsi­bility) is based on the notions of intentions and is par­

ticularly useful for ensuring coordinated behaviour in complex, dynamic environments in which agent's beliefs may change, wrong decisions may be taken and unanticipated events may occur (i.e. situations often typical of industrial control applications). We are currently coding this theory in terms of generic rules and they will form the basis of the situation

assessment and cooperation modules in future ver­sions of GRATE.

ACKNOWLEDGMENTS

The work described in this section has been partially carried out in the ESPRIT II project ARCHON (P2256) whose partners are: Atlas Elektronik, JRC Ispra, Framentec, Labein, IRIDIA, Iberdrola, EA Technology, Amber, Technical University of Athens, University of Amsterdam, Volmac, CERN and Uni­versity of Porto. In particular discussions with, and comments from, Abe Mamdani (QMW), Erick Gaus­sens (FTC) and Thies Wittig (Atlas) have been par­ticularly useful in shaping the ideas presented here. Also thanks are due to the people at CERN and to Rob Aarnts (Volmac) for building the multi-agent particle accelerator application using GRATE.

REFERENCES

Bond,A.H. & Gasser,L., (1988), "Readings in Dis­tributed Artificial Intelligence", Morgan Kaufmann.

Cammarata,S., McArthur,D. & Steeb,R., (1983), "Strategies of Cooperation in Distributed Problem Solving", in Proc. of IJCAI, pp 767-770.

Chandrasekaran,B., (1986), "Generic Tasks in Knowledge Based Reasoning: High Level Building Blocks for Expert System Design", IEEE Expert, 1 (3), pp 23-30.

Fuchs)., Skarek,P., Varga,L. & Malandain,E., (1992) "Distributed Cooperatve Architecture for Accelera­tor Operation" in Second Int. Workshop on Software Engineering, Artificial Intelligence and Expert Sys­tems for High Energy and Nuclear Physics.

Gasser,L., Braganza,C. & Herman,N., (1988), "MACE: A Flexible Testbed for Distributed AI Research", in Distributed Artificial Intelligence (ed M.N.Huhns), pp 1 19-153 Pitman Publishing.

Hayes-Roth,F., Erman,L.D., Fouse,S., Lark,J.S. & Davidson)., (1988), "ABE: A Cooperating Operating System and Development Environment", in Readings in Distributed Artificial Intelligence (eds A.H.Bond & L.Gasser), pp 457-490, Morgan Kaufmann.

Hickman,F.R., Killin) .L. Land,L., Mulhall,T., Por­ter,D. & Taylor,R., (1989), "Analysis for Knowledge­Based Systems'', Ellis Horwood.

Horowitz,E. & Munsen,J .B., (1984) "An Expansive View of Reusable Software", IEEE Trans. Software Engineering, 10 (5), pp 477-487.

Jennings,N.R. & Mamdani,E.H., (1992), "Using Joint Responsibility to Coordinate Collaborative Problem

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Solving in Dynamic Environments", in proc AAAI-92.

Jennings,N.R. & Wittig,T (1992) "ARCHON: Theory and Practice", in Distributed Artificial Intelligence: Theory & Praxis, (Ed L.Gasser and N.Avouris), Klu­wer Academic Press (forthcoming).

Jennings,N.R., Mamdani,E.H., Laresgoiti,I., Perez). & Corera,J., (1992), "GRATE: A General Framework for Cooperative Problem Solving", Journal of Intelli­gent Systems Engineering, Vol. 1 , (forthcoming).

Jennings,N.R., ( 1991) "Cooperation in Industrial Sys­tems" Proc. ESPRIT Conference, Brussels.

Jennings,N.R., (1991) "On Being Responsible", Proc. Modelling Autonomous Agents in a Multi-Agent World, Third European Workshop, Kaiserslautern, Germany.

Lenat,D.B. & Feigenbaum,E.A., ( 1991), "On the Thresholds of Knowledge", Artificial Intelligence 4 7, pp 185-250.

Lesser,V.R. & Corkill,D.D., ( 1983), "The Distributed Vehicle Monitoring Testbed: A Tool for Investigating Distributed Problem Solving Networks", AI Maga­zine, pp 15-33.

McDermott)., (1990), "Developing Software is Like Talking to Eskimos about Snow", in proc AAAI-90, pp 1 1 30- 1 133.

Neches,R., Fikes,R., Finin,T., Gruber,T., Patil,R., Senator,T., & Swartout,T., ( 1991), "Enabling Tech­nology for Knowledge S haring", AI Magazine, pp 36-56.

Smith,D. & Broadwell,M., ( 1988), ''The Pilot's Asso­ciate: An Overview", in SAE Aerotech Conference, Los Angeles, CA.

Smith,R.G. & Davis,R. (1981), "Frameworks for cooperation in Distributed Problem Solving", IEEE Trans. on SMC, 1 1 , 1, pp 61-70.

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Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

INTELLIGENT TUNING OF P+I CONTROLLERS FOR BIOPROCESS APPLICATION

I. French*, C. Cox*, M.J. Willis** and G.A. Montague**

*School of Electrical Engineering and Applied Physics, University of Sunderland, UK **Department of Chemical and Process Engineering, University of Newcastle-upon-Tyne, UK

ABSTRACT

This paper outlines two methods of advanced control which can be utilised for tuning conventional controllers. A novel AI method based upon the use of artificial neural networks is contrasted with an advanced control method utilising the PIP philosophy. Both techniques are shown to be particularly effective advanced control approaches and with appropriate structuring can be used for tuning conventional P + I controllers. This is particularly advantageous from an industrial perspective. In order to demonstrate the potential of the methodologies, a simulation of a continuous, glucose limited Saccharomyces cerevisiae fermentation is employed.

KEYWORDS

Adaptive control, Artificial intelligence, Fermentation processes, Neural nets

INTRODUCTION

While a multitude of advanced control algorithms exist which exploit the virtues of different model structures, the majority of controllers found in the chemical industry are of the Proportional-Integral-Derivative (PIO) type. Indeed well over 90% of all existing control loops are PI(D) controllers. The predominance is primarily due to the simple structure of the PI(D) algorithm which offers robust properties with respect to many common process situations, e.g. unknoWn disturbances, process nonlinearities, changing process conditions etc., provided that they are not too severe. Indeed, since control design is often undertaken using simplified first or

403

second order process approximations, a PI(D) algorithm provides the 'optimal' structure (Rivera et al, 1986). In the absence of non­linearities, time delays, input constraints, or 'known' interactions, it is not beneficial to opt for more sophisticated control strategies unless a more accurate process model is available for controller synthesis.

Over the last fifty years, many PI(D) controller tuning techniques have been suggested. The first two methods were proposed by Zeigler and Nichols (1942): the transient response and the ultimate sensitivity methods. Details of these may be found in standard texts along with another common method due to Cohen and Coon (1953). The transient response method and the approach of Cohen and Coon are both derived assuming certain model structures. More recently other model based tuning techniques have been proposed, and form the basis of a variety of tuning rules (eg. Kuo et al (1973), McGregor et al (1975), and Rivera et al (1986). Smith and Corripio (1985)). Auto-tuning techniques have also developed in recent years. Wittenmark and Astrom (1980) and Isermann (1981 ) proposed self-tuning PIO controller based upon a pole-placement approach in conjunction with a second order linear process model without time delay. Cameron and Seborg (1983) used the same type of model structure and modified the self­tuning controller of Clarke and Gawthrop (1975, 1 979) into a PID form. However, both of the latter approaches were sensitive to time delays greater than the sample interval. Gawthrop (1982), using a hybrid self-tuning controller (1980), developed a continuous

time self-tuning PID control law. Song et al (1984) developed a self-tuning feedback controller (SFC), that is globally stable in the presence of bounded, external unmeasured disturbances. This algorithm is structurally equivalent to the conventional discrete PID controller, but is, as is prevalent with other methods sensitive to time-delay systems. Self­tuning/ adaptive PID algorithms that utilise a dead time compensator to handle systems with time delays have also been suggested (eg. Tjokro and Shah (1985), Hunt and Grimble (1985)). Other tuning techniques involve the use of a relay to perturb the system (eg. Astrom and Hagglund, 1984).

It is the intention of this contribution to develop an auto-tuning Pl(D) control philosophy based upon nonlinear process models without performing linearisation. This will allow the tuning of the controller such that it can accommodate process non­linearities, input constraints, as well as any 'known' interactions/ disturbances. To obtain the 'optimum' PI(D) controller settings in conditions where some or all of the latter prevail, the dynamic response characteristics of the system are used in conjunction with a time response based objective function. This method will be compared to an auto-tuning PI(D) philosophy based upon PIP control (Billington et al 1991).

In the development of a nonlinear model based control strategy the choice of process model is of paramount importance. The most natural strategy would be to use a detailed mechanistic model of the process as the basis of the controller. However, the development of nonlinear mechanistic models for chemical processes can be a time consuming task. Moreover, any particular development is process specific. In this contribution the use of a generic nonlinear process modelling technique is considered: artificial neural networks (ANNs).

The paper is organised as follows. After introduction of the concepts behind neural network model identification, the novel auto­tuning PI(D) procedure is discussed. The PIP control philosophy is then outlined. Simulation results are used to compare the two approaches.

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NEURAL NETWORK BASED CONTROL

Whilst a number of ANN architectures have been proposed (see Lippmann, 1987), the 'feedforward' ANN (FANN) is by far the most widely applied. A reason for this being that it has been shown (Cybenco, 1989) that a FANN with two layers of non-linearity is sufficient to approximate, arbitrarily well, any continuous non-linear function. The techniques for the formulation of neural networks for modelling dynamic process data can be found in Willis et al (1991).

On having trained the model, if it is of sufficient accuracy, then it should be possible to employ the model to auto-tune a PI(D) controller. The attraction of using the neural network instead of any other model form is the ability to effectively represent complex nonlinear systems. Indeed, this attribute has been exploited in the development of alternate 'advanced' control strategies. For instance, control philosophies such as Long Range Predictive Control and Internal Model Control based on an artificial neural network model have appeared in many applications (eg. Willis et al, 1991; Lightbody et al, 1992; Hunt and Sbarbaro, 1992) and the results presented serve to highlight the benefits of the techniques. Given that the model is accurate it is obvious that performance will be improved over standard Pl(D) control. This is particularly the case for when the controller is applied to systems containing significant dead-time or severe non-linearity. Whilst the benefits of applying a modem control philosophy can be significant, adopting a non­standard controller structure may not be industrially acceptable.

An alternative approach, which should be more industrially appropriate, is to utilise the model to design a standard controller such as Pl(D). Whilst the structure of the PI(D) controller is non-optimal for non-linear systems, the performance of the controller can be tailored to yield the best response characteristics around the current process operating point. Thus non-linearity, constraints and dead-time can be accommodated for by controller parameter variation. In addition to the benefits of

common controller structural conformity, an additional industrial benefit is that an assessment can be made of the validity of the suggested controller settings.

Algorithm Formulation

The application of a PI{D) controller to any process requires selection of the controller parameters. A number of standard techniques were discussed previously. In this contribution a time response based objective function method is used to select the 'optimal' controller settings. A process model is used to simulate the response characteristics of the process for a variety of conditions around current operating point. An objective function is formulated and the PI{D) controller settings adjusted in a manner such that the 'optimum' response is sought, and hence the optimum PI(D) settings for the plant controller determined. The cost function used in the above optimisation procedure is as follows:

J= N2 I:{[ w(n)-y(n) ]2+ [). �u(n) ]2} (1) n=N1

where y(n), u(n) and w(n) are the controlled output, manipulated input and set-point sequences. Ni is the minimum output horizon, N2 is the maximum output horizon and A. is a weighting which penalises excessive changes in the manipulated input.

The neural network model is used to simulate the PI(D) controlled process up to the horizon N2 and perturbations in set-point around the current operating level are used to assess the suitability of the controller settings. An optimisation algorithm (Powell, 1964) is used to adjust the controller parameters to minimise the objective function, Eqn(l). This method is shown schematically in Fig.1 . Modification of the PI(D) controller settings can be carried out at regular intervals or when there is a significant change in process operating conditions.

OPTIMAL PIP CONTROL

The optimal PIP control philosophy is an example of one of the advanced control methodologies which exist for auto-tuning of PI(D) controllers. The full derivation of the

405

algorithm can be found in Billington et al (1991) and is based upon initial studies by Young et al (1987). Only the basic methodology of the algorithm is outlined here.

As is the case with the Neural network based controller, the PIP algorithm is model based. However, rather than adopting a generic non­linear model, a non-minimal state space plant description is assumed. The state vector is defined as:

where mk is the 'integral of error' state defined by the equation:

(3)

and wk is the desired output. Note that Xk consists of the present value of the system output as well as past values of both the plant input and output. mk is included to guarantee type 1 servo-mechanism performance. A state feedback control law is used and the feedback gains calculated to satisfy a performance criteria (similar to eqn. 1) using a dynamic programming algorithm. The resulting controller takes the form:

(4)

The process model parameters are identified explicitly using a recursive instrumental variable identification algorithm. Thus the algorithm can be implemented as an adaptive or self-tuning controller. The controller parameters, v, are calculated to satisfy the performance criteria from the current process model parameters. Whilst model order may be specified based upon engineering knowledge, in order to synthesis a PI(D) controller structure the time series model order must be specified as two or less.

BIOPROCESS MODEL

In order to demonstrate the performance of the controllers a simulation of a continuous, glucose limited Saccharomyces cerevisiae fermentation is employed. The model is based upon that developed by O'Neil and Lyberatos (1990) and accounts for cellular 'memory effects' on fermenter performance.

Experimental investigations verified the model structure and parameterisation. The model structure specified is:

x = µ x - D x (5)

s = -Asx/[Y(B+s)(C+x)] + D(s0 - s) (6)

ii = a(As/[Y(B+s)(C+x)] - µ ) (7)

where X is the biomass concentration, s is the substrate concentration, D is the dilution rate, so is the inlet substrate concentration, Y is the yield of biomass on substrate and µ is the specific growth rate. A, B, C are constants chosen to fit the experimental data. The culture adaptability, a, is chosen to also fit experimental data and accounts for dynamic culture changes. The values of these parameters and the initial conditions can be found in O'Neil and Lyberatos (1990).

CONTROL RESULTS

The control objective for both the Neural network based controller and the PIP algorithm was to design a PI(D) controller to follow a series of set point changes in desired biomass level. Dilution rate has been chosen as the manipulated variable. A fixed linear model was obtained for the PIP approach to allow the design of a PI controller. A neural network model was generated by utilising a time series of dilution rate and previous biomass values. The network training procedures to generate such a model can be found in Willis et al (1991). A PI controller was also chosen for the neural network application. Figures 2 and 3 demonstrate the quality of response attainable using the respective algorithms. Figures 2 and 3 also show the resulting dilution rate modifications to achieve the set point tracking. Figure 2 shows the performance of the PIP based PI(D) controller. Tight set point tracking can be observed, however, this is achieved by implementing major changes in dilution rate. The controller may be 'de-gained' by increasing the weighting on control changes within the cost function to provide more physically acceptable performance. This figure, however, serves to highlight the fact that excellent control can be achieved with a conventional controller with appropriate tuning. Whilst a similar response can be

406

obtained with the neural network tuned PI controller, figure 3 shows the controller tuned to give a more physically reasonable response. It may be observed that the although the biomass is at the desired level in figures 2 and 3, variations in dilution rate still occur. This is due to the slow dynamic variations in organism behaviour in response to variations in operating conditions.

While the PIP algorithm uses a fixed model, it is interesting to observe that the PI parameters of the neural network tuned controller do indeed vary in response to different desired operating levels. Figures 4 show the calculated controller gain and integral time constant variations.

CONCLUSIONS

This paper has demonstrated how a novel AI technique may be utilised to design conventional industrial controllers. Closed loop controller comparisons with an alternative advanced controller design procedure highlighted that the performance of the two controllers were similar. The system to which the algorithms were applied, a continuous bioreactor, are commonly assumed to be significantly non-linear. However, it is clear that a well tuned PI(D) algorithm is sufficient to provide well tuned servo response. The benefits gained from adopting the more complex PI(D) tuning approaches is the ability to 'auto-tune' a control algorithm. Conventional tuning approaches can be problematic with bioprocess systems (Montague et al, 1991).

The choice of the most appropriate of the auto-tuning schemes largely comes down to the appropriateness of the model structure and the system to which it is to be applied. An over-riding consideration is the need to achieve robust performance. For systems for which a fixed parameter linear time series model is sufficient then PI(D) control design via the PIP philosophy is obviously the most appropriate. When the system is more complex and a fixed parameter linear model does not suffice, then on-line adaptation of a linear model could be considered. However, this philosophy can be detrimental to closed loop robustness. This can be observed in the

low level of industrial applications of adaptive controllers. Here the neural network based model and PI(D) tuning approach may be beneficial in that the model need not adapt to changing process conditions. Further results will be presented at the conference demonstrating the utility of the techniques when applied to a range of non-linear process systems. Space limitations preclude their inclusion, however, the results serve to further highlight the relative merits of the two approaches.

REFERENCES

Astrom K. and Hagglund (1984). 'Automatic tuning of simple regulators for phase and amplitude margin specifications', Automatica, 20, pp 645-651

Billington A.J., Boucher A.R. and Cox C.S. (1991). 'Optimal PIP control of scalar and multivariable processes', Proc Control '91, Edinburgh, pp 574-581

Cameron F. and Seborg D.E. (1983). 'A self­tuning controller with a PID structure', Int. J. Cont., 2, pp 401-417

Clarke D.W. and Gawthrop P.J. (1975). 'Self­tuning controller', Proc IEE, 122, pp 929-934

Clarke D.W. and Gawthrop P.J. (1979). 'Self­tuning control', Proc IEE, 126, pp623-640

Cohen G.H. and Coon G.A. (1953). 'Theoretical consideration of retarded control', Trans ASME, 75, pp 827-834

Cybenco G. (1989). 'Approximations by superpositions of a sigmoidal function', Math. Cont. Signal & Systems, 2, pp 303-314

Gawthrop P.J. (1980). 'Hybrid self-tuning control', Proc IEE, Pt D, 127, pp 229-236

Gawthrop P.J. (1982). 'Self-tuning PI and PID controllers', IEEE Conf. on Application of adaptive and multivariable control, University of Hull, July

Hunt K.J. and Grimble M.J. (1985). 'Simple self-tuning process controllers', Proc. Advances in Process Control, Bradford, 17th-18th Sept.

Hunt K.J. and Sbarbaro D. (1992). 'Studies in neural network based control' in 'Neural networks for control and systems' Ed Warwick K., Irwin G.W. and Hunt K.J. pp 94-122

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Lippmann R.P. (1987). 'An introduction to computing with neural nets', IEEE ASSP Magazine, April, pp 4-42

McGregor J.F., Wright J.D. and Hong H.M. (1975). 'Optimum tuning of digital PID controllers using dynamic stochastic models', Ind & Eng Chem. Proc. Des. & Dev, 14, pp 398-402

Montague G.A., Morris A.J. and Ward A.C. (1991). 'Control of growth rate in fed-batch penicillin fermentation using adaptive techniques', Final U.K. SERC project report, University of Newcastle-upon­Tyne.

O'Neil D.G. and Lyberatos G. (1990). 'Dynamic model development for a continuous culture of Saccharomyces cerevisiae', Biotech. Bioeng., 36, pp 437-445

Powell M.J.D. (1964). 'An efficient method for finding the minimum of a function of several variables without calculating derivatives', Comput. J., 7, pp 155-162

Rivera D.E., Morari M. and Skogstead S. (1986). 'IMC 4 PID Controller design', Ind & Eng Chem. Proc. Des. & Dev, 25, pp 352-365.

Smith C.A. and Corripio A.B. (1985). 'Principles and practice of automatic process control', New York, John Wiley

Song H.K., Fisher D.G. and Shah S.L. (1984). 'Experimental evaluation of a robust self­tuning PID controller', Can. J. Chem. Eng., 62, pp 755-763

Tjokro S. and Shah S.L. (1985). 'Adaptive PID control', Proc ACC, Boston, pp 528-534

Willis M.J., Di Massimo C., Montague G.A., Tham M.T. and Morris A.J. (1991). 'Artificial neural networks in process engineering', Proc IEE Pt D, 138, pp 256-266

Wittenmark B. and Astrom K. (1980). 'Methods and applications in adaptive

control' in Unbehauen H. (Ed) Springer Verlag

Young P.C., Behzadi M.A., Wang C.L. and Chotai W.A. (1987). 'Direct digital and adaptive control by input output state variable feedback pole assignment', Int. J. Cont., 46, 6

Ziegler J.G. and Nichols N.P. (1942). 'Optimum settings for automatic controllers', Trans. ASME, 64, pp 759-768

Model Dlslllrbance Model

+ System State

Control Controller Network Weighting Design Tracking

K,TI Pl

System Output

Controller

Figure 1 - Neural Network tuning of Pl(D) controller

105 ,...-------------......

100

85

800 50 100 150 200 250 300 350 Tllile 0.4 ,...------------�

0.35 0.3

8 I! 0.25 .g .a 0.2 0

0.15 0.1

�o � � � 200 � � m TllilC

Figure 2 - PI(D) PIP based control

408

105

100 v

. "'

I � j 95

- 90

15 I -

•0• 50 100 150 200 251 308 351 Time

·�9 .---------------. on U7

a u' � us J U4 Ji U3 l5 0.22

Ul u

0•19 0 50 100 150 200 250 300 351 Time

Figure 3 - Pl(D) Neural Network based control

2.1

2.05

·ij "' 2 0 :ij � � 1.95 ti 0 � i= 1.9

i:: � �

1 .85

1.80

2.7 2.6 2.5 2.4 2.3 2.2 2.1

2 1.9 1 .80

50 100 150 200 250 300 350 Tune

50 100 150 200 250 300 350 Tune

Figure 4 - PI Neural network tuned parameters

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

FAULT DETECTION AND EMERGENCY CONTROL IN POWER SYSTEMS

Z.A. Vale and A. Machado e Moura

Department of Electrical Engineering and Computers, Faculty of Engineering, University of Oporto, Rua dos Bragas, 4099 Porto Codex, Portugal

Abstract . Cont rol Cent ers are responsible for the supervis ion , monitoring and cont r o l o f Powe r Systems . I n forma t i o n about the state o f the Powe r System is cont inuou s l y arriving at these cent e r s where human operators s t i l l p lay the most impo rtant role in int erpret ing this informat ion and taking dec i s i on s . However , in case o f an eme r g e n c y , the quant i t y of arriving alarms i s so great that Control Center ope rators are not able to rapi dly diagnose the fault . In this paper we present a Knowledge Based System that proce s s e s the a larm l i s t s r e c e i v e d at P o r t u g u e s e Cont r o l Cent e r s . T h i s s y s t em a s s i s t s ope rat o r s in t h e interpretat ion o f r e ce ived in format ion b e i n g a good support -decis ion t o o l for P ower Systems cont r o l . It inc ludes t emporal reasoning strategies and dea l s with real-t ime constraint s . An explanation modu le a l l ows the use o f this system as a tutor for novice operators .

Keywords . Power system contro l , real t ime comput e r systems ; a larm systems; alarm proce s s in g ; art i f ic i a l i nt e l l igence ; knowledge engineering ; expert systems ; knowledge based systems ; temporal reasoning .

INTRODUCTION

N o w a d a y s e l e c t r i c a l n e t w o r k s a r e internat iona l ly interconnected and operated with less gene rat ion reserve and c loser to the permi s s ib l e l imit s than before . This s i t u a t i o n imp o s e s a very e f f i c ient and accurate real-t ime cont ro l . Power S y s t em Con t r o l C e n t e r s are r e sp on s ib l e for the de c i s i o n s t a k e n about P ow e r S y s t e ms ope rat ion and cont rol , name ly in case of disturbance s . Due t o t h i s , the qua l i t y o f de l i vered e n e r g y d e p e n d s e n o rmou s l y on the ir e f f i c ient per formance .

Power System Cont rol Cent ers are present ly equipped with l a r g e comput e r s y s t e ms supporting many app l i cat ions such as load f l ow, state e s t imat ion , security ana l y s i s a n d l o a d forecast ing t o name only a few one s . On t he other hand, Cont rol Cent e r s h a v e a c c e s s t o a g r e a t q u a n t i t y o f informat i on about the Power S y s t em s t a t e through the i n s t a l lat ion o f met e r po int s a n d l a r g e t r a n s m i s s i on s y s t em s t h at t r a n s m i t t h e ava i l ab l e in f o r ma t i o n to

Cont rol Cent ers where it i s dealt by SCADA ( Supervisory Cont rol and Data-Acqu i s it io n )

systems .

The a r r i v i n g i n format i o n a l l ows Cont r o l C e n t e r s t o pe r f o r m e f f i c i e n t l y t h e i r funct ions when the Power S y s t em i s i n a norma l s t at e . Howeve r , in c a s e o f an e me r g e n c y , i t m a y c a u s e s e r i o u s d i f f i cu l t i e s b e c a u s e there are s o many a larms arr iving at Cont rol Cent ers at each moment that human operators are not able to rap i d l y unde r st a n d what is g o i n g on . A survey conducted by an IEEE working group ( P r ince , 1 98 9 ) about Cont rol Cent ers a l arms

revealed some important point s about this ma t t e r . Table I s hows t h e numb e r of

409

a f f i rmat ive a n s w e r s t o a c o n s i d e r i n g a t o t a l o f e le c t r i ca l companies .

f e w qu e s t i o n s 8 7 a n s we r i n g

TABLE 1 Answers to the Survey About Alarms

Que st ions Number o f a f f i rmative answers

Are your operat o r s sat i s fied with a larm proce s s ing during : - normal operation 65 - busy operation 38 - emergency operation 2 1

Do your operators feel that some a larms are a nui sance rather than he l p f u l ? 6 6 D o you fee l that the " stat e " o f the system could be automat ica l l y determined from information you have in the computer? 42

When asked about what wa s the most common ope r a t o r s comp l i a n t about a l a rms , t h e respon ses were q u i t e con s i s t ent :

- t o o many a la rms , e sp e c i a l l y in case o f a disturbance

- c ommu n i c a t i o n a l a rm s , unne c e s s a r y alarms and a larms for which no act ion can be taken by the operator

- m i x i n g of c r i t i c a l a n d a l a rms ma k i n g i t h a r d c r it i ca l a larms .

n u i s ance t o f i n d

We c a n c o n c l u de t h a t ope r a t o r s a r e de f i n i t e l y n o t sat i s f ie d with the a larm l i s t s they must int erpret and that human incapab i l i t y to p roce s s e f f i c i e n t l y the alarm l i s t s i s an evidence .

When a fault occurs in the P ower System, operat o r s mu s t make t h e d i ag no s i s and restore power de l i very . D e c i s ions must be taken according t o t ime constraint s , under great s t r e s s and often du ring the absence of the most s k i l l e d operators . The symbolic and qua l i tat ive nature o f the r e a s o n i n g i n v o l ve d i n t he s e de c i s i o n s , s t ro n g l y dependent on the o p e r a t o r s exp e r i e n c e , sugge s t s t hat an Art i f i c i a l I nt e l l igence approach i s su itable to deal with this kind o f problems .

The survey conducted by IEEE shows that the ma j o r i t y of t he res pondent companies had problems with e x c e s s i ve a l arms for t h e i r ope rators to deal with . In fac t , experience s hows t h a t a l l t h e me s s a g e s ( o ver a thousand) arriving at P o rtugue s e Cont rol Cent ers in a normal day, when n o important dist urbance has occurred, can be reduced t o one or t w o hundred messages without l o s s o f informat ion . T h e most serious problem about excess ive alarms is perhaps that , in case o f a n eme r g e n c y , due to the eno rmou s quan t i t y o f a r r i v i n g a l a rms , some t ime s ope r a t o r s f a i l t o n o t i c e t h e r e a l l y important ones .

Voltage a larms are an important part of the t o t a l n umbe r of a l a rms t h at a r r ive at Portuguese Control Centers ( F ig . 1 ) .

Number of alarms

900 soo 700 600 500 400 300 200 1 00

0 2 3 4 5 6

Days of October 1 99 0

• Power units � Contingency analysis

� Voltage 11111 Trans.formers

Iii Breakers D Control

F i g . 1 . Alarm Types

On the other hand, volt age a l a rms tend t o be repe t i t i v e , rap i d l y f i l l i n g Cont r o l Centers displays in emergency s ituat ion s .

RELATED WORK

It was only a f t e r 1 9 8 5 that Powe r Sys tems e x p e r t s i n t e r e s t f o r A r t i f i c i a l I n t e l l igence app l i cat ions became important . By that t ime s o lut i o n s had a l ready been found f o r the most imp o r t a n t p rob lems related with mathemat ical c a l c u l u s needed for Powe r Sys tems planning, operat ion and control . Howeve r , for some tasks it was not pos s ible t o develop reasonable app l icat ions

410

using the t radit ional computer languages o f p r o c e du r a l n a t u r e . H a v i n g Art i f i c i a l I nt e l l igence achieved t he s t a t e o f real app l i cat ion s , P ower S y s t ems expe rt s began f a c i n g the p o s s i b i l i t y of imp l emen t i ng Art i f i c i a l I n t e l l igence based applicat ions . T h e f i r s t s t a ge w a s t o p r ove t ha t Art i f i c ia l I n t e l l igence app roach wa s not o n l y p o s s i b l e b u t had a l s o impo r t a n t advant age s . I n 1 9 8 6 , Wo l lenberg ( 1 9 8 6 ) , T a l u k d a r ( 1 9 8 6 ) a n d Ame l i n k ( 1 9 8 6 ) pub l i shed t he r e s u l t s o f deve l oped wo rk related t o me s sage handling and diagnos i s . The early developed systems had s ignif i cant l im i t a t i o n s but t h e y made c l e a r t h a t Art i f i c i a l I n t e l l i gence app roaches cou l d repre sent a g reat improvement in P ower Systems operation and cont ro l .

The most important companies of electricity a r o u n d the w o r l d b e g a n to s u p p o r t Art i f i cial Int e l l igence projects envisaging the integrat ion of Knowledge Based Systems in Cont r o l C e n t e r s . S y s t em s f o r a l a rm p r o ce s s i n g and f a u l t diagno s i s were t he ba s i s f o r a s u rvey condu c t e d by C I GRE ( 1 9 9 1 ) .

Power S y s t ems proved t o be a cha l lenging f i e l d f o r A r t i f i c i a l I n t e l l i g e n c e a p p l i c a t i o n s , r e q u i r i n g r e a l - t i m e proc e s s ing a n d involving a great amount o f informat ion . The work carried o u t unt i l now makes P o we r Syst ems expert s s t i l l b e l i eve that they can overcome these problems and

that Art i f i c i a l I nt e l l igence app l ications a r e of g r e a t h e l p i n P ow e r S y s t ems operation and cont rol .

KNOWLEDGE BASED SYSTEM DES I GN

General Oyeryiew

The aim of our work is to deve lop a system that h e l p s Cont r o l C e n t e r operat o r s in r e a l - t i m e c o n t r o l of P ow e r S y s t e ms (Ki r s chen , 1 98 9 ) . This means that ou r system

m u s t r e a s o n a c c o r d i n g to r e a l - t ime con s t r a i n t s and p e r form its t a s k s in an e f f i c ient way even in emergency s ituat i ons . On one hand, it must c on s i de r a l l t he informat ion that is cont inuou s l y arriving to Cont rol Cent e r s , what imp l i e s a dynamic changing of the unive r s e of t rue facts . On t h e o t h e r h a n d , i t r e qu i r e s comp l e x t empo r a l r e a s o n i n g f o r i n t e rp re t i n g the available information .

In order t o h e lp Cont rol Center operators in interpret ing a l a rm l i s t s , our Knowledge B a s e d S y s t em r e d u c e s t h e numb e r o f disp layed me s sages b y making a n int e l l igent synt h e s i s and p r e s en t s the mean i n g f u l i n f o rma t i on i n a m o r e f l e x i b l e a n d structured way .

T h e K n o w l e dg e B a s e d S y s t e m we a re deve loping runs on a DEC Stat ion 5 0 0 0 / 2 0 0 and i s w r i t t e n in P r o lo g . I t de a l s with real a l a rm l i s t s rece ived at P o rtuguese Con t r o l Cent e r s and mak e s an int e l l i gent process ing of these l i st s .

F igure 2 i l lu s t ra t e s t he a r chitecture o f o u r s y s t em ( Va l e , 1 9 9 2 a ) i n v o l v i n g F a c t Ba s e , Knowledge Ba s e , I n ference Engine and User Interface .

Knowledge Base

Meta knowledge

Rules

Inference Engine

User Interface

Explanat ions external alarms Base

Fig . 2 . Knowledge Based System Architecture

The Fact Base

The F a c t B a s e co n t a i n s i n f o rma t i on concerning t he P ower System element s and topology, the a la rm mes sages arriving at the Cont rol Cente r and the Knowledge Based System conclusions .

Fact s concerning the a la rm me s s age s a re generated by a pre-processor module written in C language . This modu le receives the original me s s ages and conve r t s t hem in Prolog fact s .

Let us consider the following message :

O l -OCT- 1 9 90 0 3 : 1 5 : 1 2 PALMELA I - BREAKER

SSN BREAKER

1 0 3 CLOSED

t h a t i n f o rm s o p e r a t o r s t h a t S i n e s Substat ion ( SSN ) breaker o f the l ine 1 t o Palme la c losed a t the indicated t ime . The pre-proces sor converts this message in the fol lowing P rolog fact :

fact ( l 5 6 , message ( ' 90 / 1 0 / 0 1 ' , ' 03 : 1 5 : 12 ' , [ ' SSN ' , ' 1 0 3 ' , [ ' Palmela ' , ' l ' , ' BREAKER ' J , ' BREAKER I I ' CLOSED ' l ) I ' 2 3 5 9 8 9 1 2 ' ) .

The last element of this fact codi fies the me s sage date and t ime a l lowing an easier treatment of temporal problems .

The me s sages arriving are conve rted in P rolog fact s by the pre-proce s s ing module and t ransmit t e d to the Knowledge Based System t hat t reat s t hem o n - l ine . I t is imp o r t a n t to not i c e t hat , wh i l e the Knowledge Based System is reasoning about the P ower System state , new alarms appear and are t ransmitted to the Knowledge Based System a s P ro log fact s . This means that the F a c t B a s e is dynami c a l l y changed by external even t s , i ndependent f rom t h e Knowledge Based System conclusion s .

The Rule Base

The knowledge that al lows the Knowledge B a s e d S y s t em to reach con c l u s i o n s i s included i n the form of if . . . then . . . rules being the left hand s ide a dis junct ion of con j unct ions and the right hand s ide a set of actions t o be taken i f t he left hand s ide is veri fied .

The Rule Base of our system includes both technical and empirical knowledge . In fact , the comp l e x i t y o f P ower System cont rol requ ires the c o n s i derat ion o f emp i r i c a l knowledge in order t o make t h e performance of our system efficient . On the other hand, technical knowledge is a l s o required and

41 1

our system includes rules that mode l i z e the behaviour of P ower S y s t em e lement s ( a s breakers and automatic operators ) .

As an examp l e , t he rule concerning t he open i n g of a b reaker due to a fault is written as fol lows :

rule 1 3 [ [

' breaker t r ipping '

mes sage ( , , [ Inst , Pan, [ Inst l , NL J J , ' TR IGGER ORDER ' , 1 1 ) -at T l and mes sage ( , , [ Inst , Pan , [ In st l , NL , ' BREAKER ' ] ] , ' BREAKER ' � ' OP EN ' ) at T2 and l ine closed ( Inst , Inst l , NL ) at T and -condition ( mod t ime dif less or eq ( Tl , T2 , 6 0 ) ) - - - - -

l l ==> [

gen fact (breaker opened ( t r ip , Inst , Pan , I n s t l , NL), T2 ) , -k i l l fact ( breaker closed ( Inst , Pan , Inst l , NL ) , , TZ) -1 -:-Th i s r u l e s t a t e s t ha t i f a me s s age corre sponding t o a t r igge r o rder and a me s s age c o r r e s p o n d i n g t o t h e b r e a k e r opening arrive i n t h e inte rval of a minute and the related line is c l osed then it is concluded that the l ine breaker has been t ripped . At the right hand s ide we see that a new conclus ion about the breaker state is a c h i e ve d i n T 2 and that any p r e v i o u s con c l u s i on about the closed s t a t e o f t h e same breaker becomes f a l s e a f t e r this t ime . Note that a t ime measure is attached to any fact or rule condit ion . Fact s are t rue or f a l s e d u r i n g t im e i n t e r v a l s . T ime condit ions inc luded in the rules a l low to dea l with t ime and t o compensate for the non-chronological receiving o f mes sages .

When a fact becomes fa l s e , the use of the " k i l l fact " p r e d i c a t e s t o r e s it a s an "old fact " what a l lows i t s later use for explanat ion fac i l i t ies .

The Inference Engine

The complex temporal reason ing involved in P o w e r S y s t e m c o n t r o l r e q u i r e d t h e development o f a n inference engine capable of dealing with t ime in an e f f ic ient way . The inference engine o f our Knowledge Based System u s e s a forward cha i n ing s t rategy app l ying the adequate rules when a new f a c t , e x t e r n a l ( a l a r m ) or i n t e r n a l ( conc l u s i on ) , arrive s , in order t o derive

new conclusion s .

Mo r e o ve r , o u r k n o w l e dge b a s e d s y s t em i n c l u d e s knowledge about t h e rea s on i ng s t ra t e g y ( me t aknowledge ) improving i t s e f f ic iency . The metaknowledge i s expres sed in me t a r u l e s and dr ive s t h e r e a s o n i n g proce s s , reducing t h e reasoning t ime and al lowing real-t ime performance .

Temporal reasoning ( Perkins , 1 9 9 0 ) plays a very imp o r t a nt r o l e in t h i s in ference en g i n e , name l y due to t h e f o l l o w i n g reas ons :

- the t ime provided with the a larm messages is t he t ime when the c o r r e sponding information arrives at the Cont rol Center

and not the t ime when the correspondent event took place

- me s s a g e s coming f rom d i f fe rent p l a n t s have dif ferent t ransmi s s i on t imes

- messages are divided into categories with d i f f e r e n t p r i o r i t y l e ve l s in what concerns their t ransmi s s ion .

T h i s means t hat a l a rm l i s t s a r e o n l y appa rent l y chron o l o g i c a l a n d t h a t even messages coming from the same p lant may be in the wrong order .

In order to deal with temporal problems , we have created a set of predicates de f i n ing t e m p o r a l r e l a t i o n s h i p s ( s u c h a s " t ime equ a l t o " o r "modu l u s t ime d i f f " ) . The s e

-p r e di c a t e s a r e u sed in t i me

conditions considered in the l e ft hand s ide of the rul e s .

Another important point is that the meaning of a c e r t a i n me s s a g e depends on what happened before and, i n certain cas e s , on what may happen next . As an examp l e , let us consider that a message re lat ing a t ripping orde r to a l ine breaker has arr ived . I f , a s s oc i a t e d with t h i s me s sage , a me s sage that report s the breaker opening a r r i ve s , w e may c o n c l u de that t h e b r e a k e r was t r ipped due t o a fau l t . Howeve r , if the last me s sage does not a rr i ve and we know that t h e r e are n o p r ob l ems with t he t r a n s mi s s i o n o f i n f o rmat i o n , we may conc lude that the t r ipping mes s age was due to t e s t s to the protect ion devices . In these s i t u a t i on s , our s y s t em delays for some i n s t ant s ( me t a kn ow l edge ) the f i r i n g o f cert ain rules .

The Man-Machine Interface

The role of a human operator in supervising and c on t r o l l i n g a c omp l e x and dyn ami c system such as a P ower System requires the deve l opment of a very good man-mach ine interface .

The u s e r i n t e r fa c e mu s t be i n t e ract ive enough to be a t t ract ive and to cont ribute for the acceptance o f the system . On the othe r hand , i t must not be very demanding and must p rovide the i n f o rma t i o n t hat requ i re s an u rgent t r eatment in a very e f f i c ient way .

In the development of our system, a special attent ion was paid to the interface with o p e r a t o r s ( Va l e , 1 9 9 2 b ) . The g r a p h i c interface i s based o n the X-Window System providing the u s e r with an easy, f lexible and well s t ructured way o f pre sent ing the required informat ion .

The human interface of our system is based on a set of widget s i n c l u d i n g windows ,

s c r o l l window s , but t on s , menus and dia logue fie lds . The C ommand Window o f fe r s , in a set o f button s , the most import ant commands being the others inc luded in a menu bar . Among many o t he r s , we may r e f e r t h e existence of commands a l lowing t h e opening of a s c ro l l w indow d i s p l a y i n g a l l t h e me s s ages arr ived f rom a chosen p lant and the opening o f a window displaying a l l the available information about a chosen p lant s t a t e ( en e rg i z e d or n o t , b r e a k e r and connectors state and s o on) .

When the Knowledge Based System reaches a new con c l u s i o n , the corre sponding mes s age,

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if any, i s disp layed i n a s c r o l lwindow . The most important me s sages are presented in a sma l l area locali zed at the l e ft top corner o f the display .

The Network Window pre sent s a s imp l i f ied image o f the network , showing dynami c a l ly the changing informat ion . Us ing the mouse , operators may have a zoom of a chosen area .

The Explanation Module

In the rea l - t ime cont r o l of Power Systems , sp e c i a l l y w h e n a d i s t u rb a n c e o c c u r s , u s u a l l y o p e r a t o r s do n o t requ i r e a n Exp l anat ion Modu l e . I n fact , a r e a l - t ime system mu s t be very we l l t e sted to be in s e r v i c e . Op e r a t o r s mu s t t r u s t it i n eme rgency s i tuations when t a king de c i s ions as soon as poss ible i s o f great importance .

On the other han d , the Exp lanat ion Modu le i s v e r y i mp o r t a n t f o r t e s t i n g a n d va l idat in g t h e Knowledge Ba se . In t h e case o f Power S y s t ems cont rol , The E xp l anat ion Modu l e is of g reat ut i l i t y i n t ra i n i ng courses for Cont rol Center operators .

The i n v e s t me n t s made in P ower S y s t ems , during the last decade s , resu lted in rather r e l i a b l e n e t w o rk s , be i n g s e r i o u s fau l t s ve ry rare . D u e t o t h i s , t h e t ra i n i n g o f Con t r o l C e n t e r ope rators m u s t be based o n t h e u s e o f s i mu l a t o r s c a p a b l e o f r e p r odu c i n g s e ve r a l k i nds o f eme r gency s ituat ion s .

The use of our system as a tutor a l lows the use of rea l a l a rm l i s t s , r e s u l t ing f rom previous s ituations in the Power System, in the t ra i n i n g of operat or s . Our Knowledge B a s e d S y s t e m p r o v i d e s o p e r a t o r s an exp lanation of it s s t rategy of reasoning

and the steps taken t o interpret the a la rms in order to diagno s e the fau l t s and reach conclusion s .

EXAMPLES

As an examp l e , let u s cons ider a sma l l set o f me s s a ge s corre sponding t o the ope ning and r e c l o s u r e op e r a t i o n s of the l i ne E r me s i n d e - R i b a d ' Av e I , c o n n e c t i n g E rme s inde s u b s t a t i o n ( SED ) t o Riba d ' Ave substation ( SRA) :

0 3 -0CT- 1 9 9 0 1 6 : 0 4 : 5 3 SRA SGER GENERAL SERVICES COMMAND MANUAL

0 3 -0CT- 1 9 9 0 1 6 : 0 5 : 1 2 SED SGER GENERAL SERVICES COMMAND MANUAL

0 3 -0CT- 1 9 9 0 1 6 : 0 5 : 3 7 SRA 1 3 0 ERME S INDE I -BREAKER BREAKER OPENED

0 3 -0CT- 1 9 9 0 1 6 : 0 6 : 4 0 SED 1 0 5 R I B D ' AVE I -BREAKER BREAKER OPENED

0 3 -0CT- 1 9 9 0 1 6 : 0 8 : 0 8 SED 1 0 5 R I B D ' AVE I -BREAKER BREAKER CLOSED

0 3 -0CT- 1 9 9 0 1 6 : 0 8 : 5 1 SRA 1 3 0 ERMESINDE I -BREAKER BREAKER CLOSED

0 3 -0CT- 1 9 9 0 1 6 : 0 9 : 2 5 SRA SGER GENERAL SERVICES COMMAND AUTOMAT I

0 3 -0CT- 1 9 9 0 1 6 : 0 9 : 4 7 SED SGER GENERAL SERVICES COMMAND AUTOMATI

Ou r s y s t e m makes the s yn t he s i s of t h e s e

me s s a g e s p r e s e n t i n g conclusion s :

t h e f o l l o w i n g

03-0CT - 1 9 9 0 SED- SRA I

1 6 : 0 6 : 4 0 open ing by the operator

o f l i ne

03-0CT- 1 99 0 SED-SRA I

1 6 : 0 8 : 5 1 c l o s u re of l in e

F o r this examp l e , the s ystem explains how it reached the conclus ion that l ine " SED­SRA I" has been opened by the operator in the following way :

I have inferred fact n . 1 8 4 ( line "SED-SRA I" has been opened by the operator)

using rule n . 5 5 ( l ine opened by operator)

and verifying the fol lowing fact s :

1 8 1 ( opening by the ope rator o f the SRA breaker)

1 8 3 ( opening by the operator of the SED breaker)

I have inferred fact n . 1 8 1 ( opening by the operator o f the SRA breaker)

using rule n . 1 7 ( opening of a breake r by the operator)

and verifying the fol lowing fact s :

1 8 0 (message report ing the opening of the SRA breaker)

1 7 2 ( me s s age report ing SRA i s in manual command )

A s a n examp l e , cons idering the me s s ages arriving from Vermoim Substat ion ( SVM) at the 5th o f October 1 9 9 0 there are 5 1 h i gh voltage alarm messages out of a t ot a l of 9 5 messages arrived from Vermoim Substation on that day .

On the other hand, the f i rst two me s s ages arrived from Vermoim are the fol lowing :

0 5-0CT- 1 9 9 0 0 0 : 1 8 : 03 SVM BUS I I - 2 2 0 kV VOLTAGE

0 5-0CT- 1 9 9 0 0 0 : 2 0 : 04 SVM BUS I I - 2 2 0 kV VOLTAGE

B22 HIGH

B22 END

reporting a h igh vol tage a l a rm t hat i s active approximately for two minutes .

During that da y , these p a i r of me s sages appeared 1 6 t imes more , being the last t ime at 0 8 : 3 3 : 3 9 . Th e s e 3 4 me s s a g e s a r e summari zed b y o u r system without l o o s e o f important informat ion , in t he f o l lowing way :

0 5-0CT- 1 9 9 0 0 0 : 1 8 : 03 SVM B22 BUS I I - 2 2 0kV VOLTAGE HIGH INT 0 8 : 3 3 : 3 9

being ind icated, at each moment , the t ime when the a l a rm became innact ive for the last t ime .

As another examp l e , let us con s ide r the·

following me s sage s arr ived from Rio Maior Substation ( SRM) :

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SRM 2 0 5 BATALHA I I - BREAKER BREAKER MOVING

SRM 2 0 5 BATALHA I I - SBl D I SCON . MOVING

SRM 2 0 5 BATALHA I I - SB2 D I SCON . MOVING

SRM 2 0 5 BATALHA I I - SBP D I SCON . MOVING

SRM 2 0 6 BYPASS 2 2 0A - BREAKER BREAKER MOVING

SRM 2 0 6 BYPASS 2 2 0A - SBl D I SCON . MOVING

SRM 2 0 6 BYPASS 2 2 0A - SB2 D I S CON . MOVING

SRM 2 0 6 BYPASS 2 2 0A - SB3 D ISCON . MOVING

Thes e mes sages are f o l lowed by other 5 6 report ing movements i n several breakers and disconnectors at Rio Maior Sub s t at ion . All the s e me s sages are originated by the cut of the direct current to the pane l s . A s ingle message gives the same in formation as these 6 4 me s sages i n a much more sat i s factory way :

SRM 2 0 5 , 2 1 4 , 4 1 7 ,

d . c . cut to the fol lowing pane l s : 2 0 6 , 2 0 7 , 2 0 9 , 2 1 0 , 2 1 1 , 2 1 2 , 2 1 3 ,

2 1 5 , 2 1 7 , 2 1 8 , 2 2 1 , 4 0 8 , 4 1 1 , 4 1 6 , 4 1 8 , 4 2 2 , 4 2 4

Let u s con s ider s ome me s sage s arrived at a Portuguese Cont r o l Cent e r at the 1 st o f October 1 9 9 0 , coming from t he Ferre ira do Alent e j o Substation ( S FA ) :

O l -OCT- 1 9 9 0 0 6 : 0 4 : 5 6 SFA OURIQUE-BREAKER BREAKER

O l -OCT- 1 9 9 0 0 6 : 0 4 : 5 6 SFA OUR I QUE URGENT AL .

O l -OCT- 1 9 9 0 0 6 : 0 4 : 5 6 SFA OUR I QUE NO URG . AL .

O l -OCT- 1 99 0 0 6 : 0 4 : 5 6 SFA OURIQUE OTHER AL .

O l -OCT- 1 9 9 0 0 6 : 0 4 : 5 6 SFA SINES OTHER AL .

O l -OCT- 1 9 9 0 0 6 : 0 4 : 5 6 SFA PALMELA OTHER AL . 0 1 -0CT- 1 9 9 0 0 6 : 0 4 : 5 6 SFA AUTOMATIC OPERATOR BEGIN

O l-OCT- 1 9 9 0 0 6 : 0 4 : 5 7 SFA GENERAL SERVICES NO URG . AL .

O l -OCT- 1 9 9 0 0 6 : 0 5 : 00 SFA OUR I QUE URGENT AL .

0 1 -0CT- 1 9 9 0 0 6 : 05 : 0 0 SFA OUR I QUE TRIP ORDER

0 1 -0CT- 1 99 0 0 6 : 0 6 : 1 1 SFA OUR I QUE-BREAKER BREAKER

O l -OCT- 1 9 9 0 0 6 : 0 6 : 1 1 SFA OURIQUE URGENT AL .

O l -OCT- 1 9 9 0 0 6 : 0 6 : 1 1 SFA OUR I QUE NO URG . AL .

O l -OCT- 1 99 0 0 6 : 0 6 : 1 1 SFA OURIQUE OTHER AL .

1 0 2 OPENED

1 0 2

1 0 2 FLEET

1 0 2 FLEET

1 0 4 FLEET

1 0 6 FLEET

OPA

SGER FLEET

1 0 2 END

1 0 2

1 0 2 FLEET

1 0 2

1 0 2

1 0 2 FLEET

0 1 -0CT- 1 9 9 0 0 6 : 0 6 : 1 1 SFA 1 0 2 OURIQUE BREAKER AL .

0 1 -0CT- 1 9 9 0 0 6 : 0 6 : 1 1 SFA 1 0 4

S INES OTHER AL . FLEET

0 1 -0CT- 1 9 9 0 0 6 : 0 6 : 1 1 SFA 1 0 6 PALMELA OTHER AL . FLEET

0 1 -0CT - 1 9 9 0 0 6 : 0 6 : 1 1 SFA OPA AUTOMAT I C OPERATOR BEGIN END

0 1 -0CT- 1 9 9 0 0 6 : 0 6 : 1 1 SFA SGER GENERAL SERVICES URGENT AL .

0 1 -0CT- 1 9 9 0 0 6 : 0 6 : 1 1 SFA SGER GENERAL SERVI CES NO URG . AL .

0 1 -0CT- 1 9 9 0 0 6 : 0 6 : 1 6 SFA 1 0 2 OURIQUE URGENT AL . END

0 1 -0CT- 1 9 9 0 0 6 : 0 6 : 1 6 SFA 1 0 2 OUR I QUE TRIP ORDER

0 1 -0CT- 1 9 9 0 0 6 : 0 6 : 3 6 SFA 1 0 2 OUR I QUE NO URG . AL . END

0 1 -0CT- 1 9 9 0 0 6 : 0 6 : 3 6 SFA 1 0 2 OURIQUE BREAK . AL . END

0 1 -0CT- 1 9 9 0 0 6 : 0 6 : 3 6 SFA SGER GENERAL SERVICES NO URG . AL . END

Th i s set of me s s ages c o r re sponds t o the t r ipping o f t he b re a k e r of t he l ine t o Ourique due t o a fau l t and the reclosure by the automa t i c operator f o l l owed by another t r ipping of the breake r .

Due t o del ays i n the t ransm i s s ion o f s ome me s s age s , t h i s l i s t s eems , at t he f i r s t s i ght , t o b e d i f f i c u l t t o unde r s t and . I n fa c t , the f i rst me s s age in forming that the breaker opened ( B REAKER OPENED ) a rr i ved 4 se conds be fore t he me s s age r e l a t i n g t he t r ipping order ( TR I P ORDER ) , seeming that the last one is assoc iated with the me ssage a r r ived at 0 6 : 0 6 : 1 1 t h a t repor t s t wo chan ges in the pos i t i on of t he b re a k e r ( BREAKER FLEET ) . A more careful ana lys i s

shows that t h i s message has been caused by the bre ake r r e c l o s u r e by the aut omat i c operator ( OPA) , fol lowed b y a new t r ipping order ( TR I P ORDER at 0 6 : 0 6 : 1 6 ) and t he opening of the breaker .

Our s y s t e m s i t u at i o n , conc lusions :

i s a b l e t o f u r n i s h i n g

unde r s t a n d the t h e f o l l o w i n g

0 6 : 0 4 : 5 6 SFA opening o f l ine SFA-SOQ by tripping of the breaker

0 6 : 0 6 : 1 1 SFA rec l o s u r e of l ine S FA - S OQ by OPA fol lowed by opening of l ine SFA-SOQ by t r ipping of the breaker

CONCLUS I ONS

Cont r o l Centers are r e spon s ib l e f o r the supervi s i o n , mon i t o r i n g and cont r o l o f Power S ystems , being a ma j o r factor i n the f i n a l qu a l i t y of d e l i v e r e d e l e c t r i c a l ene rgy . Cont r o l C e n t e r ope r a t o r s have a c c e s s to the i n f o rmat i on they need t o per form e f f i c i ent l y the i r t a s k s . Howeve r , spe c i a l l y i n case o f eme rgency s ituat i on s , t h i s i n f o r m a t i o n i s o f d i f f i c u l t interpret a t i on for human operat o r s , unde r the severe imposed real-t ime con s t raint s .

I n t h i s pape r , we p r e s e n t e d a Knowledge

414

Based S y s t em that a s s i st s Cont rol Center ope rat o r s i n r e a l - t ime c on t r o l o f P ower Systems . This system rece ives and proce s s e s the i n format i on ava i l a b l e at Port ugue s e Cont rol Cent e r s providing operators a more i n t e l l i g e n t a n d r a p i d a c c e s s t o t h e mea n i n g f u l i n format i on t he y need t o base the i r de c i s i ons . I t groups some me ssages in order to p r e s ent c o n c l u s i o n s about the

Power S y st em State helping dec i s i on s about power rest orat ion procedure s .

The i n ference engine of this system uses a forward chaining s t rategy of rea soning and p e r f o rms c omp l e x t emp o r a l r e a s o n i n g in o r d e r to p r o v i de e f f i c i e n t r e a l - t i me cont rol of P o we r Systems . The explana t i on module i s of spe c i a l importance for the use o f the system as a tutor for Control Center operators .

REFERENCES

Ame link , H . , A . M. Fort e , and R . P . Gube rman ( 1 9 8 6 ) . D i spat cher a l a rm and me s s age

p ro ce s s ing . IEEE Transactions on Power Systems , .:ilQ..l...l., 1 8 8 - 1 94 .

C I GRE Working Group 3 8 . 0 6 . 02 ( 1 9 9 1 ) . Survey on e x p e r t s y s t e m s i n a l a r m handling . Electra , �, 1 3 2 - 1 5 1 .

K i r s chen , D . S . , and othe r s . Cont rol l i ng power s y s t ems during emergen c i e s : the role o f expert syst ems ( 1 9 8 9 ) . IEEE Computer Applications in Power, YQ.l....2., n . 2 , 4 1- 4 5 .

P e r k i n s , W . A . , a n d A . Au s t i n ( 1 9 9 0 ) . Ad d i n g tempo r a l reasoning t o expe rt - s y s tem­bu i l d i n g e n v i r onme n t s . IEEE Expert , YQJ....5., n . 1 , 2 3 - 3 0 .

P r i n c e , W . R . , B . F . Wo l lenbe r g , and D . B . Bertagn ol l i ( 1 9 8 9 ) . Survey on exce s s ive a l a r m s . IEEE Transactions on Power Systems , YQl......i, 95 0 - 9 5 6 .

Talukda r , S . N . , E . Cardo z o , and T . P e r ry ( 1 9 8 6 ) . T h e o p e r a t o r ' s a s s i s t a n t a n expandab l e prog ram f o r power s ys t em t rouble ana l ys i s . IEEE Transact ions on Power Systems , .:ilQ..l...l., 1 8 2 - 1 8 7 .

Va l e , Z , an d A . Moura ( 1 9 9 2 a ) . An expert system for power s y s t em c o n t r o l cente r s . I n I n t e r n a t i o n a l C e n t re f o r H e a t and Ma s s T r an s fe r ( E d . ) , Proceedings o f �n.d....International Forum on Expert Systems and Computer S j mulation in Energy Engineerj ng, E r lange n , G e rmany, pp . 1 5 . 1 . 1 - 1 5 . 1 . 6 .

Va l e , Z . , and A . Moura ( 1 9 9 2b ) . An expert system t o a s s i s t o p e r a t o r s o f t h e p o w e r s y s t e m c o n t r o l c e n t e r s . I n T h e I n s t i t u t i on o f E l e c t r i c a l E n g i n e e r s ( E d . ) , P r o c e e d i ng s of t he 1 992

I n t e rn a t i o n a l C o n f e r e n c e on Information Decision-Action Systems in Complex Organi zat ions , L ondon , pp . 1 1 0 -1 1 4 .

Wollenberg , B . F . ( 1 9 8 6 ) . Fea s ib i l it y study for a n e n e r g y m a n a g e m e n t s y s t e m i n t e l l i g e n t a l a rm p r o c e s s o r . �

Transactions on Power Systems , YQ..l......l, 2 4 1 - 2 4 7 .

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

MODEL-BASED DIAGNOSIS FOR CONTINUOUS PROCESS SUPERVISION: THE ALEXIP EXPERIENCE

S. Cauvin, B. Braunschwelg, P. Galtier and Y. Glalze

lnstituJ Franfais du Pitrole, 14 Avenue de Bois Preau, BP 311, 92506 Rueil Malmaison Cedex, France

Abstract. The Alexip knowledge-based system uses model-based reasoning to analyse Alphabutol petrochemical units' dynamic behaviour. A good understanding of what is going on is needed to suggest the corrective actions which must be taken to maintain the unit in a desirable state. This means, as a number of variables are involved, that the system must be able to take into account factors such as time-delays, combination of upsets, noisy data. In this paper we discuss the diagnostic part of the knowledge-based system. The method we present involves a qualitative description of single events that may occur in the process unit and a general reasoning mechanism (written in first-order logic) that achieves diagnosis based on the qualitative description. Since the reasoning is totally general, the method is generic and can be applied to any process. Events will only need to be described according to the procedure we define.

Keywords : Process control, Petroleum industry, Expert systems, Model-based diagnosis, Simulation

INTRODUCTION

Process monitoring is increasingly complex. Automatic control systems perform numerical tasks, but the operator must still constantly monitor the processes he is in charge of and respond to any variations he judges abnormal. This is generally a fairly complex job. The operator must process a large amount of information, analyse it quite thoroughly and make strategic decisions. From a cognitive standpoint these are high-level tasks. This is why we think that knowledge-based systems can provide considerable assistance in the operator's daily work.

IFP is currently developing ALEXIP (ALphabutol EXpert IFP) , a knowledge-based system to monitor the Alphabutol petrochemical process (an IFP process to produce 1 -butene from ethylene). A wealth of experience in running the process has been gained from installed units. The process is highly nonlinear and is very sensitive to outside upsets. Changes in the process must be anticipated and a number of parameters must be adjusted periodically to optimize operation. The role of the expert system is to analyse the operation of the unit and then determine corrective action to keep it in optimum running condition. As a result, the diagnosis phase is absolutely crucial. We will deal with its implementation in detail in this paper. First we will present the information available to us and discuss the possibilities we envisage for implementing the diagnosis. Then

415

we will present the method we adopted in detail -- it is based on a qualitative description of process behaviour in relation to a number of events. Last we will show the advantages and limits of the method.

AVAILABLE PROCESS INFORMATION

We have been able to utilize of a dynamic numerical process simulator validated on industrial plants to develop ALEXIP. The material and enthalpy balances were integrated with their accumulation terms to simulate dynamic operation in the reactor section around a steady state and in start-up phases. Simulation was performed with RSI's SORYA software and allows a number of displays: control room block diagram panels, block diagrams with the variables computed by the simulation programme, curves showing changes in different variables (Fig. 1 ) and bar charts indicating controller status.

__ !=-----� 1 . Pump_around

2. Heat_transfer

3. Pressure

4. Tempera tu re

s. Catalyst_flow

6. Water_flow

7. Total_feed

8. Water_in_temp

Fig. 1 A simulation session

By simulation, the short- and long-term consequences on the process unit of a number of events can be studied precisely based on a given steady state. The events may involve action on the controllers -- modification in set points, transition from one mode to another (automatic I manual) -- or action on v alve opening, or upsets pump breakdowns, exchanger fouling, vanat1ons in a number of outside parameters, noisy data, etc.

The knowledge can be summarized : �Actions Aj �Con•equence• Cl on J Upsets P j => variables Ve which ln state characterize the Ek process

When we speak of consequences here we mean the way v ariables change. The dynamic simulator only gives us the series of values that each variable will take on as time goes by. This is insufficient to make a good diagnosis for several reasons. However good simulation may be, it never reproduces reality exactly. A number of simplifications are always required and it is always possible to get outside the model's limits of validity. Additionally, using the simulation directly to diagnose the state of the process unit would entail making a considerable number of simulations to find out the consequences of all the combinations of events with all the possible numerical values based on a given state (an increase of 1 °C as well as 2°C would have to be simulated). This would have to be done until we found the configuration of events leading to the state we actually observed. This is obviously not feasible and means that we must analyse the situation a little more qualitatively, even though we use numerical simulation. An expert does not base his reasoning on the series of values computed by the simulator or on the series of values observed on the process unit anyway, but rather on the shape of curves, on the general trend of variables and on the orders of magnitude, i .e. on much more qualitative concepts.

Let us analyse the curves we obtain for a minute to get a better grip on the problem of diagnosis. The consequences observed on variables can be broken down into three phases: - A phase of different variations or oscillations

corresponding to transient states. This phase is due to the control system and so experts can not really explain each variation exactly.

- A phase of change leading to another stable state or to a runaway reaction. During this phase, experts can give a satisfactory explanation for the changes in the different variables. Interactions of variables wholly justify the changes. Experts can still not always tell whether a runaway reaction or a stable state will be reached since this depends on numerical values.

- A phase of stability.

The following points should be noted:

416

- The borderlines between each of the three stages are not clear-cut, i.e. it is hard to answer the question: is this the transient phase or the change phase?

- The same action can lead to a stable state or to total reactor runaway depending on the action's magnitude and on the reactor's operating range.

On one hand then we have the purely numerical information from the simulator, and on the o ther the qualitative information that corresponds to experts' knowledge of physics and chemistry. An effective diagnosis must use both types of input.

REPRESENTING INTERACTIONS BE1WEEN VARIABLES

Interactions between v ariables are hard to describe since the following points must be taken into account: - The variables are interconnected by chemical

phenomena (thermal balances, material balances, etc.).

- Controllers act on the system to keep a variable at its set point to the extent possible.

- The system is dynamic and is regulated by feedback loops.

Since the system is continuous, dynamic, controlled and has feedbacks , the consequences of one variable's variation on the others are not the same in the long and in the short term.

We could generate the long term as it is just a series of short terms. Accordingly, we worked out a diagram of short-term interactions between variables (see a subset in Fig. 2).

Catalyst BTRP05 concentration

a ..:!:.-. b Variables a and b

� -;o': have the same kind of Feed flow rate -4 Pressure

( if a i ncreases t hen + / -

b increases ) Catalyst + variations � j � I

activity + Conversion a -=--- b X / Variables a and b have Reactor

+

opposite variations ( i f a increases then b decreases)

temperature

1 " + + Action TRC300 +/ \:. Reinjection � Water temperature rate

flow

Fig. 2 Direct interactions between the variables under temperature and pressure control

Since we are dealing with qualitative data rather than computing a succession of states as the simulator does, it is very difficult to deduce how the system will evolve. Numerical gains can be added onto the arcs to give a semi­qualitative, semi-quantitative simulation of the process, as some authors propose. However, we gave up on this approach because we would have made yet another simulator. It might have been a little less costly in computer time as it

would have been more approximate, but would not really have been able to solve the problems mentioned in the first paragraph.

So we used the simulator that we had and interpreted the results. We simulated all the events that could occur in the process individually and observed the long-term consequences to describe them in the expert system.

Description is obviously possible only if process behaviour is almost always the same in a given operating range. Consequences of action are described in normal operation and in different defective operating modes.

We built the diagnosis based on the qualitative description of action in situations which were themselves defined qualitatively.

DE1ERMINING DOMINANT AND MASKED EVENTS

The core of ALEXIP's process unit diagnosis is detecting the events that influence process behaviour at any reasoning stage. Detection is particularly difficult because the process unit takes a long time to respond to single upsets. This means that process behaviour is constantly the outcome of combined actions spread out in time but with coexisting consequences.

This is why diagnosis focusses on detecting these combinations of events. The aim is not to spot "the" breakdown or "the" faulty component as in conventional fault diagnosis, but rather to identify the set of malfunctions or actions that make the process drift away from its reference s tate .

We assume that a reference state E* has been determined as explained later on in this paper. Based on the reference state, comparisons will be made, trends detected and threshold values relocated. State E* is assumed to be set and will in fact be modified only when conditions are fulfilled allowing a new reference to be established.

The system's qualitative state is analysed in terms of 1) the variables' position compared to the reference state, and 2) their change trends. If N is the number of variables measured, the qualitative state will then be determined by knowing N facts concerning the variables' positions (position related to thresholds for each variable), and 2 *N facts representing their change trends in the short term (derivative over a brief time-frame) and in the long term (derivative over a long time-frame).

Each element Pi of the set of known events in the expert system is defined by all of it consequences on the process variables, when event Pi is alone in governing the change in the process.

Pi ==> {Cj ) { P i ) = { actions undertaken by the operator, upsets, breakdowns, repairs )

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Cj <Position of variable Vj> Cj <Short term trend for variable Vj> C j <Long term trend for variable Vj>

In this facts base, which contains the qualitative causal knowledge of the change in the process, we indicate only the { Cj } corresponding to an effective modification in the v ariable under consideration. Process invariants with respect to each upset are thus defined implicitly. There is an exception to this rule though. When two different events have identical consequences but a sensor can distinguish between event Pl and event P2, then the stability of the variable that is picked up is specified for the event that is not picked up. There will therefore be consequences of the following type:

Pi ==> Cj with Cj = <stability of variable Vj>

We call an event dominant when all its consequences { Cj} are actually observed on the process. Such an event is then considered as governing the change in the process at a given time .

We will say an event i s masked when at least one of its consequences Cj is observed on the process , and w hen all its unobserved consequences are explained by the existence of a dominant event which results in the opposite consequence. This implies that the fact base must contain a description of the opposite of every consequence. There will thus be permanent facts of the following type:

X opposed to Y x, Y = <position, short or long term trend>

Example : increases decreases greater_than

opposed to opposed-to opposed::::to

decreases increases less than

We can now provide an example of diagnosis. Given events Pl and P2, with consequences on variables V l , V2 and V3, such that:

Pl ==> Vl greater_than reference value 1 Pl =a> V2 less than reference-value-2 Pl ==> Vl increases in _the_long_teriii Pl ==> Vl increases in the short term P2 ==> V2 greater_than reference value

-2

P2 ==> V3 greater_than reference-value -3

Pl results in a short- and long-term increase in variable V l , which exceeds its reference value, as well as a decrease in variable V2, which drops below its reference value. It has no consequences on V3. P2 results in V2 and V3 moving above their reference values.

Let us assume that the qualitative state of the process is as follows:

Vl V2 V3 Vl Vl

greater than less than greater than increases increases

reference_value_l reference value 2 reference-value-3 in the long term in::::the::::short_term

Here we will consider that P l is present and dominant, s ince its set of consequences is observed. We will also diagnose that P2 is present and masked, since at least one of its consequences is observed (the one related to

V3). The other consequence of P2 (the one related to V2) is masked by the effect of the dominant event that counteracts it. It should be noted that if we had no information on variable V3, event P2 could not be validated since no consequence is observable.

The diagnostic algorithm consists in looking for dominant events first, and then trying to find the events masked by them. This is an "elimination" type of algorithm. Each event is assumed a priori to be "possible " . The qualitative state of the process provides evidence that enables us to eliminate events from the list of possible events. In the end, the only dominant or masked events remaining are the ones that have not been demonstrated to be impossible.

Algorithm Step I : Determining dominant events

For any Event P such that P os s ible ( P ) =Tru e : I f there exists a consequence C such that

Ce { Consequences ( P ) } and Observed ( C ) =Fa l s e :

Then Domi nant ( P ) False

Else Domi nant ( P ) True

End i f End For any

Step 2 : -

Propagating dominant events' opp osite consequences

For any Event P such that Dominant ( P ) =True : For_any Consequence C such_that

c e { Consequences ( P ) ) : For any Con sequence C ' such that

C1 opposed to C : -Possibl y- masked ( C ' ) = True

End For any -End For-any-

End For any Step 3 :

-Determining m asked events

For any Event P such that Pos s ible ( P ) =True and Dominant ( P ) =Fa l s e :

I f there ex ists a Consequence C such that

Ce { Con sequences ( P ) ) and Observed ( C ) =Fa lse and Possibly_mas ked ( C} < > True :

Then Masked ( P ) =Fa l se

Else Masked ( P ) =True

End i f End_Fo(::any

Several simplifying hypotheses are implicitly contained in the diagnostic algorithm. So the need to observe at least one consequence of every event on the process keeps an event and its opposite from being diagnosed as coexisting. Without this restriction, all events whose consequences were a subset of opposites of the consequences of any dominant event would be diagnosed as masked by the algorithm. Additionally, we assume that only dominant events are capable of masking other events. "Compound" masking is not allowed for.

In practice, we superimpose description mechanism on the

a s ituation algorithm (a

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situation is a characterization of the state of the process at a given time, such as: "under feed flow rate control", "under pressure control", "normal operation"). The aim here is to screen the list of possible events and thereby limit the search. Furthermore, a filing system is set up for the conclusions of the diagnosis to detect changes in the process and reach conclusions of the type: "P2 is always masked by Pl ", "P2 has become dominant", etc.

We have experimented with this diagnosis in a large number of simulated cases and can state that -- since upsets, actions and consequences are limited -- a correct diagnosis of the state of the process is produced fairly often. A real­life example is reproduced later in this paper. Appendix 1 presents an excerpt of the knowledge base illustrating the diagnostic algorithm described above.

DEALlNG WITH TRANSIENT STATES

As we already stated in the analysis of available process information, detecting transient states is always rather difficult as their shape depends on the control system and the numerical values of the different parameters. The diagnosis described previously is made before we even decide whether transient states are occurring or not. In fact the conclusions of this module and some other criteria will help us with this decision. The consequences of events are described in the long term, and so if we make the diagnosis during the transient phase it is highly l ikely that we will end up w ith incompatib i l i t ies among the d i fferent conclusions. S everal symptoms are indicative of probable transient states: 1 . Several variables change. 2 . The short-term derivatives have varying

signs (variables do not have a constant variation trend).

3 . In automatic mode, not all the PID controllers manage to keep to their set points .

4 . Some action was taken in the past. Its long­term consequences can not be seen yet but a set point indicator still shows that a change has taken place.

As soon as any of these symptoms are observed, we generate the hypothesis that transient states are occurring. In this case, the diagnosis made previously m ay have mistakenly detected events. If we observe oscillations, at a given time we may accidentally see a combination of consequences in the short term which correspond to those usually seen in the long term. The event must not be accepted as dominant or masked. We consider that it is not found by the diagnostic module. The following rule is then applied:

R ule for el iminating events found b y coincidence during t h e transient phase If the a ssumpt i on

P resence of t ransient states i s made For any event-P such that

Dominant ( P } = True-or Masked ( P ) = True :

(Dominan t and masked even ts are detected by the method we proposed before)

If there_ex ists a var iable V such that V appears in C and Ce { Consequences ( P ) } and V does not have a const ant

vari at ion t rend : Then

Dominant ( P ) False Masked ( P ) Fa lse

At the end of this whole diagnosis the change in certain variables may remain unexplained, i.e. certain variables are not constant and none of the accepted dominant or masked events can explain their behaviour. Here, if some action was undertaken a few hours before -- "a few" depending on the type of action -- we assume a transient period is occurring, do not proceed any further with the diagnosis and "simply" check to see that we do not run outside acceptable operating limits. If on the contrary no action has been taken, we pursue the issue. There is incoherence somewhere and we must question some information. Either a sensor is not providing the right value -- the sensor detecting the action, the sensor for a variable that is oscillating abnormally -- or we are witnessing an event unknown by the expert system.

DETERMINING 1HE REFERENCE STATE

We have proposed a diagnosis based for the most part on the behaviour of the process compared to a reference state. However, this is not always a start-up or steady state as the diagnosis would be valid only for the first few hours of operation. The reference state must therefore be updated regularly -- this is not very complicated but means proceeding with caution. Before presenting the solution we have chosen, let us first look at the two examples below to understand exactly when the reference state must be modified.

1 . Pump_around

e i 2. Heat_ transfer

3. Pressure 0 3

4. Temperature 0 4

Q 5 s. Water_flow

' 6. Cata!yst_flow

8 � 7. Tota!_fccd

8. Water_in_temp

t O t I t 2 t3 t 4

Case 1 0 .I\ 1 . Pump_around

0 l. 2. Heat_ transfer

0 3 3. Pressure

o � 4. Temperature

:::..,..----8 : s. Cata!yst_flow

6. Water_flow 8 � 7. Total_feed

8. Water_in_temp

Case 2

Fig. 3. Two illustrations of reference state determination

Looking at Case 1 (Fig. 3), we notice first of all a temperature increase detected in comparison with the state observed on the process unit at

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time tO. The consequences of the action "catalyst flow rate increase" are observed at time tl on the feed and water flow rates. The subsequent decrease in catalyst flow has consequences on the water flow rate from time t3 onward, and on the feed flow rate from time t4 onward. Between the two, a problem has arisen on the pump-around circuit, and a substantial drop in the heat transfer coefficient can be observed in comparison with its state at tO.

Now in Case 2 (Fig. 3), the catalyst flow rate was first increased. It was then decreased because events occurring on the process unit after the catalyst flow increase kept the unit from running properly and some "back-tracking" was required. However, the water and feed flow rates keep rising as a result of that first catalyst flow increase. This first action remains the dominant event and the reference s tate continues to be the initial state. Past actions can also remain dominant either because of their magnitude or due to process response time.

These two brief examples show that:

a) There is a reference state for each variable; the reference state must not be changed for all the variables picked up on the process unit at the same time (Otherwise, either we would not have detected the actions on the catalyst or we would have missed the problem of the heat transfer coefficient in Case 1 . )

b) The reference state can not be changed as soon as a new action is detected, since a past action may still predominate. We could think of changing reference points when the action becomes dominant, but this is not possible either. As our thinking would not be based on the right reference point, the action would never be detected as dominant!

The solution we have chosen is therefore to change reference s tates when a variable actually changes its variation trend (i.e. it had a constant v ariation trend over one period and has another trend over a given new period), and if there is a dominant event that justifies this new change when the new reference state is taken. This means that we might decide to take a past state as a reference rather than the state observed on the process unit when the reference state is determined. In addition, we do not update the reference states of all the variables at the same time. This allows us to take all the past events into account. The algorithm is therefore as follows (provided that transient states are not occurring):

S t e p l Determ i n i n g a new p ossible reference state : For any va r i able V

If Change of va riati on_t rend (V) = True Then - -

New_possible_re ference state ( V ) Observed_value ( V )

Else New_pos s ible_re ference state (V)

Previou s_reference_state ( V )

Step 2 Dete rmining dominant and masked events by reasoning with respect to the new reference state

Step 3 : Selecting the new reference state For any variab le V

If Change of va r i at ion t rend (V) = True And Fo r_any- Con sequence c in which V appears

Then

There exi st s an Event P such that Dominant (P) = True and C e { Con sequences ( P ) } :

New reference state (V) New=pos sible_reference_state (V)

It can be noted that our solution implies that when the same action is performed two times in a row, the reference state is not modified the second time. In fact doing the same thing twice boils down to performing one action of greater magnitude .

DISCUSSION

A conclusion can be drawn from the points presented above. Monitoring a petrochemical process run with complex instrumentation and control systems entails using methods and reasoning far more sophisticated than LOe diagnostic systems currently employed in artificial intelligence. The difficulties in the concept of real-time supervision, and especially in taking dynamic process behaviour into account, are the following: a ) In terpre ting time- dependent s ignals ,

considering widely differing time constants. b ) Manipulating qualitative concepts. c) Dealing w ith hypotheses , questioning

information read by sensors. d ) Continually determining a reference frame. e ) Diagnosing multiple causes coexisting at any

time. f) Providing a response in a limited time­

frame. g) Reacting quickly in critical situations.

We should also add the problems of man I machine interface especially for process operators -- as well as the technical interface with computerized process control systems and their real-time data bases.

At this point in time there is no general methodology that can be applied systematically to developing on-line knowledge-based systems. Every single difficulty listed above is the subject of considerable research in university laboratories and industry and results have been obtained in each area. The problems of symbolic interpretation of continuous time-dependent signals with their time constants are dealt with by signal processing methods, fuzzy logic and neural networks. Qualitative or naive physics studies the propagation of qualitative variables in complex causal networks. Truth maintenance systems are used to manipulate multiple hypotheses, generally to diagnose breakdowns in static systems or systems whose dynamics are not governed by complex feedback loops. Real- time inference engines are used for

420

applicat ions requiring response times compatible with the time constants in the monitored systems. Reactive inference systems are continually attentive to outside inputs to react immediately to any new information.

We have theoretical and practical tools to implement all these methods independently. By contrast, integrating this body of characteristics in a single process monitoring system does pose problems. First of all a problem of the tool, since none of the development environments on the market has large enough potential or flexibility. Second a problem of methodology, because even if we had a generic tool that could implement these widely dissimilar methods, we would have a very hard time defining a coherent procedure to assemble the different pieces of knowledge and processing. The most commonly used methodologies for developing knowledge-based systems, such as KADS or KOD, do not provide solutions to real-time and time-dependent problems. Accordingly, we need to do some long-range thinking about developing high­performance monitoring systems that are integrated in existing computer systems, able to make diagnoses as relevantly as the best experts and capable of communicating simply with operators. Actual-size applications such as ALEXIP provide a basis for this type of thinking; they are also an environment for experimenting and validating the advanced methods that will be produced.

ACKNOWLEDGEMENTS

We are grateful to the lnstitut Franyais du Petrole for authorizing the publication of this paper and we particularly acknowledge Mr B amberger, Mr Franckowiak, Mr Freund and Mr Commereuc .

REFFRENCES

Boucot, P. ( 1987). Le simulateur de raffinage de l'ENSPM, Outil de developpernent de modeles dynamiques de procedes. Revue of Institut Francais du Petrole, Vol. 42 n°2 Cauvin, S . , B . Braunschweig, P. Galtier and Y. Glaize ( 1 992). Alexip, Expert system coupled with a dynamic simulator for the supervision of the Alphabutol process. Revue of Institut Francais du Petrole. Vol. 47 n°3 Commereuc, D., Y. Chauvin, J. Gaillard, J. Leonard and J. Andrews ( 1984). Dimerize ethylene to butene- I . Hydrocarbon Processing. N ov ember 1984. p. 1 1 8 Morgan, A.J. ( 1 988). The qualitative behaviour of dynamic physical systems. Wolfson Col lege. dissertation submitted for the degree of Doctor of Philosophy in the University of Cambridge. Penalva, J.M., L. Coudouneau, L. Leyval and J. Montmain ( 1 99 1 ) Diapason : Un systeme d'Aide a Ia supervision. 1 1 e m e J o u r n e e s Internationales sur Jes Systemes Experts . Avignon 91. Systemes experts de seconde i:eneration. Vol. 2. p 41-52

APPENDIX : Excerpt of the knowledge-base concerning the diagnosis In GENESIA2 software language

In the rules, the terms in brackets are the variables on which the unification mechanism or "pattern matching" will operate. The sign ' (quotes) refers to the status of the object or triplets follows. The sign: (colon) followed by a variable declaration indicates the creation of a new variable which contains the value of the corresponding instantiation. Examples :

( E ) ' =DOMI NANT (V) EVOLUTION

NOT OBSERVED

sets the value DOM INANT to the status of the variable (E) (EV2 ) ' NOT_ OBSERVED tests if the status of the triplet EVOLUTION ( EV2 ) is

(V) EVOLUTION ( EV2 ) (V) EVOLUTION ( EV2 )

' NOT OBSERVED : ( c l declares that the variable (C) is equivalent to the triplet

The remaining aspects of the syntax can be understood without further more information.

Examples of GREATER THAN GREATER-THAN LESS THAN LESS-THAN EQUAL TO EQUAL::::To

declaration of OPPOSED TO OPPOSED-TO OPPOSED::::To OPPOSED TO OPPOSED-TO OPPOSED::::To

the oppositions LESS THAN EQUAL TO GREATER_THAN EQUAL TO GREATER THAN LESS THAN

AUTOMATIC OPPOSED TO MANUAL OPPOSED-TO

MANUAL AUTOMATIC

INCREASES OPPOSED TO DECREASES OPPOSED-TO

DECREASES INCREASES

(Facts base)

Examples of declarations of causality (facts base) (B TRC300 IN Sl) IMPLIES (TEMPERATURE LESS THAN EQUILIBRIUM VALUE) (B-TRC300 IN Sl) IMPLIES (FEED FLOW RATE INCREASE TREND) -(B-TRC300 IN Sl) IMPLIES (FEED-FLOW-RATE LESS THAN EQUILIBRIUM VALUE) (B::::TRC300 IN Sl) IMPLIES (WATER_FLOW_RATE INCREASE TREND) -

(B TRC300 IN S2) IMPLIES (TEMPERATURE LESS THAN EQUILIBRIUM VALUE) (B-TRC300 IN S2) IMPLIES (PRESSION INCREASE TREND) -(B-TRC300 IN S2) IMPLIES (PRESSION GREATER THAN EQUILIBRIUM VALUE) (B-TRC300 IN S2) IMPLIES (WATER FLOW RATE INCREASE TREND) -(B::::TRC300 IN S2) IMPLIES (WATER::::FLOW::::RATE GREATER_THAN EQUILIBRIUM_VALUE)

Excerpt of the rule base : the core of the detection

This rule screens dominant events when all their consequences have been observed RULE DOMINANT-EVENT-DEIERMINATION IF (E) ' <> ELIMINATED

(E) ' <> DOMINANT THERE EXISTS NOT OBSERVED CONSEQUENCES OF (E) ' NON-EXISTENT THERE::::EXISTS OBSERVED_CONSEQUENCES_OF (El

THEN (E) ' -DOMINANT

The following two rules generate the opposite consequences of dominant events. Those opposite consequences will be used to screen of masked events.

RULE DOMINANT-EVENT-IMPLICATIONS-1 IF (E) IMPLIES ( (V) (EV) TREND)

(V) ( EVl ) SHORT TERM TREND (EVl) <> CONSTANT -

THEN

(EVl ) OPPOSED TO (EV2) (V) (EV2) TREND ' NOT OBSERVED ; (C) (E) ' =DOMINANT -

THERE_EXISTS A_DOMINANT_EVENT_WHICH_IMPLIES (C)

RULE DOMINANT-EVENT-IMPLICATIONS-2 IF (E) IMPLIES ( (V) (P ) EQUILIBRIUM VALUE)

(V) POSITION (Pl) -(Pl ) <> EQUAL (Pl) OPPOSED TO (P2) (V) (P2) EQUILIBRIUM VALUE ' NOT_OBSERVED : (C) (E) ' -DOMINANT -

THEN THERE_EXISTS A_DOMINANT_EVENT_WHICH_IMPLIES (C)

This rule screens masked events RULE MASKED-EVENT-DETERMINATION IF (E) IMPLIES (NC)

(NC) ' =NOT OBSERVED THERE EXISTS A DOMINANT EVENT WHICH IMPLIES ( (NC) ' NOT_OBSERVED) THERE::::EXISTS AN_OBSERVED_CONSEQUENCE_OF (E)

THEN (E) ' = MASKED

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Copyright © IF AC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

REACTIVE PROCESS CONTROL USING A BLACKBOARD ARCHITECTUREl

A. Vliia* and J.M. Domfnguez**

•Dpt. ofTelemaJic Systems Engineering, Technical University of Madrid, C!Ciudad Universitaria sin, 28040 Madrid, Spain

••Dpt. of Electronics and Systems, Universidade da Coruiia, Castro de Elvina, 76, 15071 A Coruiia, Spain

Abstract

A software architecture to engineer complex process control applications must combine into the same paradigm efficient reactive and real-time functionalities and mechanisms to capture dynamic time­pressured intelligent behaviors, and must provide convenient high level tools to free the programmer from having to think at an unappropriate level of detail. We implement such characteristics into a blackboard framework that builds the basic abstract elements of reactive behavior and the blackboard computational model on top of low level real-time operating system functions. Under this approach, the engineer gets a powerful and flexible high level medium to map a complex system design that requires artificial intelligence techniques, like intelligent monitoring, and reactive planning and execution, with fully support for real-time programming. The paper also reviews other alternatives which have been explored in the past recent years for implementing complex reactive planning and execution systems.

1. INTRODUCTION

Many physical device control systems work under rigid

temporal constraints between the time when environmental

events occur and the time when control systems effectively

respond to those events. For instance, when an obstacle

appears in the path of an autonomous vehicle, the vehicle

control system must react to avoid a collision by changing the

followed path within some time interval. Other temporal

constraints are more flexible, like deadlines pointing out the

beginning of a monotonic degradation of the system under

control. An example for such a deadline is a situation when a

failure occurs in a communications network. This kind of

failure can usually be assumed during a short period of time;

after such period expires the network performance starts to

deteriorate and can eventually produce a complete chaos in the

communication system. In these situations, the real-time

system has to optimize the physical system global performance

by continuously balance the quality and the speed of possible

control actions. Finally, a third class of deadlines can imply

coordination and synchronization constraints when performing

actions and plans.

Temporal constraints in the behavior of physical devices

determine temporal constraints in the computer-based system

that implements the physical device control. In such a system,

it is not sufficient to execute all the required control tasks in all

possible situations. In addition, the behavioral temporal

constraints have to be satisfied. We will call this kind of

systems reactive agents. They are sensor-actuator systems that

deal with asynchronous events, that operate with a high degree

1This research is supported by the Comisi6n lnterminist�rial de Ciencia y Tecnologia of Spain, project numbers TIC92-0267 and TAP92-1 1 16-E of the R&D National Plan. We thank B. Hayes-Roth and L. Brownston, from the Stanford University, for giving us support for developping those projects.

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of autonomy, and that positively modify the environment working under temporal stress. They are always embedded in environments which are either dynamic, or unpredictable, or both, and they can be identified by two temporal characteristics:

( I ) There is a pace of change in the environment in terms of passage of time or how fast external events happen. For this reason, any real-time controller has to accommodate its computations to confom1 to this rate of variation.

(2) The result of a particular computation may depend upon the variable time at the instance of execution of the control programs or the time taken to execute the

programs and the external actions. Time acts as a new agent variable, and time bounds, soft, hard and coordination temporal constraints, pla)' an important role in scheduling computations and external actions and in assigning resources to those computations and actions.

The t�chnolog� to build this kind of systems is rapidly changmg, mamly fostered by advances in computer arc�itecture, operating systems and artificial intelligence. Dunng the past recent years, the rapid evolution in those three areas has changed priorities in computer-based real-time control �ngineering: from focusing basically on making com?utauons faster and response times shorter, to having predictable response times, guaranteeing deadlines satisfaction and capturing more complex dynamics. Modern reactiv� agen�s engineering

. research tries ro find technological

soluu.ons �or 1mprovmg and augmenting of system's autonomy,

functionality, adaptability and intelligence when working under real-time constraints.

Our work in this area integrates standard low level Unix �echn�logy with a neat blackboard approach to the high level mtelhgent agent architecture. Since the low level topics are not

within the scope of this paper, they will be referred throughout the paper in a simplified way. A set of deterministic real-time unix platforms forms the low level layer, which offers to the high level blackboard software all functionalities defined by the Posix 1003.4 standard. The determinism is achieved by means of a set of execution facilities, such us preemptive assignment of priorities to tasks, worst-case time limits in context switching, absolute and relative timers, and other time­bounded memory management and input/output facilities.

That low level gives a solid and powerful foundation to construct an architecture for intelligence applicable in real­time control problems. Traditionally, the artificial intelligence community has put the emphasis of their work on simulating intelligent behaviors without caring enough about the engineering perspective of their work. We take into account the advances in workstations and operating systems technology to build a blackboard architecture that supports artificial intelligence techniques for intelligent monitoring, situation evaluation, planning and intelligent execution of actions and plans. We incorporate into the same software framework the following functions:

( 1 ) Symbolic modeling techniques to represent and process in real-time the information about the control system and its environment [Hewett and Hayes-Roth, 1 989; Vina and Hayes-Roth, 199 l b].

(2) Dynamic scheduling techniques, which allow the continuous adaptation of a real-time system to the changes of a dynamic environment. The adaptation is achieved by making decisions about resource assignment and task scheduling and dispatching at execution time [Hayes-Roth, 1985].

(3) Real-time functions in a blackboard context.

The paper starts reviewing other approaches which have been used in the past recent years for engineering reactive agents. Then we define a reactive control agent from the architectural point of view, by identifying its functional components. Section 4 describes the real-time blackboard architecture and the basic system execution cycle. Finally we outline the architectural principles and techniques that strengthen a blackboard solution for implementing reactive control agents.

2. RELATED WORK

In this section we analyze three different approaches in dealing with the engineering of complex reactive agents for real-time process control applications. We begin with a brief discussion about what can and can not be done within the limits of computer-based discrete control theory. Then, we move to the domain of artificial intelligence to study how planning, and the most real-time oriented reactive planning, has regarded the identification of the environmental state and the generation and execution of control plans under time pressure. Finally, we explore how actional deliberation has been treated in the AI literature, specially the characterization of a real-time computation as a problem of limited rationality, in which limits have been imposed in the availability of time to compute and execute the control plans.

2.1 Discrete control theory

Conventional discrete-control theory has addressed the real­time problem regarding the environment and the agent as black-boxes, which are modeled by transfer functions relating outputs to inputs. The calculus of a correct sample period guarantees the time constraints, the rejection of disturbances of undesirable values, and the stability of the whole system. There is a well-established straightforward methodology to

424

design these control algorithms using the theory of difference equations or the theory of finite automata [Bollinger and Duffie, 1988; Dorf, 1 986; Kuo, 1 987] .

Of special interest in dynamic environments i s the combination of feedback and feedforward control. In feedback control, the desired closed loop response is defined in terms of output­input, error-input, or output-disturbance ratios. Feedforward control provides effective elimination of undesirable response to disturbances, feeding the sensory information forward through a feedforward controller and combining it with manipulations generated by a feedback controller. In both techniques, the real-time constraints are considered to calculate the controller sample period. In a sample period the controller is supposed to sensor the environment and to execute the adequate external operations to control the environment. Thus, �he concepts of variation rate of the environment and deadlines for a particular application are implicitly considered in the design of the sample period.

Discrete-control theory has been successfully applied in a number of computer-based control systems, and is the foundation of a modern theory of control. But despite its broad used, there are some inherent limitations in this approach to be the basis of a theory of intelligent control:

Most of the applications of control theory are associated with low level primitive behaviors. The approach relies on good mathematical input-output models of the process to be controlled. When the environment under consideration is complex or requires more intelligence in the controller, to find a control algorithm can be mathematically intractable.

The only knowledge the agent has about its environment is functional. The input-output discrete functions do not incorporate structural and internal functional knowledge, which makes impossible the integration of control operations with real-time diagnosis, prediction, and long term planning.

A discrete control algorithm is rigid: there is no flexibility to change goals, to interact with operators, to adapt to new contingencies, or to be modified by the designer.

The external situation is assumed totally identified by reading the current sensory information. No further computation is needed to know about the state of the environment.

2.2 Al Reactive Planning and Control

In order to overcome this difficulties, the AI community has been trying to apply results on planning and problem solving to real-time control. It has been proved that planning is non­decidable unless the search space for possible plans is finite [Chapman, 1 985]. Thus, planning without this restriction is not applicable in real-time control problems since no upper bound can be guaranteed in the amount of time required to find a control plan.

Even assuming a finite search-space, planning is a very time consuming task, because the search space grows exponentially with the number of possible environmental situations. At the same time, classical planning commits to plan formation until a plan is found, and to plan execution once its execution has begun. Those commitments limit the agent's ability to notice new events as soon as they occur, and to replan if necessary. Although highly conditional plans which consider a number of possible external contingencies have been used, real-time control of dynamic environments usually demand the

interleaving of plan formation and plan execution in 11nkr h' conform the real-time constraints of the environment.

Reactive systems with pre-computed plans have been proposed \o gain efficiency over classical planning in finite search­spaces. In reactive planning, plan formation is merely a search process to find the appropriate pre-computed plan for the current situation. Reactivity is achieved by limiting the scope of the plan as much as the control application requires, and repeating the cycle search for plan-execute plan iteratively.

Research work has been done on data structures to represent plans, on efficient interpreters to .search for and to compute plans, and on software tools to specify plans using high level languages. Absent from this research are explicit representation of time, relations to the rate of variation of the external world and deadlines. Real-time constraints are assumed to be satisfied by using the pre-computed plans which are compiled into the structure of the machine, thereby decreasing the amount of computation required at run time.

A pre-computed plan can be understood as a declarative specification of what is a transfer function in classical discre,te control theory in which not only time is a discrete variable but lnputs and outputs as well. This approach has two clear advantages over the classical discrete control theory approach.

First, by using a declarative representation of plans, modifications and additions are easier to change than the control procedures of discrete computer-based controllers.

Secondly, because the agent usually is programmed with a number of pre-computed behaviors, one fqr each possible environmental situation and possible goal; its behavior is equivalent to the sum of behaviors of the same number of conventional discrete computer-based controllers.

But apart from these advantages, some inconveniences still remain.

The use of pre-computed plans has been shown to be adequate for low level routine operations, such as avoiding obstacles in robot motion, but they still have not been applied successfully to encode high level cognitive functions.

Further, these plans do not differentiate situation identification, plan formation and plan execution as three high level interactive tasks which define the agent behavior.

The agent is blind to the scheduling of actions; it has no idea of deferring actions until they have to be made.

- Moreover, the achievement of real-time constraints relies on the experimental calculus of how fast the pre­computed plan can be interpreted, but there is no correlation between the temporal patterns of the external world (rate of variation and deadlines) and the internal operation of the agent.

A number of architectures for reactive systems have been proposed in the last few years. A list of the most relevant and a short description of every one is summarized below.

- Spanning trees of state-space graphs and its interpreters [Nilsson, 1989; Schoppers, 1987].

- Trees of triangle tables and its interpreter [Nilsson, 1989]. - Action networks [Nilsson, 1989]. - Situated automata [Rosenschein and Kaelbling, 1986]. - Subsumption architecture [Brooks, 1985].

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- Procedural reasoning systems [Georgeff, 1987]. - RAPs and its interpreter [Firby, 1987]

Nilsson has proposed three different formalisms to represent programs of actions. All are equivalent: plans that can be represented in one of the languages can also be represented in the others. The principal difference is their interpretation algorithm.

I. Spanning trees of state-space graphs. They represent the solution path from all or pan of the states of the environment to a goal. If the spanning tree is complete, that is, all paths from all possible states for every goal, we have what Schoppers calls a universal plan.

2. Triangle-table trees. A triangle table is a representation of a solution path from one state to one goal as a NxN

trianglular array which shows in column i the effects of action i and in row i the preconditions to execute action i. The solution path plan is the action sequence a1, •.. ,aN. A

tree of triangle tables represent solution paths for all or part of the possible states of the environment.

3. Production rules. A special form of production rules is considered to construct plans: (C1 and Cp and CT => a),

where C1 is the set of preconditions to execute the action,

Cp is the logical sentence which define the purpose of the

action, and CT is the set of trigger conditions of the rule.

When the trigger conditions hold, and the preconditions of the rule are true, and it is not the case of the purpose of the rule, the action a is executed. A set of rules that share the trigger conditions can be regarded as a subplan.

The interpreters of the preceding formalisms share the following execution cycle:

1 . Find out which of the environmental states is satisfied by the current state.

2. Execute the action in the path from the current state to the goal.

3. Go to 1 .

Nevertheless, the procedure used to identify the current state varies. In the case of tree plans, the current state is identified by performing a blind sequential, a guided sequential, or a parallel testing of the tree nodes. In triangle tables the current state is identified by checking what is called the active kernel of a triangle table. Finally, when production rules are used, the current state is identified by feeding an action network, a kind of binary circuit which represents a compiled version of the production rules, with the sensory information.

The situated automata approach is based on modeling the agent as a hierarchical automaton that interacts with another automaton which represents the environment. The agent is divided into two components: the perception component, whose transfer function is the state-transition function of the automaton, and the action component, whose behavior is represented by the output function of the automaton.

Rosenschein and Kaelbling have focused their efforts in the development of software tools to specify the agent's state­transition and output functions. They include the Gapps, Ruler high level languages, and the lower level Rex language. Plans are generated at design time reducing Gapps specifications of goals to programs of actions using goal reduction rules. This reduction yields a Rex program which is equivalent to a binary circuit, pretty much like action networks, which receives as inputs a stream of sensored signals and states and outputs actions. Thus, a goal reduction rule is like a parameterized

plan which once evaluated generates a binary circuit or program that leads to the goal from a set of possible input conditions

In the subsumption architecture, the agent is built bottom up, in several layers, in such a way that each lower set of layers is fully operational. Higher layers override lower layers. Higher level of competence is considered in higher layers, and an action is always available at the lowest layer of the hierarchy. In Brooks work, declarative representation of the system's actions and the ability to reason about them is surrendered to favor procedural representation of knowledge. A similar idea of subsumption of lower intelligent behaviors to other with higher lever of cognition has been used in other systems since they were proposed.

Procedural representation of plans is also used in PRS. Georgeffs knowledge areas (KAs) define particular behaviors of the system, each one involving both the processing of sensory in,formation and the execution of effector actions. The PRS interpreter decides which KAs are applicable by checking their trigger conditions. The selection and integration of behaviors is made up by metalevel procedures represented as KAs as well, and by communication protocols among applicable behaviors.

Using the metalevel KAs, the agent is able to choose between acting or reasoning. Reasoning can be made forward from its set of beliefs or backward from its set of goals. Metareasoning introduces a higher level of intelligence that does not exist in the previous reactive architectures, since the agent is able to reason about when to act and when to refine the decisions about acting.

The PRS interpreter allows two mechanisms to avoid degradation in the agent's responsiveness and timeliness. First, the metalevel KAs can be interrupted by KAs which define external operations. Secondly, PRS checks the KAs triggering conditions using only unification, bypassing the use of time­consuming deductive checking.

Firby's RAPs (reactive action packages) are also procedures, each one defined to achieve a goal. Every RAP represents a number of partially ordered sets of subtasks to achieve a goal. These subtasks can be primitive operations or subgoals. To achieve a subgoal, another RAP has to be executed. Each RAP has three parts: the goal check, which defines the trigger conditions; the task net, which defines the various methods (solution paths) to achieve the goal, and the validity check, which is used to determine whether or not a RAP is valid in the current circumstances. The selection of RAPs for execution is done using the information about temporal deadlines and the ordering constraints placed on RAPs by the task networks.

The architecture is purely reactive because in every step the goal and validity conditions of all RAPs are checked, and the decision about which RAP to execute depends on the current monitored sensory information. Its adequacy to real-time domains is based in the assumed high speed of this reactive cycle, and the efficient search of task nets the interpretation of RAPs.

2.3 Real-time and actional deliberation

Instead of looking at plan formation (in planning systems) and pre-computed plan search (in reactive systems) as tasks that only deliver a result when their execution end, both can be regarded as computational intensive tasks which produce partial, suboptimal or uncertain plans throughout their execution. In this case, and under conditions of time pressure, the agent has to make decisions about whether or not to execute the found plans before the solution search-space has been exhaustively explored. We have called this problem

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actional deliberation.

The relationship between actional deliberation and real-time control can be stated as follows: in a control process in which there are upper time bounds to correct undesirable situations, the behavior starts to deteriorate beyond some point in time (soft deadline), and actions will be useless after some other point in time (hard deadline); the agent has to decide at which moment the immediacy in acting becomes more important than the accuracy of the control action that has been found, taking into account the previous deadlines. Actional deliberation allows the incorporation of higher levels of intelligence in controllers at the cost of spending some time doing metareasoning to decide about the scheduling of actions.

Several researchers have proposed sc:hemas to deal with this problem. Dean and Boddy [Dean and Boddy, 1988] have introduced the notion of anytime algorithms to describe the kind of inference techniques whose processes can be terminated at any time and always return a result, and their results improve in some well-behaved manner as a function of time.

Georgeff [Georgeff, 1 987] includes metalevel KAs in the procedural reasoning system (PRS) which has been described before. Although temporal constraints and knowledge for the scheduling of actions can be programmed using the metalevel KAs, PRS is a too general framework and does not offer an intuitive straightforward way to capture and to process this kind of knowledge.

Russell [Russell and Wefald, 1988] draws a theory of metareasoning that treats internal computations for making decisions about acting as actions themselves. Using probability and decision theory he proposes an empirical approach to determine the expected value of each possible computation at every point in time. The resulting scheduling policy for external actions is as follows:

1 . Delay the execution of the best-found control plan and perform the most valuable of the available computations until none of the computations have positive value.

2. Commit to the best-found plan according to the result of the computations carried out in the previous step .

The expected value o f an action (or computation) i s composed by a positive factor and a negative factor: the former is its intrinsic utility, and the later the cost derived from the passage of time. The precision of the action increases with the passage of time, and its utility degrades as time passes. Finding the optimum in this precision-utility space is the goal of the metalevel process.

The use of some sort of reasoning, usually metareasoning, to decide when actions have to be made, allows the inclusion of some rationality in the agent in scheduling actions. For real­time purposes, this possibility opens doors for a declarative representation of temporal constraints and knowledge about utilities of actions and computations. However, this intelligence is achieved by consuming time. This time has to be taken from the execution time of this control process, and that is not always possible when working under real-time constraints.

We conclude that actional deliberation is essential to achieve an acceptable degree of intelligence in the control task. However, to be able to use actional deliberation in real-time control domains two requirements must be satisfied:

! . The agent's architecture has to provide an intuitive and declarative representational mechanism to express

temporal constraints and other important knowledge for the scheduling of actions.

2. The cost of doing metareasoning has to be negligible in comparison with the length of the deadlines.

3. REQUIREMENTS FOR INTELLIGENT PROCESS CONTROL

We approach the introduction of intelligence in process control focusing on techniques for flexible management of limited resources (like time, space, memory, processors, communication links, or sensors) under time stress,' and methods for creating and continuously modify off- and on-line plans of actions to achieve the control goals. We explicitly avoid any references to learning techniques as a way to incorporate intelligence in controllers. Dynamic resource allocation and planning, when performed in real-time, are very complex knowledge intensive tasks that, just by themselves, raise formidable engineering problems.

Fig. 1 shows the basic building blocks for implementing intelligent reactive agents for process control. It is based on the vertical decomposition of the agent's functionality into two units:

1 . The situation identification task 2. The plan synthesis and execution

Both components are also horizontally decomposed into two layers following the classical multilevel model for reasoning processes. The base layer includes the approximate reasoning processes that (1) identify the situation, and (2) synthesi;re the set of actions to reach the goal from the identified situation. The metalevel layer deals with the time stress, cost and value of actions to decide first when to acquire new information in order to reduce the uncertainty about the situation of the environment, and, second, when to schedule for execution the plan which was previously generated. The proposed functional decomposition of an agent is shown in fig. 1 .

.......

Fig. I : Intelligent control agent functional decomposition

At the basic layer, the situation identification module keeps track of the history of sensored signals to decide what the possible state or set of states of the environment is more possible. This module can range from a complex identification process to a very simple state-situation map. It has been conceived as a computational intensive process that allows functional abstraction. It is computational intensive because the refinement and confidence in the identification monotonically increases when additional time is allocated to the computation. It has the anytime property because there is

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always some identification available; initially there is a default identification, and lately, the identification results are a refinement of the previous ones, and there is always a guess about what the possible situation of the environment is. Finally, functional abstraction is achieved by means of decisions about taking or not the discretionary available sensory operations, hence hiding or disclosing information about the external world.

For every identified situation, a planner synthesizes a plan to reach a desirable state. The planner takes as input the current identification result (most probable situation) and yields the set of effector actions to execute.

The metalevel (see also fig. 1) is also divided into two actional deliberation functions: the control for executing new sensory actions, and the control for plan execution. Both modules implement the agent's intelligence at run time.

4. PROCESS CONTROL IN A REAL-TIME BLACKBOARD FRAMEWORK

Agents which have been built using the architecture described above, can be aware of the dynamic state of its operating environment, and can react to changes in each state by managing its resources, planning and acting in a timely manner. A software environment based on the blackboard paradigm offers an excellent framework for building that kind of intelligence. Fig. 2 shows the basic structure of our blackboard framework.

Fig. 2: High level real-time blackboard architecture

It has conventional blackboard systems features [Hayes-Roth, 1985; Engelmore and Morgan, 1988], but it also includes two important features that make the software applicable in real engineering scenarios: the concurrency of execution tasks, and the blackboard architecture integration with low level deterministic execution.

This architecture includes concurrent systems for cogmuve activities and for different modalities of perception and action. These systems communicate by means of a communication interface. The information interchange is implemented throughout input output bounded buffers, in which a best-first

strategy is used for retrieving information and a worst-first

strategy is used to discard information when an overflow occurs. The system inputs environmental signals into the monitoring buffers throughout the perception subsystem. This subsystem selectively filters and interprets the monitored information using the active strategies and heuristics in the cognitive subsystem. The results are stored in blackboards which are accessible by the cognitive subsystem.

The cognitive subsystem reads the monitored values in its input buffers and incorporates these data to the knowledge base. Then it executes processes for identifying the situation and determine the adequate plan to be executed. Finally, it communicates the decisions about how to act to the percepcion and action subsystems. Each one of these subsystems reads the description of action to be performed in their input buffers, controls the execution of actuators and sensors using performance parameters which have been previously determined by the cognitive subsystem, and returns info1mation about the execution of plans.

This architecture has been built by implementing an execution cycle which is based on a three steps iteration:

1. Interpretation Concurrent dispatching and execution of processes which have been scheduled for execution.

2 Ag;enda Mana�ement The agenda manager incorporates the new external synchronous and asynchronous events plus the internal cognitive events to update the agenda of processes. It arranges the set of processes into three classes : triggered and suspended, triggered and executable and obviated.

3. Task Prommming; Once the new agenda of active executable processes has been created, the rater applies the current control plan and the scheduler compares temporal constraints of processes against the performance parameters of available executors to decide what to execute next.

There are several properties that stand out this software architecture for engineering reactive controllers against others:

a) The inte�ration of conventional and co�nitive tasks into the same execution model.

A knowledge source (or program) is an object that includes the following attributes:

(def-ks :level :links :trigger-conditions :preconditions :obviation-conditions :context :action-variables :action

<ks name> <System-name> ((implements <Skillname>)) (<form>*) (<form>*) (<form>*) (<context>) (<action-variable>) (<action>*)

The trigger conditions are always based on a single event. All conditions should be chained to the event. The trigger event specifies a trigger object, and the trigger object some attributes or linked objects which match the trigger condition. All trigger conditions must be simultaneously true at time of triggering and must have no side effects. These constraints on the triggering conditions give the architecture an event-driven flavor, with a very efficient evaluation of responses to new events. That characteristic makes the software very reactive.

The preconditions are always based on state, not on event. They are evaluated repeatedly, at settable intervals, after triggering. All preconditions must simultaneously be true if

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a process is to execute. They are mainly used to implement synchronization and coordination constraints, to indicate the suspension of a process in execution or the dispatching or a suspended process.

The obviation conditions determine when a process must be definitely withdrawn. They are also evaluated repeatedly, at settable intervals, after triggering.

Context variables are used to generate multiple processes when a knowledge source is triggered, and action variables determine variable bindings to be used during the execution of actions.

Finally, actions take the form of a list of at least one rule. Rules executed conditionally in order written, and do not return values. Their syntax is

<rule> ::= (<number> <lhs> <rhs>) <lhs> : == <form> <rhS> : := <execute-rhs>

The number is a monotonically increasing identifier. The left hand side part of the rule (<lhs>) is a form use as a Boolean guard that when true indicates that the right hand side of the rule must be executed. The right hand side of the rule can be a piece of code, a direct operation on a blackboard or any other thing the programmer wishes to define.

Within this framework it is straightforward to program in terms of blackboard operations, but, at the same time, it is totally direct to implement a rule-based process (by using a knowledge source as complete rule-based knowledge base) or a conventional imperative process (eliminating the left hand side of an action and written the code on the right hand side of the action).

The potential use of this representation schema is wide enough to accommodate all sorts of programming. At the same time, the flexibility of the execution environment makes possible to fit different kinds of information processing paradigms into a common blackboard framework. This will be the topic of the next point.

b) The use of up to date technolo�y to represent information in an object oriented fashion.

Objects are the primitive data type in our system. They are represented as symbols that include information to address the object: the blackboard and the level in the blackboard where the object is located. Objects are the building blocks of a semantic network, where objects are the nodes, they can have properties or attributes, and links implement relationships among them. Links "is-a" and "instance" determine inheritance of other links and attributes among nodes in the semantic network.

The object structure is as follows :

(def-object :level :attributes :links

<Short-name> <level-long-name> <attribute-list> <link-list>)

All information in our system is represented in terms of objects organized in blackboards. Events, rules, knowledge sources, processes, strategies, heuristics, agenda items, all are objects stored in different blackboards. Manipulation of objects is the result of all processes in the system. Objects can be created, modified, deleted and accessed to read their attributes and links by primitive blackboard operations.

c) The combination of a1�orithmic and heuristic control of action execution and resource mana�ement to achieve adaptive intelli�ent behaviors.

When a set of knowledge sources that can solve the application problem has been programmed, it is time to write control knowledge sources to generate a control plan. A control plan is a declarative representation of desirable problem-solving behavior that is generated and updated at runtime by control knowledge sources. Control knowledge sources have the same format as task problem-solving knowledge sources and compete with them for resources.

A Control Plan is made up of two levels of information. At the upper level there is a set of strategies. A strategy is a partial control plan which applies in a certain situation. They are implemented by a set of rating functions, that can have a neat algorithmic foundation or a "scruffy" heuristic nature. Depending on the kind of functions that the programmer decides to use the control can be implemented

either for working with a fixed priorities rating process for scheduling tasks, or for working under an heuristic-based flexible dynamic scheduling policy, or a combination of both techniques.

d) The support for real-time proerammin�.

The low level deterministic unix platform supplies the high level with enough functions to support real-time programming. Besides time bounded primitive context switching operations, the unix real-time platform offers standard system calls to perform the following functions:

- Absolute and interval-based timers. - Absolute control for resource allocation to tasks. - Preemptive scheduling of tasks. - Support for interprocess communications in real-time.

5. CONCLUSIONS

Digital computer systems are being used as computational

components in physical device control for a growing spectrum

of applications. These applications range from the control of

simple devices implemented as embedded systems, to the

control of large, complex systems such as an automatic

manufacturing facility, or a telecommunications network

(workstation-based systems). A physical device control system

must be aware of the dynamic state of its operating

environment, and it must react to changes in that state by

planning and acting in a timely manner. We call these systems

reactive agents. To implement these agents for process control

we propose a well engineered real-time blackboard framework

that combines the qualities of reactivity and adaptability of

conventional blackboard architectures with a well founded

executing environment that takes advantage of the emerging technologies in real-time unix operating systems.

6. FURTHER WORK

Further work is needed to exploit all the potential benefits of our approach to the engineering of reactive agents. We are focusing our effort on two main areas: the development of a toolkit for temporal analysis and evaluation of tasks and plans, and the mapping of our software to distributed computing environments.

To guarantee correct responses it is important to validate the

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control system temporal behavior. To reach this goal, we are developing a toolkit to help the engineers to evaluate and to analyze the deadline satisfaction of applications. This toolkit will provide tools to accomplish:

( 1 ) an exhaustive off-line simulation of the dynamic behavior of applications, and

(2) the generation of the temporal information to include in task blackboards that has to be used by planners and schedulers at execution time. Examples of such informations are worst-case execution times, task resource requirements, deadlines, and performance measurements.

A second topic for research in order to refine our architecture is to deal with cooperation and communication problems in distributed computing environments. Complex process control often requires several computing units, some of them embedded, some on workstations, most of the time working at different levels of task automation. All those computers have to communicate and cooperate. We are extending our architecture to incorporate facilities for working with these distributed systems into our real-time blackboard framework.

7. REFERENCES

D. Ash, A. Vina & B: Hayes-Roth [1990], "Action-Oriented Diagnosis under Real-time Constraints", Stanford University, Tech. Memo.KSL-90-39.

J.G. Bollinger & N.A. Duffie [1988], Compu1er Conlrol of Machines and

Processes, Addison Wesley, Reading, MA.

F. Armand, M. Oien, M. Guillemont & P. Leonard [1986], "Towards a Distributed UNIX System - The Chorus Approach", en Proceedings of the

EUUG'86 Conference. Machester, UK.

R.A. Brooks [1985], "A Robust Layered Control System for a Mobile Robot", Artificial Intelligence Laboratory, MIT, Technical Report 864.

D. Chapman [1985], "Planning for Conjunctive Goals". Artificial Intelligence Laboratory, MIT, Technical Report 802.

T. Dean & M. Boddy [1988], "An analysis of Time-dependent Planning", in Proceedings of the Seventh National Conference on Artificial

Intelligence, Minneapolis, MN, Morgan Kaufmann, San Mateo, CA, 49-54.

R. Dorf [1986], Modern Control Systems, Addison Wesley, Reading, MA.

R. Engelmore & A. Morgan (eds.) [1988]. Blackboard Systems, Addison Wesley, London, UK.

R. Firby [1987], "An Investigation into Reactive Planning in Complex Domains", en Proceedings of the Tenth International Joint Conference on

Artificial Intelligence, Milan, Italia, Morgan Kaufman, San Mateo, CA, 202-206.

M. Georgeff [1987], "En Embedded Real-time Reasoning System", Nasa Ames Al Research Forum.

B. Hayes-Roth [1985], "A Blackboard Architecture for Control", Artificial Intelligence 26, 251-321.

B. Hayes-Roth, R. Washington, D. Ash, A. Collinot, A. Vina y A. Seiver, "Guardian: A Prototipe Intelligent Agent for Intensive-Care Monitoring". Artificial Intelligence in Medicine, vol. 4, no. 2, 1992 (en imprenta).

R. Hewett & B. Hayes-Roth [ 1989], "Representing and Reasoning about Physical Systems using Generic Models" en Formal Aspects of Semantic

Networks, J. Sowa, S. Shapiro y R. Brachman (eds.).

L. Kaelbling [1986], "An Architecture for Intelligent Reactive Systems", en Proceedings of the AAA! Workshop on Planning and Reasoning about Ac1ion.

B.C. Kuo [ 1987], Automatic Control Systems, Prentice-Hall, Englewood Cliffs, NJ.

N. Nilsson [1989], "Teleo-reactive agents", Stanford University, Computer Science Dpt., Internal Technical Report.

S. Rosenschein & L. Kaelbling [1986], "The Synthesis of Digital Machines with Provable Epistemic Properties", en Proceedings of the

Conference on Theoretical Aspects of Reasoning abom Knowledge, J. Halpern (ed.), Morgan Kaufman, San Mateo, CA, 83-98.

S. Russell & E. Wefald [1988], "Principles of Metareasoning", en Proceedings of the First International Conference on Principles of

Knowledge Representation and Reasoning, Toronto, Canada, Morgan Kaufman, San Mateo, CA, 400-4 1 1 .

J . Stankovic & K . Ramamritham [1991], "The Spring Kernel: A New Paradigm for Real-time Systems", IEEE Software, vol. 8, no. 3, pp. 62-72.

M. Schoppers [1987], "Universal Plans for Reactive Robots in Unpredictable Environments'', en Proceedings of the Tenth International

Joint Conference on Artificial Intelligence, Milan, Italia, Morgan Kaufmann, San Mateo, CA, 1039-1046.

A. Tanembaum, R. van Renesse & H. van Staveren [1989], "A retrospective Hnd Evaluation of the Amoeba Distributed Operating System'', Vrije University, Technical Report, The Nederlands.

A. Vina, D. Ash & B. Hayes-Roth [199!a] "Engineering Reactive Agents for Real-time Control", Stanford University Technical Repon KSL-91-43. (Also published in the Proceedings of the I Ith International Conference on Expert Systems & Their Applications, General Conference: Tools, Techniques & Methods, pp. 439-454. Avignon, France).

A. Vina & B. Hayes-Roth [199lb] "Knowledge-based Real-Time Control: The Use of Abstraction to Satisfy Deadlines", Stanford University Technical Report KSL-91-71 .

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Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

PATTERN RECOGNITION FOR BIOPROCESS CONTROL

B. Sonnleitner and G. Locher

Institute for Biotechnology, ETH Ziirich Honggerberg, CH 8093 Ziirich, Switzerland

Abstract Pattern recognition is used to identify a distinct state of a biopro­cess; most interesting is the recognition of physiological states. This method is an excellent means for relevant bioprocess monitoring and the respective knowledge can be effectively used for decision making. The multitude and multiplicity of data is treated as a 3 dimensional picture of a process and compared to prototypes, i.e. pictures from, for instance, a reference process. This method was successfully used to detect unique phases in bioprocesses, to initiate certain process operation activities automatically, or to detect faults on line with little time delay.

Keywords Pattern recognition; Automation; Bioprocesses; Decision making

INTRODUCTION

Control of technical processes - and among these, of course, also bioprocesses - requires reliable monitoring of the respective process. Although physical variables are significant de­terminants, i.e., of great importance for the be­havior of a bioprocess they are not of greatest interest when evaluating biotechnological pro­cesses. Simply, physical and a few chemical variables can be easily and reliably measured in strictly monoseptic processes, but they do not reflect the physiological state of a biosystem satisfactorily. For instance, temperature, pH, pressure and the gases' partial pressures may well be around the desired set points but, in spite, the culture may be totally nonproductive. This is only one good reason for evaluating even qualitative attributes of a biosystem such as type of growth behavior, transition from one physiological state to another, or bioregulatory behavior. Unfortunately, there are neither direct measures for these attributes nor are appropri­ate sensors available. The characteristic proper­ties of a certain physiological state of a bio­system are quite complex and not sufficiently describe by a few isolated values; they are cer­tainly also determined by the 'history' of tem­poral development, e.g., the fate of the precul­ture (inoculum) is likely to have a decisive in­fluence on the main culture.

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PATfERNS

One among several reasonable methodologies for evaluation of a process' (physiological) state and a sound basis for decision making is pat­tern recognition. The patterns are derived, i.e. created, from a series of several concomitant direct measures or estimates of state variables. The link between the time courses of more (than only one single) variables provides more information than the sum of the same number of isolated trajectories does because the interre­lations of the individual state variables are ex­ploited. The patterns need not describe the en­tire process duration (full length trajectories), they can code individual fractions (e.g. typical phases) of a process. However, patterns must first be created from raw data because (at least) 2 types are required to be available for recog­nition, describing 1 . : the prototype(s) or reference(s) and 2.: the actual process.

Monitoring of biotechnological processes com­prises the analysis of a multitude and multiplici­ty of data: every sensor, intelligent analytical subsystem or manual (off line) analysis delivers a scaled variable either continuously or discon­tinuously. This results in a 3 dimensional data array. Such arrays are most probably evenly spaced if only continuous on line signals are exploited but they are unevenly spaced, if on

line and off line signals or signals from differ­ent types of analytical equipment are com­bined. However, all 3 dimensions must be used for data evaluation (i.e. pattern creation) in or­der to avoid loss of significant information. We have considered such 30 arrays as patterns which can be analyzed manually, i.e. graphical­ly/optically, or by algorithms derived, e.g., from image or picture analysis.

Prototype patterns can be easily created, espe­cial�y for routine bioprocesses or routine op­erations. The prototype patterns can be either

unfiltered experimental raw data or a mean calculated over a multitude of in­dividual experiments (but identical ones such as industrial productions) or a set of model simulated time courses or even generously hand drawn time trajecto­ries (e.g. for routine operations like pulses or shifts).

In the simplest way, a pattern is organized as a 2 dimensional matrix in which each single trajec­tory occupies a row and all the row vectors span the same time window (this resembles most ob­�iouslr the straigh� forward way of storing dig-1tzed images or pictures). This solution, how­ever, turned out to be too simple for several practical and numerical reasons. We, therefore, prefer to either normalize (length of vector = 1 ) or scale (into the window [O 1]) the individual data vectors equally in both prototype and ac­tual pattern generation. Further, Fourier trans­formation (from time into frequency domain) renders the patterns invariant to time shifts and is, therefore, recommended. Remark: a second Fourier analysis with respect to the sensor-di­mension was expected to introduce invariance towards bias on several sensors (especially those that cannot be calibrated against absolute stan­dards; e.g. optical density or culture fluores­cence) but did not improve recognition and is, therefore, no longer applied.

EXPERIMENTAL EXPERIENCE

According to experience extending over some years, a typical pattern should be created from not less than 5 independently generated and most likely different signals, and it should span a time window of not less than I h - for in­stance in the case of yeast cultures, but the latter value may vary considerably with the biosystem in use. Following these rules of thumb, we f�und that the association of actual patterns with a prototype pattern (usually something like 1 �mong a dozen) was rapid and mostly also umque; the latter fact, however, depends greatly on a reasonable choice of prototypes. We found the scalar product a useful measure for the quality of match between 2 patterns (actual and

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prototype pattern; each matrix converted to a row vector and multiplied).

1. PHASE DETECTION

Pattern recognition allows to associate a pattern, which is created from some recent but limited time interval of the actual data set, with a most similar prototype pattern, which encodes a cer­tain phase of such a culture (e.g. exponential growth, declining growth, product formation, sporulation, lysis). This gives a good indication about the actual phase or state of a bioprocess.

Since the algorithm in use 'must' find an asso­ciation, independent of how good or bad it may be, it is wise to include more prototype patterns in the reference set than those representing the expected culture phases (e g Fig l ) ; there should some patterns be added that describe typical misdevelopments of a culture such as infection, degeneration of population, and the like. Of course, it is not easy to foresee all possible misdevelopments but the experience with unlucky cultivations - and they happen to exist everywhere - is of great help in these cases, provided data are evaluated and not just discarded. A similar extension, however, in the field of modelling, was recently reported by King et al. (199 1 ).

Generally, we observed good recognition of in­dividual phases whenever the actual pattern (encoding a culture) did not overlap 2 adjoint reference patterns in similar fractions (around 50:50). Even though, the association toggled between those 2 references exclusively and in­dicated in this way the transition of the culture from one to the next prototype phase reliably. There were only very few cases where an unrea­sonable (=mis)match with an obviously distant phase was calculated. The reason was mostly an improper choice of phase duration, i.e. too short. However, this pitfall is very likely to oc­cur because the longer (in time) the patterns are the greater is the delay of the results (i.e. the di­vergence from real time).

2. DECISION MAKING

As indicated, it is easy to check the 'correct' se­quence of occurrence of patterns (i.e. cultiva­tion phases). As a matter of fact, this check widens the basis for and improves reliability of decision making. The only necessary extension to the above said is the creation of a vector filled with the most probable membership (to a distinct phase during the time course of a culti­vation). If the sequence of the elements in this vector does not diverge from the expected se­quence (qualitatively and/or quantitatively) then is the conclusion most likely that the most re­cent association is also most probable. This

additional information improves safety/proba­bility of the correctness of decisions based on the occurrence(s) of (a) certain event(s). In our lab, we have successfully exploited this facet to initiate step sequences like harvest, refill, feed, next_pulse etc. For instance, more than 200 repetitive batch cultivations could be performed on one single reactor unit within a man-year without any operational fault caused by mal­function of this decision making algorithm (remark: faults occurred but were due to human errors or malfunctions of mechanical/electrical components of the equipment).

3. FAULT DETECTION Faults can be detected and different possible alternatives can be discriminated if - besides phase detection - a statistical criterion is evalu-

ated to quantify the degree of similarity be­tween actual and prototype patterns. A 'faulty' variable can be positively identified if this cri­terion can be improved by omitting one or an­other variable from pattern generation. This allows to recognize malfunctions of sensors or of the biological system (e.g. infection) as well.

REFERENCES

King R (199 1 ) On-line supervision and control of bioreactors. In: B iochemical engineering -Stuttgart, 69-77, Reuss M, Chmiel H, Gilles ED, Knackmuss HJ (eds), G Fischer, Stuttgart, New York

Locher G, Sonnleitner B, Fiechter A (1990) Pat­tern recognition: a useful tool in technological processes. Bioproc Eng 5 : 1 81 - 1 87

reference pattern

actually measured pattern

tbne (150 min)

Fig 1 : Typical pattern of a synchronous culture of Saccharomyces cerevisiae at a diluti­on rate of 0. 13 h- 1 (top) and fractional pattern (i.e. phase) on bottom. Only signals of non-invasive sensors are shown.

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Copyright @ IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

ENHANCING FERMENTATION DEVELOPMENT PROCEDURES VIA ARTIFICIAL NEURAL NETWORKS

J. Glassey•, G.A. Montague•, A.C. Ward** and B. Kara•••

*Depart!Mnt of Chemical and Process Engineering, Newcastle University, UK ••Depart!Mnt of Microbiology, Newcastle University, UK

•••!Cl PharmaceuJicals, UK

ABSTRACT

This paper describes how artificial neural networks can aid in recombinant fermentation process development. Two specific areas are addressed. Firstly, neural networks are used to increase the quality of information available during the course of a run. Available on-line

measurements, together with a network model, are used to estimate key bioprocess parameters. Secondly, neural networks are used to formulate process models to aid in the specification of fermentation operational procedures. The ability to capture non-linear bioprocess characteristics is particularly significant and is an enhancement to existing experimental design procedures. Both the off-line experimental design and on­line parameter estimation techniques can aid in the progression from shake flask scale to large pilot scale operation.

KEYWORDS

Artificial Neural Networks; Experimental Design; Recombinant Fermentation

INTRODUCTION

The development of a process for recombinant protein production can involve several time consuming and costly stages. A number of key decisions in project development can be identified, such as the selection of a suitable host and plasmid combination, as well as specification of operational conditions to achieve acceptable levels of recombinant protein. Whilst this may appear an onerous task, the choice of host microorganism is limited by its characteristics, in that it must be able to

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synthesise the desired protein. Furthermore, the growth and genetics of the organism must be understood in sufficient depth so that a reasonable level of protein production can be achieved. In these studies Escherichia coli has been chosen as the basis for production. The fermentation development problem therefore reduces down to the specification of the strain of E.coli and the fermentation operational

procedures.

Currently fermentation development proceeds via a structured series of experiments specified by fermentation scientists. Considerable technical expertise is necessary in order to evaluate results and postulate improvements in operation. Improvements in fermenter operation are hindered by the poor level of on-line information. Bioprocess state can only be ascertained from off-line sampling. The delay in sample analysis essentially precludes the use of off-line samples for current batch modification, the off-line information can serve to adjust operational procedures for future experiments. As a consequence of the existing experimental design scheme many experiments must be undertaken, therefore this stage is a 'bottle-neck' in progression from shake flask to 'large scale' production. One means of overcoming the problem is to resort to experimental design procedures in order to reduce the number of experiments which must be carried out. 'Standard' statistical experimental design procedures are however limited in that process linearity assumptions are made. Since the fermentation process is far from linear, these

techniques are not ideally suited.

Rather than utilise a linear approximation, a more effective means of experimental design

would be to quantify knowledge gained from experimental trials in the fonn of a more

realistic process description. With an accurate bioprocess model available not only would conventional experimental design procedures be enhanced, but the possibility of on-line process

variable estimation becomes feasible. In determining a process model a wide range of approaches can be taken, however, the complexity of process dynamics limits the applicability of many techniques. An essential prerequisite is that the model must be capable of describing system non-linearities and interactions. The 'conventional' approach is to formulate a model from a basic system

understanding (structured model). There are a number of structured models describing recombinant E. coli fermentation behaviour,

each one emphasizing slightly different characteristics of the process (Lee and Bailey, 1984; Betenbaugh and Dhurjarti, 1990). These

strain I plasmid specific models have taken

many man months to construct. Such time­scales obviously preclude their use for experimental design. A more rapid method of quantitatively describing process non-linearities is essential and one means of doing so is to exploit artificial neural network (ANN) technology. The power of the ANN approach is that it is generic in structure and it possesses the ability to 'learn' complex non-linear relationships with limited a priori knowledge

about the process structure.

Neural networks are composed of highly interconnected, simple processing units which

are inspired by neural processes observed in the human brain. Successful applications can be found in areas such as: process engineering;

design and simulation; process control and

estimation; pattern recognition; fault detection

and image analysis. A common theme of these

applications is the ability of the ANN to learn complex non-linear input - output relationships. This ability is highly appealing for bioprocess application.

FEEDFORWARD ARTIFICIAL NEURAL NETWORKS

The architecture of a typical feedforward artificial neural network (FANN) consists of

nodes arranged in layers. There is always an

input and an output layer and between these are

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hidden layers. The number of neurons in these layers depends on the number of process factors

being considered and are detennined through an

engineering appreciation of the problem. The

number of hidden layers and neurons in each of them may vary and must be pre-specified prior to network training. Furthennore it is necessary

to specify the processing element activation function and the method of determining the network weights - the learning law.

Processing Element Activation Function

The neurons in the input layer simply introduce,

via the interconnections, the scaled inputs to the

hidden layers. Following the procedures of

linear regression, raw data scaling is carried out (usually over the range 0- 1 ) in order to improve

the integrity of weight determination. The nodes in hidden and output layer perform two tasks. Firstly they perform a summation of weighted

inputs to the neuron, including addition of a bias in order to shift the space of non-linearity. The

weighted sum is then passed through a processing element activation function. A number of different activation functions (also referred to as threshold, squashing or transfer functions) have been used in the literature. Cybenko (1989) has shown that any differentiable continuous function can be employed. The most widely applied non-linear

function is given by the relationship:

Neuron output = 1/(1 + exp(-0)) (1)

where e i s the sum o f the neuron inputs.

ANN Architecture

The problem of selecting the 'optimum' network

architecture for a given data set is difficult. A

number of researchers have tried to show that any continuous function defined on an n­

dimensional space can be unifonnly approximated by a single hidden layer network (eg. Hornik et al, 1989). However, other authors claim that two hidden layers are necessary (eg. Cybenko, 1989). Clearly, the number of neurons and hidden layers must be sufficient to perfonn the required task. However, if too many nodes and layers are used, the network can become 'brittle', i.e. capable of fitting the training data very well but incapable of generalising for

unknown inputs. Moreover, chosing an

excessively large number of neurons may significantly increase the required learning time.

In the absence of firm guidelines for topology specification, the most straightforward procedure is to start from a 'small' network and increase the number of neurons I layers until an acceptable model is attained. Acceptability is assessed on the quality of network fit to data other than that used for training. An alternative philosophy has also been considered in these studies. Several researches have shown the ability of genetic algorithms to cope with a large search spaces. This ability makes them an interesting tool for searching for 'optimal' neural network architectures. A genetic algorithm is an iterative procedure which maintains a constant­size 'population' of possible problem solutions. During each iteration step, called a generation, the structures in the current population are evaluated, and, on the basis of those evaluations, a new population of solutions is formed by means of idealized recombination operators. Again, the evaluation was based on the performance of ANN model on test rather than training data. Although some encouraging results were obtained using this method, further experiments are necessary in order to clarify the efficiency.

Algorithm for Network Training (Weight Selection)

Once the ANN topology has been specified, the network is 'trained' on process data. There are a variety of training methods, for example supervised, graded and unsupervised (Hecht­Nielsen, 1990). During supervised training, a set of past input-output data is presented to the network in order to determine appropriate values for the weights (including the bias terms) associated with each interconnection. The data is propagated forward through the network to produce an output which is compared with the corresponding output in the data set, hence generating an error. This error is minimised by changing the weights and may involve many passes through the training data set. When no further decrease in error is achieved, the weights are retained as the parameters of the ANN model.

A numerical search technique is applied to determine the weights as this task is not amenable to analytical solution. Clearly,

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determining the weights of the network can be regarded as a non-linear optimisation problem where the objective is to minimise the training error. In this contribution the objective function has been minimised using the Chemotaxis algorithm (Bremermann and Anderson, 1989). This algorithm adjusts weights by adding Gaussian distributed random values to old weights. The new weights are accepted if the resulting error is smaller than that recorded using the previous set of weights. This procedure is repeated until the reduction in error is negligible. During the minimisation the variance of the increments may be adjusted to assist network convergence.

DYNAMIC NEURAL NETWORKS

The ANNs discussed above merely perform a non-linear mapping between inputs and outputs. Dynamics are not inherently included within their structures. Although, dynamics can be introduced in a rather inelegant and inefficient manner by making use of time histories of the data, a rather more attractive approach is inspired by analogies with biological systems. It has been suggested (Terzuolo et al, 1969) that a first-order low-pass filter may provide the appropriate representation of the dynamic characteristics. Using a discrete representation, these filters transform the neuron output in following manner:

yf(t) = n yf(t- 1 ) + ( 1 -n)y(t) (2)

Suitable values of filter time constants cannot be specified a priori, and thus the problem becomes one of determining n in conjunction

with the network weights. The Chemotaxis approach to network training does not require any modification to enable incorporation of filter dynamics. The filter constants are determined in the same manner as network weights. Thus neurons in hidden layers not only sum the inputs (including the bias term) and pass the resulting sum through an activation function, but also each neuron has associated with it a dynamic first order response. Dynamic system modelling using this approach, rather than adopting a time series of inputs, results in a smaller number of parameters to be determined (Montague et al, 1992).

ON-LINE BIOPROCESS VARIABLE ESTIMATION

Measurements of biomass and product concentration using existing sensor technology are currently performed off-line in the laboratory and provide only delayed information about the fermentation. The delay is such that off-line information is of little use in on-line modification of fermentation behaviour. If, however, an estimate was available then any deviations from desired performance could be corrected promptly. This increase in the level of information would assist in experimental operation. On-line secondary measurements, such as output gas composition (giving carbon dioxide evolution rate (CER) or oxygen uptake rate (OUR)), alkali addition rate and feedrates provide a means of obtaining an estimate of biomass and product concentration. The effectiveness of such a scheme is limited by the quality of the model relating on-line to off-line measurements. If the claims regarding the modelling capabilities of ANNs are justified then on-line estimation becomes feasible.

Preliminary neural network studies considered a range of input variables. Results showed that although several possible factors could be used as inputs to the ANN, careful selection of them is required to obtain accurate estimations. Again, these conclusions are in-line with experiences in linear regression where poor choice of inputs (for example correlated input data) leads to identification problems. Carbon dioxide and oxygen concentrations in the outlet gas, as well as on-line measurements of feed addition, were shown to give the best estimates of biomass and protein estimation from the available on-line measurements. For on-line biomass estimation, a (3-3-1) network was utilised (i.e. a network with 3 input neurons, 1 hidden layer with 3 neurons and 1 output neuron) and 'trained' on process data. The training data was chosen to span the range of likely operating conditions. Several sets of fermentation data were used to assess the quality of the resulting model. Fig. 1 . shows the fit for one of the sets as an example. It can be seen that the ANN model provides good estimates of biomass from the on-line measurements. This quality of fit is also achieved on fermentations carried out under different operational conditions within the training span.

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The on-line estimation of recombinant protein concentration was initially adversely affected by the quality of off-line protein data available. Recent improvements in the method of protein measurement is now providing more reliable data. A neural network model of topology (3-3-1) using the same input data as the biomass model was trained to predict protein levels. Fig. 2. demonstrates the fit for one of the testing sets used to evaluate the neural network estimation.

In specifying biomass and protein prediction models of this form, an assumption has been made that the plasmid is stable over the time­scales of interest. This presumption is made in­light of present understanding of fermentation behaviour and is, to an extent, verified by the quality of the results.

EXPERIMENT AL DESIGN

During the process research phase under consideration the two principle stages are initial shake flask experiments, followed by fed-batch fermentations. The aim of shake flask experiments is to select the best combination of E. coli host strain and recombinant plasmid with respect to specific properties of the protein. The selected combination then undergoes a series of fermentations under different conditions in order to determine the feed, temperature and pH profiles and media composition for acceptable biomass and protein production.

One of the primary process variables to be optimised during the fermentation stage of experimental design is the feed. Here initial batch concentrations, the time of initiation of feed addition and its rate during the course of fermentation need to be specified. Although there are other process variables influencing process efficiency, eg. temperature or pH, in these studies initial attention is focused on the feed. The ANN models for experimental design were thus trained using batch medium composition, the time of continuous feed initiation and its rate during the course of fermentation to predict production levels. Once the network is trained the model can be used to perform simulations of fermentation behaviour for different experimental conditions without having to carry out the individual fermentations. Again, the training data must be selected to span

likely operating conditions to attempt to avoid

extrapolation problems.

The first stage in verifying the concept was to concentrate upon one design variable. Thus an ANN model considering only the feedrate was developed. Whilst ultimately protein concentration will be the primary process variable to optimise, these studies have demonstrated the concept of experimental design by considering biomass. The use of

biomass was due to the poor quality of protein data available initially. Improvements in measurement technique have now been made and results of the trials on protein optimisation will be presented at the Conference. Fig. 3. demonstrates the ability of this model to predict different levels of biomass for a variety of feedrates not used in model determination. Here

optl shows the results from a fed-batch fermentation. opt2 to opt5 show the predicted effects of increasing feedrate on this batch. It can be seen that final concentration of biomass is higher with increasing feedrate. However, there is a decrease in yield of biomass on substrate as feedrate increases. The ANN predicted biomass concentration profiles have proved to be consistent with the results of subsequent experiments.

The results shown in Fig. 3 have demonstrated that reasonably accurate prediction of fermentation behaviour can be made. The model was therefore expanded to include batch media composition and feed initiation time. The model can be used to predict fermentation behaviour and integrated within an optimisation scheme to maximise fermentation profit (Fig. 4).

An optimiser was utilised incorporating a profit

function accounting for production levels and costs. The optimiser determines the network inputs which will maximise the network predicted fermentation profit. Fig. 5 shows an example contour plot of the profit function against varying feedrate and feed initiation time with constant batch concentration. A distinct profit maximum can be observed for certain combinations of the input variables. Although this graph illustrates only the determination of two process conditions, in practice initial batch concentration would also be determined by the optimiser. Once the maximum profit has been attained the experiment is carried out and the network updated with these new results.

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Another iteration of the optimisation

experiment loop is then undertaken.

DISCUSSION

This paper has described how artificial neural networks can aid in recombinant fermentation process development. Two specific areas were addressed. Firstly, neural networks were used to increase the quality of information available during the course of a run. Available on-line measurements, together with a network model, were used to estimate key bioprocess parameters. Results from experimental trials confirmed the validity of the concept, however, important considerations in the use of neural networks were also highlighted. For example, in order to attain a realistic process representation it was essential for the training data to span the range of likely process operation. Furthermore, the quality of training data should be reasonable; poor training data inevitably leads to a poor model. Whilst further conclusions can be drawn as to the use of neural networks, there is a clear parallel with the principles of linear regression. Secondly, neural networks were used to formulate process models to aid in the specification of fermentations. Preliminary

studies highlighted how an optimisation routine could be integrated with a neural network to provide an experimental design tool. Experiments are now underway to verify the procedure. Here again, the need for caution in applying neural networks was highlighted. However, with appropriate training methodologies neural network based models can aid in the progression from shake flask scale to large pilot scale operation.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the support of the Dept. of Chemical and Process Engineering, University of Newcastle-upon­Tyne, ICI Pharmaceuticals and the U.K. Science and Engineering Research Council.

REFERENCES

Betenbaugh, M.J. and Dhurjati, P. (1990). A comparison of mathematical model predictions to experimental measurements for growth and recombinant protein production in induced

cultures of E.coli. Biotech. Bioeng., �. pp 124-134.

Bremermann,HJ., Anderson,R.W. (1989). An alternative to Back-Propagation: a simple rule for synaptic modification for neural net training and memory, Internal Report, Dept. of Mathematics, Univ. of California, Berkeley

Cybenko,G. (1989). Approximation by Superpositions of a Sigmoidal Function, Mathematics of Control. Signals and Systems, 2, 303-314

Hecht-Nielsen R. (1991). Neuro-computing, Addison Wesley

Hornik K., Stinchcombe M., and White H. (1989). Multilayer feedforward networks are universal approximators, Neural Networks, 2, pp 359-366

Lee, S.B. and Bailey, J.E. (1984). Genetically structured models for lac promoter - operator function in the chromosome and in multicopy plasmids: lac promoter function. Biotech. Bioeng., 2Q, pp 1372-1382

Montague, G.A., Willis, MJ., Morris, AJ. and Tham M.T. ( 1992). Dynamic modelling of industrial processes with artificial neural networks. Submitted to the J.Proc.Cont.

Terzuolo,C.A., McKeen,T.A., Poppele,R.E., Rosenthal,N.P. (1969). Impulse trains, coding and decoding, In: Systems Analysis to NeurophysioJogica} problems, (Terzuolo, Ed.) Univ. of Minnesota, Minneapolis, pp.86-91

Time

- Actual -- Estimate

Fig. 1 On-line prediction of biomass concentration

Time

- Actual - - Estimate

Fig. 2 On-line prediction of protein concentration

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.-.

.,.../ ......

........... ··

; ... :: ,-P

Time

. ........ • ... ro·········-··---·-·---•·•••

-Opt 1 ---Opt 2 ·-·Opt 3 -opt 4 ···--Opt 5

Fig. 3. Prediction of biomass profiles for varying feedrates

Model update

A y NN Model

x Experiment

Optimiser

Profit

Fig. 4 Experimental design scheme

IniL time

Fig. 5 Contour plot of fermentation profit

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

ARTIFICIAL INTELLIGENCE IN THE CONTROL OF A CLASS OF FERMENTATION PROCESSES

N.A. Jalel, F. Shui, D. Tsaptsinos, R. Tang, W. Vanichsrlratana, J.R. Leigh

Industrial Control Centre, Polytechnic of Central London, London, UK

Abstract. The control problems that arise in a fed- batch process are caused by the poorly understood nature of the process, its nonlinearity, the wide range of operating states passed through during a batch and the unmeasurability of key process variables.

In this paper alternative approaches to modelling and state estimation of the process will be outlined and a summary given of the comparative performance of numerically based and neural net derived models. A Self organising system based on fuzzy logic controller has been adapted to control the state variables of the process. The feasibility of using pattern recognition for modelling and state estimation of the process will be illustrated. Finally a brief treatment on the software structure, including expert system shells, that will allow these emerging AI techniques to be applied in real time to the fermentation process will be described.

Keywords. Expert Systems; Fuzzy Control; Modeling; Neural Nets; Pattern Recognition

INTRODUCTION

In the fermentation process there are three types of variables, the controlling inputs to the fermenter such as feeds, pH, temperature, etc. , the measured outputs in the gas components leaving the fermenters such as oxygen, carbon dioxide, etc. and the state variables, such as biomass, glucose and product concentration.

The problem with the industrial fermentation process is to find a model to represent the unmeasurable state variables and to design a suitable controller for the process. In controlling a fermentation process the most difficult problem is to determine its current state. This problem can be overcome if a suitable process model can be found for then an estimator can be used to determine the

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non-measurable variables and the model parameters.

In this contribution, the feasibility of using different techniques for modelling the Oxytetracycline (OTC) fermentation process are investigated. An identification technique is applied where autoregressive models have been developed from the process data. Neural networks have been developed to model the process. To control the state variables around a desired trajectory self organising fuzzy logic controller has been used.

THE AUTOREGRESSIVE (AR) MODEL FOR THE FERMENTATION PROCESS

The identification approach, Autoregressive (AR), is adopted to develop a model for the batch process from the available data [ l ] . For

the OTC fermentation process two models have been derived to describe the process . In the first a model has been derived to express the relation between the inputs, the carbon dioxide evaluation (RC02) and the carbon fed, and the unmeasurable state variables, potency, residual carbon, and residual nitrate. The second model is used to express the relation between the state variables and the measured output oxygen uptake rate (ROJ Figure 1 . The Kalman filter has been applied to estimate the unmeasurable state variables, in which the A, B, and C matrices and the model output (ROJ have been used to derive the Kalman filter [2] . Figure 2 illustrates the model output, Kalman filter estimation and the offline line measurement for the potency. Since fermentation is a time varying process, sequential modelling approach has been adopted. It has been decided to divide the fermentation process into three phases. Each phase has been treated separately in that a model for each has been derived. The unmeasurable state variables of the process have been taken to be the combination of the three phases. Of course, an important point is to find the change-over between the three phases. The change-over point between phases was chosen by inspection of the data. Figure 3 illustrates the offline measurement, the model output and the Kalman filter estimation for potency.

NONLINEAR MODEL OF THE PROCESS

The identification technique is a linear approach while fermentation is a highly non-linear, time varying and uncertain dynamic process. In this work, different techniques are investigated to create a general non-linear model to represent the process over the whole operating range.

The approaches are based on transforming the linear model derived using the AR technique into a non-linear model . In the first, the constants of the A and B matrices for the three models derived using the sequential modelling has been expressed in a time series polynomial . So instead of having three linear constants for the coefficients of the A and B matrices a time variant polynomial has been derived which represent the constants . The derived polynomial is used to represent and cover the time varying of the process over the whole operation. The described approach has

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been tested on one batch of data and Figure 4 illustrates the off-line measurement and the model output for the potency.

In the other approach, a varying window technique is used to model the process. In this approach an AR model has been derived over a data window which represent one phase of the procf.ss. The window is moving by a fixed step along the time axis of the process data. After each overlapping a new AR model has been derived. At each moment of time, several overlapping AR models have been derived and the average of them is used to represent the process. Figure 5 illustrn::es the offline measurement and the model output for potency.

SELF ORGANIZING FUZZY LOGIC CONTROLLER

The basic design of self organizing fuzzy logic controllers has been described in many papers [3,4] . It is composed of two levels, the first containing a simple fuzzy logic controller and the second containing the self organizing mechanism. There are many parameters involved in the design of SOFLC such as fuzzification, the choice of the input and the output variables, the type of the fuzzy control rules, defining the implication and inference procedure, and the defuzzification procedure, Figure 6.

The input signals to the controller taken at each sampling instant are, the error signal calculated by subtracting the process output from the set-point, and the change in error calculated · �'Y subtracting the error of the last sample from the present one. The signal is then mapped to the corresponding discrete level by using the error and change in the error scaling factors and prior to rule evaluation. The output signal is scaled to a real value using the output scaling factor and fed to the process being controlled.

The control rules are usually viewed as I inguistic conditional statements and symbolised in the form of a relational matrix R given by the Cartesian product.

R = Ek x CEk x Uk

The output from the fuzzy controller can be

obtained from its inputs, the error (E) and the change in the error (CE) using Zadeh's compositional rules of inference

U = ( Ek x CEk) o R

Then the output is defuzzified using defuzzification procedure to obtain a control action.

SOFLC has been applied to control a desired trajectory of the OTC product, by controlling the amount of Carbon fed inside the fermenter and using the derived AR model, described previously, to estimate the process. Figure 7

shows the desired trajectory and the process output of the product. From this figure it is possible to indicate that SOFLC has achieved a good control strategy in following the desired trajectory.

PATTERN RECOGNITION FOR MODELLING AND CONTROL OF

FERMENTATION PROCESS

Pattern recognition is an alternative approach for ill-defined process modelling, control and diagnosis. It can be regarded as a procedure for mapping a pattern correctly from pattern space into class membership space. Usually it comprises of two distinct steps as described by Pao [5] and illustrated in Figure 8.

There are two principal ways by which one can design a pattern recognition system. Firstly, the supervised approach consists of gathering representative patterns from each acceptable category and using these patterns to adaptively 'train' the machine to recognize the sample sets . Secondly, the unsupervised approach deals with techniques that accomplish learning without a prior knowledge of the categories present in the sample sets .

Pattern recognition technique could be used to obtain an accurate and robust identification model of the state variables for the fermentation process. The unsupervised approach is applied to analysis process data to get a prior knowledge of the process, for example, classify the process into normal or abnormal classes, or subclassify normal processes into several other classes . Eventually, the supervised approach would be used to diagnose the abnormal process,

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evaluate the process performance, and recognize fermentation phases using on-line measurements.

The control strategy could be accomplished using the integration of adaptive control and pattern recognition techniques. The basic framework is essentially a generic self-tuning controller containing three modules: A plant identification module; a controller design module; and a control implementation and validation module.

The identification module uses the on-line measurements to select a non-parametric model based on historical data. This is followed by a controller design module to design a control rule, and finally a control implementation and validation module will be used to implement the control rule and evaluate the control action. This information would feedback to the first module to conform the pattern recognition process as well as the control rules . Hence, this controller would have learning and self­organising capability with the advantage of effectiveness, high insensitivity to noise and operational simplicity for fermentation process control.

ARTIFICIAL NEURAL NETWORKS

The objectives of the research are twofold. First, the suitability of neural networks for the modelling and control of the OTC fed-batch fermentation process is being investigated. This part of the work has resulted in a number of publications where the use of multi-layered perceptrons (MLP) employing the back­propagation learning algorithm has been reported. The employment of different architectures, such as recurrent ANN's, will be explored in the future. The second objective is the foundation of a generic methodology for the development of ANN's. Obviously the two objectives are related. The need for a methodology arises when one considers the vast number of options confronting a user. For instance, the topology of the network and the selection of the appropriate inputs and training set are two aspects that need addressing.

In our research the use of correlation analysis between inputs and weights has been tested and proved to be a useful tool for post-pruning a neural network [6] . Correlation analysis assists

towards: Matching of the topology of a neural network to a particular problem; the identification of networks which learn faster; the recognition that a network does not improve its performance and that changes are required; and the elimination of hidden nodes, input nodes and connections.

Other post-pruning techniques have been attempted as well, for example weight analysis and activation analysis [7] .

Alternative input schemes have been tried for the modelling of the product concentration of the OTC process. The present values of the feeds, the present and previous values of the feeds, and the present values of the two feeds plus a third input which received the input were three such schemes [8] . Regarding the representation of the dynamic we are considering three alternative approaches : recursive nets, time staggered multiple inputs and dynamicaly enhanced neural nets . Our evaluation of these approaches is continuing.

Comparisons between ANN and Kalman filters demonstrated that with an appropriate learning set the ANN's will outperform the identification approach. This is mainly due to the ability of ANN's to handle the non­linearities of the data set. On the other hand the use of an identification technique within an overall control strategy is well defined whereas the integration of ANN models into control architectures need to be further investigated [9] .

The use of machine learning algorithms as tools for identifying relevant inputs and for modelling are also investigated. In particular the AIM tool which synthesizes abductive networks is currently evaluated.

THE INTELLIGENT SYSTEM APPROACH

With the above modelling and control methodology described, the software structure for the Intelligent Supervisory Monitoring And Control System is illustrated in Figure 9.

Three knowledge sources (Data Qualifier (DQ), Process Estimator (PE) and Process Controller (PC)) and a System Controller (SC) are required to accomplish the task of data screening, state variable estimation and to

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suggest desired control values to the process operator. The function of the DQ knowledge source is to ensure that all the data collected from the batch are reasonable for use by the subsequent knowledge sources. This could also result in providing early fault detection about measurement devices.

The PE 1�nowledge source is required to determine the unmeasurable state variables as well as providing information about the state of the batch. This can be accomplished by using the modelling techniques described above to estimate the state variables on-line. Further, information about the productivity of the batch at this moment in time or how healthy is the batch could also be determined by this knowledge source. Alarms would be generated if unusual activities (for example, the batch is biological contaminated) inside the fermenter is concluded.

The third knowledge source PC, is used to determine the desired control values in order to max1m1ze the production of OTC. Additionally, the system requires a SC to manage the sequence of knowledge sources execution.

With the system architecture designed in such a way that it could be implemented by one software tool or another. COGSYS Real-Time Expert System Shell has been selected for this project.

CONCLUSION

This paper examined various approaches for modelling and estimation of the state variables in the process. These included numerically­based and neural-net derived models. SOFLC has been used to control the state variables of the OTC fermentation process. The feasibility of using pattern recognition in the fed-batch process has been described. A brief description of the intelligent software structure that will allow the emerging AI techniques to be applied in real time has also been illustrated.

REFERENCES

1 . Mirzai A.R., Dixon K., Hinge R.D., Leigh J.R. (1991) . Approaches to the Modelling of Biochemical Processes. IEE International Control Conference. Edinburgh. U.K.

2. Leigh J .R. ( 1985). A1mlied Digital Control. Prentice-Hall .

2. Zadeh L.A. (1973). Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. IEEE Transactions on Systems. Man. and Cybernetics, Vol. SMC-3,

NQ...l. 4. Procky T.J . , Mamdani E.H. (1979). A Linguistic Self-Organizing Process Controller. Automatica, Vol. 15, pp. 15-30.

5. Pao Y.H. ( 1989). Adaptive Pattern Recoenition and Neural Network, Addison­Wesley.

6. Tsaptsinos D. , Mirzai A.R., Leigh J .R. (1992). Matching theopology of a neural net to a particular problem: Preliminary results using correlation analysis as a pruning tool, accepted for publication in ICANN'92 conference. Brighton. England.

7. Tsaptsinos D. , Jalel N.A., Leigh J.R., Mirzai A.R. (1992). Neural networks for estimating fermentation state variables, accepted for publication in AIENG'92 conference. University of Waterloo. Canada.

8 . Jalel N.A. , Tsaptsinos D., Mirzai A.R., Leigh J.R., Dixon K. (1992). Modelling the Oxytetracycline fermentation process using multi-layered perceptrons, acce.pted for publication in ICCAFT 5/IF AC.BIO 2 conference. Keystone. Colorado.

9. Tsaptsinos D. , Jalel N.A., Leigh J.R.(1992). Estimation of state variables of a fermentation process via kalman filter and neural network, Colloquium on the application of neural networks to modelling and control. Livemool University/Polytechnic.

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Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

A T ASK DECOMPOSITION APPROACH TO USING NEURAL NETWORKS FOR THE

INTERPRETATION OF BIOPROCESS DATA

G.K. Raju and C.L. Cooney

Biotechnology Process Engineering Center, Department of Chemical Engineering,

Massachusetts Institute of Technology, Cambridge, MA 02139, USA

AIWDa:1. During the course of most bioprocess development programs a large amount of process data is generated and stored. However, while these data records contain important infonnation about the process, little or no use is made of this asset. The work described here uses a neural networlc: approach to "learn" to recognize patterns in fermentation data. Neural networks, trained using fermentation data generated from previous runs, are then used to interpret data from a new fennentation. We propose a task decomposition approach to the problem. The approach involves decomposing the problem of bioprocess data interpretation into specific tasks. Separate neural networks are trained to perform each of these tasks which include fault diagnosis, growth phase determination and metabolic condition evaluation. These trained networks are combined into a multiple neural network hierarchy for the diagnosis of bioprocess data The methodology is evaluated using experimental data from fed-batch, Saccharomyces cerevisiae fermentations. We argue that the task decomposition approach taken here allows for each network to develop a task specific representation and that this in turn, can lead to network activations and connection weights that are more clearly interpretable. These expert networks can now be pruned to remove nodes that do not contribute significant additional infonnation.

Keywords Neural network; task decomposition; Saccharomyces cerevisiae; learning, pattern recognition, data interpretation, bioprocess, modular approach, bioprocess development, fed-batch

Introduction

During the course of bioprocess development there is often a need to make inferences about the state of a complex biological system using a very limited number of measurements. However, due to the scarcity of measurements and the complex, nonlinear, and time-varying nature of cell growth and product formation, there is both a severe limitation in our ability to measure system "performance" (often formulated in terms of yield, productivity, product quality, concentration and purity) and a serious lack of models to relate observed parameters to performance. This leads to the need for a large number of experimental runs to be performed in order to approach statistically meaningful optimal conditions for product synthesis. However, since the experimental space for process optimization is large, only a part of it is investigated because of the considerable amount of time and effort required to do so. As a result, bioprocesses continue to be plagued by variability in performance despite the effort to maintain tight control.

Figure 1 , summarizes three different approaches to dealing with this problem. We characterize the traditional approach to solving the bioprocess monitoring problem over the last

20-30 years as being a model based engineering approach3,l6. While this is an appropriate approach to use for some simple model systems, the time constraints (which determine the economics of process development) and effort involved make detailed modeling and sensor development difficult to justify for more complex systems. In these cases, simplified models tend not to reflect the real situation because of the large number of assumptions required before the model takes on a form that is tractable for actual use. To deal with these difficulties an expert system approach has been developed over the

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last few years as a solution to some of the problems encountered during bioprocess development. We characterize this second approach as being a knowledge based engineering approachll . This approach is aided by the large number of "generic rules" associated with process diagnostics and process performance. While this approach attempts to capture the known expertise about a process, experience has shown that it is limited by the ability of getting an expert(s) to formalize a consistent set of rules for a process that fundamentally is not yet well understood.

In this paper, we propose a third alternative to dealing with the bioprocess data inteipretation problem. It is motivated by the fact that a primary asset in most bioprocess development programs is the large amounts of process data recorded during the course the experimental runs. Early on in the life of the process, detailed models and specific expertise have not yet been developed. They have to be "learned" by doing more runs and by analyzing the results of the previous runs. We propose a neural network engineering approach. The ability of feedforward networks to model arbitrarily complex relationships toitether with their ability to learn from examples!� motivates us choose that network architecture to demonstrate our methodology!3.14.

Materials and Methods

A fed-batch Saccharomyces cerevisiae fermentation was used as a model system to test the neural network engineering approach. This system is well understood and is one for which models have been developed. In addition, a knowledge based expert system. has been developed for this model system! ! . Using a well understood model system for which other techniques have already been developed I ! gives

us a basis to evaluate the neural network engineering approach. The details of the experimental work are given by O'Connor et aJ.11 Given a set of measurements and calculated :van�bles, the pattern recognition task is to identify the growth phase of the fermentation, the cell's current metabolic state, and equipment or sensor faults. Figure 2 shows fermentation data from a fed-batch S. cerevisiae fermentation. The data is from a fermentation where certain metabolic conditions are deliberately inflicted on the culturel l . Hence the metabolic condition during the fermentation is known.

.The training. algorithm involves finding the optima! set of hidden nodes and connection weights for �he ta.sk. This is done by training networks with different numbers of hidden nodes. The fermentation data is partitioned into three sets - a training set, a cross-validation set and a testing set. An optimal set of connection weights is defined to be one that leads to the maximum generalization accuracy (minimum error) on the cross-validation data set. The optimal number of hidden nodes is one that leads to the maximum generalization accuracy (on the cr<?ss validation data set) among all the fully trained netw?rks. The training data set is used to actually tram the network and determine the optimal set of weights. The cross-validation data set is used to decide when the training is complete. A network is fully trained when it has achieved its highest generalization accuracy on the cross validation data set. The testing set is then used only to report results on. Each of the networks were trained to minimize using two different objective functions: mean squared error and cross entropy.

Blackbox Approach

Figure 3 illustrates the typical "blackbox approach" to the pattern recognition task we chose. This approach is similar to that taken in recent work using neural networks for pattern recognition in chemical engineerings.11. The network shown in Fig. 3 was trained on experimental data obtained from the S. cerevisiae fermentation with deliberately inflicted abnormalities. Inputs to the neural network are variables that are typically recorded during the course of bioprocess development programs. (Table 1).

Type of variable Variable

Measured variables Temperature pH %02 in outlet gas %C02 in outlet gas time

Manipulated variables Agitatof speed Air flow rate

Calculated variables 02 uptake rate C02 evolution rate respiratory quotient

Table 1: Variables used as inputs to network

Time is included as an input. In addition to variable values, their average trend over the last 3 time steps is also used in order to deal with the dynamics involved in the pattern recognition task. There are twenty-one inputs to the network. Sixteen possible categories were chosen as outputs based on knowledge of the different kind of possible states the fermentation could be in. (Fig. 3).

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Results

This network was previously trained on data from one fermentation where abnormalities were deliberately inflicted on the culture. The

blackbox network resulted in a generalization accuracy of 64%. This generalization accuracy depicts the number of correct interpretations made by the trained network on a fermentation that the network had not seen before. This generalization accuracy did not depend on the choice of objective function. That is, the same generalization accuracy was obtained for networks trained using the mean squared error objective function and those trained using the cross entropy objective function 1.

Task decomposition Approach

While it has been shown that a feed forward neural network can simulate any relationship to an arbitrary degree of precision, this assumes that the necessary training data is available and that the network can be trained until a global minima is reached. This is usually not the case when dealing with more practical pattern recognition problems. The training data are often incomplete and inconsistent. Error backpropagation and any other gradient descent method are local techniques. Hence, there is a need to use a-priori knowledge to constrain the number of possible solutions when using such methods for real world problems where the training data is finite. There are many ways to introduce this a-priori knowledge. Some of them include the choice of the activation functions (e.g. . logistic vs. radial basis fu n c t i o n s B ) , objective functions4 and constraining the network weights to satisfy certain constraints (e.g .. scale and rotation invariance).

Another way to use a-priori knowledge is to decompose the problem into simpler, well­defined tasks. This is one way of constraining the number of possible representations. Modular architectures can be designed to reduce the effect of conflicting training information referred to as "crosstalk"6. "Crosstalk" can be spatial or temporal. Spatial crosstalk occurs when the output units of a network provide conflicting error information to a hidden unit during training. If a separate network was designed for each of these outputs, then this crosstalk would be eliminated. Temporal crosstalk occurs when a network is trained to perform different functions at different times. Training a system to compute one function may affect the system's ability to learn a second function. This transfer of training can be positive or negative. The goal in designing suitable modular architectures is to have similar functions learned by the same network (resulting in the positive transfer of training) and dissimilar functions learned by different networks (avoiding the detrimental effects of negative transfer of training)6.

The outputs from the single large network can be divided into three sets of outputs; each associated with a separate task. The first set involves the identification of the phase of the fermentation and is only the required classification if the fermentation is normal. The second involves the detection of an abnormal metabolic condition. The third set involves the detection of equipment and sensor faults. This task decomposition is based on the rationale that it does not make sense to try to recognize the phase or metabolic condition if there are sensor or equipment faults.

Figure 4 shows a task decomposition approach to the pattern recognition task of monitoring a fermentation. The task involves breaking down a network that learns to perform many different and contradictory functions at the same time, into a set of networks, where each learns a set of similar functions. The approach involves breaking the problem of fermentation control into specific tasks of fault diagnosis, growth phase determination, and metabolic condition evaluation. The different neural networks are trained for each of these tasks. These trained networks are then combined into a multiple neural network hierarchy for fermentation control. These expert networks are then combined with an "observer" network which is trained to assign the pattern recognition task to the appropriate expert network based on the input pattern.

We expect that modular architectures will develop representations that are more easily interpreted. That is, will be easier to understand how a modular architecture implements a function than to understand how a single network implements the same function. In the modular approach a different set of hidden units is used to represent information about each different task. The functions learned by the modules can be thought of as building blocks to be used in more complex tasks. Modular architectures localix.e functions and develop more interpretable representations and hence are easier to debug. An advantage of the modular approach is that each network becomes an expert at a certain subset of the classifications. Since the

smaller specialist networks have a smaller, m� well defined, task, it is more likely that they will develop interpretable representations of the input output relationship. Because much of expert knowledge is modularized, it is easier to embed domain knowledge into a connectionist system when it is organized in a modular fashion. Each of the four networks were trained independently using data relevant to the task that the network was trained to perform. That is, the fault network was trained only with data that contained faults, the phase network was trained with data known to be normal and the metabolic network was trained using data generated during abnorm�l metabolic condition. The observor network 1s trained with all the data and is used to classify data as indicating normal metabolism, abnormal metabolism, and equipment and sensor faul_ts. The softmax2 output function was used with cross entropy was the objective function. This combination allowed for the network outputs to be interpreted a-posteriori probabilities2. While this combination resulted in the same generalization accuracy as in the case where mean-squared-error was used, the probabilist!c interpretation of the netw<?rk outj�uts 1s convenient and can form a basis for a ngorous interpretation of network outputs. It _also �lows for multiple networks to be combmed mto a multiple network hierarchy.

Results

The modular approach using task decomposition resulted in a generalizat�on accuracy of79%. This is an increase over usmg a single large network.

It was difficult to get interpretable representations from the single large nc:twork. Figure 5 summarizes the propagation of activations from the hidden layer to the output layer of the fault network �ault for the seven different classes. The opumal fault network network architecture consisted of twenty one input nodes (described earlier), three hidden

449

nodes and seven output nodes. Figure 5 does not show the input layer. Filled circles indicate nodes with an activation of 1 while the empty circles indicate no activation at all. Figure 6 shows the connection weights between the hidden layer and the output layer. The pattern of activations through the network together with the connection weights depicted in Fig. 6 indicate that the three hidden nodes have learned a rough binary representation of the inputs to the networks. The different combinations of these three higher order binary features are then all that are required to classify the set of faults. It can be argued that the fault network has "learned" to extract the three higher order features present in the bioprocess data and used these features then to make the classifications.

Pruning

Pruning is useful because it allows for the removal of nodes or connections that are not being used to make the classifications. Previous researchers 10,9 have developed pruning algorithms for feedforward networks. Here we use a statistical approach developed by Boger et al.I to prune the input nodes not contributing to the final classification. Each of the three expert networks were pruned to remove inputs that were not contributing to classification. Table 2 depicts the pruning of their input nodes.

Network

Phase net Metabolism net Fault net

Inputs nodes Inputs nodes beCore pruning after pruning

21 3 21 9 21 6

Table 2: Pruning of input nodes As depicted, there is a significant reduction in

the number of inputs required.

Conclusions

This work investigated the use of artificial neural networks as an way to "learn" to recognize patterns in bioprocess data. Using a fed-batch S. cerevisiae as a model system, the neural network approach has been demonstrated for the interpretation of bioprocess data.

It was found that a task decomposition approach to designing neural networks has certain advantages over a single large network approach. Decomposing the pattern recognition task into smaller specialix.ed subtasks improved ability to generalize. Analysis of the fault network showed that the modular approach allowed the smaller expert networks to develop representations that are more interpretable. This opens the possibility of trying to understand what these features represent. Network pruning resulted in a significant reduction in the number of hidden nodes.

Literature

1. Boger, Z., H. Guterman and M. A. Kramer. Neural Network Reduction: Application of a Statistical Relevance Approach. Submitted to IEEE Transactions on Neural Networks, August, (1990).

2. Bridle, J. S. Probabilistic Interpretation of Feedforward Classification Network Outputs, with Relationships to Statistical Pattern Recognition. In Neuro-computing: algorithms, architectures and applications, Springer Verlag, 1989.

3. Cooney C. L., H. Y. Wang and D. I. C. Wang. Computer aided material balancing for prediction of fermentation parameters. Biotechnology and Bioengineering, 19, 55-67, (1977).

4. Geman, S., E. Bienenstock, and R. Doursat. Neural Networks and the BiasNariance Dilemma. Neural Computation 4, 1-58, (1992).

5. Hoskins, J. C. and D. M. Himmelblau. Artificial Neural Network Models of Knowledge Representation in Chemical Engineering. In Computers and Chemical Engineering, 12, No. 9/10, pp. 881-890, (1988).

6. Jacobs, R. A., M. I. Jordan and A. G. Barto. Task decomposition through competition in a modular connectionist architecture: The what and where vision tasks. COINS Technical Report 90-27, University of Massachusetts, Amherst, MA .. March, (1990).

7. Lippmann R. P .. An introduction to computing with neural nets. IEEE ASSP Mag., 4, 4-22, (1987).

8. Leonard, J. and M. A. Kramer. Neural Networks and Pattern Recognition Techniques for Fault Tolerant Control. In Proc. American Institute of Chemical Engineers Annual Meeting, San Francisco November (1989).

• •

9. Le Cun, Y., J. S. Denker, and S. A. Solla. Optimal Brain Damage. In Touretzky, D., editor, Neural Information Processing Systems, 2, (1990).

10. Mozer, M. C., and P. Smolensky. Skeletonization: A Technique for Trimming the Fat from a Network via Relevance Assessment. In Touretzky, D., editor, Neural Information Processing Systems, 1 , Denver, Morgan Kaufman. (1988).

1 1 . O'Connor, G. M.. Development of an Intelligent Fermentation Control System. Ph.D. Thesis, Massachusetts Institute of Technology, September (1989).

12. O'Connor, G. M., F. Sanchez-Riera and C. L. Cooney. Design and Evaluation of Control Strategies for High Cell Density Fermentations. Biotechnology and Bioengineering, Vol. 39, 293-304, (1992).

13. Raju, G. K. and C. L. Cooney. Using Artificial Neural Networks for bioprocess control. ACS 200th National Meeting, Washington D. C., August, (1989).

14. Raju, G. K. and C. L. Cooney. Using Artificial Neural Networks to aid the interpretation of bioprocess data. IFAC Symposium on Modeling and Control of Biotechnical Processes, Keystone, Colorado, April, (1992).

15. Rumelhart D. E. and J. L. McCelland (Eds), Parallel Distributed Processing: Explorations in the Microstructure of Cognition. MIT Press, Cambridge, Mass. (1986).

16. Stephanopoulos, G. and Ka-Yiu San. Studies on On-Line Bioreactor Identification. I . Theory. Biotechnology and Bioengineering, 26, 1 176-1 1 88, (1984).

17. Venkatasubramanian, V. and K. Chan, A Neural Network Methodology for Process Fault Diagnosis, AIChE Journal, Vol.35, 12, 1993-2002, (1989).

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Model based engineering approach

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452

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

HARDWARE AND SOFIW ARE REQUIREMENTS

TOP-DOWN DESIGN OF EMBEDDED REAL-TIME AI SYSTEMS

J. Hooman

Department of Mathematics and CompuJing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Abstract. A formal method is proposed for the specification and verification of em­bedded real-time systems. We consider distributed systems in which parallel processes communicate by sending messages along synchronous or asynchronous channels. To verify that a program satisfies a specification, a compositional proof system is given. Compositionality enables verification during the process of top-down program design. This is illustrated by an example of a rail road crossing. Starting from an assertional specification, we design a program that controls lamps and barriers using information from sensors that signal the passage of trains at a certain distance from the crossing.

Keywords. decomposition; failure detection; distributed control; real time computer systems; software development; specification languages.

INTRODUCTION

To specify and verify timing properties of real­time systems, a formalism based on classical Hoare triples (precondition, program, postcondi­tion) is introduced. These triples are extended with a third assertion, called commitment, by which the real-time communication interface of distributed reactive systems can be specified. To prove that a program satisfies such a specifica­tion, we give a proof system, i .e. a set of axioms and rules which axiomatize the functional and the timing properties of programs.

To be able to split up correctness proofs, we for­mulate a verification method which is composi­tional. This allows us to reason with the spec­ifications of components rather than their imple­mentation, and verify design steps during the pro­cess of top-down program development. This is demonstrated by the top-down derivation of a pro­gram to control a railway crossing. Given sig­nals from sensors along the tracks the task is to control lamps and barriers that guard the cross­ing. Barriers may fail, which can be detected by the control system. Starting from an assertional specification we first split up the system in par­allel components and show that the specifications of the components imply the top-level specifica­tion. Next we implement these components inde­pendently according to their specification.

453

PROGRAMMING LANGUAGE

We consider real-time systems implemented in a concurrent programming language with communi­cation by message passing along synchronous and asynchronous channels. Let CHANs be a set of synchronous channels and CHANA a set of asyn­chronous channels. Then the language contains the following communication statements.

• Input statement c?:x , for a channel c E

CHANs U CHANA , to receive a value via channel c and assign this value to the vari­able :x. Such an input statement has to wait until a message is available.

• Synchronous output c!e, for c E CHANs, to send the value of expression e on channel c

as soon as a corresponding input command is available. Such a synchronous output state­ment is suspended until a parallel process ex­ecutes an input statement c?:x .

• Asynchronous output c!!e, for c E CHANA , to send the value of expression e along channel c. It does not wait for a receiver but sends im­mediately. There is no buffering of messages; the message is lost if there is no receiver.

Other programming language constructs will be discussed in subsequent sections.

The timing behaviour of a program is expressed from the viewpoint of an external observer with his own clock. Since this global notion of time is not incorporated in the distributed system itself, it does not impose any synchronization upon pro­cesses. In this paper we use a time domain TIME which is dense, i.e. between every two points of time there exists an intermediate point.

In our proof system the correctness of a program with respect to a specification, which may include timing constraints, is verified relative to assump­tions about the execution time of atomic state­ments. For instance, for communication actions we assume that there exist parameters T1yn > 0 and Taayn > 0 such that each synchronous com­munication takes T,yn time units, and each asyn­chronous communication takes Taayn time units. Further we have to make assumptions about the progress of actions. In this paper we use the max­imal progress model in which an enabled action will be executed as soon as possible, represent­ing the situation that each parallel process has its own processor. An input or synchronous output command can cause a process to wait, but only when no communication partner is available; as soon as a partner is available the communication must take place. Thus maximal parallelism im­plies minimal waiting. In [2] we show that the framework can be generalized to multiprogram­ming where several processes may share a single processor and scheduling is based on priorities.

SPECIFICATIONS

Our formalism is based on classical Hoare triples [1] , that is, formulae of the form {p} S { q} where S is a program and p and q are asser­tions expressed in a first-order logic. Informally, a triple {p} S { q} has the following meaning: if S is executed in a state satisfying precondition p and if S terminates then the final state sat­isfies postcondition q. To extend a Hoare triple {p} S {q} to real-time, a special variable time is introduced. Consider, for instance, the formula {time = 3} c!!5 {time = 3 + Taayn} · In the pre­condition the variable time specifies the starting time of the program, whereas in the postcondition time denotes the termination time. Thus the for­mula {time = 2} S { 17 < time < 23} expresses that if the execution of S is started at time 2 and if S terminates, then it terminates after time 17 and before time 23.

With Hoare triples, however, we can only ex­press partial correctness of programs, i.e. proper­ties that hold if the program terminates. Hence a specification {p} S { q} is trivially satisfied by non­terminating programs. This is not appropriate for embedded real-time programs which are usually

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non-terminating, having an intensive interaction with their environment. Therefore we extend a Hoare triple with a third assertion, called com­mitment, which should be satisfied by both termi­nating and non-terminating computations. This leads to formulae of the form C : {p} S {q}, where commitment C expresses the real-time communi­cation interface of program S. In general , commit­ment C reflects the real-time communication in­terface between parallel components, whereas the pre- and postconditions facilitate the reasoning at sequential composition .

The assertions C, p, and q in an extended Hoare triple C : {p} S { q} are expressed in a first­order logic. To express termination in the commit­ment, the special variable time is allowed to occur in commitments where it denotes the termination time of computations. Since our aim is to specify and verify timing properties of open systems that communicate with their environment by message passing along channels, the logic contains the fol­lowing primitives to express this communication behaviour.

• ( c, exp1 ) at exp2 to denote the start of a com­munication, when both sender and receiver are ready to communicate, along channel c with value exp1 at time exp2 .

• (c! ! , exp1) at exp2 to denote the start of an asynchronous output along channel c with value exp1 at time exp2 .

Recall that our maximal progress assumption im­plies minimal waiting for communications. To ex­press this assumption in our compositional frame­work, we include the following primitives in the logic:

• c? at exp to express that a process is waiting to receive a message along channel c at time exp.

• c! at exp to express that a process is wait­ing to send a message along a synchronous channel c at time exp.

We frequently use intervals of time points such as [to , t 1 ) = {t E TIME I to � t < t i } , etc. Hence­forth we use = to denote syntactic equality. Fur­ther, we define the following abbreviations, for a predicate P at t and an interval I C TIME.

• P at I =: Vt E I : P at t • P in I =: 3t E I : P at t • await (c?, v) at t = c? at [t , oo)V

(3t1 E [t , oo) : c? at [t , t 1 } /\ (c, v) at t 1 ) • await (c!, v ) at t = c! at [t , oo}V

(3t1 E [t , oo} : c ! at [t , t1} /\ (c, v) at t 1 ) • We often abstract from the value that is com­

municated, using c at t = 3v : (c, v) at t , c ! ! at t = 3v : (c! ! , v ) at t , awaitc? at t = 3v : await (c? , v) at t , and await c! at t = 3v : await (c ! , v) at t .

EXAMPLE RAILWAY CROSSING

As an example, we design a real-time program to control lamps and barriers of a railway crossing, as specified informally in [4] . We consider a segment of a railway with two one-way tracks on which trains run in opposite direction. The tracks cross an ordinary road and the crossing is guarded by barriers and lamps. The crossing section (CS) is the part of the railway that crosses the ordinary road and has a length of 20 m. On each track there are two sensors on a distance of 3000 m before the crossing. On track i we have sensors Ai and Bi with distance 10 m, for i = 1 , 2 . These sensors can be used to determine when trains enter and exit the crossing section. They give a signal on an asynchronous channel when a wheel of the train is detected. The minimal distance between wheels is 3 m and the maximal distance is 20m. The min­imal speed of trains is 10 m/s (36 km/h) and the maximal speed is 30 m/s ( 108 km/h). We assume that the speed of a particular train is constant between the sensors and the crossing. Further we assume that the distance in time between trains on the same track is at least 100 sec.

Given signals from the sensors along asynchronous channels SensA1 , SensA2 , Sens Bi and SensB2 , the task is to design a program CONTROL which controls the lamps and the barriers (see Fig. 1) . Lamp i can be set to three positions: off, slow

CONTROL

Figure 1: System to control the crossing

(i.e . , slowly flashing, 1 sec on and 1 sec off) , or hold (continuously on) by sending signals, 0, S, or H, resp. , along asynchronous channel Li , for i = 1 , 2 . We assume that the lamps never fail. Barrier i is controlled by sending signals U (up) or D (down) along asynchronous channel Bi . Bar­riers may fail, and to detect a failure we have syn­chronous channels done1 and done2 indicating the completion of an opening or closure operation. If a barrier does not fail then the opening or closure operation takes at most 4 seconds. Thus if barrier i does not fail then we receive a signal along chan­nel done; in less than 4 sec after sending a signal on Bi. Barrier i is considered to be failing if the control system has sent two successive signals on

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Bi , with a distance of at least 4 sec, without re­ceiving a signal via done2 in less than 4 sec.

Specification of CONTROL

We start with a specification of the program CONTROL in terms of trains, lamps and bar­riers. We use train in CS at t to express that a train is in the crossing section at time t . For the status of lamp i we use (lampi , off) at t , etc. A similar notation is used for the barriers with (barrieri , fa ult) at t to indicate that barrier i is in a failure mode at time t . We define the follow­ing abbreviations for the relation between barriers that are down (or fail) and the lamps. OKDNi at t ::

(barrieri , down) at t /\. (lampi , slow) at t FA/Li at t ::

(barrieri , fault) at t /\. (lampi , hold) at t DOWNi at t :: OKDNi at t V FA/Li at t DOWN at t :: DOWN1 at t /\. DOWN2 at t Similary, we have abbreviations for barriers that are up (or fail). OKUPi at t ::

(barrieri , up) at t /\. (lamp; , off) at t UP; at t :: OKU P; at t V F AIL; at t UP at t :: UP1 at t /\. UP2 at t

The control system CONTROL is specified by

C : {time = O} CONTROL {false}

where C :: C1 /\. C2 /\. C3 /\. C4 with, for to E TIME and v 2:: 0 ,

C1 = train i n CS at (to + v) /\. v < 30 __.. DOWN at to

(If there will be a train in the crossing section in less than 30 sec then a barrier is either in failure mode or down.)

C2 = train in CS at (to + v) /\. v < 40/1. -i(barrier; , fault) at to __.. (lamp; , slow) at to

(If a train will reach the crossing section in less than 40 sec and barrier i is correct then lamp i should be slow. )

C3 = /\.;=1,2(/amp; , off) at to __.. -i(barrier; , fault) at to

(If lamp i is off then no failure is detected for bar­rier i.)

C4 = (-it rain in CS) at [to , to + 90} __.. UP at (to + 15)

(If no train will reach the crossing section in less than 90 sec then a barrier which is not in failure mode should be up in less than 15 sec.)

This specification, however, is not in terms of the interface of the system. We have to make assump­tions about the relation between trains and sen­sors to be able to translate train in CS at t in terms of signals along the channels SensA; and SensB; . Similarly we have to give a relation be-

tween the status of lamps and barriers and signals along channels L; , B; , and donei . Thus we define the predicates used in the specification above as abbreviations in terms of the interface of the con­trol system.

Interface with the Trains

By the signals from the sensors we can com­pute when a train will enter or exit the cross­ing section. Thus, first define, for i = 1 , 2 , train enters CSi , and train exits CS; at t in terms of SensAi and SensB; (see [3] ) . Given these ab­breviations the number of trains that have en­tered or exited the crossing section before a cer­tain point of time t can be determined, that is, we define # train enters CS; at t , and then #train enters CS at t = #train enters CSi at t+ # train enters CS2 at t . Similarly, we define # train exits CS at t . This leads to train in CS at t = # train enters CS at t > # train exits CS at t .

Interface with the Lamps

For the interface with the lamps we use a param­eter 61 for the maximum time between a signal on channel Li and a corresponding change of lamp i. Initially the lamps are off.

• (Lampi , off) at t = (.,Li ! ! ) at [O, t}V 3ti � t - 61 : (Li ! ! , 0) at ti/\ (.,Li ! !) at (ti , t}

• (lampi , slow) at t = 3ti � t - 61 : (Li ! ! , S) at ti/\ (.,Li ! !) at (t i , t}

• (lampi , hold) at t = 3ti � t - 61 : (Li ! ! , H) at ti/\ (.,Li ! !) at (t i , t}

Interface with the Barriers

Similarly, we define the status of the barriers in terms of the channels Bi , B2 , donei and done2 . Initially the barriers are up.

• (barrieri , up) at t = (.,Bi ! !) at [O, t}V (3ti � t : (Bi ! ! , U) at ti /\ (.,Bi ! !) at (ti , t}/\

3t2 � t : t i < t2 � ti + 4 /\ donei at t2)

• (barrieri, down) at t = 3ti � t : (Bi ! ! , D) at ti /\ (.,Bi ! ! ) at (ti , t}/\

3t2 � t : ti < t2 � ti + 4 /\ donei at t2

• (barrieri , fault) at t = 3ti , t2 : ti < t2 - 4/\ t2 < t - 4/\ Bi ! ! at ti /\ Bi ! ! at t2/\ ( .,donei) at [ti , t}/\ 3ta > 0 : await donei? at [t1 + 4 - ta , t i + 4}/\ 3t4 > 0 : await donei? at [t2 + 4 - t4, t2 + 4}

Note that we only have (barrieri , fault) ifthe sys­tem has detected a failure, that is, if it has sent along Bi twice without receiving a signal on donei , although it was ready to receive such a signal.

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DECOMPOSITION OF CONTROL

As a first design step we decide to implement the system CONTROL as a parallel composition

RAIL I I WAY with the intention that RAIL uses the sensors to generate signals along internal asynchronous channels Close and Open, and that WAY controls the lamps and the barriers using these signals. This is expressed in the specifications of RAIL and WAY below. Since the precise timing constraints to be imposed upon these components are not yet clear, we use parameters Y1 , Y2 , etc. Parameter 6r indicates that there is some uncertainty about the time at which signals are generated.

Specification of RAIL

Ru = Close! ! at t -+ train enters CS in [t + Yi , t + Yi + 6r}

Ri2 = train enters CS at (t + Yi) -+ Close! ! in (t - 6r , t]

R2i = Open!! at t -+ train exits CS in (t - 6r , t]/\ (.,train in CS) at [t , t + Y2 - 6r}

R22 = train exits CS at ti\ (.,train in CS) at [t , t + Y2} -+

Open!! in [t , t + 6r} Ra = (.,Close! ! ) at [O, Ye} R4 = Close! ! at t -+ (.,Open!!) at [t , t + Yeo} Rs = Open!! at t -+ (.,Close ! !) at [t, t + Yoe} Note that by Ra, R4, and Rs we express that there is some distance in time between successive Close and Open signals. Let R = Ru /\ . . . /\ Rs. Then program RAIL is specified by

R : {time = O} RAIL {false}

Specification of WAY

Define, for i = 1 , 2 , Wo = (.,Close) at [O, t } -+ UP at [O, t} Wi = Close at to /\ (.,Open) at [to , t i } -+

DOWN at [to + Xd, ti} W2 = Open at to /\ (.,Close) at [to , ti } -+

UP at [to + Xu , t i } Wa = A:i,2(lampi , off) at to -+

.,(barrieri, fault) at to W4 = Close at to /\ (.,Open) at [to, ti]/\

.,(barrieri , fault) at t1 -+

(lampi , slow) at [to + X1 , ti] Ws = await Close? in [O, Xe] W6 :: Close at to -+ await Open? in [to , to + Xeo] W1 = Open at to -+ await Close? in [to, to + X0e]

Note that here, in Ws, W6 , and W1, we specify that WA Y is ready to receive signals along chan­nels Open and Close within some time after the last communication. Let W = Wo /\ . . . /\ W1. Then for WAY we have the following specification

W : {time = O} WAY {false} .

VERIFICATION

The aim is to verify the correctness of this de­sign step and proceed with the implementation of RAIL and WAY according to their specification. Therefore the proof system contains the following rule for parallel composition.

Rule 1 (Parallel Composition)

C1 : {pi} S1 {qi } , C2 : {p2} S2 {q2} C1 /\ C2 : {p1 /\ p2} S1 l lS2 {q1 /\ q2}

provided, for i = 1 , 2, Ci and qi refer only to pro­gram variables and channels of Si , and time does not occur in Ci and qi . Such a rule expresses that the formula below the line can be derived, provided the formulae above the line are derivable. Note that this rule is com­positional, i.e. only depends on the specif cations of S1 and S2 without using their internal structure. Further, the proof system contains a consequence rule.

Rule 2 (Consequence)

Co : {po} S {qo} , P - Po , Co - c, qo - q c : {p} s {q}

In our example, the parallel composition rule leads to

R I\ W : {time = O} RAIL II WA Y {false} .

Hence, by the consequence rule, RAIL I I WAYim­plements the system CONTROL for the railway crossing if we can prove that R /\ W implies com­mitment C of CONTROL. Note, however, that R is terms of Open!! and Close ! ! , whereas W is in terms of Open, Close, Open? and Close?. Thus we have to axiomatize the relation between input, output, and communication actions. The proof system contains separate axioms for synchronous and asynchronous channels. For a synchronous channel c E CHANs we define • P1(c, t) = -i(c! at t /\ c? at t) (Minimal waiting: it is not possible to be simul­taneously waiting to send and waiting to receive on a particular channel .) • P2(c, t) = -i(c at t /\ c? at t)/\ -i(c at t /\ c! at t) (It is not possible to be simultaneously commu­nicating and waiting to communicate on a given channel.) • P3(c, t) = (c, v1 ) at t /\ (c, v2) at t - v1 = v2 (At any time at most one value is transmitted on a particular channel.) Define • Sync =: Vt : P1 ( c, t) /\. P2( c, t) /\. P3( c, t) .

Axiom 1 (Synchronous Channel) Sync : {true} S {Sync}

Define, for an asynchronous channel c E CHANA , • Ai(c, t) = -i(c!! at t /\ c? at t)

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• A2(c, t) = -i(c at t /\ c? at t) • A3(c, t) = (c! ! , v1) at t /\ (c, v2) at t - v1 = v2 • A4(c, t) = (c, v) at t - (c!! , v) at t • Async = Vt : Ai (c, t) /\ A2(c, t)/\ A3(c, t)/\

A4(c, t).

Axiom 2 (Asynchronous Channel) Async : {true} S { Async}

To add these properties to a specification, the proof system contains a conjunction rule.

Rule 3 (Conjunction)

C1 : {pi } S {q1 } , C2 : {p2 } S {q2} C1 /\ C2 : {P1 /\. P2} S {q1 /\ q2}

In the railway example we can derive with these axioms and rules that RAIL I I WA Y satisfies the commitment R/\. W /\Asynopen /\Async1oae · First we observe that by R3, R4, and Rs of R and Ws , W6 , and W1 of W, no signal along Close or Open is lost, provided

Ye � Xe , Yeo � Xco , and Yoe � Xoc · In [3] we prove that then we obtain commitment C of CONTROL, provided we have the following additional constraints on the parameters:

Y2 - Y1 > 26r , Y1 > Xd + 30, Y1 > X1 + 40, Y2 � 90, 6r + Xu � 15, Y1 < 75 - 6r .

It remains to implement RAIL and WA Y accord­ing to their specification.

IMPLEMENTATION OF WAY

Before we consider the implementation of WAY in detail, we describe some of the programming constructs and their proof rules. More informa­tion can be found in [2] . Real-time is incorpo­rated in the programming language by a delay e statement which suspends the execution for (the value of) e time units if e is positive, and 0 time units otherwise. Then the proof system contains the following rule, using p[ezp/var] to denote the substitution of each free occurrence of variable var by expression ezp.

Rule 4 (Delay)

p[to/time]/\. time = to + maz(O, e) - C /\ q C : {p} delay e {q}

Note that by the substitution p[to/time] the vari­able t0 represents the starting time of the state­ment . For an assignment z := e we have the fol­lowing rule, using parameter Ta to represent the execution time of an assignment.

Rule 5 (Assignment)

p[to/time, v/z] /\. z = e [v/z]/\ time = to + Ta - C /\. q

C : {p} z := e {q}

Next we give a rule for asynchronous output.

Rule 6 (Asynchronous Output)

p[to/time] A (c! ! , e) at to fl.time = to + Ta1yn -+ C A q

C : {p} c!!e {q}

To obtain a compositional proof system we do not make any assumption about the environment of a statement. Thus in the rule for a synchronous output statement no assumption is made about when a communication partner is available, and hence this rule includes any arbitrary waiting pe­riod (including an infinite one). In the rule below the commitment is split up in Cnt , representing a non-terminating computation in which the syn­chronous output statement waits forever to com­municate, and C to express properties of termi­nating computations.

Rule 7 (Synchronous Output)

p[to/time] A c! at [to , oo} A time = oo -+ Cnt p[to/time]A 3t E [to , oo} : c! at [to , t}/I.

(c, e) at t /I. time = t + T,11n -+ C /I. q (Cnt V C) : {p} c!e {q}

In the input rule we allow any arbitrary input value, since no assumption should be imposed upon the environment, and hence any value can be received. Let Tcomm = T,11n if c is a syn­chronous channel, and Tcomm := Taayn if c is an asynchronous channel.

Rule 8 (Input)

p[to/time] /I. c? at [to , oo} /I. time = oo -+ Cnt p[to/time]/I. 3t E [to, oo} : c? at [to, t}/I. (c, v) at t /I. time = t + Tcomm -+ C /I. q[v/.x]

(Cnt V C) : {p} c?.:z: {q}

We have sequential composition S1 ; S2 of state­ments S1 and S2 with an inference rule which is an extension of the classical rule for Hoare triples.

Rule 9 (Sequential Composition)

C : {p} S1 {r}, C : {r} S2 {q} C : {p} S1 ; S2 { q}

The programming language contains a guarded command G of the form

(Df:1bi ; ci?.:Z:i -+ Si fi bo ; delay e -+ So] where b1 , . . . , bn , b are boolean expressions. A guard, i.e. the part before an arrow, is open if the boolean part evaluates to true. If none of the guards is open, the guarded command terminates. Otherwise, wait until an input statement of the open input-guards can be executed and continue with the corresponding Si . If the delay guard is open (bo evaluates to true) and no input-guard can be taken within e time units, then So is executed.

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Boolean guards equivalent to true are often omit­ted. Iteration *G indicates repeated execution of guarded command G as long as at least one of the guards is open. When none of the guards is open *G terminates. We refer to [2) for rules con­cerning these constructs.

In our railway example we can prove that the fol­lowing program satisfies specification W. * [Close? -+ (Dn1 l lDn2) ;

Open? ; (Updl UP2) ] with

Dni ::L; !!S ; B; ! !D ; [donei? -+ skip fidelay 4 -+ B; ! !D ; [done;? -+ skip

Il delay 4 -+ L; ! !H] ] and

Up, ::B; ! !U ; [done,? -+ L, ! !O fi delay 4 -+ Bi ! !U ; [done;? -+ L, ! !O

fi delay 4 -+ L; ! !H] ] Note the use of a time-out, implemented by a guarded command with a delay branch, to detect a failure of a barrier. Under suitable assumptions on the timing of atomic statements, we can prove specification W with Xu = Xd = 9 , X1 = 1 , X0 = 0 . 1 , Xco = 9 , and Xoe = 9. Using these values we can express the requirements from the previous section for the decomposition of the sys­tem in terms of requirements for the parameters of RAIL:

Ye � 0 . 1 , Yeo � 9 , Yoe � 9 , Dr $ 6 , Y1 > 41 Y2 $ 90 , and Y1 < 75 - Dr .

Observe that it is possible to find Y1 and Y2 sat­isfying these restrictions. Hence, RAIL should satisfy specification R with

Ye � 0 .1 , Yeo � 9, Yoe � 9, and Dr $ 6. The development of a program for RAIL can be found in [3] .

REFERENCES

[1] C.A.R. Hoare. An axiomatic basis for com­puter programming. Communications of the ACM, 12(10) :576-580,583, 1969.

[2] J. Hooman. Specification and Compositional Verification of Real-Time Systems. LNCS 558, Springer-Verlag, 1991 .

[3] J . Hooman. Top-down design of embedded real-time systems. Deliverable ESPRIT-BRA project 3096 (SPEC), Eindhoven University of Technology, 1992.

[4] E. Zijlstra. The rail road crossing. Deliver­able, Esprit project DESCARTES, Foxboro, The Netherlands, 1988.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

A TEMPORAL BLACKBOARD STRUCTURE FOR PROCESS CONTROL*

F. Barber, V. Botti, A. Crespo, D. Gallardo, and E. Onalndfa

Grupo de Automatica e Informatica Industrial, Universidad Politecnica de Valencia, Apdo 22012,

E4(J()7J Valencia, Spain

Abstract. Complex control systems require the use of new A.I. techniques to cope all the variable relations. One of the open topics is the use of temporal information and the ability of reason about it. Blackboard systems are one of the most promisin� proposal

. for

real time expert system. In this paper a temporal blackboard to be used m a real time expert system is described. In order to represent the information a tempor� model

. and

its methods will be presented. Finally, some temporal features has been explamed usmg a small scenario of a cement kiln process.

Keywords. Temporal reasoning, blackboard systems, real time expert system

INTRODUCTION

The temporal representation and reasoning problem arises in a wide range of Knowledge-Based System (KBS) application areas, where time pl�ys

.a crucial

role such as in process control and momtormg, fault detection, diagnosis- and causal explanation, resource management and planning, etc. In these cases, tem­poral data representation is needed in order to obtain conclusions about the problem. Moreover, temporal dependence of knowledge relations (temporal cons­traints and parameterization of their application) is possible. However, neither the several Expert Sys­tem (ES) prototypes developed to handle these appli­cations [ISERMANN87, LAFFEY88, PERKINS90, TSANG88, etc.] nor the several expert system de­velopment tools which have a certain temporal ca­pacity offer a general solution to the problem and the temporal representation and reasoning capacity of the ES has an ad hoc treatment in each case, which is too restrictive for the wide range of tempo­ral domains. Temporal constraint and parameteriza­tion about rule application is not usually considered and the dynamic of the problem has not a natural

* Partially supported by a grant of CICYT No. ROB89-0442 of Spanish Government and the ESPRIT Project REAKT 4651 (Thomson Syseca CRIN GMV UPV Mar­coni Etnoteam Computas)

459

representation.

In order to handle this problem in Artificial Inte­lligence (AI) areas (action-planning, qualitative re­asoning about processes, explanation of the world at some earlier time, and prediction or tempo­ral projection of the future) in a more specific way, several temporal logic-based models, from ini­tial situation calculus [McCARTHY69], were de­fined [ALLEN84, McDERMOTT82, KOWALSKI86, SHOHAM88]. Thus, these temporal models in AI have an explicit time representation, based on time­points or intervals.

With a particular representation, the Temporal Imagery concept is related to representation and inference methods with large amounts of temporal information, and events and facts are arranged in a time map, based on temporal intervals [ALLEN83] or time points (DEAN87]. Other models are included in the Qualitative Reasoning concept (DeKLEER84, KUIPERS84, FORBUS84], with a qualitative consi­deration of the problem dynamic, about which the laws of change are defined.

However, some important points are not completely solved when temporal reasoning is used under time constraints. The need of manage past and future facts and the number of possible variable relations

can produce large operations for update and retrieve temporal information. Thus, an efficient manage­ment must be addressed.

In this paper a temporal blackboard (TBB) struc­ture is described. The blackboard is a component in a real time expert system under development in the framework of the REAKT Esprit project [RE­AKT90]. In the following section, a revision of tem­poral information representation will be done. Next sections describe the temporal model assumed and the main methods for temporal management, and temporal functions provided by the blackboard to be used in rules. Finally, an example of a cement kiln subprocess will detail the use of the main functiona­lities.

TEMPORAL INFORMATION

Temporal information in control systems is relevant to know the evolution of the process and deduced variables and reason about it. The need of tempo­ral information is related to past and future values. From a general point of view, a temporal value can be:

1. exactly known: when the time, where values were taken, is known (the alarm was 'on' from 10:20:03 till 10:28:45)

2. partially known: when a value is result a of sampling and this value is maintained till the next (the temperature at 10:23:22 was 120 degrees)

3. known with an uncertainty: when a variable will take a value in some instant of an interval (the kiln status will be HIGH before 20 minutes)

4. dependent: when the exact instant of a tem­poral value depend on other temporal facts (the alarm will be ON 20 minutes after the tempera­ture be HIGH)

In terms of process control, 1 and 2 can be assumed as equivalent due to incoming values are produced at known instants (sampling period), and, if no more information is added, the same value can be maintai­ned. This behavior if can be modeled by means of a data persistence as the time which the variable main­tain its value. If this time is exceed a lack of informa­tion is produced and no value is assumed. When this persistence is oo, the last value is always maintained.

Past values are always related to the instant they were produced, so, an absolute date can be used to store them. In this case there is not relation between temporal information, all of them are related to the clock and the relations must be deduced using clock values.

Future or prediction values introduce more difficulties due to the lack of knowledge about the exact instant they will be produced. In the third case, we predict

460

that a status will be HIGH in some instant before 20 minutes, but we do not know the concrete instant it will start, finish or its duration. So, a model to represent and manage prediction has to represent this uncertainty and be able to reason about it.

Besides, fourth case introduces more complexity be­cause of the dependency with another fact, when a fact occurs the dependent fact is equivalent to the third case, if it does not occurs neither the second one.

Moreover, the system behavior defines a set of tem­poral dependencies: a material in a cement kiln, from the input to the output takes about 10 minutes, so if we measure the temperature at the input, some pre­diction can be done about the future temperature in the middle and the output of the kiln, taking into account the process model, delays, etc. On the other hand, the system can take actions based in predic­tions in order to avoid problems in temperature.

In rule based systems, it means that rules should be fired with present and future facts and actions, in the right hand side of a rule, should be executed in the instant the values are deduced or when they are present.

TEMPORAL MODEL

The developed system is based on time-points (tp) as primitive for time representation. A tp represents a time instant in a discrete temporal line. An addi­tional concept is the temporal duration( td) as the temporal distance between two tp's.

The temporal relations relating two tp's are:

• (BEFORE tp1 , tdk , [tpi]): expresses that tp1 is temporally before tpi plus a certain temporal duration tdk.

• (AT tp1 , tdk, [tp,]): expresses that tp; is tem­porally at tpi plus a certain temporal duration tdk.

• (AFTER tp1 , tdk, [tp,]): expresses that tp; is tem­porally after tpi plus a certain temporal dura­tion tdk .

The tdk value, which stands for a temporal dura­tion, may be positive or negative. The tpi is op­tional and, by default, it represents the initial time reference (clock). With all these relations, the follo­wing temporal constraints can be set between time points:

• Temporal relation between a time point and the clock; the time point tp; occurs at 8h:15':34" , would be represented as: (AT tp; (duration 8:15:34))

• Temporal distance between two time points; tp; occurs at 10' AFTER tpj is represented as: (AT tp, (duration 0:10) tpi)

• Relative constraints between two time points, when tdi.=O; tp; occurs before tpi is represented as: (BEFORE tp; (duration 0) tp,) .

These temporal relations are represented in a graph (Time Map) where nodes are the time points and the labeled directed edges show the temporal cons­traints between them:

Nodes: time points ( tp; )

Edges: Temporal constraints between time points: (Before, At, After tdi.)

With this model as background, application objects are instances of classes with static and temporal at­tributes or slots, for instance:

Class Temperature has static attributes :

name , location , units , temporal attributes :

value End class

Each object in the blackboard has a pointer to the parent class description and a set of static and tem­poral slots. The structure of a temporal slot is formed by the following pointers:

• object: which this slot belongs

• current: pointer to the temporal value that cu­rrent now

• past: list of pointers to past temporal values

• future: list of pointers to future temporal values

The TEMPORAL-VALUE class is defined by means of a value and the begin and end points as the ins­tant limits where the value was, is, or will be ta­ken. Both time points are pointers to tp (instances of TM_NODE) in the Time Map. Each tp has a pointer to the slot which it belongs, and three lists of tp's with relation of BEFORE, AFTER, and AT asso­ciated with a temporal distance.

The following figure 1 shows the relations between these data structures.

TEMPORAL MANAGEMENT

The set of management routines of a Time Map is called Time Map Manager (TMM). TMM func­tions manage the basic operations of creation, de­letion, and temporal relations management between temporal values. In order to manage future values

461

History buffer ��IT:"' Future values

( ooe• • • ) • � Time

TEMPORAL VALUE

Figure 1 : Temporal data structures

in a proper way, a suitable solution is to provide a reason maintenance system (RMS) cooperating with the TMM. Both components allow to manage logical dependencies and coherence of temporal values.

The main operations of a TMM are the updating and retrieving temporal information. Following sections describe these processes in depth.

Updating process

The function for updating a temporal constraint bet­ween two time points with relation rel (BEFORE, AF­TER, or AT) and a distance is:

a.ddTemporalRelation(tp, , rel, tdi., tpi)

The updating process of a new constraint performs a consistency and non-redundancy checks. If the new constraint is consistent and non-redundant with the existing ones, the new constraint is asserted in the Time Map. Thus, the result of this operation may

be:

• Contradictory, whether the temporal constraint to be updated is inconsistent with the informa­tion already represented in the TBB. In this case the TBB keeps with no modifications.

• Redundant, whether the temporal constraint to be updated can be retrieved from the ones exis­ting in TBB, and so it will not be introduced.

• Updated, whether the temporal constraint is up­dated.

Retrieval process

Two ha.sic retrieval operations are performed by the Time Map Manager: retrieve a concrete temporal constraint between two time points and evaluate the more constrained temporal distance between two time points.

(retrieveTemporalRela.tion ( tp; , AFTER, tdi., tp;)

(retrieveTemporalDura.tion ( tp; , tpi)

The retrieval of an specific temporal constraint bet­ween two nodes is stated a.s a path searching process between the two nodes throughout the rest of no­des in the Time Map. Due to the existence of many possible paths between the two nodes, the goal is to find a restrictive path according to the inquired cons­traint by combining the temporal constraints of the edges in the pa.th. That is, to obtain a pa.th which permits to provide an answer 'true' or 'false', if it is feasible to be deduced from the Time Map. The result of this function may be: True, False, or Pos­sible. A response Possible can be obtained in two cases: i) There is no pa.th relating both nodes, or ii) Though existing a path, the information provided is not enough to deduce neither the constraint nor the opposite one.

In this way, the stated retrieve operation consists of obtaining the shortest combined pa.th between two time points in a directed graph whose edges are labe­led with a temporal relation and a weight (positive or negative). This algorithm is based in a bidirectional search from ea.ch time point involved in the expres­sion looking for the direct and inverse relation in the graph.

The second recovery processes obtains a response a.bout a concrete temporal constraint between two time points. In order to evaluate the more constrai­ned temporal distance between two time points the same process can be used. Thus, the exact tempo­ral distance between the two tp's, or, the maximum and minimum temporal distance between tp's can be obtained.

462

Evaluation

Above operations are the most complex in the tem­poral information management. They can decide whenever a model is appropriated for real time sys­tems or not. The described temporal model proces­ses has been implemented by means of efficient al­gorithms [BARBER92] in Common-Lisp running on a Sun SparcSta.tion 2 and tested by running a. great number of representative empirical proofs on Time Maps randomly generated. Figure 2 shows the ma­ximum time for ea.ch TMM process for a Time Map with 30% of nodes related with the clock and, four temporal constraints for ea.ch node as average ratio.

msec. 6 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0

0 0

-- Retrieval - · ·· · · Updating

,' ,' . . . . . . . . . . . . - . - . . . - � · ........• .: ... . . . . . . . . . . . . . . . . . . . . . . . \ . . �<·· ,(

. . . . . . . . . . . . . . . . . . . ·::.· � · "" · : : i-;' :

. . . . . . . ..., .... . -:' . . . 5 0 0 1 0 00 1 5 0 0 2 0 0 0 n2 nodes

Figure 2: Updating and retrieving processes eva­luation

In this Time Map, 1800 nodes has been introduced with 600 numerical constraints between a node with the clock and 7200 between two nodes. Computatio­nal times have been measured each 10 nodes. Ta.king into account the test results, a nearly linear beha­vior for the updating and retrieving processes can be assumed. The computational cost for the deletion process is constant (10 msec). Moreover, the spatial cost in all cases was not relevant.

BLACKBOARD STRUCTURE

Blackboard structure provides storage and manage­ment of application objects used by concurrent reaso­ning processes. Figure 3 shows the relations between all components in a real time expert system.

Blackboard interface provides a set of functions that can be used by a user language to express actions, such as class definition, object instantiation, and temporal updates and queries. Some of these fun­ctions can be used as rule predicates in the left hand side, and others, called in the right hand side, that updates the internal information.

With respect to the Left Hand Side temporal func­tions provided by the blackboard, they can be stated as:

Expert Process Data

Adquisltion

Timer

Agent 1

Agent 2

Agent N

Figure 3: Blackboard relations

• when_occurs (object slot begin end) This predicate is satisfied for those temporal va­lues (current or predicted) which, belonging to the temporal slot, match the value. The begin and end of the temporal value may be instantia­ted in variables. They can be either an absolute value or a tp.

• past_value (object slot value begin end) This predicate is satisfied when a current value in the defined slot is outdated and is moved from current to past.

• temporal_test (any temporal expression) Time-test function is used for asking about i) temporal relations between dates or begin or end of temporal values or ii) between a date or time points obtained from the begin or end of a tem­poral value and the current time (NOW).

The temporal_test management is achieved by using the TMM internal functions to to inform in the moment that a time point value changes its temporal window.

Blackboard functions in the Right Hand Side of the rule modify the internal state by adding values and predictions about slot values of nodes.

• put_value (object slot value begin end depen­dencies)

This function adds a value to a slot. If the slot is a temporal slot, then the function is used to create a current or a predicted temporal value according to the premises of the rule:

if there is at least one premise instantiated to a predicted temporal value, then the as­serted value will be predicted

463

if all the premises are instantiated to cu­rrent temporal values then the asserted va­lue will be current.

In the former case, when all the predicted pre­mises supporting the asserted value change to current, then the created value also change to current. In this case, the existing temporal cons­traints for its end-time are retracted and only the temporal constraint (after begin) is main­tained. And if some predicted premise is not fulfilled, then the asserted predicted value will be deleted. When a current value is asserted in a slot, if there is a previous current value in it, then this current value is moved to its historical buffer of past values. The end time of this previous current value is modified with the date corres­ponding to the begin of the new created current value.

• predict_value (object slot value begin end de­pendencies) Adds a predicted value to a temporal slot. The user specifies the begin and end date for the va­lue, by writing temporal restrictions expressing BEFORE, AFTER or AT a time point. The status of the created value is always predic­ted. It may change according to the following specification

to current: a predicted value created with this function is changed to current when the prediction is fulfilled, this only can occurs when a new value (that matches with the prediction) arrives by means of a put_value.

deleted: a predicted value is deleted in two cases: i) when arrives the upper time of its begin temporal window and the predic­tion has not been fulfilled and ii) when was created with predictions in the LHS of the rule and one of this predictions is not ful­filled.

The following meaning for the predicted values is as­sumed: a prediction is matched by a new (predic­ted) temporal value when it has the same value and the begin and the end of the new temporal value are respectively within the temporal windows of the be­gin and end of the prediction. Then the temporal window of the matched prediction can be constrained according the new prediction. In this case, pending queries can be updated. A prediction is fulftlled by a new (current) temporal value when it has the same value and the begin and the end of the new temporal value are respectively within the temporal windows of the begin and end of the prediction.

If there is some prediction about the slot which is fulfilled by the put_value (current value), then it is not created a new current temporal value. Then the status of the fulfilled prediction value is changed to current. In this case, the temporal constraints for its

end time are deleted, since a current value has not end temporal constraints. Only the temporal cons­traint (after begin) is maintained.

Blackboard informs to other components in the sys­tem when new current, past or prediction values are created or predictions fulfilled or deleted.

EXAMPLE

In order to illustrate the main features of the propo­sed functionalities a small example is described. The example is based in the temperature subprocess of a cement kiln.

There are three temperature sensors at beginning, middle and end of the kiln. From these inputs, some internal variables (kiln status as hot normal or cold) can be deduced. There are three variables that per­mit control the kiln status at beginning, middle and end: the input of fuel, fl.ow of fumes, and external air fl.ow, respectively. There is a delay in the raw material fl.ow along the kiln.

The system can be modeled by means of three clas­ses: SENSOR, VALVE, and STATUS, with some static attributes as name, location, range, etc., and a tem­poral attribute value. Another class KILN models the relations between all objects. There are defined th­ree temperature sensors TS! , TS2 and TS3, three kiln status KS! , KS2, and KS3, and three valves VI, V2, and V3. A persistence is assumed for the sensor inputs.

The following rules express the system behavior:

Rl: Determines the value of the status from its sen­sor. when a new sensor data is added, if the temperature value is high, then the status is hot.

Some alternative Rl rules deduced the normal and cold status.

R2: Predicts a change in the next temperature point taking into account the fl.ow delay. A minimum dmin and maximum dmax delay is assumed. When a new status is added, if the kiln status is hot then predict high for the next temperature value with a begin point after(dmin) and before{dmax).

R3: Takes decision about open or closed the associa­ted valves to a determined point. When a new status is added, if the kiln status is hot (cold) then closed (open) now the associated valve.

Let consider the following situation: at time Tl a new sensor data TS! arrives, and the reasoning process is performed at T2 producing the results showed in figure 4.

464

Tl T2 TS T4 T& T6 TT Ta

TSl

KSl -TS2 -

D KS2 E TSS - -. D -KSS u c Vl E V2 D vs

current

Figure 4: Initial deductions

KS! is deduced as hot in [Tl , oo], TS2 is predicted as high with a delay and as consequence KS2 hot. As a prediction on KS2 is produced rule R3 is instantiated with this new fact and another prediction on TS3 and consequently on KS3 is produced. Each time a value for some KS is added an action of open or close the associated valve is produced but in the current time T2.

In this scenario if a time T3+o a new value of TS2 is read matching the prediction, the following situation is obtained (figure 5) .

Tl T2 TS T4 T& T6 TT Ta

TSl -TS2 .

K S l KS2

T TSS -.

M KSS M

Vl -.

V2 . vs .

current

Figure 5: Prediction matched

Note that the temporal window of TS3 and KS3 are updated being more restricted due to the new added knowledge.

Now, let consider when a prediction is not matched. If any TS2 match the prediction, at time T4 (end of begin window) predictions about TS2, KS2, and obviously TS3 and KS3 are removed (figure 6).

Tl T2 T3 4 T& T6 TT TB

TSl

KSl - � . TS2 - -

KS2 T TS3 -

M -KS3

M -

Vl -

V2 : V3 :

-

current

Figure 6: Prediction not matched

CONCLUSIONS

In this paper, a temporal blackboard has been pre­sented. The temporal information is associated to the temporal attributes of objects stored using a model based on time points. The proposed model permits to represent a great number of situations including uncertainty. In order to have efficient methods to be applied under time constraints, past facts are sto­red with respect an absolute clock and future using a graph when there is no possible due to the facts dependencies. Fast algorithms permits to update and retrieve temporal information in the Time Map. Some results of these operation has been showed.

Finally, some temporal features has been explained using a small scenario of a cement kiln process.

Acknowledges

The authors acknowledge to T. Chehire, A. Mensch, J.Y. Quemeneur, D. Kersual, J.J. Galan, I. Rodriguez, E.

Pezzi, C. Luparia, A. Lupi, M. Shenton and R. Fjellheim its comments and its participation in the global architec­ture described in this paper.

REFERENCES

[ALLEN83] J.F. Allen "Maintaining knowledge about temporal intervals" . Comm. of the A CM. VOl 26, No. 11 , 1983.

[ALLEN84] J.F. Allen "Towards a general Theory of Action and Time" . Artificial Intelligence, 23, 1984.

[BARBER92] F. Barber, E. Onaindfa, M. Alonso. "Representation and management of temporal re­lations" . Novatica. 1992.

[DEAN87] T. Dean and D. McDermott "Temporal Data Base Management" Articial Intelligence, 32, 1987

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[DeKLEER84] J. De Kleer, J.S. Brown. "A Qua­litative physics based on confluences." Articial Intelligence, 24 August (1984), pp. 7-83.

[FORBUS84] K.D. Forbus. "Qualitative process the-ory" Articial Intelligence, 24 August (1984) pp.85-168.

[ISERMAN87] R.Isermann (Ed.) . Procc. of the 10th world congress on automatic control. IFAC-87, vol.6, (1987).

[KOWALSKI85] R.A.Kowalski, M.Sergot. "A logic­based calculus of events." New Generation Com­puting,4 (1).(1985).pp.67-95.

[KUIPERS84] B.Kuipers. "Commonsense reasoning about causality: Deriving behavior from struc­ture" Artificial Intelligence, 24, pp.169-203.

[LAFFEY88] T.J. Laffey, P.A. Cox, J.L. Schmidt, S.M. Kao and J.Y. Read Real-Time Knowledge­Based Systems. AI Magazine. Spring. 1988.

[McCARTHY69] J.M. McCarthy, P.J. Hayes. "Some philosophical problems from the standpoint of ar­tificial intelligence." Machine Intelligence,4. Edin­burgh Univ. Press. (1969).

[McDERMOTT82] D.V. McDermott. "A temporal logic for reasoning about processes and plans." Cognitive Science,6. (1982). pp.101-155.

[PERKINS90] W.Perkins, A.Austin. "Adding tem­poral reasoning to expert-systems building envi­ronments" . IEEE-Expert. Freb.1990.

[REAKT90] Thomson, Syseca, Crin, GMV, UPV, Marconi, Etnoteam, Computas. REAKT: Environment and Methodology for Real-time Knowledge Based Systems. ESPRIT II 4651. 1990-93

[SOHAM88] Y. Shoham. Reasoning about change. MIT Press.(1988)

[TSANG88] E.Tsang. "Elements in temporal reaso­ning in planning" Procc. of ECAI-88 Munchen. pp.571-573.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

REINFORCEMENT LEARNING AND RECRUITMENT MECHANISM FOR ADAPTIVE DISTRIBUTED CONTROL

H. Berslnl

/RID/A - Universite Libre de Bruxelles CP 19416, 50 av. Fr. Roosevelt, B-1050 Bruxelles, Belgium

Abstract The work presented in this paper is an attempt to spread further the inspiration gained from the knowledge of biological systems into the field of adaptive control. After the neural controllers and the evolutionary based mechanisms, new hints for the control of complex processes might be derived from other biological domains such as immunology or the study of conditioning learning. The conception of a system equipped with a complex controller, interacting with an uncertain and varying environment, and basing its learning on its own experiences entails quite naturally the integration of a reinforcement learning mechanism. Two learning processes characterized by two different time scales will be introduced, will be connected to their respective biological origins and will be illustrated on the classical cart-pole control problem. These two learning processes are the rapid reinforcement learning and the slower recruitment mechanism.

Keywords Process Control; Reinforcement Learning; Dynamic Programming; Distributed Control; Immune System; Recruitment Mechanism

INTRODUCTION

The work presented in this paper is an attempt to spread further the inspiration gained from the knowledge of biological systems into the field of adaptive control. After the neural controllers (Barto, 1990) and the evolutionary based mechanisms (see (Renders, Nordvik and Bersini, 1992) for a survey on applying genetic algorithms to process control), new hints for the control of complex processes might be derived from other biological domains such as immunology or the study of conditioning learning. Very briefly, two learning processes characterized by two different time scales will be introduced, will be connected to their respective biological origins and will be illustrated on the classical cart-pole control problem. These two learning processes are the rapid reinforcement learning and the slower recruitment mechanism.

As stated by Barto (1990), when the performance measure for a "weakly supervised" system is not defined in terms of a set of targets by means of a known error criterion, reinforcement learning addresses the problem of improving performance as evaluated by any measure, "informative enough", whose value can be supplied to the learning system. Roughly, systems exhibiting reinforcement learning adapt themselves in response to hardly informative feedback such as : "it's good", "it's bad". While it is difficult to imagine any different type of learning for biological or behavioristic systems, the increasing interest raised by this learning approach in the control community is a direct consequence of the

467

wish for more and more complex and autonomous systems. A very representative example of this new class of projects is the conception of robots which, wandering in an environment cluttered with obstacles and able to pick and carry some objects, must learn to do so while avoiding the obstacles.

The complexity can be inherent to the control mechanism itself when the precise knowledge of how to tune the control parameters in order to obtain a precise control behaviour is lacking i.e when the controller does not possess a sufficient self­knowledge. This can be the case for distributed or "emergent" control when the interesting resulting behaviour is an holistic phenomenon. Each actor "has no view" on the final objective it contributes to satisfy. Therefore the effect of one actor modification on the global behaviour is not easy to predict and the learning must be more of a "trial and error" than of a "gradient" type. However the complexity can also be inherent to the process or environment the controller is interacting with. This environment can be uncertain, varying and hard to specify. In such case, the precise impact a change in the control parameters provokes in the environment is unknown and there again, the controller needs to adjust its parameters not according to a gradient completed by a sensitivity analysis of the environment but through trial and error instead. Then reinforcement learning is partly due to an uncertain knowledge of both the controller and what is controlled.

On the other hand, an autonomous system reveals autonomy with respect to two different things: the

human operator or programmer and the system environment. Firstly, the controller should not rely any more on attentive human supervision, teaching it the exact way it must behave. Moreover it must interact with an environment whose feedback will never be as precise as a quadratic error to minimize by any gradient but purely qualitative and hardly informative instead. For instance the robot bumps yes or no into the obstacles, reaches yes or no its target, etc .... The environment must not be seen any more as an instructor but rather as a mean to trigger or to select the controller potential way of behaving (Bersini, 1992). In short, the conception of a system equipped with a complex controller, interacting with an uncertain and varying environment, and basing its learning on its own experiences entails quite naturally the integration of a reinforcement learning mechanism.

In addition it is very rare to see the qualitative feedback following the control actions occurring without any delay. In general (think about the robot) a sequence of control actions is executed before to receive any information on the quality of the whole sequence, and once received, the impact of this information on each step of the sequence can be a serious difficulty. Recently Barto, Sutton and Watkins (1990) have derived a new type of reinforcement learning algorithm in order to account for this feedback delay. The idea is simple although ingenious. When the effective impact of the environment, whatever it is (positive or negative), is delayed, it is still possible to provide the controller with an intermediary reinforcement measure. This information is obtained while the controller is acting and it allows to improve on-line the successive choices of actions.

A decision policy at a certain stage of the control sequence is adjusted only on basis of what will happen at the subsequent stage (not the final one). The nature of this intermediary reinforcement measure (the whole methodology is called Temporal Difference (TD) and presented in a more formal way in Sutton (1988)) has led to a family of algorithms whose simplest member is the Q_learning algorithm which will be presented later in the paper. Since in dynamic programming too, a decision at an certain stage is only a function of data retrieved at the subsequent stage, the connections of the delayed reinforcement learning family with dynamic programming is a very advantageous point and make such learning very promising in the control community (Barto, 1990; Barto and Singh, 1990).

The immune network model proposed and developed by Varela and colleagues ( 1988,1989,1990) comprises two major aspects. The first aspect concerns what has been called the dynamics of the system i.e the differential equations governing the increase or decrease of the concentration of a fixed set of lymphocite clones and the corresponding immunoglobins. The network view relates to the immunoglobins interactions by mutual binding. The binding of two species is defined by an affinity value

468

between these two species. Such value is function of the species physical and chemical properties and then does not change. The second aspect concerns what has been called the meta-dynamics of the system. It governs the intermittent recruitment of new species from an enormous pool of lymphocites freshly produced by the bone-marrow. This recruitment process selects for the generation of a new species on the basis of the current global state of the system i.e. according to the sensitivity of the network for this candidate species. This complementary process is fundamental because it modifies continuously the actors in presence like a neural net whose structure (the number and the nature of neurons) would change in time.

In the methodology exposed in this paper, this recruitment mechanism is responsible for the time to time renewal of some control actors. Then two learning mechanisms occur characterized by two different time scales: a rapid reinforcement learning during which the current actors are punished or rewarded such as to improve the control resulting from their collective behaviour, and a slower recruitment mechanism generating new actors in the system necessary if the current population of actors is not satisfactory enough. It is worth mentioning that the methodology described here is close in spirit to the Holland's Classifiers Systems (Holland and colleagues, 1986) and enters in a large family of biologically-inspired systems whose common feature is a three time-scales dynamics (a state dynamic + the two learning mechanisms: a parameter dynamic and a graph dynamic, see (Farmer, 1991)) and which comprises: GENET (Hebbian Leaming + GA for optimizing neural net structures), Classifiers Systems (Bucket Brigade Algorithm + GA for generating new rules), Immune Network (varying concentration of cells + recruitment of new cells) and autocatalytic network.

In the next chapter, the general approach and the role played by the reinforcement learning are exposed in details. Then the recruitment mechanism is presented. The final chapter contains experimental results of the methodology applied to the simple cart-pole problem.

THE GENERAL APPROACH

x2 x2 ' �

--

xi xi

a) b)

Fig. 1. The general framework

Suppose the process to be controlled characterized by a state vector X(t) = {xi(t)} represented in the state space Rn. This state space is partitioned in several sub-zones or cells. Each variable Xi has its do�n of variation divided in Ki intervals: [xi

m(k),xi (k)] with xiM(k) = xim(k+l). Then, the total number of cells is IliKi. Figure la illustrates such partition for a two variables process.

Here we will consider a control problem with one objective: the process must reach a certain specific cell, and one constraint: the process must not leave a specific zone (which will be called a zone of viability (this denomination comes from Aubin (1989)). Such constraint of viability might relax the objective to follow a referential trajectory for processes either too complex or interacting with an open, hard to formalize and unpredictable environment. On the other hand this constraint fits the objective of reliability or safety which are generally stated via the establishment of a bounded zone for some variables of the process. In the present approach the zone of viability will be a certain union of the cells. For each cell c, a quality measure is defined Qc. For sake's of clarity we will suppose simple values: Qc=O for the cells in the zone of viability, Qc = -1 for the cells outside the zone and Qc = 1 for the target cell. Figure 1 b illustrates these values of cells quality.

The control is then in the hands of a large amount of small operators whose responsibility is limited to their cell. The same operator acts on the process as long as the process stays in its cell. One and only one operator has to be found out in each cell. Initially a random set of n operators is generated by cell. At the end of the reinforcement learning stage, only one operator will be preferentially selected in each cell. An operator acting in a cell c: Oc is characterized by k values to optimize and then can be described by a vector W in a k dimensional space W = { w l • w2 ..... Wk} . Consequently, it can be symbolized by Oc(Wi) with c indexing the cell and i indexing the operator (from 1 to n).

Distributed control is closely connected to real-time control and the appearance of more and more sophisticated parallel computing architectures is backing up this claim. Distributed control is in the hands of a set of very simple operators. Each operator has a localised responsibility and a localised access to the information either when acting or when improving itself from the result of its act. The larger the distribution, the easier a future hardware parallel implementation. Generally the local communication existing among the operators amounts to trivial excitatory or inhibitory signals. The improvement of each operator depends on the behaviour of its closest neighbours namely the whole system exhibits local plasticity. The interesting resulting behaviour is an holistic phenomenon. No operator has any privilege view on the final objective it contributes to satisfy.

Since the Selfridge's Pandemonium updated today into the blackboard methodology, the idea of

469

distributed control is nothing very new in AI. It participates to this recent enthusiasm for auto­organising systems demonstrating emergent functionalities (Forrest, 1991) like an Hopfield-like neural net or a colony of insects. It is deeply involved in Minsky's society of minds and Brooks' subsumption architecture. Distributed control can achieve two different kind of objectives: l)cooperative control where different operators can act simultaneously on different parameters of the process. The responsibility is distributed on space. 2)sequential control where at any time one and only one operator is acting on the whole process. The responsibility is distributed on time. Direct control based both on production rules (Jager and colleagues, 1990) and fuzzy rules (Lee, 1990) can be classified in the second category. The paper concrete part will be restricted to this category.

Q_LEARNING

The basic learning problem turns to be the discovery in each cell of the appropriate operators i.e the ones which collectively guarantee the attainment of the objective: reach the target while keeping the process viable. Each operator Oc(Wi) is characterized by a quality value: QOc(Wi). The selection of the operator which acts when the process accesses its cell is achieved through a probabilistic Boltzmann distribution. The probability of selecting operator i in cell c is given by:

Pi = eQOc(Wi)ff n L eQOc(Wj){f

j=l

(1)

T is a temperature parameter that adjusts the degree of randomness.

Once an operator i has been selected in the cell c, it will control the process as long as the process stays in this same cell. When the process leaves that cell to get into a neighbouring one c+ 1 , the quality of the just acting operator is updated by:

QOc(Wi) <== (1-a)QOc(Wi) + aR (2)

with a < 1.

R is called the critic in the reinforcement learning literature and it is the only information feedback the operator receives:

R = (Qc+ 1 - Qc) + 6Maxj(QOc+ 1 (Wi)) (3) 6 is the discount rate and 6 < 1

Maxi(QOc+ 1 (Wi)) is the quality of the best operator (i.e the one with the highest probability to act) acting in the next cell.

The formula for R clearly indicates the connection with dynamic programming. It is supposed that the best strategy is already discovered in the next cell although the learning is incremental, on-line and direct (without any prior knowledge of the process).

Qc+ 1 - Qc = 0 as long as the process stays in the viability zone; Oc+ 1 - Qc = -1 when the process leaves the viability zone (the control is punished). Qc+ 1 - Qc = 1 when the process accesses the target cell (the control is rewarded).

It can be shown (Barto, Sutton and Watkins, 1990) that the value of the operators quality tends to:

QOc(Wi) ==> Lj=l ..msi<Qc+yQc+G-1)) (4) which is called the discountive cumulative reward.

According to this, the quality of the operator will be as great as its action contributes to keep the process viable the longer the better i.e (Qc+m - Qc+m-1)= -1 for m>>>>>, and to access the target cell the faster the better i.e (Qc+m - Qc+m-1) = 1 for m<<<<.

When applying Q_learning in the field of process control, the kind of problems to be faced is stochastic i.e the exit cell c+ 1 is not only dependent on the action taken in the current cell c but also on the way the process accesses that specific cell c (in a sense it depends on the previous cell c-1 ). Applying dynamic programming to this problem would require the knowledge of the state-transition probabilistic matrix i.e p(c+ l/c,i): the probability to access cell c+ 1 when the operator i acts in cell c. This would require either an important amount of prior simulation or a preliminary analysis of the problem. In (Barto and Singh, 1990), it is explained why Q_learning avoids these very computationaly expensive preliminary data and compares favourably with dynamic programming despite this absence of the explicit transition probabilistic matrix.

Recently several additions have been proposed in order to reduce the problem search space so as to accelerate Q_learning. For instance, Whitehead (1991) suggests to rely, when available, on external teacher which might provide shorter latency feedback. A biasing function BOc(Wi) is then associated to the quality function of the operator and the selection is based on the sum of the two contributions: BOc(Wi) + QOc(Wi). The biasing function is updated by:

BOc(Wi) <== (1-a.)BOc(Wi) + a.Re+ 1 (5)

with Re+ 1 provided by an external teacher immediately following the operator Oc(Wi) action and no more at the end of a sequence of actions.

Other improvements address the computation of the operators quality QOc(Wi). Suppose that in each cell a same set of operators can act: Oc(Wi). Now define a quality measure for each operator (the indices have

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to be inverted) OOwi (c) which is now function of the cell it is acting in. Instead of updating the quality each time the process leaves a certain cell, a better strategy might be to store a sequence of operations and effects, that is to say a sequence of: (c,Oc(Wi),c+ l ,R) i.e in cell c, the acting operator was Oc(Wi) driving the process to c+ 1 and receiving a critic R. This sequence can be replayed backward several times and the function QOwi (c) can be learned by any gradient technic. Indeed QOwi (c) must be equal to the discountive cumulative reward and then the error to minimize is the desired value: (Qc+1 -Qc)+ BMaxiQOwi (c+l ) minus the current value QOwi (c). On account of its non-linear mapping capabilities, Lin (1991) makes the quality function to be implemented by a neural network. For each operator, the input of the net is the cell indices and the output is the quality value of the specific operator in that cell. Besides, the use of neural nets can avoid the pre-partition of the state-space and it is worth to mention that the existence of this state­space checkerboard implies a prior analysis of the problem and hampers greatly the "generalisation" capability of the technic (an important issue discussed in (Chapman and Kaebling, 1991)).

The strategy called experience replay is connected to Sutton (1990) relaxation planning technic in which Q_leaming is both performed in the real world during real experiments of the control system but also in a model of the process which is learned progressively in function of the actions that have been done so far on the process. This leads to a combination of reactive planning (search of the solution by trials and errors in the real world) and strategic planning (search of the solution by trials and errors in an hypothetical world). All these proposed improvements are based on the blending of supervised or teaching strategy (when some external teacher or any hypothetical model of the process is available) with pure unsupervised reinforcement learning for further refinement

As already stated a crucial point of the methodology is the partition of the state space. Complementary works are in progress to leave the controller to discover alone an economic but satisfactory partition of the state space. This partition is important for 1 ) the quality of the final control 2) the speed of learning (less cells accelerate the search) 3) the input generalization capability. This partition is a sensible problem and has recently deserved a special treatment in (Chapman and Kaebling, 1991). Instead of fixing from the beginning a specific partition of the state space, the authors derived an algorithm which performs a recursive splitting of the state space based on statistical measures of differences in reinforcements received. The state space is divided in an incremental way and the gain in the critic information content is verified. This division stops when a further step would not improve the information to be received.

Two extensions are needed when Q-leaming is being compared with other adaptive control methodologies

1) relaxing the need to observe the behaviours of all variables namely the necessity to make a partition for each variable of the process 2) extending the control objectives to include the smoothness of the controller.

Suppose the process to be controlled characterired by some variables xi and their temporal derivative dxi/dt. In order to avoid the controller to be an explicit function of the derivatives variables generally hard to observe (i.e to avoid any partition of these variables, the reduced state-space will no more contain the derivatives), one can make the operator in each cell to be function of the inlet cell: Oc c-1 (Wi). The selection will only concern the sub­set' of operators Oc c-1(Wi). When the operator has just acted it is upruited in considering the quality of the exit cell operator itself a function of the inlet cell, in our case c:

QOc,c-1<WO <= (1 - a)QOc,c-1(Wi) + cxR (6)

with R = (Oc+ 1 - Oc) + BMaxiOOc+ l ,c<Wi) (7)

When the process accesses cell c coming from cell c-1 , the probability of selecting operator i in cell c is given by:

Pi = eQOc c-1 (Wi){f n L eQOc,c-1 (Wj){f

j=l

(8)

Generally speaking the objective of process control is more than making the process to follow a referential trajectory or than forcing certain variables to reach a steady value. Requirements are also imposed on the quality of the control. One of these classical requirements is for instance to keep the variation of the control parameters as small as possible. The resulting control objective turns then to be expressed through a weighted combination of these two sub-goals. The methodology described in this paper can be extended to satisfy similar requirements. Suppose the quality of an operator to be a vector rather than a number: QOc(Wi,k) with each coordinate k related to a specific objective to satisfy. Here we will suppose a two-dimensions vector, the first dimension (QOc(Wi,l) playing the same role as the one described in the previous chapter, the second dimension (QOc(Wi,2)) relating to the objective of a smooth control. The global quality will be given by a weighted combination of the two qualities.

The updated mechanism turns to be:

QOc(Wi,l ) <== (1-a) QOc(Wi,l ) + a R(l) (9) QOc(Wi,2) <== (1-a) QOc(Wi,2) + a R(2) (10)

with

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R(2) = dist(Wi(c+l),Wi(c)) + BMaxiQOc(Wi,2) (12)

dist(Wi(c+l ),Wi(c)) is the Euclidean distance in the space W of the operators parameters.

The global quality which bases the final selection is given by:

with A l and A2 two weighting parameters.

Such extensions of the Q_learning algorithm are being implemented and the first experimental results are presented and discussed in (Bersini, 1991).

THE RECRUITMENT MECHANISM

A second and slower learning mechanism is responsible for the intermittent renewal of some actors in the cells. Either if the solution was not present in this first random set of operators or if the current solution can be improved, a fresh sub-set of operators can be "injected" in the cells and a next phase of reinforcement learning be initiated. Figure 2 illustrates these two learning strategies.

x2 Reinforcement learning: !J,. t = 1 Q0c(W,t+1 ) = ( 1 - a)QOc (W,t)+aR

ecruitment of new operators: Wi in cell j : !J,. t = 500;

Fig. 2. The two learning mechanisms

The way a new operator is recruited in a cell depends on a recruitment threshold which guarantees the new operator to be more similar with the best operators already present in this same cell and in the neighbouring cells. Since each operator in cell c is characterized by a certain vector Wi, a possible candidate Wk will be recruited for acting on the process if: Lim(Wk,Wi)QOc(Wi) > T (14)

m(Wk,Wi) is a similarity function of two points in the space W (i.e inversely related to their distance, (see (Bersini and Varela, 1990) for some possible profiles of this similarity function)). T is a threshold whose value can be adjusted in order to increase or to decrease the selectivity of the recruitment. In addition, this imposed resemblance of an operator with the operators in the contiguous cells ensures the

respect of continuity constraints in the controller space which both accelerates the learning and satisfies the important requirement of a smooth control. When an operator is newly recruited in a cell, it replaces the worst operator acting in this cell (i.e Mini(QOc(Wi)) and receives the quality value of the best operator in that cell (i.e Maxi(QOc(Wi)). Consequently, its probability to be tested in the next Q_learning phase is very high.

EXPERIMENT AL RESULTS

In order to illustrate and validate the two learning processes of the methodology, simple experiments have been achieved for the control of the cart-pole (this problem is largely described in the literature, for instance (Barto, Sutton and Anderson, 1983)). This process is characterized by four variables: x ,0 ,dx/dt,d0/dt making the distribution and the partition to be achieved in a four dimensional space. The aim of the learning is to find in each cell a force between - ION and +I ON (the force can have whatever value between -10 and + 10 so it is no more a classical bang-bang control) to exert on the pole so as to keep the pole viable the longer the best (the zone of viability is the same as the one described in Barto, Sutton and Anderson (x in (-2.4, 2.4) and 0 in (-I5°,I5°) ). The algorithm was the following:

1) Initially, 5 operators with random values in (-ION, ION) are present in each cell. Q_leaming runs for 500 steps (one step takes place as long as the process stays viable).

2) Each 500 steps, 5 new operators are recruited in whatever cells according to the recruitment mechanism. It makes the new value of the force to be closer to the two best operators currently acting in the specific recruiting cell.

3) Q_learning is released once again and so forth, back to the first stage.

The partition of the state space was adequately assumed to be a critical feature of the problem. Indeed, in case of the same partition as the one in (Barto, Sutton and Anderson) (I62 cells: 3 for x, 6 for 0, 3 for dx/dt, 3 for d0/dt), no recruitment was necessary to find a solution. On the whole, one solution was always in the prior random set and ±400 steps sufficed to keep the cart-pole viable. Since Q_learning algorithm has been mainly applied to Markovian problems (like the discovery of trajectory in (Sutton, I990)), very non-Markovian environments (here we mean that the exit cell depends not only on the operator applied in the current cell but equally on the inlet cell) like the cart­pole or any real process to control could become problematic. Surprisingly, the performance of the algorithm was pretty good and recently Barto and Singh (1990) have plead for the exploitation of Q_learning for direct adaptive control to the detriment of more formal and indirect approaches.

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Nevertheless, decreasing the partition of the state space, the difficulty of the problem increases and the experiments results testify to the need of the complementary recruitment mechanism. For instance with a 36 cells partition (3 for x, 4 for 0 , 3 for d0/dt), a good solution was generally absent from the initial random set and several recruitment generations were needed. In order to confirm the usefulness of the recruitment instead of leaving Q_leaming runs for more time, statistics were realized which indicate that the final solution always contains several of the recruited operators. In addition further tests were run to validate the quality of the recruitment based on the immune mechanism instead of just random recruitments. There again, the greater selectivity of the renewal through the recruitment test was responsible for better results than simple random renewal.

CONCLUSIONS

Q_learning algorithm has been proposed and extended to process control. It is a powerful methodology to be used when the control is distributed in a sequential way and the information feedback is given in a delayed and qualitative manner. It performs an on-line and computationaly cheap optimization of the control policy i.e the discovery of the best operator to act at any moment which compares favourably with the more demanding approach based on exact dynamic programming. The first feature i.e sequential distribution is becoming more and more current when exploiting AI technics such as crisp or fuzzy production rules for process control. Indeed, generally the premise of the rule encodes the variables domain in which the action part of the rule must be applied to the process. The second feature i.e the poor quality of the information feedback is typical of complex processes where no prior knowledge of the process to control is available, only few and crude observations are possible and complex controllers, distributed and highly non­linear, have to be used.

The recruitment mechanism inspired from the recruitment of new cell species in the immune system allows an intermittent refreshing of the current actors. This second adjustment is necessary if either no solution is in the current population of actors or if one solution exists but needs to be improved. In a related paper (Bersini, 1991) the presence of this complementary mechanism is further justified to improve the adaptability of the controller interacting with an unstable process. In case of failure or modification of the process to control the process could get in various cells it has never passed through before. In the immune system, the adaptability relies in a large part on the randomness of the recruitment mechanism (Bersini and Varela, 1990). Here too, the optimization algorithm allows the contingent recruitment of operators in cells never visited before just in case these cells would be visited. Once the process gets in a virgin cell, an operator is available to react. In the same time, the

two learning mechanisms initiate a search procedure to improve the operator acting in that cell.

REFERENCES

Aubin, J.P. (1989). Learning Rules of cognitive processes. In C.R. Acad. Sc. Paris. T. 308.

s.tritl Barto, A., Sutton, R. and C. Anderson. (1983).

Neuronlike adaptive elements that can solve difficult learning control problems. IEEE Transactions on Systems. Man a n d Cybernetics. 13(5).

Barto, A. (1990). Connectionist Learning for Control. Neural Networks for Control (Thomas Miller III, Richard Sutton and Paul Werbos eds.) MIT Press.

Barto, A.G., Sutton, R.S. and Watkins, C.J.C.H. (1990). Sequential decisions Problems and neural networks. Advances in Neural Information Processing Systems 2. D.D. Touretzky, ED. Morgan Kaufmann, San Mateo, CA.

Barto, A.G. and S.P. Singh (1990). Reinforcement Learning and dynamic programming. Procee<lings of the Sixth Yale Workshop on Adaptive and Leaming Systems, New Haven, CT.

Bersini, H. and F. Varela. (1990). Hints for adaptive problem solving gleaned from immune networks. Parallel Problem Solving from � - H.P. Schwefel (Ed.) Springer Verlag.

Bersini, H. and F. Varela. (1991). The Immune Recruitment Mechanism: A Selective Evolutionary Mechanism. Proceedings of the fourth conference on genetic algorithms.

Bersini, H. (1991). Immune Network and Adaptive Control. IR ID IA Internal R ep o r t IRflRIDINJ 1-9.

Bersini, H. (1992). Animal's I. Towards a Practice of Autonomous Systems - Procee<lings of the First European Conference on Artificial Life -F.J. Varela and P. Bourgine (Eds.)

Chapman, D. and L. P. Kaebling. (199 1). Input Generalization in Delayed Reinforcement Learning: An Algorithm and Performance Comparisons. Proceedings of the 12th UCAI Conference.

Farmer, D. ( 1 99 1) . A Rosetta Stone to Connectionism. Emergent Computation. Forrest S . (Ed). MIT Press.

Forrest, S. (Ed) (1991). Emergent Computation. A Bradford Book - MIT Press.

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Holland, J.H., Holyoak, K.J., Nisbett, R.E. & Thagard, P.R. (1986). Induction: Processes of inference. learning and discovery. Cambridge: MIT Press.

Jager, R., H.B. Verbruggen, P.M. Bruijn and A.J. Krijgsman (1990). Direct real-time control using knowledge-based techniques. Proceedings of 1990 European Simulation Symposium.

Lee, Chuen-Chien (1990). Fuzzy Logic in control systems: fuzzy logic controller-part I and part 2. IEEE Trans. on Syst. Man Cyber. 20 (2).

Lin, L-J. ( 199 1). Programming Robots Using Reinforcement Learning and Teaching. In Proceedings of the 9th MAI Conference.

Renders, J.M., Nordvik, J.P. and H. Bersini (1992). Genetic Algorithms For Process Control: A Survey. In Proceedings of the second European Conference of AI for Real Time Control.

Sutton, R.S. (1988). Learning to predict by the methods of temporal differences. Machine Learning, 3, pp. 9-44.

Sutton, R.S. (1990). Reinforcement Learning Architectures for Animats. Procee<lings of the SAB Conference - 24-28 September, Paris.

Varela, F., A. Coutinho, B. Dupire and N. Vaz. (1988). Cognitive networks: Immune, neural and otherwise, in A. Perelson (Ed.), Theoretical Immunology. Vol.2 SFI Series on the Science of Complexity, Addisson Wesley, New Jersey.

Varela, F., V. Sanchez and A. Coutinho ( 1989). Adaptive strategies gleaned from immune networks, in B. Goodwin and P. Saunders (Eds.), Evolutionary and e.pigenetic order from complex systems: A Waddington Memorial Volume. Edinburgh U. Press.

Varela, F. and Stewart, J. ( 1990). Dynamics of a class of immune networks. I) Global behaviour. J. theoret. Biol. Vol. 144.

Whitehead, S.D. (199 1). A Complexity Analysis of Cooperative Mechanisms in Reinforcement Learning. In Procee<lings of the 9th AAAI Conference.

Copyright @ IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

USING NEURAL-NET COMPUTING TO FORMULATE REAL-TIME CONTROL STRATEGIES

Yoh-Han Pao

Department of Electrical Engineering and CompuJer Science, Case Western Reserve University, Cleveland, OH 44112-7221, USA and Al Ware, Inc., Cleveland, OH 44106, USA

Abstract. In this paper, we propose a new neural-net approach to learning appropriate control actions. It is not based on the more commonly accepted approach of learning a system emulator and a control-action generator with supervised learning implemented through minimization of errors. Instead, the net observes and records, and adjusts .WW activation and attention to reflect the frequency of occurrences. Such a net can track the time variational characteristics of physical plants and is compatible with the learning of real-time fuzzy controls.

Keywords. Real-time control; fuzzy controls; concept learning; frequency-based learning.

INTRODUCTION

In recent years, considerable progress has been achieved in the evolution of a hypothesis of how system control might be implemented effectively with artificial neural-net computing.

We choose our words carefully. We do not imply that researchers who evolved that understanding necessarily subscribe to the view that biological systems do indeed operate in that mode. Nor do we mean that this is a well explored and well verified understanding. Nor do we imply that there is no possibility or need for further advances. Quite the opposite.

Briefly, the key elements of that understanding include the following.

A supervised learning type of neural-net learns a system emulator. This is a 'next-step' system state predictor. With the same data, another neural-net learns a control-action generator. Again this is only valid for evolving the physical system to attainable next-step states. These two components can then be used in a variety of modes to control the system along desired trajectories and towards desired states. The work of others are concerned with the ultimate goals, with reward/punishment learning and with the control path. This area is contained in Pao, Phillips and Sobajic ( 1992) and articles in the book edited by Miller, Sutton and Werbos (1990) are relevant.

In all those considerations, there is of course the concern that the 'physical plant' might not be time invariant and the neural-net system emulator might

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gradually become inaccurate over a period of time. The question is how such system emulators might automatically update themselves in robust manner even in noisy environments. The idea that such nets might take time off to retrain is not plausible nor practicable. We pro.pose another i\PProach instead. In its present form, our proposed method of learning and exercising control is well suited to learning Fuzzy controls.

This paper is based on the work of Pao and Hafez ( 1992) on the learning of concepts in a manner suitable for real-time analog computing.

In the following, we switch our language to that of concept learning and to the recognition of whether a pattern is of positive or negative class. This is to be understood that in control situations we do indeed deal with scenarios or patterns which are not neatly formatted in the manner of artificial toy problems, but more in the manner shown in our discussion. In other words, let us imagine that a neural-net system of the type described in this paper is to learn how to control the setting of a 'regulator' switch in a physical plant. Both the net and the human control operator has access to the outputs from a number of sensors. On the basis of the sensor readings, the human operator sets the regulator setting to 'on' or 'off. However no one informs the net why the human operator acts in that manner, nor indeed whether all sensors are relevant, or what combinations are relevant. In other words, what are the concepts on which the control actions are based? This is why the concept learning discussion of the remaining part of this paper relates

to real-time control and we do not further translate from one domain to the other.

The difference between this approach and the previously cited understanding of neural-net controls, in that the net learns not by minimizing error, but merely by observing and recording. Also the net accommodates different operational environments ranging from clear-cut deterministic situations to somewhat stochastic situations, and then to situations where the net automatically augments its features to attain more discrimination powers.

THE LEARNING OF CONTROL ACTIONS: CONCEPT IDENTIFICATION

In cognitive psychology research, there is interest in trying to understand how people do conscious hypothesis formation. Anderson (1985) describes a typical concept-formation task in the following manner:

"Consider the following:

A dax can be large, bright, red and square, A dax can be large, dull, red and square, A dax cannot be small, dull, red and square, A dax cannot be large, bright, red and triangle, A dax can be large, dull, blue and square.

What is a dax?

The best answer is probably that a dax is a large square, .. "

As an illustrative example for our work, we use the same kind of material used by Bruner, Goodnow and Austin ( 1956) shown in Fig. 1 . The stimuli varied among themselves along four dimensions: number of objects (one, two, or three); number of borders around the boxes (one, two, or three) , shape (cross, circle, or square), and color (green, black, or red; represented in the figure by white, black or gray). Human subjects were shown number of such stimuli and were asked to discover the concept common to all the instances shown.

Three columns of cards are also shown in Fig. 1 . Each column i s made up of instances identified as members of a concept (+) or not (-). Each column represents a different concept. In the psychology experiments, the human subjects would be presented with the instances in a column, one card at a time. From these instances the subjects would try to determine what the concept was.

In our concept identification procedure, each positive or negative instance of a concept is represented in terms of a pattern of features. As shown in Fig. 2, the feature names are shape, color, count and border­number. Each feature can have any one of three values which are (circle, cross, square), (white, gray, black), (one, two, three) and (single, double, triple), respectively.

In this concept learning approach, we utilize a network of interconnected processing elements. This

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net differs significantly from many others in that processing is determined by parameters which are stored locally. Thus, although there is indeed much connectionism each node does not need to collect a great deal of information on parameter values from afar before it can decide on how to proceed computationally.

Of prime importance are the ideas of activation and attention. Fig. 2 can be understood better with the help of the schematic illustration of Fig. 3. In Figure 2, we see that the feature value 'cross' is activated three times in the training experience. However, two of the three times belonged to the positive concept whereas the third instance did not. Accordingly, the processing element splits its output activation in proportion to the relative frequency of the positive and negative classes. Therefore, we say that the frequency parameters are learned and are stored at the output gate. And the output energy which is finite is split among the outgoing connectivities in accordance with the frequency information.

On the input side the processing element needs to divide its attention among the various incoming channels which are connected to it. Accordingly, in Fig. 2 and Fig. 3, it so happens that a 'positive' node is able to devote its entire attention to the channel from a 'cross' while the 'negative' node only devotes half of its attention to the 'cross' channel.

When the cross node is activated, an activation of (2/3) x (1) = 2/3 goes to the 'positive' node while an activation of ( 1/3) x ( 1/2) = 1/6 goes to the 'negative' node, indicating that the 'cross' is likely to be a strong positive indication of the concept. Similarly, we see that 'two' also sends a strong activation to the positive node.

DISCUSSION OF THE METHOD

Bruner, Goodnow and Austin ( 1 956) state that concept 1 is 'two crosses', a conjunctive concept. Under some circumstances conjunctive concepts can be learned with a linear net. but under other circumstances it can be shown quite clearly that a linear net, such as we advocate, would not be adequate. In fact, we are now revisiting the old Perceptron discussion (Minsky and Papert, 1969) under very interesting and new circumstances.

To illustrate some points, let us now modify concept I to 'two crosses or one square', a disjunctive statement of two conjunctions. We encode the relevant subset of cards in terms of patterns with two binary-valued features, as shown in Fig. 4. As can be seen in Fig. 4, there is a total of sixteen concepts that can be constructed with the four patterns (in general, for an n-dimensional space of binary-value variables there are 22• boolean functions). It is known that if we represent the patterns as points in a 2 dimensional space then there are two functions, namely the exclusive OR and its complement, for which one cannot separate the 'true' points from the 'false"' by a linear equation, (Kohavi, 1978).

It is interesting that this situation is signaled by our network as shown in Fig. 5. When the complexity of the concept becomes greater than that which the network can handle, the entropies at individual feature nets attain their maximum values.

In our approach, we take note of what features are no longer effective indicators of class membership and build conjunctive features from those primitive ones. In the present case, we use threshold logic elements to synthesize the new conjunctive features 'one AND square', 'one AND cross', 'two AND square' and 'two AND cross'. Use of these new features results in a zero-entropy network, as shown in Fig. 5.

In this series of steps, we have shown and explained how the frequency-based concept learning approach using strength of actiyation and attention as local parameters determined by experience can learn concepts in three different modes. In the initial mode, when learning the concept of 'two crosses', it is not clear whether we are learning the concept f 1 = 'two AND cross' or the concept of /2 = 'some degree of two or some degree of cross'. It is interesting that the natural language expression of the two crosses does not distinguish between the two concepts, and ordinarily no one cares.

However, mathematically there is a difference and a linear net of the original set of feature values can gradually become increasingly inadequate either because there is noise or randomness in the instances or because the true complexity of the concept begins to be experienced. In practice this can be tolerated until the classification mistakes become too annoying or too costly. This second phase is of increasing entropy.

The third phase is initiated by the formation of new features consisting of conjunctions of those original features which have failed to provide classification information. It is highly likely that these new (contextual) features can result in a zero-entropy, i.e. highly deterministic mode of concept learning.

The first mode is the normal mode of human endeavor of mostly hypothesis-testing with some biasing by frequency. The second mode is that of heavy reliance on experience to cope with increasing randomness, and the third mode is that which is the result of new insight and deterministic hypothesis testing can be resumed. Concept 2 is circle or one border and concept 3 is equal number of objects and borders. All of those are also readily learned.

The proposed concept network architecture is simple and modular. Very large and extended connectionist networks can be built from the elements described in this paper. The output of one concept network can be used as an input feature by other concept networks, i.e. forming a hierarchy of concepts. Furthermore, the network can accommodate feature values which are linguistic, symbolic as well as numeric.

Processing is dependent on two values of locally synthesized and locally stored parameters. The complexity of communications (interconnections)

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does not increase significantly with the increase of the size of the net. The learning mechanism is plausibly described in terms of strength of activation and attention.

Both the learning and processing can be implemented with Analog VLSI.

We find that this methodology is eminently suitable for automatic learning of controls through observing an operator, without need of explanations. However the acquired knowledge can be extracted and stated in the forms of rules.

In this brief note, we do not have the opportunity to expand on the theoretical background of this work. However there are many interesting issues of computational complexity (Abu-Mostafa, 1 986; Kolmogorov 1968) and how networks automatically react to cope with increasing complexity. There are also other issues of how to 'chunk' the nets into another representative, namely that of production rules. These matters will be discussed in future communications. At present we conclude by saying that the network described in this paper is extendible and seems to be appropriate for implementing rather complex real-time control mechanisms.

REFERENCES

Abu-Mostafa, Y. ( 1 986). The complexity of information extraction. IEEE Transaction on Information Theory. IT-32, 4, 5 1 3-525.

Anderson, J.R. (1985). Cognitive Psychology and its Implications. W.H. Freeman and Company, NY.

Bruner, J., J. Goodnow, and G. Austin ( 1 956) . ..A Study of Thinking. J. Wiley, NY.

Kohavi, Z. ( 1 978). Switching and Finite Automata �. 2nd ed. McGraw-Hill, NY.

Kolmogorov, A. ( 1 968). Logical basis for information theory and probability theory. IEEE Transactions on Information Theory. IT-14. 5,, 662-664.

Miller, W.R., R.S. Sutton and P.J. Werbos (Eds.) ( 1990). Neural Networs for Controls. MIT Press, Cambridge, MA.

Minsky M. and S. Papert ( 1 969). Perce.ptrons. MIT Press, Cambridge, MA.

Pao, Y.H. and W. Hafez, ( 1 992). Analog compu­tational models of concept formation, Special Issue on Neural-Net of Analot Integrated Circuits and Signal Processing, Kluwer Academic Publishers, Boston, MA.

Pao, Y.H., S. Phillips, and D.J. Sobajic ( 1 992). Neural-net computing and the intelligent control of systems. To be published in the International Journal of Control Special Issue on Intelligent Control.

Concept 1

Concept 2

Concept 3

Fig. 1 . Concept Formation Task. A well-known concept formation experiement from the literature on cognitive psychology (Bruner, Goodnow and Austin, 1956; Anderson, 1985). For each concept, the subjects were shown a set of labeled cards. Cards that belong to the concept to tbe learned are labeled '+' while others are laneled '-'. Each card has four features; shape, color, count and number of bounders. Each feature can assume only one of three possible values. The set of all possible cards consists of 81 cards. Example cards for three separate concepts are shown above.

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Fig. 2. Network for Concept 1 .

Class + Class -

white grey black one two three

Concept 1

Pattern Class Network Pattern Type Label Output

I c{?{? I + + t I mm I - -

m --

Training I mmm l - - j I ++ I + +

1 ++ 1 + + Consulting

[±] + + (Generalization)

The network response for the training patterns and consulting patterns indicate that the network have acquired the concept of 'two crosses or black color'. Orginally, in (Bruner, Goodnow and Austin; Anderson, 1985), the ocncept was claimed to be 'two crosses', however the last training pattern justify the network response for the second consulting pattern.

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Upper layer processing nodes

Lower layer processing nodes

"Cross"

" "

1(2 1(2

D "Square"

Fig. 3. Illustration of a Small Portion of a Concept Learning Net.

Input gate

Frequency parameters are stored locally at the output gates of the processing elements of the input layer, while attention parameters are stored at the input gates of the output layer. Strength of activation from a processing element is distrubuted among output gates in accordance with frequency parameters. Spatial integration of incoming activation at input gates is governed by how much attention is devoted to each gate.

pattern x y fO fl f2 f3 f4 f5 f6 n f8 f9 no n 1 n2 f13 f14 ns PO 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Pl 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

P2 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

P3 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

PO = (O 0) P2 = (1 0)

[QJ [±] lool I <{}><{}> I

Pl = (0 1) P3 = (1 1)

Fig. 4. Concepts Representation in Terms of Boolean Valued Functions. There are 16 concepts with two binary-valued features. Each concept can be represented by a boolean functio non the two variables for visulation purposes, each of the four input patterns can be encoced into graphical displays of one or two squares or crosses. In this encoding, the square shape is assigned the value 'O' and the cross shape is assigned the value '1 '. The count 'one' is assigned the value 'O' while the count 'two' is assigned the value ' l '.

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+

one I\ D one I\ +

[QJ GJ loo! I c{}>c{}> I

two I\ D two I\ +

f9 = 0010101001 1 1

+

(1) Shape Feature Net (2) Count Feature Net (3) AND Operator Net (4) Shape&Count Feature Net (5) one I\ D (6) two I\ D (7) one I\ + (8) two I\ +

Fig. 5. Increasing Complexity of Hardware to Cope with Complexity of Concept. The concept of 'one' square or two crosses' is equivalent to the boolean function 'Exclusive OR', which can be encoded as a binary string 0001 101 1 1001 . The complexity of the concept, the function and the binary string is reflected in the Shape and Count feature networks, as their entropies are maximum. this cinmplex concept can be acquired only through the use of the AND operator's network, resulting in a zero-entropy network.

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Class + Class -

0 c{? D white grey black one two three

Concept 2

Pattern Class Network

Pattern Type Label Output

[QQJ j + +

I ++ I - *

[[] + + J ooo J - - Training

III - -

[ill + + l mmm l - -

* No classification -- Evidence for '+' is equal to evidence for '-'.

Fig. 6. Leaming Concept 2 with Original Set of Patterns The concept is cirle or 2 borders, a disjunctive statement of two simple concepts. The network response for the training patterns indicate that it could not clasify the second pattern. For that pattern, the output of the processing element 'Class +' is equal to the output of the processing element 'Class -'.

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Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

A SURVEY OF COMMERCIAL REAL-TIME EXPERT SYSTEM ENVIRONMENTS

K.-E. Arl.fn Department of Automatic Control, Lund Institute ofTechnology, Box 118, S-221 00 Lund, Sweden

Abatract: A technical survey of commercial real-time expert system environments is given. The real-time aspects of expert systems are dis­cussed. The differences between real-time and non real-time tools are described. A more de­tailed description is given of G2, RTworks, RTAC, COGSYS, and TDC 3000 Expert.

1. Introduction

The industrial interest in knowledge-based system (KBS) techniques has led to a number of proto­type implementations during the 1980s. This ap­plies to the process industry, power systems, and manufacturing industry as well as the aerospace industry. A large part of the prototypes have con­cerned real-time, on-line applications such as data analysis, fault detection and diagnosis, control, de­cision support, modeling and simulation, training simulators, etc., (Arzen, 1991 ) . However, in spite of the high activity the number of fielded systems has remained surprisingly low. A major reason for this has been the lack of expert system tools aimed at real-time applications. During the peak of the expert system boom in the beginning and mid 1980s the available expert system tools such as KEE, ART, Knowledge Craft, S .1 , etc., were not intended for and, hence, did not work well for real-time applications.

The first real-time system was PICON from LMI developed in 1984. PICON introduced many of the ideas and technical solutions which are now common in real-time expert system tools. Running PICON required a LMI Lisp machine. This was one of the reason why PICON never became any commercial success. In 1988 G2 from Gensym Corporation was released and has since dominated the market. G2 was developed by the same team that developed PICON and can be seen as the second generation of real-time expert system tools.

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The developers of real-time expert system tools can be divided into three groups. The first and largest group consists of software companies with an AI orientation. During the last few years sev­eral new systems have been released, e.g., RTAC from Mitech, COGSYS from Cogsys Ltd, RTworks from Talarian Corporation, Chronos from Sagem and Euristic, Nemo from S20, Pamela-C from Alcatel-Austria, Muse from Cambridge Consul­tants, Escort from PA Consultants, and Activa­tion Framework from The Real-Time Intelligent Systems Corporation. In process control applica­tions these systems are intended to be used as an add-on to conventional control systems as shown in Fig. 1 . In some cases the connection between the expert system and the conventional control system is bidirectional, e.g., when the expert sys­tem generates set-points to the control system.

The second group consists of the companies devel­oping traditional distributed control system. Com­panies like Honeywell, Hitachi, Toshiba, and Yoko­gawa all have their own real-time expert system tools. The tools are placed as optional add-ons to the control system in a similar way to Fig. 1. The tools are integrated in the sense that they have the same man-machine interface, a well-defined communication interface, and come from the same supplier. Bailey Control's Expert 90 system (Oyen et al, 1988) takes another approach. Expert 90 is a rule-based software module that can be embedded as a control block among the other control blocks in the Bailey Infi 90 control system.

The final group is the companies developing computer-aided control system design software. A good example of this is Integrated Systems that together with the engineering analysis and design tools MatrixX and xMATH has developed System­build, an integrated graphical model editor and simulator. Using a function library of linear and non-linear dynamic systems a hierarchical block editor is used to capture system topology and be­haviour. From the block diagram System build au-

Operator

Knowledge­based

system

Numerical module

Conventional control system

Figure 1. An add-on system solution

tomatically builds a simulation model. Using Au­toCode, a separate product, C, Fortran, or Ada code can be generated from the simulation model. What makes Systembuild relevant in the real-time expert system contexts is the optional System­build modules State Transition Diagram (STD), RT /Expert, and RT /Fuzzy. STD is a facility for designing finite state machines. RT /Expert and RT/Fuzzy are non-object-oriented, forward chain­ing rule modules applying boolean logic and fuzzy logic respectively. All the modules can be graphi­cally interconnected with the other types of blocks in Systembuild and run-time code can be gener­ated automatically.

The aim of this paper is to give a technical survey of the real-time expert system market. The pa­per does not discuss general expert system tools not aimed specifically at real-time applications al­though some of them, e.g., Nexpert Object and Clips, can also be used for this. Section 2 describes the special requirements that real-time operation imposes on KBSs. The general functionality of real-time expert system tools is discussed in Sec­tion 3. Finally, in Section 4 G2, RTAC, COGSYS, RTworks, and TDC 3000 Expert are described in more detail. The reason why these specific tools have been selected is primarily that these are the ones which the author is most familiar with. The focus of the survey lies on knowledge representa­tion and language, and on real-time issues.

2. Real-time aspects

Real-time, on-line applications of KBSs contains a set of special problems (Laffey et al, 1988) that differ substantially from the off-line consultation applications for which knowledge-based systems originally were developed.

Nonmonotonic reasoning: The reasoning sys-

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tern operates in a dynamic environment. Incom­ing sensor data, as well as inferred facts, do not remain static. Data are either not durable and de­cay in validity with time, or they cease to be valid due to events which have changed the state of the system. In order to maintain a consistent view of the environment, the reasoning system must be able to automatically retract inferred facts.

A synchronoua e11enta: The system must be responsive to asynchronous events. This includes interrupting less important processing and focus attention on the currently most important issues.

Temporal reasoning: Time is an important variable in real-time systems. A real-time system must be able to represent time and reason about past, present, and future events as well as the sequence in which the events occur.

Reaaoning under time constraint.: This cov­ers the problem where the system must be able to come up with a solution in time when the so­lution is needed. Furthermore, the best possible solution within a given deadline is desired. The topic includes the problem of estimating the time needed for internal reasoning. A measure of good­ness of the solutions or the different reasoning mechanisms that lead to solutions is also needed.

Several other real-time aspects are also important. The system must be able to cope with uncertain or missing sensor data. Interfaces must be provided to both conventional software and the external en­vironment. Finally, the execution speed must be sufficiently high. Many consider this the crucial problem. In comparison with the other problems and in light of the rapid hardware development this is, however, probably the leaat difficult prob­lem.

Many of the problems described above are ex­tremely difficult and very far from general solu­tions. In most cases, however, practical approaches exist that to some extent solve the problems. These practical approaches are being adopted by the real-time expert system tools.

3. Functionality

The kernel of a real-time expert system tool is the inference engine. In addition to the standard forward and backward chaining rule invocation it is usually possible to invoke rules at regular time intervals, at a specific time, or asynchronously when some event, e.g., that a variable receives a new value, occurs. It is often also possible to explicitly invoke a rule or group of rules, thus mimicing that the system focus its attention on some specific problem. In object-oriented systems it is often possible to write generic rules that apply

to all instances of some class. This greatly reduces the number of rules in the system. The rule syntax varies all the way from program code style to natural language style syntax.

The inference engine is either based on pattern­matching using some version of the RETE algo­rithm or on static links maintained by the infer­ence engine. The links connect the variables that the rules operate upon with the appropriate rules, and rules with other rules. During inferencing the inference engine follows the links to determine which rule should be tested next.

The data that the rules operate upon can be of varying complexity. In the simplest case only one data type, real values, is allowed. In more advanced systems different data types such as real values, integers, booleans, symbolical values, (e.g. Pascal style enumeration types), text strings, and lists may be used. Usually variables can be grouped together into user-defined structured variables. In some cases a full object-oriented ap­proach is used with class definitions, inheritance of object attributes, object instances, etc. In an object-oriented system objects can have different ways of referring to other objects. One possibil­ity is to use name references, i.e., the name of the referenced object is stored as the value of an at­tribute of the referring object. Another possibil­ity is to treat a reference between two objects as an instance of a special connection or relationship object. In graphically oriented systems objects are represented by icons and connections between ob­jects by graphical connections.

In most systems time stamps are associated with variables. Using these the system can check how old the current value of a variable is. In several systems time stamps are combined with validity or currency intervals that define how long the value of a variable should remain valid. Usually validity intervals are propagated to facts that are inferred or calculated from the variables. Using validity in­tervals is one way of handling the problem of non­monotonic reasoning in the case of measurement data whose values expire. History buffers where old variable values are stored are normally associ­ated with variables. This is combined with built-in functions operating on time histories for calculat­ing, e.g., past variable values, mean values, rate of change, etc.

Rules are not well-fitted for problems of a strong sequential, algorithmic nature. Two different ap­proaches for supporting procedural programming exist. Some tools include an integrated procedu­ral programming language. The procedures in this language are usually interpreted. The second ap­proach is to provide call-in and call-out hooks to the underlying implementation language, in many cases C, where the user is required to write the

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procedural parts of the application.

Some tools have built-in simulation facilities. These can be used for, e.g. , testing the applica­tion before it used on the real process. The func­tionality of the simulators varies. In the simplest case it is only possible to explicitly set variable values. In the more advanced cases the simulator contains numerical integration routines for solving differential and difference equations.

The process interface is an important part of a real-time expert system. Usually the process inter­face consists of two parts, one part that connects to the expert system tool and one part which the user must connect to his specific control system or data acquisition system. The process interface nor­mally supports bidirectional communication. Data can be requested at regular time intervals or when needed. In many cases the system also can handle unsolicited data.

The development environment of a real-time ex­pert system allows the developer to enter the data structures and the rules into the system. The de­velopment environment can be either text-based or graphics based. In a text-based system a nor­mal text editor, e.g., Emacs, is used. In a graph­ics based environment the input is defined partly graphically using mouse and menus and partly as texts.

The user interface of a real-time expert system allows presentation of information for the end­user, often the process operator. Two distinct ap­proaches can be found among the available tools. Some tools have the ambition to provide the oper­ator interface as a part of the tool itself. These tools have the possibility to define, sometimes quite powerful, operator interfaces consisting of animated process schematics, trend curves, bar graphs, etc. The tools that adhere to the second approach view the operator interface as a service that should be provided by the underlying dis­tributed control system. Therefore the operator output is restricted to ASCII-form text messages and parameter values that are intended to be sent to and presented at the standard operator console. This approach limits the functionality of the inter­faces that can be implemented. However, having all operator information on one monitor is also clearly an advantage.

The tools on the market are either intended to be used as general programming tools for real­time applications or specifically developed for one specific application type, e.g., rule-based, symptom-oriented diagnosis. The more general tools with their increased functionality require the developer to be more or less an expert on the specific tool whereas the more specialized tools usually are intended to be used by non-expert application developers, e.g., process engineers.

4. Tool survey

G2

G2 from Gensym Corp. (Moore et al 1990) is the dominating system on the market both in terms of functionality and in terms of market share. This description of G2 is based on Version 2 . 1 . G2 can be seen as a general programming environ­ment that combines three paradigms: rule-based programming, object-oriented programming, and procedural programming. It also has a very strong graphical orientation.

The G2 inference engine is based on static links. Rules can be invoked through forward chaining, backward chaining, at regular time intervals, ex­plicitly, or asynchronously when some event oc­curs. The actions that can be performed by a rule include assigning new values to variables (a con­clude action), starting procedures, invoking rules, creating and deleting objects, and graphical ac­tions for, e.g., moving, rotating, and changing the colours of objects. Generic rules that apply to all instances of a class are allowed. The G2 language has a very rich grammar with a large variety of ways to, e.g., make references to objects. The syn­tax is of natural language type.

The basic data types in G2 are numbers, logicals (boolean or fuzzy), symbols (enumeration types), text strings, lists, and objects. Objects are defined in class definitions where the superclass of the ob­ject, the attributes of the object, and the graph­ical icon representing the object are defined. The object-oriented part of G2 supports single inher­itance. Methods are not directly supported. Ev­ery G2 object is represented graphically by its icon. Objects can be interconnected by G2 con­nections. Using this feature graphical structures such as process schematics or fault trees can be conveniently represented. The connections estab­lish a relationship between the objects that can be used in general G2 expressions. Non-graphical relationships between objects are represented by G2 relations.

Time stamps and validity intervals can be associ­ated with G2 variables. Validity intervals are prop­agated. History buffers can be attached to all vari­ables. G2 contains several pre-defined functions operating upon time histories.

G2 contains a built-in procedure language of Pascal or C type. Procedures take arguments, have local variables, and may return values. The allowed statements in a procedure body include conventional programming language constructs such as if-then-else, case, repeat, for loops, etc. in addition to all the rule actions.

G2 includes a built-in simulator containing numer­ical integration routines for solving differential and

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difference equations.

The G2 process interface is based on GSI, a separate Gensym product. Using GSI the user can connect G2 to various external signal sources. GSI supports bidirectional communication, unsolicited inputs, regularly updated data, and data updated on demand.

In G2 the development environment and the user environment are integrated. G2 includes display and interaction objects that can be used to imple­ment advanced graphical user interfaces. The de­velopment interface includes a syntax driven text editor that is used to enter all textual parts of the system, e.g., procedures and rules.

G2 is a general tool with a large applicability. It requires substantial expertise from the developer. G2 is developed in Lisp. However, the Lisp imple­mentation layer is not available to the user.

RTAC

RTAC, an acronym for Real Time Advisory Con­trol, from Mitech Corporation has, in the same way as G2, its roots in PICON. This description is based on version 1 .6. RTAC has a modular ar­chitecture with the RTAC kernel containing the inference engine being the center of the system. Attached to the kernel are the following modules:

Dneloper 's Interface: The development in­terface is based on syntax structured templates. RTAC runs in two execution modes. In develop­ment mode the knowledge base is defined and in execution mode it is executed. Before execution the knowledge base is automatically compiled and loaded. Restricted modifications can be performed also on an executing knowledge base without dis­turbing the execution.

Dynamic Graphics: Using the dynamic graph­ics application, colour graphics interfaces can be implemented.

The Performance Monitor: Through this module performance information and network sta­tus summaries can be displayed.

The Value Monitor: The value monitor allows the user to inspect tables of sensor and variable values.

The Ezaminer: The examiner is a debugging tool that allows the user to view internal schedul­ing information from the RTAC kernel.

The Message Processor: The message pro­cessor displays advice messages chronologically. It also supplies the supporting information that caused the generation of the message.

The Ezternal System Interface: The interface is based on a subroutine libraries called ESIL and ESIL+.

The Simulator: The simulator allows limited testing facilities. It contains, however, no methods for solving differential equations.

The RTAC inference engine is based on static links. Rules can be invoked through forward chain­ing, backward chaining, at regular time intervals, or explicitly. The rule actions normally involves assigning a new value to a variable or sending a message. Generic rules are supported.

RTAC contains only one data type, floating point numbers. Logicals, integers, and even strings are internally represented as floating points. RTAC is not object-oriented. The RTAC language contains 10 different items: sensors, variables, set-points, devices, external systems, rules, generic rules, parameters, messages, and destinations.

Currency intervals, history buffers, and flags that may trigger rule execution are associated with variables as default attributes. RTAC contains a number of built-in functions operating on time histories. Sensors are variables that receive their values from the external system or the simulator. Set-points represent variables that are sent from RTAC to the external system. Device items are used to collect associated variables, sensors, and set-points. A device can be compared with a C structure.

The external system item defines the external ap­plication used by sensors, set-points, and mes­sages. Parameters provide default values for the behaviour of the compilation, help functions, etc. A destination item defines where messages are sent and determines the behaviour at the destination when the message is received. A message item rep­resents a text string that can be sent to a message destination.

COGSYS

COGSYS (COGnitive SYStem) (Morgan, 1990) was developed in a collaborative club with 35 UK and European companies involved. Cogsys Ltd was founded to be responsible for market­ing and future development. COGSYS consists of two parts, the Generator System which provides the development facilities, compiler, and linker, etc., and the Runtime System that interprets and runs the execution file. The Generator System uses a sub-set of the POPLOG/POP-11 environment whereas the Runtime system is written in C. The two main features of COGSYS are the Knowledge Based System (KBS) where the application knowl­edge is expressed in the Knowledge Representa­tion Language KRL, a modular text-based lan­guage, and the General Purpose Interface (GPI) that links COGSYS to the external environment. As COGSYS contains no built-in operator inter­face, GPI is used both for process communication and operator communication.

487

COGSYS is closer to a conventional real-time lan­guage than, e.g., RTAC. For example, COGSYS contains a complete real-time procedural language with concurrent procedures, synchronization, mu­tual exclusion primitives, etc. The block struc­tured KRL resembles languages like Pascal or Ada.

The basic data structures of COGSYS are called Cognitive Entities. It is possible to have structured cognitive entities and arrays of cognitive entities. A cognitive entity may have a pointer to another cognitive entity as its value. History buffers may be associated with cognitive entities. Data are time stamped but validity intervals are not used. Instead truth maintenance is obtained by, when a value is retracted or deleted, also have any dependent values similarly treated.

A KRL module consists of a number of block structures. The structures consist of activity blocks, demons, rule sets, and functions. Activ­ity blocks may be either Control Blocks, used to control the knowledge base, and which provide access to system scheduling facilities, or Action Blocks, which are used to represent application procedures. The action statements specify the con­ditions on which the action is taken, e.g., ON and WHILE. The actions may be used to assign values to cognitive entities, retracting assertions, setting outputs, or calling function.

Demons are one of the means by which Activity Blocks are fired; the other way is by activation from other Activity Blocks. A demon can be set to fire at a preset time, after a duration, on a change in a cognitive entity value, or as a result of an explicit signal from the GP!.

A rule set consists of a set of rules of if-then-el8e or 8Witch-ca8e type. The rules operate upon the values of cognitive entities. Forward and backward chaining is supported. By the use of wild-card specifiers rules can be made generic. Function blocks return a value. They can be implemented by an action block, a rule set, or by an external function.

A blackboard approach is used to exchange data between different KRL modules. The blackboard can be partitioned into different zones and thus protected from access by certain modules.

GP! collects real time data. It is not possible for the inference engine to, on demand, invoke exter­nal data collection. Normally, a scan interval is associated with each GPI data point. Unsolicited input is supported. When new data arrives to a cognitive entity, a demon may be triggered and invoke, e.g., an activity block.

RTworks

RTworks from Talarian Corporation is a suite of tools or modules for real-time expert system ap­plications. The RTworks architecture is based on a distributed client server model. An application is composed of multiple modules working together across a network of, possibly, heterogeneous work­stations. All modules are implemented in C. This description is based on version 2.0 of RTworks.

The modules of RTworks are:

The interprocess communication ser1'er {RTser,,er): RTserver allows the RTworks pro­cesses to communicate with each other, as well as with user-defined processes.

The data acquisition process {RTdaq): RT­daq acquires, filters, and groups incoming data and sends it to RTserver for further distribution.

The inference engine process (RTie): RTie consists of the application knowledge and the inference engine.

The human-computer interface {RThci): RThci provides a graphical user interface based on Dataviews from VI Corp. RThci receives di­rect data from RTdaq and derived data and text messages from RTie.

The data generator process {RTgen): RTgen allows the user to generate test data that can be read by the other process. It is similar in functionality to the RTAC simulator.

In addition to this RTworks has archiving and playback modules that allows saving of variables in permanent storage and playback of the stored data for in-depth analysis. The shared database {RTsdb) contains all information that is shared between the processes, i.e., information about data points. The information includes the name of the data point, its type (e.g., numeric, enumer­ated, boolean, or string), the datagroups that the data point is part of, and the object attribute in RTie which the data point will be linked to.

RTie is based on an object-oriented language, the Frame Representation Language (FRL). FRL sup­ports multiple inheritance between classes. Frame slots may point to history ring buffers where a se­ries of values and their associated time stamps are kept. Objects can be created and deleted dynami­cally. A variety of functions for trend analysis such as linear and nonlinear regression analysis, least squares, moving averages, rate of change, mean, standard deviation, exponential smoothing, etc., are pre-defined. It is also possible to define new functions. The inference engine in RTie is based on static links. Rules, of if-then-else type, can be invoked by forward chaining, backward chaining, and at regular time intervals. The rule actions in-

488

eludes assigning new values to variables and send­ing messages.

RTie can compare current data with past, as well as reason about the order in which events have occurred. The latter is done using the operators before, after, and during. Focus of attention ca­pabilities are provided through changing the set of sensors the system is currently investigating, bringing a new set of rules to bear, or changing the sampling rate or compression scheme of the data being analyzed.

RTworks has no built-in procedural language. Instead RTworks has call-out and call-in facilities to C.

RThci displays are developed using an interactive menu-driven drawing editor called RTdraw. RT­draw contains a variety of pre-defined primitive shapes, graph formats, and input objects. Displays can be hierarchically organized into a tree struc­ture. A RThci graphics object connected to a vari­able will change in some pre-defined way when the data changes.

RTworks includes a point-and-click development interface based on Motif.

TDC 3000 Expert

TDC 3000 Expert is a real-time expert system tool developed by Honeywell that runs integrated in the TDC 3000 distributed control system. The sys­tem is intended for operator assistant applications such as monitoring and diagnosis. TDC 3000 Ex­pert runs on DEC V axstations running VMS and is written in Objective-C.

TDC 3000 is interfaced to the Local Control Net­work through a computer gateway and provides its operator output on the Universal Station, the TDC 3000 operator console. A preformatted op­erator display which the user can configure is pro­vided. The display allows the operator to view and acknowledge situations and advisories, sort them in their assigned priority, scroll through them, an­swer questions issued by the knowledge base, re­quest "why" and "how" type information, call up related existing custom displays {built by the TDC 3000 Picture Editor) on the same or another Uni­versal Station, and view and enter data in the knowledge base using data display tables.

The alpha-numerical development interface con­sists of an editor through which the user can enter, view, syntax check, and compile a knowledge base. TDC 3000 Expert also includes an Engineers Run­time Interface {ERi) through which the user can load, run, debug, and test a compiled knowledge base.

The TDC 3000 Expert language contains eight types of language items: classes, instances, situ-

ations, locations, views, constants, functions, and alternate expressions.

A clau element gives a name for the class and defines the attributes which the instances of that class have in common. An instance object inherits the attributes defined in its class definition. The type which is assigned to an object attribute can be the name of a class (in which case the attribute acts as a pointer to another object) , a one-of specifier (which includes a list of valid values which the attribute may assume) or one of the basic data types of the language which include numbers, logicals, strings, time stamps, and durations. It is also possible to define that an attribute should take its value from the TDC 3000 Local Control Network. All instances and attributes have associated with them one or more facets in addition to their value. The facets contain information about when the value facet was last changed; the previous value of the attribute; the data refresh interval; limits determining when the attribute is very high, high, low, and very low; what should be considered a significant change in a numerical attribute; the size of the history buffer for the attribute; and whether some condition function should be automatically applied to the raw value, e.g., rejecLas_noise, moving...average, firsLorderJag, etc.

Transition rules may be associated with an object attribute. A transition rule contains a logical condition and a new value for the attribute. The new value is applied when the condition applies. It is also possible to define different contexts where different sets of transition rules should apply for an attribute.

TDC 3000 Expert contains pre-defined classes for querying the operator. An attribute can be defined to take its values from one of these pre-defined classes. When the attribute value is needed the question is posed to the operator. Together with the query classes it is possible to define the query text string, possible valid answers for the question, etc.

TDC 3000 Expert uses three-valued logic. Logi­cal expression may have the values true, false, or unknown. Within expressions a large number of built-in functions for testing data against limits or expectations and for computing trends can be used. These include functions to calculate aver­age values, maximum and minimum values, slopes, and standard deviation over time intervals; func­tions that returns true if a value has changed sig­nificantly, has decreased or increased, or has ex­ceeded some high or low threshold; and functions for time and date calculations.

The major part of a TDC 3000 Expert knowledge base consists of cause-effect hierarchies of situa­

tions. A situation can be seen as a description of

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an abnormal operating condition that the TDC 3000 Expert system should monitor, detect, diag­nose, etc.

The inference engine does a parallel "breadth­first" investigation of the situation hierarchy un­til one or more problems or opportunities are detected. It then searches down those situa­tions' cause branch or branches, issuing engineer supplied correction advisories and/or queries as needed. The search is dynamic and based on the latest scanned data from the Local Control Net­work. Monitoring continues after advice is issued. Inferencing will continue after a user-set period of time and not wait for operators to confirm ad­visories or follow the advice. When a triggered situation is corrected via operator actions or on its own, any advice generated is automatically re­tracted and the operator is notified the situation is no longer active. Similarly, if a cause situation becomes active during an investigation of another part of the hierarchy, the inference engine auto­matically issues any supplied advice associated with correcting the new cause.

The knowledge encoded in the situation elements is used to indicate when to monitor the process for such conditions, how to tell when a given condition is in fact occurring, how to determine what is causing the condition, what actions to take to correct these causes, and how to tell when the actions have been effective. Since TDC 3000 Expert is an assist-only system, all the actions must be manually performed by the operator.

There are two types of situations: primary and sec­ondary. Primary situations can be self-activating, whereas secondary situations are only activated by other situations. Primary situations include logical conditions determining when the situation should be active, i.e., monitor the process for cer­tain undesirable conditions. When these undesir­able conditions are observed, the primary situa­tion begins an investigation. Secondary situations are activated when some other situation, either primary or secondary, is performing an investi­gation and identifies that situation as a possi­ble cause. In active situations a test is continu­ously consulted to determine whether the condi­tions they describe actually exist; if so, then other situations listed as causes are activated. When all the possible causes for a confirmed situation are themselves either ruled-out or resolved, the situ­ation issues advice to the operator to remedy its own condition. Finally, it monitors the process to determine whether the issued advice has the de­sired effect, resolving the situation.

The location items describe how variables are to be physically organized into the data display screens which are viewable by the operator. Views

describe the appearance of attributes' values if

and when they are displayed on the data display screen. This includes colour, whether the value blinks or appears steadily, display intensity, and reverse or normal video.

Con&tants are used to specify default values for various system parameters used by the inference engine. They are also used to specify user-defined constants or short-hand notations. It is possible for the user to write and call simple functions. It is not possible to call functions written in other languages. The body of a user-defined function may contain assignment statements and if-then­else conditional blocks.

A TDC 3000 Expert application gets most data from the Local Control Network or from oper­ator's answers to queries. By using an alternate ezpression element the engineer is allowed to de­fine an alternate data source for an attribute. The purpose for alternate expressions is to provide the engineer with a means for testing the application.

TDC 3000 Expert has no built-in procedural language.

5 . Summary

In this paper five real-time expert system tools have been described. Several similarities can be seen. The systems are based on rules with the exception of TDC 3000 Expert that uses situations instead. All the systems have ways of associating time stamps and history buffers with variables.

The user interface solution is solved differently in the systems. In G2 it is integrated with the devel­opment interface. Each object has a unique iconic representation through which it can be manipu­lated. An advantage with this strong coupling is that it quite easy to use G2 to develop graphi­cal programming languages for, e.g., Petri nets, Grafcet, block diagram languages for control and diagnoses, etc. In, e.g., RTworks graphical user in­terfaces also can be developed but the graphical object showing, e.g., some process component, are different from the object representing the process component in the knowledge base. COGSYS, fi­nally, leaves the operator interface to the underly­ing control system.

The generality and functionality of the tools varies quite a lot. On one extreme is G2 that can be used for a variety of applications applying a large number of different implementation techniques. The other extreme is TDC 3000 Expert that

490

is tailored for symptom-oriented diagnosis and difficult to use for other diagnosis methods. The generality of the tools naturally also affects how easy the systems are to use. Systems like TDC 3000 Expert and RTAC are designed to be used by process engineers whereas systems like G2 and COGSYS clearly require a substantial amount of training by the application developer.

G2 and RTworks runs on multiple platforms, typi­cally workstations or high-range personal comput­ers whereas RTAC, COGSYS, and TDC 3000 Ex­pert have been developed primarily for DEC com­puters running VMS.

The material which this survey is based upon has been collected in the Swedish IT4 project "Knowledge-Based Real-Time Control Systems" (Arzen, 1990) performed jointly by the Depart­ment of Automatic Control, Lund Institute of Technology and Asea Brown-Boveri AB.

References

ARZEN, K-E. (1990): "Knowledge-based control Systems," Proc. of the American Control Con­ference, ACC 90, San Diego, CA.

ARZEN, K-E. ( 1991): "Knowledge based applica­tions in the process industry: Current state and future directions," Keynote address, Proceed­ings of the IFAC Workshop on Computer Soft­ware Structures Integrating AI/KBS in Process Control, Bergen May 29-30.

LAFFEY, T.J . , P .A . Cox, J .L. ScHMIDT, S .M. KAO and J.Y. READ ( 1988): "Real-time knowledge-based systems," AI Magazine, 9, 1 , 27-45.

MooRE, R.L . , H. RosENOF, and G . STANLEY ( 1990): "Process control using a real time ex­pert system," Proc. 1 1 th IFAC World Congress, Vol 7, Tallinn, Estonia, pp. 234-239.

MORGAN, T. (1990): "Real time expert systems in the COGSYS environment," Proc. of Expert Systems 90, London, Cambridge University Press.

OYEN, R.A. , M.A. KEYES, and M.P. LUKAS (1988): "An expert system shell embedded in the control system," Preprints of the IFAC Workshop on AI in real-time control, September 21-23, Swansea, UK.

Copyright © IFAC Anificial Intelligence in Real-Time Control, Delft The Netherlands, 1992

DESIGNING REAL-TIME KNOWLEDGE BASED SYSTEMS WITH PERFECT

J.M.A. Sassen* and R.B.M. Jaspers**

*Delft University of Technology, Faculty of Mechanical Engineering, Mekelweg 2, 2628 CD Delft, The Netherlands

**TNO-lnstitute of Applied Computer Science, P.O. Box 6032, 2600 IA Delft, The Netherlands

Abstract. For real-time knowledge based systems (RTKBS) to beco�e viable complemen!s to traditional information systems the application of proven methodologies for system analysis and design is of utmost performance. However, these methodologies d.o not provide any support to knowledge engineers about issues that are related to the �es1gn of RTKBS, s�ch as: What is the necessary knowledge for the RTKBS to perform a certam task? How can this knowledge be used by inference strategies? How shoul� the know!edge

. m�el and the

inference strategies be implemented, such that the resultmg model 1s mamtamable and meets all time requirements? Answers to these questions are also not provided by tools that are suitable for implementing a RTKBS, such as COGSYS or G2. In this paper ":"'e �il l show

.that . PERFECT (Programming EnviRonment For Expertsystems Constramed m reas�mn� Time)

does support knowledge engineers in answering these questions, an� hence that _it bndges the

gap between the traditional analysis and design methodologies, and 1mplemental!on tools for RTKBS.

Keywords. Artificial Intelligence; Knowledge engineering; Computer-aided system design; Programming support: Real-time knowledge based systems

INTRODUCTION

Real-time knowledge based systems (RTKBS} often cooperate with Distributed Control Systems, Database Management Sys­tems and other "traditional" information systems to perform supervisory tasks such as process m?nitoring, alarm handling, process optimization, etc. Although.m.

the. development of

"traditional" software systems the d1stmclion between system analysis and system design is general�y c?n.sidered .to be essen­tial (see e.g. Sommerville ( 1985)), this d1stmct10n 1s certamly not common in knowledge based system development. In the latter case, emphasis generally lies on knowledge acquisi

.tion

. (which is part of system analysis}. Technical s�stem des1�n 1s often not considered at all, especially when rapid prototypmg techniques are applied. In ��r vie".", for R�KBS to become viable complements to trad1t1onal mfonnallon systems, the ap­plication of proven methodologies for project management a�d systems analysis and design is of utmost importance. For this purpose, traditional methodologies and tools, s�ch as Y o.urdon (Hatley and Pirbhai, 1987) for systems analy�1s and design, and software project management methodologies have. to be supplemented by specific methods for RTKBS analysis and design.

At the moment, there exist some powerful tools for the implementation of a RTKBS, such as COGSYS (COGSYS, 1990) and G2 (G2, 1990). TNO has been involved in the development of COGSYS. It offers a generi� i�t.e!1'ace to in­dustrial processes, a high performance, poss1b1ht1es for . reasoning with uncertainties, temporn! and non-monotonic reasoning, and concurrency to deal with asynchr�nous events (Van Steen and Sassen, 1989). However, even with a tool as COGSYS three types of questions arise when one wants to build a RTKBS. These questions are respectively related to I } the knowledge level (Newell, 1 981 ) •

. 2) the level of (real.-ti�e)

software engineering. and 3) the design of human-machme m­terfaces: I } What is the necessary knowledge for the RTKBS to per-

. form a certain task? How can this knowledge be used by m­ference strategies? In order to overcome some of the prob­lems reported with first generation knowled�e. �ased sys­tems, such as difficulties in knowledge acqms1t10n, brit­tleness of the problem-solver, and weakness of explana­tions, these questions need to be answered

. (Steels, 1990).

2) How should the knowledge model and the mf�rence . strategies be implemented, such that the resultmg RTKBS 1s

maintainable and meets all (time) requirements? Typical design decisions which are to be made concern the division

491

into program modules, definition .of interfaces be_twe

.en

modules the choice for representmg knowledge m either a declarati�e or procedural manner, etc. Guidelines for struc: turing the knowledge base can substantially benefit the mam­tainability of an expert system (Bacha�! �nd �oloway, 1989). Annenise ( 1989) states that opl!m1za1Ion o� a system in order to meet (time) requirements should be achieved by assisting programmers with tools integrated in the software development environment.

3) How should the output of the RTKBS be presented to human operators to achieve effective human performance? De Keyser ( 1987) notes that many of the comp�ter di�plays currently available in control rooms she had v1s1ted, did not always help the operators to perfO!ffi their task. 1:hei;efore, it is necessary that knowledge engineers know pnnc1ples that can be used to design human-machine interfaces.

Since neither the traditional methodologies for software analysis and design, nor the implementation tools for RTKBS, address the three raised questions, we have undertaken the construction of PERFECT (Programming EnviRonment For Expert systems Constrained in.reasoning Time), in order to provide the necessary support m RT��-developm�nt. PER­FECT bridges the gap between the traditional analysis and design methodologies, and the implementation tools for RTKBS. It does so by providing the means to analyse and design RTKBS, and by translating the resulting design to a skeleton program in an implementation tool like COGSYS. At the moment of writing, PERFECT supports the development of knowledge based systems that can monitor and diagnose an industrial installation. Extensions, like optimal control; plan­ning and scheduling; and start-up and sh.ut-down �ill be developed in the future. PERFECT consists of an mtegrated set of tools based on a single modeling techmque (Fig. I ). 11: •••••••• ••••• ,races•

K••••••a• M•••I tllat Skelet•• mara9r•• ta ••••I •eets tl•e C85S9S aatl l•MeNaes

ca•stnl•t• •�••t Hie •••••­••clll•e laterface

"'

Fig. I . An overview of PERFECT

With the graphical interface, a knowledge engineer builds a knowledge model. Certain properties of this model are checked by the analyzer. For instance, the analyzer checks whether the knowledge model contains sufficient knowledge for diagnosis of disturbances. It also calculates the response-time of the knowledge model, i.e. how long it will take a reasoning strategy to diagnose a disturbance. If response-times are not as required, the analyzer can propose a different structure of the knowledge model with improved response-time. Once a knowledge model is obtained that is satisfactory, this model can be compiled automatically to a skeleton program in a lan­guage suitable for implementing RTKBS, eg. COGSYS.

In this paper, we describe how knowledge engineers can build a RTKBS with PERFECT. To show how PERFECT bridges the gap between a traditional software analysis tool (Yourdon) and an implementation tool for RTKBS (COGSYS), we use an example RTKBS that can monitor and diagnose a nuclear power plant simulation, the Generic Nuclear Plant developed by RIS0 (Goodstein and coworkers, 1 984).

DESIGNING THE COOPERATION OF THE RTKBS WITH EXISTING SOFrW ARE SYSTEMS

Suppose that we want to design an intelligent supervisory con­trol system for the Generic Nuclear Plant (GNP) in order to operate it safely and economically. The software that is already available to us consists of a Distributed Control Svstem (which uses a Data acquisition function to gather sensor data), and a Human Machine Interface. The task of the anticipated RTKBS is to monitor on-line whether the operation of the GNP is cor­rect and to predict if it will remain so in the near future. If this is not the case, the RTKBS should find the cause and the con­sequences of this malfunction and present these to the operator. The first phase in the RTKBS life cycle would be the system definition, for instance by means of Yourdon System Analysis. Figure 2 shows a dataflow diagram of the intelligent supervisory control system, constructed with the graphical Yourdon-editor of PERFECT. It shows the data-processing functions (indicated by a circle), the datasources (indicated by two parallel lines), and the environment (indicated by rectangles). The arrows show how data flows from one element to another. The elements in the dotted rectangle already exist in the available control system. The other elements should be designed in such a way that they can cooperate with the ex­isting functions and dataflows. Since the Human Machine In­terface receives new information that must be presented to the operator this function must be redesigned as well. Hence, the data-processing functions to be designed are: Monitor and Diagnme and Hunuin-Machine Interface. The datasources to be designed are: knowledge model and diagnosis. In the next sections we will show how PERFECT can be used to design these functions and datasources.

knowledge model

Fig. 2. A dataflow diagram of the Intelligent Supervisory Control System of the GNP

THE MODELING TECHNIQUE OF PERFECT

The design primitives of PERFECT to develop a knowledge model for a realtime knowledge based system are called units. Each unit models the knowledge about a single component, a subsystem or an abstract function of the target process of the RTKBS. Units can be fully decomposed or aggregated to form a hierarchical structure, in the same way as subsystems of the

492

target process can be decomposed into components, or aggregated to realize a function. Units corresponding to se!1-sors that provide input to the RTKBS are called hooks, to m­dicate their function as an interface between the target process and the RTKBS. Some variables which are used during a reasoning process of the knowledge based system do not cor­respond directly to one measured value, but can be derived from a set of sensorvalues and constants through data­abstraction. For instance, the energycontent of a volume of mass cannot be measured directly, but can be derived from the measured amount of mass, the mass' measured temperature, specific heat, and specific density. Such variables are modeled as virtual hooks. Units (and thus hooks and virtual hooks) have attributes and relations in order to represent knowledge about the corresponding part of the target process. Figure 4b and 4c show respectively a unit and a virtual hook. The unit is graphically represented by a ( large) rectangle. Its children are represented by rectangles within the unit. Virtual hooks are represented by tripple-lined rectangles, while hooks are represented by double-lined rectangles (QI is a hook). Attributes are represented by rectangles with rounded comers. There are two kinds of attributes, which differ in scope. Inter­nal attributes are placed inside a unit. They can only be used in relations of that same unit. Hence, the attribute behaviour _OK cannot be used in relations of the unit mass_trans_prim. External output attributes are placed on the right vertical edge of a unit. They can be used in relations of that same unit, and of its parent-unit. Hence, the attribute U _tot_prim can be used in relations of the virtual hook U_tot_prim, but also in relations of the virtual hook ebal_trans_prim. A hook will not have any relations, since its only task is to read a sensor and to provide its value to the knowledge model. Hence QI will only be used in the relations of ebal_trans_prim. A virtual hook al­ways has relations to define its external output attribute. This modeling technique is sufficiently generic to allow the construction of many different kinds of hierarchical process models. We will now show how it can be used to build a mul­tilevel flow model (Lind, 1 990) of the GNP.

Fig. 3. Goals and functions of the Generic Nuclear Plant

A knowledge model for the GNP The goal of the supervisory control system to be designed is to detect as soon as possible that the GNP is not operating optimally with respect to either the safety, production or economics, to diagnose why this is the case, and to present the result to the operators. This required functionality can be achieved by using a multilevel flow model of the GNP as a knowledge model. A multilevel flow model describes the nor­mative behaviour of the goals, functions and components of an industrial process by means of mass- and energy balances and transfer functions. Figure 3 shows the multilevel-flow model of the GNP. There are three goals: safety, production and economics. Safety is guaranteed when there is no radioactive mass leaking to the environment (modeled by prevent_loss_<!{Jadioactive_material), and when there is no energy accumulation somewhere in the plant (modeled by prevent_loss_of_cooling). The production goal specifies that the power generated should be equal to the amount that is demanded, the economics goal specifies that energy losses in the plant should be minimal. To meet the production and economics goal there are three main functions in the plant: energy__generation, energy_transport and energy_conversion.

Energy _generaJion models the relation between the demanded amount of energy and the generated amount. Energy_transport models the transportation of energy generated in the reactor to the turbine/generator. The means of this function are energy transport in the primary circuit (en_trans_prim), energy transport in the secondary circuit (en_trans_sec), and exchange of energy between the primary and the secundary circuit (en_tran�fer_l->2). To transport energy in the primary circuit it is necessary that there is mass circulation (modeled by mass_transyrim ), that there are no significant heat losses during transportation in different parts of the circuit (maintain­_enyrim), and that a high pressure is maintained (maintain_pressyrim). Based on the multilevel flow modeling philosophy, the other functions can be decomposed in a similar way. In Sassen, Riedijk and Jaspers ( 1 99 1 ) a detailed multilevel flow model of the GNP is described.

Designing the knowledge model of the RTKBS with the graphical interfaces To represent a multilevel flow model in the design primitives of PERFECT a unit is defined for every goal and function, and the relations between the goals and functions are mapped to parent-child relations between units. This can be done with one of the graphical editors of PERFECT. Figure 3 is a typical ex­ample of a model built with this editor. Subsequently, the nor­mative behaviour of each of the units must be described. PERFECT supplies two graphical editors for this purpose: one is especially tailored to multilevel flow modeling, another is suitable for every type of description. Figure 4a shows the normative behaviour of the function en_trans__prim described with the multilevel flow model-editor, and Fig. 4b and 4c show this same function described in the general purpose editor. When the user has described the normative behaviour of a function as in Fig. 4a, PERFECT automatically generates the description as in Fig. 4b and 4c. Figure 4c shows all the details of the virtual hook ebal_transyrim, while Fig. 4b shows that the external output attribute of ebal_trans_prim is used in the unit en_trans_prim.

a)

b)

c)

cl. heater Q7 Q_to_ vct ml contr tank

en trans nrim < behaviour OK l ( c� ) !behaviour OK := ABS (ebal trans prim) < cps I cps := 20

maintain_ m cn_prim

main tam -press_prirr

eblli_trans Ill _pnm

I I

CJ (eblli trdlls onm

cblli_trans_prim Ce""' trans

( nctto meut)

I cbal_trans_prim := U_tot_prim{O} - U_tot_prim{- 1 } I +(netto input{- ! } + netto_input{O} )/2*delta_t lnctto_input := Q I + Q7 - Q_prim_scc - Q_to_vct I u �,,,Q_primcd�m sec)

lllU_tot_primlll 1111Q_to_vctJll �

I U tot --m ({) to vd ta t

Ill nmJ

Fig. 4. Normative behaviour description of the function en _trans _prim

The symbols used in Fig. 4a are defined by Lind ( 1990). The picture shows that the primary circuit of the GNP acts as a large storage of energy; it contains U _tot _prim MJ of energy. Incoming sources of energy are QI MJ/s from the reactor, and Q7 MJ/s from an electrical heater. The energy flowing out of the primary circuit is equal to Qyrim_sec MJ/s to the secun-

493

dary circuit and Q_to _vet MJ/s to a volume control tank.Figs. 4b and 4c show how PERFECT automatically translates the semantics of the multilevel flow model-picture to a knowledge model in the PERFECT modeling technique.

Figure 4a does not specify how the quantities Q7, Qyrim_sec, Q_to_vct and U_totyrim that have to be estimated from temperatures, mass flows and pressures, can be determined. This is done with the editor of Fig. 4b. By clicking on ebal_transyrim Fig. 4c is obtained. Here we can click on for instance U _totyrim or another virtual hook (a tripple lined rectangle), to describe how this value can be cal­culated from sensor data that is available in the datastore raw plant data of Fig. 2.

THE MONITOR AND DIAGNOSE FUNCTION OF THE RTKBS

Now a knowledge model of the GNP is available, how can it be used by an inference strategy to monitor an industrial process, to detect threats to goals and to determine the conse­quences of a certain malfunction? PERFECT supplies the in­ference strategy establish-generalize to achieve this.

In the knowledge model the normative behaviour of each unit (a goal, function or component) is described by a mass- or energy balance or transfer function. If all units are behaving as described by their normative behaviour, the total process is well-functioning. However, if for at least one of the units its observed behaviour does not correspond to its normative be­haviour, there is a malfunction somewhere in the process. The origin of the malfunction must be found. Also, the consequen­ces of this malfunction have to be predicted, to allow the operators to develop a good plan of compensating actions. For this purpose, establish-generalize uses the decomposition rela­tions between individual units in the knowledge model. In a multilevel flow model a node's children indicate how the node is implemented, or which support functions are necessary for the well-functioning of the node. Consequently, when a node and one of its children are both malfunctioning, the cause of the node's malfunctioning is the malfunctioning of the child. Reasoning the other way around is valid as well: the consequence of the child's malfunctioning is that its parent is malfunctioning. Hence, to search for causes of a disturbance it is necessary to search downwards in the knowledge model, and to search for consequences of failures it is necessary to search upwards. This fairly simple diagnostic process is one of the strengths of using a multilevel flow model for diagnosis. When another type of process models is used for doing diag­nosis (for instance a model based on the physical structure of the plant) the diagnostic process can be a seemingly complex search problem due to system interactions (Lind, 1990). With a knowledge model which correctly models the means-ends relations that exist between different functions and components of the industrial process, a node can only start malfunctioning when at least one of its children is malfunctioning. Therefore, establish-generalize first investigates all units at the lowest level of the knowledge model, it does so by comparing the normative behaviour of each of the units to their observed be­haviour. The units which are found to be malfunctioning are "established" malfunctioning. The consequences of the malfunctions that are found are determined by investigating the parents of the nodes that are established, and recursively the parents of the established parents.

To illustrate the reasoning of establish-generali:.e, the example knowledge model of the Generic Nuclear Plant is used. Sup­pose the steamgenerator has deteriorated, and cannot transport the necessary amount of energy from the primary circuit to the secundary circuit. This causes the malfunctioning of the func­tions en_transfer_l->2 and energy_transport, since not all generated energy is transported to the turbine/generator. Prevent_loss_of_cooling and the safety goal will fail as well, since energy accumulates in the primary circuit. The economics goal will fail since the relation between the generated amount of energy in the reactor, and the delivered amount of power is not as it should be. All other nodes are well-functioning. The malfunctioning of the steamgenerator would be diagnosed as follows. The behaviour of the leaves of the knowledge model are periodically investigated, and en_transfer _1->2 is established malfunctioning. In the "generalize" step, the establish-generalize reasoning strategy will compare the nor-

mative behaviour of each of en_transfer _l->2's parents to their observed behaviour. The only parent is energy transport, and it is established malfunctioning as well. This implies that its parents will also be investigated. Production will be found well­functioning, but prevent loss of cooling and economics are es­tablished. The only parent that still needs investigation is safety, and it is established as well. Now, all consequences of the original malfunction are known, and hence the diagnostic process stops and returns the diagnosis.

Establish-generali:.e can reason progressively (Winston, 1984) to provide an answer at any moment in time, because the knowledge model is a hierarchical model. Since the diagnostic process is triggered by the identification of the malfunctioning of a leaf, a coarse diagnosis is directly available. This can serve as the required answer if immediate action is necessary, for example in emergency situations. If more time is admissible for reasoning, this coarse answer can be elaborated. And again, this more detailed answer might be elaborated fur­ther if there is enough time to do so.

ANALYZING AND COMPILING THE RTKBS

Thus far, the design of the RTKBS yielded a knowledge model of the target process and an inference mechanism that can use this model to monitor and diagnose the process. Two important software engineering aspects remain: I . To assure that the RTKBS contains sufficient knowledge to

diagnose faults. 2 . To assure that the RTKBS meets its time-constraints.

These aspects are taken care of by the analyzer of PERFECT. To check whether the knowledge model built in the PERFECT modeling technique contains sufficient knowledge for diagnosis, it is checked that there are enough relations in each unit of the knowledge model for establish-generalize to decide whether a unit is malfunctioning. (In other words, is it possible to decide whether the value of the attribute behaviour­_ OK of each unit evaluates to FALSE or to TRUE). To assure that the RTKBS meets its time-constraints the knowledge en­gineer must know the response-times of the RTKBS based on the current knowledge model. If the response-times are not good enough, he can decide to change the knowledge model. The analyzer of PERFECT supports this process by first deriving a heuristic which guides the search process of establish-generali�e during run-time. This heuristic is based on the probability that a component fails and the costs related with the investigation of a unit. The use of this heuristic during run­time assures that e.wablish-generali:.e searches units in a best­first order. If this heuristic does not lead to response-times that are good enough, the analyzer proposes some additional short­cuts in reasoning which further improves the efficiency of the RTKBS. This is described in detail in another paper we pre­sent at this conference (Sassen, Ollongren and Jaspers, 1992).

After it is checked that the knowledge model contains sufficient knowledge for diagnosis, and the heuristic to guide the search process during fault diagnosis is derived, the knowledge model and the inference strategies can be compiled to a skeleton program in COGSYS.

� Figure 5 shows an overview of the architecture of COGSYS. The main components of each COGSYS-knowledge based system are a h/ackhoard containing values of frame-like knowledge representation entities, so-called cognitive entities, a rule base consisting of declarative knowledge about these cognitive entities, and a set of activities (shown in Fig. 5 as "A l " and "A2") that can execute procedural code. A change of a value of a cognitive entity can trigger a demon ("D I " and "02" in Fig. 5) which in tum activates an activity by submit­ting it to a scheduler. The latter determines when an activated activity may actually access the blackboard. Besides these components, each COGSYS-knowledge based system has an inference engine for inferring values of cognitive entities using the rules in the rule base. The inference engine is triggered by activities when they query values of cognitive entities. These components are connected to the environment in which the knowledge based system is embedded by means of an interface hus. This bus makes it possible to access each of the compo­nents from outside the knowledge based system, as well as to interface to programs written in traditional languages like "C".

494

Fig. 5. Architecture of a COGSYS-knowledge based system

Developing a knowledge based system with COGSYS requires development of a COGSYS-KRL (Knowledge Representation Language) program. The language strongly reflects the architecture as discussed above. In particular, a system developer specifies activities, demons, cognitive entities and a rule base of the knowledge based system by means of the KRL. The interface bus of the architecture, i.e. the communication facilities with the environment of the expert system, is specified by means of a runtime-library, combined with the COGSYS-General Purpose Interface (GPI). The GPI allows for the specification of data structures for low-level communication with peripherals such as sensors and PLCs. These data structures can subsequently be accessed by a KRL program.

COGSYS has been chosen as a target language for the com­piler of PERFECT because of its unique set of facilities for the development of RTKBS, such as an interface to the environ­ment, the possibility to reason with uncertain data, flexible problem solving strategies, possibilities for temporal and non­monotonic reasoning, concurrency to deal with asynchronous events, and because it satisfies the generally accepted criteria for support of well-engineered software development.

Compiling to COGSYS In this section we will show the translation of the PERFECT knowledge model, and the establish-generalize inference strategy for which the analyzer has derived an order of inves­tigating units, to a COGSYS-program. The heuristic assures that the diagnostic strategy is doing the best that is possible in the available reasoning time. In the COGSYS-program that the compiler produces, the diagnostic strategy is forced to publish partial results on the blackboard, as soon as they come available so that they can be presented to the operator.

Figure 6 shows the optimal order of investigating units for es­tablish-generalize. It should periodically investigate the behaviour of respectively energy _conver.fion, energy_generation, maintain_press_prim, maintain_mass_sec and the other units in the order indicated in the left-most column of Fig. 6. When one of these is established malfunctioning, the generalize step is made by searching the parents of the established unit in the order indicated by the dashed arrow pointing to the right. Establish-generalize is implemented in such a way that the parents of an established unit are investigated immediately, and that the other units (brothers) which still require investigation are visited when all parents of an established unit have been investigated. This implies that when for instance maintain_press_prim is malfun­ctioning, the next unit to investigate is en_trans_prim. If en_trans_prim proves to be well-functioning, prevent_los.f_oj­_cooling is investigated. If en_trans_prim were malfunctio­ning, prevent_loss_of_cooling would be investigated only after energy_transport and possibly its parents had been inves­tigated.

The compiler of PERFECT produces a skeleton program in COGSYS, which consists of a collection of modules with clearly defined interfaces. In this way, the maintainability of the RTKBS is enhanced. Each unit of the PERFECT-model is translated to a seperate module in COGSYS. Each module con­tains knowledge (rules) about the normative behaviour of the unit, and it contains part of the diagnostic strategy, which is

implemented in activities. Each activity of a module knows which activity to activate next, depending on the status of its own behaviour. For instance, the activity belonging to the unit ener�:_v_conversion (called energy_conversion_activity) activates economics activity when its own behaviour is not as it should be, in the other ca5e it activates energy__generation­_activity. In case economics activity was activated, it will on its tum ·activate prevent_losi_of_c<wling_activity. If the behaviour of prevent_loss_of_cooling is OK it will activate production_activity. Production activity needs information about which units ·were investigated before, to decide which module's activity to activate next. In this example, production­_ activity would query the blackboard and find that energy_generation-activity would be the next activity to be ac­tivated.

---··s I I I

I I I I

.__ � - - - - - -: ..---� I I I

- - -t - - - - - - -1 I - � :+i..:::.Jf 1 1 I -¥i I 1 1 I

- +- - - J 1 1 ' 1 � 1 1 1 1 _1 1 I I I

Legend:

I

points to next unit _ _. to be investigated

when unit is established

points to next unit to be investigated when unit is not established

Fig. 6. An analyzed PERFECT-model for establish-generalize

A COGSYS-knowledge based system consists of a KRL­program, a GPI-specification and possibly some programs written in another language. In COGSYS all communication with the enviroment (in our case the datasources "raw plant data" and "diagnosis" of Fig. 2) occurs via the GP!. Therefore, the GPI-specification produced by the PERFECT-compiler consists of the hooks and virtual hooks that occur in the PER­FECT-model, and of the facts that are derived by the KRL and that occur in the datasources "diagnosis". The value of each of the hooks is taken from the datasource "raw plant data" of Fig.2, while the values of the virtual hooks are derived from variables of this same datasource through a seperate data­abstraction module. It is possible to do this data-abstraction in KRL, but it is most efficient to use a C-program for this pur­pose. Therefore, the PERFECT-compiler generates a C­program that can be linked in the application. The following piece of KRL-code is the result of the compilation of the unit en_trans_prim of Fig. 4.

495

MODULE en_trans_prim

!***** Interfaces of this module with other modules *****/ IMPORT maintain_en_prim

maintain_en_prim_inv _before ENDIMPORT IMPORT pump_prim

pump_prim_inv _before ENDIMPORT IMPORT maintain_level_pressurizer

maintain_level_pressurizer_inv _before ENDIMPORT EXPORT

COG en_trans_prim_inv _before: TRUTH; END EXPORT

/** Declaration of cognitive entities used in this module**/ COG behaviour_ OK: TRUTH; COG eps: NUMBER;

/** The cognitive entities used in this module that are part of the GPI**/ EXTERNAL COG INPUT Hooks: Hook_type; EXTERNAL COG I NPUT VirHooks: VirHook_type; EXTERNAL COG OUTPUT unit_ OK: unit_OK_type;

!** The set of rules which contain knowledge about the normative behaviour of this unit **/

RULESET en_trans_prim_rules RULE behaviour OK value

behaviour OK IS -ABS(VirHook.en_bal_en_trans_prim)<eps;

ENDRULE RULE eps_value

eps IS 20; ENDRULE

ENDRULESEf

!** The activities which contain the part of the establish­generalize diagnostic strategy that is relevant for this unit **/ CONTROL en_trans_prim_activity I

ON behaviour OK DO OUTPUT -

unit_OK.en_trans_prim JS TRUE; ENDOUTPUT ACTIVATE prevent_loss_of_cooling_activity2

OTHERWISE OUTPUT

unit_OK.en_trans_prim IS FALSE; ENDO UT PUT ASSERT en_trans_prim_assertion

en_trans_prim_inv _before IS TRUE; ENDASSERT ACTIVATE energy _transport_ activity

ENDON ENDACTIVITY

CONTROL en_trans_prim_activity2 ON behaviour OK DO

OUTPUT -unit_OK.en_trans_prim IS TRUE;

ENDOUTPUT ON maintain_en_prim_inv_before DO

REfRACT maintain_en_prim_assertion ACTJV ATE en_transfer_2_3 _activity

OTHERWISE ON pump_prim_inv _before DO

REfRACT pump_prim_assertion ACTIVATE maintain_level_pressurizer_activity

OTHERWISE ON maintain_level_pressurizer_inv _before DO

REfRACT maintain_level_pressurizer_assertion ACTIVATE energy _conversion_activity

EN DON ENDON

EN DON OTHERWISE /*behaviour OK is FALSE */

OUTPUT unit_OK.en_trans_prim IS FALSE; ENDOUTPUT ACTIVATE energy_transport_activity

EN DON END ACTIVITY

END MODULE

This KRL-code should be interpreted as follows: Since en_trans_prim (which occurs twice in Fig. 6) does not have a vertical successor the second time it occurs, it must be able to decide whether it should activate en_transfer _2->3, maintain_level_pressuri::.er or energy_conversion. Therefore, it needs to know whether the beginning of the path started at the unit maintain_en_prim, pump _prim or main­tain_level_pressurizer. In the IMPORT statements it can be seen that en_trans_prim imports certain cognitive entities from these three modules which provide the necessary information. Moreover, since in the first occurrence of en_trans_prim it does have a vertical, as well as a horizontal successor, en_trans_prim must write on the blackboard when it has been investigated, and hence it must EXPORT a cognitive entity that represents this knowledge and that can be used by the modules energy_transport and production. The next statements show that behaviour _OK and eps are local cognitive entities. The ex­ternal cognitive entities Hooks and VirHooks are GPI­variables. The fact that they are INPlIT implies that their values can be used in the KRL, but that it is not possible for the KRL to make any changes. The external cognitive entity unit_OK is an OlITPlIT GPI-variable, which means that the KRL can derive a value for it, and write it to the GP!, where it can be used by the Human Machine Interface. The next part of the module is the RULESl:IT. This is a translation of the rela­tions of the unit. Each relation is translated to a seperate rule. The rules are used to assert whether the behaviour of the unit is according to its normative behaviour. The following control­activities En_trans_prim_activityl and En_trans_prim_ac­tivity2 assure that inferencing is done in the optimal sequence that was calculated by the analyzer. En_trans_prim_activityl invokes the inference engine of COGSYS to derive the value of the cognitive entity behaviour _OK. In case behaviour _OK was TRUE, its value is send to the GP! by means of the OlITPlIT-statement, and the activity prevent_loss_of _cooling2 is activated. In the other case, the value of be­haviour _OK is also send to the GP! and energy_transport_ac­tivity must be activated, but energy_transport_activity must know that it was en_trans_prim that was investigated before. Therefore, it first ASSERTs on the blackboard that the cognitive entity en_trans_prim_inv _before IS TRUE.

The activity en_trans_prim_activity2 (which corresponds to the second occurrence of en_trans_prim in Fig. 6) also first invokes the inference engine to infer the value of behaviour-_ OK, this value is written to the GP!. In case behaviour OK is TRUE, the activity must now decide what the next activity to activate is. Therefore, it queries the blackboard to find out whether maintain_en_prim was investigated before. In case that it is true, this value can now be retracted (cleared) on the blackboard, and en_transfer _2_3 _activitv can be activated. In case pump_prim_inv _before is TRUE, it retracts pump_prim­_assertion and then activates maintain_level_pre.uurizer­_activity. In the other case, it retracts maintain_level_pres­suri::.er _assertion and activates energy _conversion_activity.

To summarize. the compiler of PERFECT yields a RTKBS in which the knowledge contained in the relations of a unit are translated to rules. The heuristic derived by the analyzer to guide the search strategy of establish-generalize are translated to efficient procedural code in activities. Hence, a clear separa­tion exists between the knowledge and the inference strategy.

CONCLUSIONS

For real-time knowledge based systems (RTKBS) to become viable complements to traditional information systems the ap­plication of proven methodologies for system analysis and design is of utmost performance. However, these methodologies do not provide any support to knowledge en­gineers about issues that are related to the design of RTKBS, such as: What is the necessary knowledge for the RTKBS to perform a certain task? How can this knowledge be used by inference strategies? How should the knowledge model and the inference strategies be implemented, such that the resulting model is maintainable and meets all time requirements? How should the output of the RTKBS be presented to human operators to achieve effective human performance? Answers to these questions are also not provided by tools that are suitable for implementing a RTKBS, such as COGSYS or G2. PER­FECT (Programming EnviRonment For Expertsystems Con­strained in reasoning Time) does support knowledge engineers

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in answering these questions.

By means of an example RTKBS of the Generic Nuclear Plant, we have shown that it is possible to draw Y ourdon Sys­tem Analysis-diagrams with one of the graphical editors of PERFECT, in order to design the cooperation of the RTKBS with existing software. From this diagram the interfaces bet­ween the RTKBS and existing software can be defined, and it can be seen which datasources and data processing functions must be (re)designed. We have also shown that PERFECT provides guidelines and principles to make the (re)design. The datasource "knowledge model" of Fig. 2 can be specified by the knowledge engineer by using the graphical editor of PER­FECT. This editor provides design primitives to build a hierar­chical and modular knowledge model, that is maintainable. The analyzer checks whether it contains the necessary knowledge for monitoring and diagnosing an industrial process, and warns the knowledge engineer when this is not the case. Moreover, the analyzer derives a heuristic that is used by establish-generalize to investigate the units of the knowledge model in a best-first order. Hence, the data processing function "Monitor and Diagnose" need not be designed by the knowledge engineer, but is provided by PERFECT. The datasource "diagnosis" is also provided by PERFECT. It con­sists of all malfunctioning units. In this paper we did not show which guidelines PERFECT gives with respect to the Human­Machine Interface, that will be the topic of a future paper. Finally, we have shown how the design of the knowledge model and inference strategy is translated to a COGSYS­program.

From this, it can be concluded that PERFECT supports the en­tire life cycle of RTKBS, from analysis to implementation, and hence it bridges the gap between the traditional analysis and design methodologies, and implementation tools for RTKBS.

REFERENCES

Armenise, P. ( 1989). A structured approach to program op­timization. IEEE Transactions on Software Engineering. 12. 2: 101- 108.

Bachan!, J. and E. Soloway. ( 1 989). The engineering of XCON, Communications of the ACM. ;2b 3: 3 1 1 -3 1 7.

COGSYS, 1990. COGSYS manual. COGSYS Ltd, Salford, United Kingdom.

De Keyser, V. ( 1987). How can computer-based visual displays aid operators? Int. J. Man-Machine Studies. n, 471 -478.

Hatley, D.J. and I.A. Pirbhai. ( 1 987). Strategies for Real Time System Soecification. Dorset House Publishing, New

York, NY. G2. ( 1990). G2 Reference Manual. Gensym Cooperation,

Cambridge, MA. Goodstein, LP., J. Hedegard, K. Soe H¢jberg, and M. Lind

( 1984). The GNP testbed for Ooerator Supoort Evaluation. RIS0 report M-2460, Roskilde, Denmark.

Lind, M. ( 1 990). Representing goals and functions of complex systems. Report, Institute of Automatic Control Systems, Technical University of Denmark, Lyngby, Denmark.

Newell, A. ( 1 981). The Knowledge Level. AI Magazine. Summer . 1 -20.

Sassen, J.M.A., P.C. Riedijk, and R.B.M. Jaspers. ( 199 1 ). Using multilevel-flow models for fault-diagnosis of industrial processes. In Proceedings of the 3th European Conference "Cognitive Science Approaches to Process Con trol". Cardiff, UK, 207-216.

Sassen, J.M.A., A. Ollongren and R.B.M. Jaspers. ( 1 992). Predicting and improving response-times of PERFECT­m�els. Proceedings of the 1992 IFAC/IFIP/IMACS Inter na!Ional Symoosium on Artificial Intelligence in Real-Time Control . Delft, The Netherlands.

Sommerville, I. ( 1985). Software Engineering (2nd ed.) Addison-Wesley, Reading, Mass.

Steen, M.R. van and J.M.A. Sassen. ( 1 989). COGSYS-KRL: A knowledge representation language for real-time knowledge based systems. In H.J. van den Herik (Ed.), Proceedings AI Toepassingen '89. SIC, The Hague, The Netherlands, (in Dutch), 33 1 -340.

Steels, L. ( 1990). Components of Expertise. AI Magazine. Summer. 29-49.

Winston, P.H. ( 1984). Artificial Intelligence. Second Edition. Addison-Wesley, Reading, Mass.

Copyright © IFAC Artificial Intelligence in Real-Time Control, Delft, The Netherlands, 1992

RIGAS: AN EXPERT SERVER TASK IN REAL-TIME ENVIRONMENTS*

A. Crespo, J.L. Navarro, R. Vivo, A. Garcia and A. Espinosa

Grupo de AUlomatica e Informatica Industrial, Universidad Politecnica de Valencia, Apdo 22012, E4(J()7J Valencia, Spain

Abstract. The integration of expert systems in real time environments provides new pos­sibilities to the process control of complex systems. Intelligent tasks working together with traditional control tasks under real time constraints introduce some problems in order to guarantee a response time of the system. In this paper, the use of a a real time expert sys­tem for process control, called RIGAS, encapsulated in an expert server task is described. The expert server is formed by an scheduler, a blackboard, and a set of task with real time constraints.

Keywords. real time expert systems, intelligent control, blackboard system

INTRODUCTION

Real time and expert systems provide a general framework to solve a great number of problems not completely solved by means of traditional ap­proaches. One of the most interesting fields to apply these techniques is the control of complex systems.

There is a significant number of topics in research re­lated with this subject. Some of them are: real-time scheduling, temporal representation and reasoning, guaranteed response time, uncertainty management, efficient inference, etc. [Laffey88)

Blackboard systems are being used to experiment knowledge based systems in real time frameworks and it has been seen as one of the best alternatives to match complexity and variety of actual applications.

However, expert system need to be integrated with other software components to complete the overall system including critical and non critical tasks. One of the main problem emerged is the predictable be­havior of the tasks with Al techniques.

Most of the real time expert system are based in blackboard architectures [Hayes90) [Erickson90)

*Partially supported by a grant of CICYT No. ROB89-0442 of Spanish Government

497

[Paul91) [REAKT90).

Real time expert systems knowledge bases use the ob­ject oriented approach to represent the knowledge. It allows an easy understanding, redundancy avoidance, and modularity, among other interesting issues.

The features above stated require:

• Guaranteed response time When we combine process control with expert systems techniques and we try to apply them under real time con­straints, some criteria have to be applied in or­der to guarantee the response time of the sys­tem. This guaranteed response time may be obtained at different levels:

1 . Scheduling: establishing a plan to execute the appropriated tasks. The appropri­ated with respect to the deadline speci­fication and the resources used.

2. Knowledge Base: Rules are defined at dif­ferent levels of knowledge (deep knowl­edge), and several sets of rules cooperate in a problem. The inference engine knows which rules are appropriated and the time they require in order to solve a subprob­lem.

3. Inference engine matching algorithms: us­ing RETE or TREAT pattern matching al­gorithms to improve the inference process.

4. Data Base: providing concurrent and real time methods to access to object instances.

• Temporal representation and reasoning Com­plex processes require some kind of temporal information and reasoning about time. So, an efficient model to represent past, current and fu­ture facts and reason about these facts should be considered. Several temporal models have been proposed as [Allen84] , [Dean87], [Barber90] based on time intervals or time points. The last one offers many options to handle temporal knowledge, but, in order to have a simple and efficient model of the reasoning process when applied to real­time systems.

• Continuous operation: The system have to op­erate in a known loop based on: i) data acquisi­tion, ii) output calculation (using IC and other classical regulators), and iii) actuation.

• Focus of attention: when a concrete situation that requires a specific treatment is recognized, the system should change its mode and concen­trate its attention over a concrete number of variables or processes. In this case, the system should follow the process and correct the situa­tion putting all resources on it.

• Nonmonotonicity: due to new information (in­coming from sensors), as well as deduced facts, do not remain static during the execution. Each period of acquisition data values are updated and old information or decay in validity with time or is obsolete.

In this paper a real time expert system, called RIGAS, [Crespo91] [Garda90] that incorporates most of the features above described is presented. First, we will describe the global architecture and the design criteria to be decomposed. Next, the in­ternal structure of the expert server will be detailed. Finally, implementation details will be given.

ARCHITECTURE

Several architectures have been proposed for real time expert system, [HAYES90], [RAUF89], etc. Most of them enlarge the features of expert systems to real time environments. However, this approach has some problems due to the the differences between expert and real time systems.

In order to improve predictability it is needed to tackle two levels:

1. Global architecture: In a distributed environ­ment some nodes perform real time activities implying AI components. Tasks in a node can

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be split into critical tasks, other tasks (no critical), and expert server tasks where AI techniques relevant to a concrete problem are embodied. All these tasks run on top of a real time operat­ing system that provides priority based schedul­ing. The priority of each task is determined based on periods, computation time and re­sources used.

2. Expert task architecture: which provides archi­tectural foundations to be applied in complex environments with temporal constraints. The expert task can be based in a blackboard ar­chitecture with extensions for real time problem solving.

Figure 1 shows the two proposed levels.

Critical ta•k• Otber ta.aka

Expert ta•k•

I

I t'!natrod ""'"

R.T.O.S.

Figure 1 : Global architecture

-

Critical and non critical tasks can be managed by means of a conventional real time operating system using mechanism based on priorities. However, a more sophisticated method to execute the intelligent tasks is needed due to the complexity, number of tasks, unpredictability of the reasoning process, etc. So we need to isolate intelligent tasks in the expert server task in order to apply other methods to offers the best solution in time.

From the global architecture point of view, it is possi­ble to apply the rate monotonic theory to all tasks in the system calculating a priority to each task. This first step, using the computation time of all tasks (ex­cluding server tasks), determines the system schedu­lability and the computation time that can be used by expert task.

Expert task has a period of execution related with data acquisition task, so, a determined priority is as­signed. With the available time, the expert server can offer answers with a quality. If more time is available the quality of the response will be higher.

Data from external tasks to expert server is sent by means of mechanism (messages) provided by the op­erating system. An internal process in the expert system get this information and store it in the asso­ciated objects.

RIGAS ARCHITECTURE

The internal structure of the expert server is shown in figure 2.

blackboard

reg '#

O.S. Exten•loa•

Figure 2: Internal structure

The main components in the internal architecture are:

• Blackboard Database: It stores the applica­tion objects. Objects are instances of classes with static and temporal attributes. Temporal slots in objects store past, present and future facts. A set of internal methods has been de­fined in order to manage temporal information, maintain dependencies of future facts and rea­son about time. Additionally, some mechanism to permit multiple access to objects have been defined.

• Regulators: which includes a domain specific knowledge. Global problem is partitioned into several regulators -knowledge sources (KS)- each one contributing to solve a control subproblem. Regulators are objects instances of determined classes that can be implemented as procedures (classical algorithms) or sets of rules. Several versions of each regulator can be defined in or­der to express more level in a specific knowledge. Each higher version is able to obtain a. better answer (more quality) but with more time con­suming

• Processes: Blackboard and regulators compo­nents pla.y a. passive role in the system. The activity, as response to external or internal stim­ulus, is carried out by active objects structured as processes. Because of these processes define the response a. set of real time constraints are

I

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associated to each one that ha.ve to be guaran­teed. Several set of processes can be defined in order to model different control situations (nor­mal mode, alarm mode, etc.). Actions are mes­sages to passive objects, or event to the control, or mode changes.

• The Control Component: The main objec­tives of control are to manage processes in re­sponse to dynamic changes in the environment, guarantee the response time, and maximize use of resources. All above components emit events to the control in order to notify changes in the system. Control component selects the most appropriated versions of the regulators needed by processes ta.king into account used resources, a.va.ila.ble time, a.nd quality of the response. In­teresting points a.re: selection of most a.ppro­pria.ted events, to guarantee the response time, parallel execution of regulators.

• Operating system extensions: This compo­nent provides functionalities on top of a resi­dent operating system to create processes with real time constraints, manage and execute, fast mechanisms to synchronize processes, and mem­ory management.

A more precise description of ea.ch component is done in the following sections.

Blackboard database

The blackboard database provides mechanisms to ob­ject access, a.nd ma.na.gement. Objects a.re instances of classes where static a.nd temporal attributes ca.n be defined. In this case some attributes a.re constant or we do not wa.nt to remember old values, a.nd others a.re temporal where we ca.n store old values (evolu­tion of a temperature, in which instants a.n alarm was produced) or perform predictions a.bout it (in 30 minutes the temperature will be high, or a.n ala.rm will be signaled before one hour).

Temporal information is based in a. point based model where ea.ch value has information a.bout its begin a.nd end time a.nd duration. In real time systems, things occurs a.t time impulses, so it is easy to assume tha.t past facts a.re perfectly known (begin a.nd end time) a.nd all of them a.re related to a.n exact da.te. With respect to future facts, they a.re predictions a.bout future behavior tha.t has to be confirmed by means of field da.ta.. This kind of facts ca.n be assumed as present when its time is actual a.nd has been con­firmed, or eliminated when its temporal window has been overlapped by the current time without confir­mation.

Blackboard provides methods to retrieve past infor­mation ( a.t a. concrete time, before another value) calculate trends, put future values, deduced things depending on future values, a.nd inform when predic­tions a.re fulfilled.