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MODELING VISUAL REASONING ON GRAPH USING

QUALITATIVE INTERPRETATIONS.M.F.D. Syed Mustapha

Faculty of Computer Science and Information Technology

University of Malaya, Lembah Pantai

50603, Kuala Lumpur

Tel:+(603)7560022 ext 6346 Fax: +(603)7579249 e-mail:symalek@fsktm.um.edu.my

Abstract: Human visual reasoning and understanding are important in the study of human cognition

(Pisan, 1995). It is a constituent discipline in the field of artificial intelligence. Such research study

advocates to various orientations such as image processing, neural networks, parallel distributed

processing, machine learning and others. Human graph recognition through subjective visualization

substantially plays the role in various applications such as engineering, fluid mechanics and education.

Particularly, in reasoning towards the behavior of physical relations and processes via the piece-wise

graph representation. In this paper we discuss an artificial intelligence technique so-called qualitative

reasoning which is used to generate qualitative interpretation in analyzing graphs. Selection on graph

models can be misleading and require qualitative understanding about the nature of the graph. We

define briefly the scope of qualitative reasoning, discuss the reasoning techniques by providing several

selected research works as case studies.

1.. INTRODUCTIONGraph expresses relationships between variables in a pictorial form. It serves both as devices toaid in the representation of obscured raw data and make holding information in the humans

memory easier (Pisan, 1994). Different types of graphs indicate distinctive refinements during the

process of recognition. For instance, in pie chart, the relative size of portions are observed, bar

graphs show the relative height or amount, scatter plots display the pattern of the data and line

graphs portray the continuous relationship between two variables.

The graph recognition on the line graph is our main interest because of its usage in variousapplications are far-reaching. Human being recognizes a graph through subjective visual

inspection. Interpretation of the graph is done by giving qualitative description based on the

physical appearance of the slope, direction, continuity and spatial relationship. A monotonic x-yrelationship commonly described as linear model or non-linear model if it shows a continuous

change in slope and direction. Nomenclatures such as the parabolic, the hyperbolic and the

sinusoidal wave posses qualitative term which are frequently referred by human. For anonymous

graph, separate parts of the graph have to be labeled individually so that a single-named reference

can be made by concatenating the labeled parts. The application of such technique has been

shown in (McIllraith, 1989; Ritter and Will, 1990).

In this paper, we describe an approach of artificial intelligence, so-called qualitative reasoning. Itis a technique incorporated into a computer system such that interpretation of a piece-wise linear

graph can be automated. The idea of the qualitative reasoning are introduced in section 2,

followed by its implementation in several areas such as in well-test data interpretation in section

3 and modeling the fluid behavior in section 4.

2.QUALITATIVE REASONINGThe notion of qualitative reasoning emerges in the realm of physics (Forbus, 1988). Theobjectives are to represent and reason about the physical behavior of a system. Professor Kenneth

Forbus (Forbus, 1998) and his research group are the founder of this theory. They expounded this

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concept with an example of an object attached to a spring sliding through a friction-free surface

as illustrated in Fig. 1 (Cohn 1989).

If we posed a question what would happen if the extended spring of the object is released fromposition 2?. Without a need to engendering any mathematical expression such as F = kx, human

being qualitatively explain the object oscillates back and forth several times for a short time

until it eventually stops. A simple conjecture of this has been employed extensively in various

simple to complex areas such as modeling the coffee machine problem (Bonissone and Valvanis,

1985), automotive circuit simulation (Snooke and Price, 1997) and reasoning towards the

structural behavior of fluids (Yip, 1995). Several organizational structures, so-called ontology,

have been introduced. Among the prominent ones are contraint based (Kuipers, 1986),component centered (Kleer and Brown, 1984) and process centered (Forbus, 1988).

In this paper, we focus the implementation of the qualitative reasoning in graph recognition andunderstanding. We also mention the essential of this technique in steering to the selection of

correct model. The dominant properties of qualitative reasoning over the other reasoning methods

such as rule-based reasoning and expert system are:

I.The ability of performing reasoning on the behavioral of physical system without thenecessity of building up a precise model (Cohn, 1989).

II.Reduce the computational time cost on many occasions where approximate results aresuperior to exactness.

III.Exploring the symbolic modeling paradigm, so-called qualitative model, whichreasons from the fundamental theories and incomplete data or knowledge. This allowsthe generation of qualitative simulation (Kuipers, 1986).

IV.Simplify the parameter setting and model selection of quantitative model. Thisreduces the searching space and selection complexities (Mustapha, 1997, 1998).

The graph recognition process undertakes two main stages namely, qualitative modeling andquantitative modeling. The qualitative modeling, which resorts to qualitative reasoning technique,

captures the behavioral of the graph and its physical features. At this stage also, the class of

model library can be determined. This can reduce computational cost by narrowing the range of

possible graphs to more accurate ones (Capelo et al., 1991, 1992, 1993, 1995, 1996). In the

quantitative modeling stage, parameter values are estimated. The accuracy of this work depends

on the well-chosen graph model from the early stage. In the next section we review the

application of this technique in interpreting graph displaying an actual well pressure build up

data.

3.WELL-TEST DATA INTERPRETATIONTwo relevant cases on the well-test data interpretation are discussed here. In the first example,Ritter and Will (Ritter and Will, 1990) showed an interpretation system assembled with the aid of

an expert system shell complimented with graphical displays of an actual well-pressure build up

Figure. 1 A sliding object on a friction-free

surface

ObjectSpring

2

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data. The transient pressure analysis is essential for a good estimation of permeability formation,

well damage and average pressure in the drainage volume of the well.

Figure 2 shows a diagnostic model produced by the interpretation system. The small triangularshapes are the real well-test data. The continuous lines are the master curves, which are split into

three period of time, early time, middle time and late time.

User input an appropriate names (some examples are given in Table 1) to the expert system. Theauthors in (Ritter and Will, 1990) claimed that there is no need to automate the labeling process,as the task is obvious and trivial to users and experts. The rule-based expert system will perform

reasoning to select suitable model solution such as Homogeneous, Dual_Porosity,

Frac_Layer_Fault and Frac_Homo_Closed.

We elaborate the work of McIllraith (McIllraith, 1989) as second example. Unlike Ritter andWill, labeling the components of a curve in her work is fully automated. The adoption of

qualitative reasoning in the graph recognition is shown to be an effective method. The selection

of possible quantitative model is augmented by the knowledge of physical appearance of thegraph, prioritizing the region to be assessed and classifying the data sets to a smaller range of

possible graph models. The diverse sources of knowledge can be incorporated into an

interpretation system. The graph is described using qualitative description language, which is

represented using BNF notation. Some of these are given below:

EarlyTime MiddleTime LateTime Model Solution

Missing Stabilized MissingHomogeneous

UnitSlope FlatMinimum Stabilized Dual_Porosity

HalfSlope SmoothMinimum Increasing Frac_Layer_Fault

QuarterSlope SharpMinimum FallingOff Frac_Homo_Closed

Table 2. Model solution for time periods

EARLY TIME MIDDLE TIME LATE

Figure 2. Diagnostic Model (after Ritter and Will)

UnitSlope

HalfSlope

QuarterSlope

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A graph is composed of a region and another graph. The region is the important part of a graph inwhich its features are essential to be assessed. A region can be an entire graph or part of a graph.

The length and region-type characterize the region. The attributes such as gradualness, rapidness,

concavity characterized the curve descriptor, which are also component types of a region-type.

There are four levels of visual interpretation introduced by McIllraith (McIllraith, 1989). Theyare namely, regionalization, labeling, smoothing and curve characterization. In the regionalization

stage, curve discontinuity and abrupt change of direction is detected. The curve is then

partitioned into several segments. In labeling, each segmented curve is mathematicallycharacterized by fitting to low-order polynomial function. Each region is mathematically

described in terms of shape and length (McIllraith, 1989). Symbolic pattern language

characterization mentioned earlier is used to map the mathematical characterization to qualitative

description language. The smoothing performs subjective smoothing to detect anomalies behavior

of a graph. The occurrences of spikes, outliers or a line between two curves are repaired. There is

a need to re-label if mislabeled has been found. The final stage of visual interpretation is curve

characterization, which is executed in two different manners. The first is the identification of

characteristic curve forms in the observed data. This leads to the production of physical features

such as positive skin, wellbore storage and partial penetration. This can be done by performing

curve description parsing. For example, the following qualitative curve description,

AVERAGE GRADUAL CONCAVE CURVE + LONG GRADUAL CONVEX SHAPEcan produce the following physical features POSITIVE SKINWELLBORE STORAGEPARTIAL PENETRATION.The three interpreted physical features above indicate that at least three rules have matched thecurve description. The second type of curve characterization is determination of statistical model.

The two of these models are Gringarten SAS model and Agarwal SAS model. Each model

displays a set of master curves. The observed data is matched to one of these curves. The first

stage of curve matching is the symbolic matching of the qualitative shape of the observed data tothe ones in master curves. Heuristic knowledge is applied to decide which part of the region is to

give priority. The set of master curves of the statistical model is reduced to several potential

models. The second stage involves more stringent mathematical matching. The weighted least

squares fit is used to guide the selection of best-matching curve.

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The two examples mentioned above proved the necessity of qualitative reasoning. Humanssubjective visual inspection on the graph can be automated using this technique.

4.MODELING FLUID BEHAVIORIn the field of fluid mechanics and modern study of non-Newtonian fluid such as in rheology

(Barnes et. al, 1989), numerical modeling is essential in estimating accurate parameters. Before

selecting the appropriate accurate models, experimental data are observed and parts of the graph

are analyzed qualitatively. There are several pronged-reasons for doing this, among them are:

1.To analyze graph components to detect physical response such as elasticity, viscous,recoverable or irrecoverable deformation.

2.To determine the relevant class of constitutive equations.3.To eliminate inappropriate models through qualitative observation on regions of a

graph.

4.To refrain ill-posed problem (Winter and Baumgaertel, 1993) and evaluation onmisleading models. These models may be proven mathematically valid but can be

unphysical.

We explain the first two reasons with an example. Figure 3 shows a graph model of a creep test.

A creep test is a process of applying stress on a fluid sample and measured the strain in a

cessation of stress (Ferguson, 1995). Segmenting the graph into several components namely OA,

AB, BC, CD, DE and EF enables the analysis of a graph. The strain responses, t0 t1, are the

instantaneous elastic deformation, delayed elastic strain, viscous and labeled as OA, AB, and BC

respectively. This is followed by cessation of stress, t1 t, where CD is the instantaneous elastic

deformation, DE is partial recoverable deformation caused by the delayed elastic strain (AB)

during the imposition of strain and EF shows irrecoverable deformation due to linearity at BC.

Qualitative observation can be made by analyzing the general properties such as linearity,

concavity, vertical or horizontal line and asymptotic. The general properties can be used to

determine the physical responses of the graph. The vertical lines OA or CD indicate the existence

of an instantaneous deformation. The concavity of AB or DE exhibits the delayed response. Thelinear line of BC or the non-asymptotic EF means an irrecoverable deformation. The qualitative

behavior can be represented in logical triplet as

QB = (, , ),

Figure 3. An anatomy of creep test graph model (strain vs. time)

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where , and respectively are instantaneous elasticity, delayed elasticity and irrecoverabledeformation. These symbolic representations accept, T, for existence and, F, for non-existence of

the physical responses. The logical triplets can lead to any one of the four admissible classes of

constitutive equations,

It is not the intention to flaunt the elegance of the equations above but rather to emphasize that

there are numbers of possible quantitative models, which have been categorized into four classes.

The amount of computational time and problem-state space for an algorithm to traverse indetermination of an accurate model from these possibilities is unattainable. The knowledge of

existence and non-existence of the physical responses will help to reduce the searching to a single

class. This can be achieved by the recognition of physical appearance of the graph.

The last two reasons explain that purely statistical model-fitting is able to produce numerical

values with the lowest least-squares errors. However, parameter values such as negativity and

infinity do not have any physical meaning. The selection of appropriate models has to givepriority to physical consideration. Figure 4 compares two viscosity models, Power Law and

Carraeu-Yasuda models. Both models can describe mathematically the three regions, namely,

First Newtonian region, Power Law region and Second Newtonian region. However, for the

Power Law, this is not physically possible. Power Law model is given as,

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When n < 1 (for shear thinning fluid), approaches which is impossible for fluids. At a veryhigh shear rate, the Power Law model also fails when the viscosity eventually reaches constant.

Qualitative reasoning is applied to find the appearance of data at the plateau regions and avoid

them from fitting to the Power Law model. Instead, other models such as Carraeu-Yasuda model

is used.

5. CONCLUSIONWe briefly described the application of qualitative reasoning in the areas of graph recognition

and understanding. The impacts of such studies have led to several significant usage such as in

education. Graphs have become essential visual aids in explaining the nature of a business,

engineering process, economics, mathematics and many others to students. The qualitative

interpretation and description of a graph lends itself in generating discussion using natural

language. This has opened avenues to new teaching paradigm, so-called, intelligent tutoringsystem. This contradicts to the traditional mathematical descriptions of using figures and

primitive equations. Qualitative interpretation also allows descriptor labeling to be input

automatically to other reasoning system such as the expert system in which was manually done

previously.

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