neural and neuro-fuzzy networks in fault diagnosis of dynamic systems józef korbicz university of...
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NEURAL AND NEURO-FUZZY NETWORKS
IN FAULT DIAGNOSIS OF DYNAMIC SYSTEMS
Józef Korbicz
University of Zielona Góra Institute of Control and Computation Engineering
www.issi.uz.zgora.pl
Józef KorbiczUniversity of West Bohemia, Czech Republic,
12 May 2011
Outline of the talkIntroductionModel-based diagnosis systemsSoft computing in fault diagnosis artificial neural networks fuzzy logic neuro-fuzzy networks
Applications – intelligent actuators, DC motorConclusionsFuther reading and research directions
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 20112
Introduction
Fault diagnosis: determination of the kind, size, locations and time of the occurrence of a
fault
Fault diagnosis problem in: automatic control systems telecommunications networks transmission pipelines and lines electrical and electronic circuites and others
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 20113
Diagnostic steps
Fault diagnosis most important and difficult task to achieve
fault accommodation
Goals of fault diagnosis detection and isolation of occurring faults
as well as providing information about their size and source
Isolation
Detection
Identification
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 20114
Two-step procedure of the diagnosis process
Symptom generation (fault detection) generation of signals or symptoms which reflect the faults
Symptom evaluation (fault classification) logical decision-making on the time of the occurrence and location of a fault Fault analysis determination of the type of fault as well as its size and cause
SYSTEM
InputsResidual
generation ClassificationFault
analysis
Residual evaluation
MeasurementsResiduals
Time andlocationof faults
Type and caseof faults
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 20115
Fault diagnostic strategies
Model-based approach analytical models (e.g. Luenberger observers, Kalman filters) knowledge-based models (neural networks, fuzzy logic, neuro-fuzzy
networks) combination of both along with analytical or heuristic reasoning
Data-based approaches pattern recognition statistic methods
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 20116
Model-based approach
PROCESS
MODEL
ClassifierR=>S
RelationS=>F
Residualevaluation
Faultisolation
faults
outputs
R-residual
inputs
S-diagnostics signals
F-faults
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 20117
Data-based approach
PROCESS
RelationS=>F
Generator of diagnostic signal
Fault isolation
faults
Y-outputsU-inputs
S-diagnostics signals
F-faults
ClassifierU Y=>S
∩
University of West Bohemia, Czech Republic, 12 May 2011Józef Korbicz 8
Importance of research
IFAC Symposium on Fault Detection Supervision and Safety forTechnical Processes, SAFEPROCESS since 1991 every 3 years, next: Mexico, 2011
Polish National Conference on Diagnostics of Processes and Systems, DPS since 1996 every 2 years, next: Warsaw, 2011
Applications, i.e. chemical industry, power plants, automotive and aircraft industries, etc.
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 20119
Models for symptom generation
Parityspace
DETECTIONMODELS
Analytical Knowledge-based Data-Based
ObserversParameter
identificationExpertsystems
Qualitative(fuzzy) Fuzzy Neural
Neuro-fuzzy
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201110
Why do we need so many models?
Diagnosed system can be: complex: processes, actuators, measurements non-linear dynamic noised and disturbed – unknown input with imprecise mathematical models
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201111
Models for symptom evaluation
ThresholdsPattern
Classification
Neural
SYMPTOM EVALUATION
ApproximateReasoning
Adaptive•analytical•fuzzy•neural
Constant Parametric•geometrical distance•fuzzy•neural•neuro-fuzzy
Parametric•statistical
Probabilistic•fuzzy
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201112
n Fault tolerant control system Multidisciplinary feature
FTC is a control system that possesses the ability to accommodate system component faults/failures
automatically and is capable of maintaining overall system stability and acceptable performance in the event of such failures
Fault Detection and Isolation (FDI)
Computing, Communication,
Simulation,I mplementation
(hardware/ software), and Display
techniques
Optimal, Adaptive,Robust Control
(Reliable Control or Passive FTC)
Reconfigurable/ Restructurable Control
Active FTC
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201113
n Modern control and fault diagnosis system
Problem how to design a robust
fault diagnosis system for non-linear systems?
Solution with analytical or soft computing techniques
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201114
n Where can fault tolerant control systems be applied?
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201115
Neural networks in fault diagnosis
Main advantage of ANNs do not require an accurate analytical model of the diagnosed process need representative training data
ANNs in fault diagnosis
Modelling problem dynamics of the diagnosed processes
–
+
PROCESS
Neuralmodel
)(ˆ ky
)( q1,2,...,ii f
)(ku )(ky
r Neuralclassification–
+
PROCESS
Neuralmodel
)(ˆ ky
)( q1,2,...,ii f
)(ku )(ky
r Neuralclassification
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201116
Networks with external dynamics
Neural residual generator with external Tapped Delay Lines (TDLs)
Input-output representation
where - non-linear function of the network - non-linear function of the diagnosed process
)](),...,1(),(),(),...,1(),([ˆ)(ˆ nkykykymkukukufk y
)(ˆ f
)(fu(k–m)
…
PROCESS
Staticneural
network
TDL TDL
u(k)
y(k)
u(k)
y(k)
r(k)+
–
…
…
…y(k – n)
u(k–m)
…
PROCESS
Staticneural
network
TDL TDL
u(k)
y(k)
u(k)
y(k)
r(k)+
–
…
…
…y(k – n)
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201117
Networks with internal dynamicsDynamic neural networks with global recurrence: drawback – the stability problem local recurrence: dynamic neuron modelsDynamic neuron model
Mathematical description
adder module
filter module
activation module
sg
...
w1w
2
wP
1( )u k
2 ( )u k
( )Pu k
IIR( )y k
)(F)(k )(kx
1
mT
p pi
k k w u k
( ) w u( ) ( )
)]([)]([)( kxgFkxFky s
n
ii
n
ii ikbikxakx
01
)()()(
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201118
n Dynamic multilayered neural network
Training algorithm Extended Dynamic Back-Propagation (EDBP)
1mu
mju
m
mSu
1u
2u
0Su
1S1MS
MS
M1M 1
0S
11
1
ny
2y
1y
dynamic neuron model
1mu
mju
m
mSu
1u
2u
0Su
1S1MS
MS
M1M 1
0S
11
1
ny
2y
1y
dynamic neuron model
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201119
n Application problems of neural networks
Architecture designing there are no effective formal methods kind of network and its structure is selected based on:
- known properties of various networks, e.g. MLP, RBF or GMDH- character and complexity of the process considered, e.g. nonlinear,
dynamic, multi-input and multi-output
Training and learning needs representative data convergence is a pretty slow
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201120
Examples of fault diagnosis systems
Two-tank system with delay aim of system control: to keep up
a constant level of water in Tank 2 possible faults:
- Valve V2 closed and blocked- Valve V2 opened and blocked- leak in Tank 1
S P IR A LP IP E L IN E
V E
Q 1
h 1
h 2
Tan k 1 Tan k 2
V 2
V 3V 4V 1 Q n
P U M P
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201121
Residual generation
1 0 0 0
0 .0 5
-0 .0 5
0
0
2 0 0 0
M O D E L 0
N orm al cond itions Fault N o . 1
a )0 .1
-0 .1
0
0 1 0 0 0 2 0 0 0
M O D E L 1
N orm al cond itions Fau lt N o . 1
b )
0 .0 5
-0 .0 5
0
0
1 0 0 0 2 0 0 0
M O D E L 2
N orm al cond itions Fault N o . 2
c )
0 .1
-0 .1
0
0 1 0 0 0 2 0 0 0
M O D E L 3
N orm al cond itions Fault N o . 3
d )
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201122
n Fuzzy logicGeneral fuzzy-logic systems
Advantages of fuzzy systems transparent representation of the system under study linguistic interpretation in the form of rules rules extracted from data can be validated by an expert
Knowledge BaseRules Data
Inference mechanism
Crisp/Numerical Outputs
Crisp/Numerical Inputrs
Fuzzy inference system
Fuzzy sets
Fuzzy sets
Fuzzyfication Defuzzyfication
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201123
Fuzzy residual generationKnown fuzzy observers qualitative observer functional observer relational observer
PROCESS
z-
1
z-
1
z-
1
z-
1
Fuzzy
Relation
Fuzzy-fication
Fuzzy
Cartezian
Product
Defuzzi
- fication
Fuzzy relation model
)(ˆ ky )(kr
)(ku )(ky+
–
YX
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201124
Neuro-fuzzy networksCombination of the fuzzy system with neural networks Mamdani neuro-fuzzy networks
Takagi-Sugeno neuro-fuzzy networks
i-th rule:
IF x1 is A1i and … and xn is An
i THEN y1 = b1i and … and yn = bm
i
i-th rule:
IF x1 is A1i and … and xn is An
i THEN y1=b0,1i+b1,1
ix1+…+bn,1ixn and ...
... and ym=b0,mi+b1,m
ix1+…+bn,mixn
where
x1,…,xn are inputs
A1i,…,An
i are fuzzy sets
b0,1i,…,bn,m
i are parameters of linear consequents
y1,…,ym are outputs Józef Korbicz
University of West Bohemia, Czech Republic, 12 May 201125
Neuro-fuzzy networks
/
n
/
b11
m
b12
b13
b1N
bm1
bmN
bm2
bm3
L. 1 L. 2
L. 3 L. 4
N
N
NN
1
N
n
N
y1
ymxn
x1
where x1,...,xn - inputs y1,...,ym - outputs n - no. of inputs, m - no. of outputs N - no. of rules, L.1,...,L.4 - layersN1,...,Nn - no. of fuzzy partitionsbj
i - singletons
where x1,...,xn - inputs y1,...,ym - outputs n - no. of inputs, m - no. of outputs N - no. of rules, L.1,...,L.4 - layersN1,...,Nn - no. of fuzzy partitionsbj
i - singletons
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201126
Neuro-fuzzy networks
Advantages of neuro-fuzzy networks ability to represent some kind of uncertainty present in real processes ability to combine quantitative and qualitative knowledge non-linear mappings parameters of membership functions are adjusted by the training process,
i.e. the mean value and variance of bell-shaped membership functions
Disadvantages for large numbers of fuzzy sets the number of adjusted parameters
increases drastically
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201127
Models uncertaintySources of model uncertainty mathematical or/and neural and neuro-fuzzy models of supervised systems
are never perfectly accurate and complete parameters of the systems may vary with time in an uncertain manner characteristics of disturbances and noise are unknown
Conclusion there is always a mismatch between the actual process and its model even
if there are no process faults
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201128
Robustness in model-based fault diagnosis
Robust model-based FDI methods insensitive or even invariant to modelling uncertainty
Why do we need robust methods? to increase robustness to modeling uncertainty without losing fault
sensitivity to minimise false alarms and improve the quality of the diagnosis Józef Korbicz
University of West Bohemia, Czech Republic, 12 May 201129
Uncertainty problem in diagnostics and its solutionRobust observer unknown input observer, unknown input filter design strategy: minimization the effect of unknown inputs
Model uncertainty statistical techniques (many restrictive assumptions)
Neural and neuro-fuzzy models uncertainty design strategy: using the Bounded-Error Approach (BEA)
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201130
n Approaches to robust fault detectionActive approaches principle: to eliminate model uncertainty - unknown input observers (Witczak, 2007) - parity relation (Chen and Patton, 1999)
Passive approaches principle: to provide and adaptive threshold taking into account model
uncertainty (approaches for linear systems (Frank, 2002)) key design principle: to estimate the parameters of the model and the
associated model uncertainty and then use this information for adaptive threshold determination
main tool: least-square method-based approachesJózef Korbicz
University of West Bohemia, Czech Republic, 12 May 201131
n Adaptive threshold n Concept
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201132
Uncertainty of soft computing models
Takagi-Sugeno fuzzy model Korbicz and Kowal, 2007
GMDH neural model Witczak, Korbicz, Mrugalski and Patton, 2006
Multi-layer perceptron model Mrugalski and Korbicz, 2007
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201133
n Dynamic neural networks of GMDH(Group Method of Data Handling)
Why GMDH? successful identification depends on proper selection of the model structure determination of the appropriate structure and parameters of a non-linear
model is a very complex task GMDH approach can be successfully employed to automatic selection of the
neural network structure, based only on the measured data structure of the network is designed by gradually increasing its complexity
Idea of GMDH replacing the complex model of the process with partial models (neurons) by
using the rules of variable selection
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201134
Network development procedure GMDH
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201135
n Dynamic GMDH neural networkDynamic neuron structure
System description
)())(()( kkzky T
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201136
GMDH networks Uncertainty determination and fault detection
BEA-based parameter estimation non-linear parameter estimation problem
due to the invertibility of the activation function it is possible to write
this makes it possible to use the error-in-regressor BEAAs a result of using the BEA, we have- an estimate of - the feasible parameter set
MTm kkzkyk )())(()()(
)(
))()(()())()(( 11 mTM kkykzkky
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201137
GMDH networksUncertainty determination and fault detection
Termination condition procedures of
- parameter identification- partial models evaluation- partial models selectionare repeated over till the transition error starts growing
Uncertainty propagation
uncertainty of the neurons is propagated through the layers during the development of the GMDH network
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201138
GMDH networks Uncertainty determination and fault detection
Fault detection An adaptive threshold generated with the output neuron (Witczak, 2006):
where
Fault detection rule: When the output signal does not satisfy the constraints of the adaptive threshold then a fault symptom occurs
Computational aspects:
exact BEA: where V stands for the set of vertices of a polytopeimplicit BEA (e.g. OBE): the adaptive threshold is described by analytical formulae (see e.g. Mrugalski, Witczak and Korbicz, 2007), i.e. there is no need for solving the max/minproblem
MMTmmT kkxkykkx ))()(()())()((
,)(maxarg)(
kxk T
V
M
)(minarg)( kxk T
V
m
,)(maxarg)(
kxk TM
)(minarg)( kxk Tm
)(ky
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201139
Passive approachAdaptive threshold
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201140
DAMADICS benchmark Valve actuator case study
Realization 5FP EC, RTN DAMADICSIndustry Lublin Sugar Factory (Cukrownia Lublin S.A.)
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201141
Intelligent actuator
ACQ – data acquisition unit CPU – positioner central processing unitE/P – electro-pneumatic transducerV1,V2 and V3 – valvesDT – displacementPT – pressureFT – value flow transducer CV – control valueF – flow measurementT1 – juice temperatureX – rod displacementP1 and P2 – juice pressures at the input and outlet of the control value
T1 P1
V3Control valve
Pneumatic actuator
Positioner
P2
E/P CPU
ACQPT
DT
F
CV
V1
V2
FT
X
S
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201142
Industrial application DAMADICS benchmark
FaultFault DescriptionDescription SS MM BB II
f1
f2
f3
f4
f5
f6
f7
f8
f9
f10
f11
f12
f13
f14
f15
f16
f17
f18
f19
Valve cloggingValve plug or valve seat sedimentationValve plug or valve seat erosionIncreased of valve or busing frictionExternal leakageInternal leakage (valve tightness) Medium evaporation or critical flowTwisted servomotor's piston rodServomotors housing or terminals tightnessServomotor's diaphragm perforationServomotor's spring faultElectro-pneumatic transducer faultRod displacement sensor faultPressure sensor faultPositioner feedback faultPositioner supply pressure drop Unexpected pressure change across the valveFully or partly opened bypass valves Flow rate sensor fault
x
xx
x
xxx
x
xx
x
xx
x
xxx
x
xx
xx
xx
x
xxxxxxxx
xxxxxx
x
x
x
xx
FaultFault DescriptionDescription SS MM BB II
f1
f2
f3
f4
f5
f6
f7
f8
f9
f10
f11
f12
f13
f14
f15
f16
f17
f18
f19
Valve cloggingValve plug or valve seat sedimentationValve plug or valve seat erosionIncreased of valve or busing frictionExternal leakageInternal leakage (valve tightness) Medium evaporation or critical flowTwisted servomotor's piston rodServomotors housing or terminals tightnessServomotor's diaphragm perforationServomotor's spring faultElectro-pneumatic transducer faultRod displacement sensor faultPressure sensor faultPositioner feedback faultPositioner supply pressure drop Unexpected pressure change across the valveFully or partly opened bypass valves Flow rate sensor fault
x
xx
x
xxx
x
xx
x
xx
x
xxx
x
xx
xx
xx
x
xxxxxxxx
xxxxxx
x
x
x
xx
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201143
Pneumatic motor and valve models
Model of the positioner and the pneumatic motor
Model of the control valve
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201144
Structure of GMDH models
),,,( juice of rate flow for the Model 121 TPPXfF f
),,,(nt displaceme rod sactuator' for the Model 121 TPPCfX vx
P 1
P 2
T
C V
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201145
Robust detection of faults f4 and f7 with GMDH
f4 – bushing friction f7 – medium evaporation
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201146
Robust detection of faults and with MLPFaults and17f 18f
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201147
n DC motorLaboratory stand DC motor M1 DC motor M2 rotational speed sensor S clutch K
The shaft of the engine M1 is connected with the engine M2 by the clutch K
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201148
n DC motor Model
DC motor model
whereT – revolutions per minute (RPM)Cm – motor excitation signal
Neural network with dynamic neurons
)(CfT m
)3
3.02sin(3
)7
1.12sin(3)7.12sin(3)(
k
kkkCm
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201149
n DC motor Model
DC motor response (solid line) and neural model response (dotted line) closed-loop system (Patan and Korbicz, 2007)
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201150
n DC motor Fault detection
Fault description (Korbicz and Kowal, 2007)
Faults incipient (I), abrupt small (S), abrupt medium (M) and abrupt big (B)
Fault Description S M B I
f1 Tachometer fault
f2 Mechanical fault of the motor
Fault Description S M B I
f1 Tachometer fault
f2 Mechanical fault of the motor
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201151
DC motorFault detection
Takagi-Sugeno neuro-fuzzy model with linear consequents
wherexi – input variable, y – output variable, N – number of fuzzy rules, Nj – number of fuzzy partitions, μ – membership function, p – parameters of linear consequents
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201152
n DC motor Fault detection
Takagi-Sugeno local linear models
General data number of rules: 9 number of faults: 7
,43211 043211 bkubkubkubkubkyaky ii
where: kyi - output of the i-th local linear model ku - motor control signal
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201153
DC motor Fault detection
Confidence interval for DC motor and model outputs small fault f1
Confidence interval for residuals small fault f1
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201154
DC motor Fault detection
Confidence interval for DC motor and model outputs incipient fault f2
Confidence interval for residuals incipient fault f2
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201155
Conclusions
General problem in fault diagnosis how to design a system that will be
- robust to uncertainties- sensitive to small changes
Future research activity combination of analytical methods and soft computing techniques, i.e.
expert systems
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201156
Further reading and research directions
2004 2010Józef Korbicz
University of West Bohemia, Czech Republic, 12 May 201157
Further reading and research directions
2007 2008Józef Korbicz
University of West Bohemia, Czech Republic, 12 May 201158
Thank you!
Józef Korbiczhttp://www.uz.zgora.pl/~jkorbicz/
University of Zielona Góra Institute of Control and Computation Engineering
www.issi.uz.zgora.pl
Józef KorbiczUniversity of West Bohemia, Czech Republic, 12 May 201159