neural and neuro-fuzzy networks in fault diagnosis of dynamic systems józef korbicz university of...

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


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


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


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


Model-based approach

PROCESS

MODEL

ClassifierR=>S

RelationS=>F

Residualevaluation

Faultisolation

faults

outputs

R-residual

inputs

S-diagnostics signals

F-faults


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.


Models for symptom generation

Parityspace

DETECTIONMODELS

Analytical Knowledge-based Data-Based

ObserversParameter

identificationExpertsystems

Qualitative(fuzzy) Fuzzy Neural

Neuro-fuzzy


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


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


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


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


n Where can fault tolerant control systems be applied?


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


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)


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

)()()(


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


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


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


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


c )

0 .1

-0 .1

0

0 1 0 0 0 2 0 0 0

M O D E L 3


d )


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


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


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


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


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


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


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)


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


n Adaptive threshold n Concept


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


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


Network development procedure GMDH


n Dynamic GMDH neural networkDynamic neuron structure

System description

)())(()( kkzky T


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


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


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


Passive approachAdaptive threshold


DAMADICS benchmark Valve actuator case study

Realization 5FP EC, RTN DAMADICSIndustry Lublin Sugar Factory (Cukrownia Lublin S.A.)


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


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


Pneumatic motor and valve models

Model of the positioner and the pneumatic motor

Model of the control valve


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


Robust detection of faults f4 and f7 with GMDH

f4 – bushing friction f7 – medium evaporation


Robust detection of faults and with MLPFaults and17f 18f


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


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


n DC motor Model

DC motor response (solid line) and neural model response (dotted line) closed-loop system (Patan and Korbicz, 2007)


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


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


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


DC motor Fault detection

Confidence interval for DC motor and model outputs small fault f1

Confidence interval for residuals small fault f1


DC motor Fault detection

Confidence interval for DC motor and model outputs incipient fault f2

Confidence interval for residuals incipient fault f2


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


Further reading and research directions

2004 2010Józef Korbicz


Further reading and research directions

2007 2008Józef Korbicz


Thank you!

Józef Korbiczhttp://www.uz.zgora.pl/~jkorbicz/

University of Zielona Góra Institute of Control and Computation Engineering

www.issi.uz.zgora.pl


neural and neuro-fuzzy networks in fault diagnosis of dynamic systems józef korbicz university of...

Documents