Fuzzy Logic Application for Fault Isolation of Actuators Jan Maciej Kościelny Michał Bartyś Paweł Rzepiejewski April 5-7, 2004 DAMADICS 2004 5-th DAMADICS

Fuzzy Logic Application for Fault Isolation of Actuators

Jan Maciej KościelnyJan Maciej KościelnyMichał BartyśMichał BartyśPaweł RzepiejewskiPaweł Rzepiejewski

April 5-7, 2004April 5-7, 2004

DAMADICS 2004DAMADICS 2004

5-th DAMADICS Workshop on 5-th DAMADICS Workshop on Integration of Qualitative/Quantitative Integration of Qualitative/Quantitative

Methods for Fault DiagnosisMethods for Fault DiagnosisPresentation of Final ResultsPresentation of Final Results

Łagów/PolandŁagów/Poland

• IntroductionIntroduction• Fault detectionFault detection• Fuzzy residual evaluationFuzzy residual evaluation• Fuzzy reasoning rules Fuzzy reasoning rules • Fault isolation algorithmFault isolation algorithm• Industrial benchmark problemIndustrial benchmark problem• Final remarksFinal remarks

Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project

IntroductionIntroductionActuator FDI approaches


• parity equation - (Massoumia and Van der Velde, 1988; Mediavilla et al.,1997)

• unknown input observer Phatak and Wiswandham, 1988)• extended Kalman filter (Oehler et al., 1997)• signal analysis (Deibert, 1994)• fuzzy logic (Kościelny and Bartyś, 1997; 2000)• b-spline (Benkhedda and Patton, 1997)• spectral analysis (Previdi and Parisini, 2003)• pattern recognition (Marciniak et al., 2003)• structural analysis (Frisk et al., 2003)• timed automata (Lunze and Supravatanakul, 2003)

IntroductionIntroductionIntelligent actuators supporting auto diagnostic andauto validation functions


Bayart and Staroswiecki, 1991 Isermann and Raab, 1993 Kościelny and Bartyś, 1997 Yang und Clarke, 1997; 1999 Tombs, 2002

IntroductionIntroductionFuzzy logic applications for development of FDI algorithms of actuators


Frank, 1994 Garcia et al., 1997 Kościelny et al. , 1999 Kościelny 1999; 2001 Sędziak, 2001 Calado et al. 2003 Korbicz et al. 2004 Yang und Clarke, 1997; 1999 Tombs, 2002

IntroductionIntroductionModel based fuzzy FDI system scheme Fuzzy approachFuzzy approach

Residual generation

Fuzzy residual evaluation

iXjS

jr

y

-+

Fault isolationFault isolationFault isolationFault isolation

Set of pairs: <fault, fault certainty >

<f<fkk,,kk>>

Fault detectionFault detectionFault detectionFault detection

XX={={xxii: i=1,2,...,I }: i=1,2,...,I }

Process data set

R={rR={rjj: j=1,2,...,J }: j=1,2,...,J }

Set of residuals

SS={={ssjj: j=1,2,...,J: j=1,2,...,J } }The set of diagonostic signals

Fuzzy reasoning

jS kf

1,0k


Actuator fault detectionActuator fault detection

10

20

50

40


)(ˆ1 CVZZr

),(ˆ212 PPZFFr

30 ),(ˆ213 PPCVFFr

)(ˆ4 ZFFr

)(ˆ5 CVFFr

S

ZT

FT

E/P ZC

Positioner

CVIPs

V

V3

V1 V2

F

CV

X’

PSP

Pz

Pneumatic servomotor

Valve

PTPT

P1 P2

Fv3

FvT1

TT

P

X

Fault detectionFault detectionFeed forward perceptron neural networks (MLP)


- easiness of learning

MA models because:

- satisfactory modeling errors

- no significant improvement of

model quality

- ability of fault learning

ARMA models not because:

Fault detectionFault detectionExamples of modelling results achieved


- easiness of learning

Exemplification of flow rate model (3) quality in fault free state (normal process state). Flow rate in technical units [t/h] versus time in [s] is shown. Significant (ca. 50%) flow drop was observed.

Illustration of fault sensitivity of

the flow rate model (3).

Fuzzy residual evaluationFuzzy residual evaluationTri-valued fuzzy residuum evaluation (idea)Tri-valued fuzzy residuum evaluation (idea)

(r )1.0

0.0-1.0 1.0

-1

0

rnj

nj 1

0.75

0.25

0.50

Tnj-T nj

(rnj )0

(rnj )1


DefinitionsDefinitions

10 Fuzzy fault symptom is the k dimensional fuzzy set such that for each residual rj assign k-plets

20 Fuzzy multiple-valued symptom

jjkjkjj Vvvvvr :..., 21j

jjiji Vvvv :, jij

where:

- membership function of the j-th residual to the fuzzy set vji

Vj – the set of fuzzy values of j-th fuzzy diagnostic signal

ji


Setting parameters of membership Setting parameters of membership functionsfunctionsStatistical approach


Examples of experimental histograms of residual of flow rate model of control valve of Actuator Benchmark Problem in fault free process state. Additional filtering technique (low pass moving average filer) applied for the instrumentation measurements may reduce the span of residual distribution (right chart).

Setting parameters of membership Setting parameters of membership functionsfunctionsAbrupt fault occurrence


Examples of histograms of residual of flow rate model of control valve of Actuator Benchmark Problem in faulty process state. The occurrence of abrupt fault is documented. Additional filtering technique (low pass moving average filter) applied for the instrumentation measurements increase separation between neighbourhood residual values in fault free and faulty states an lower the number of intermediate residual values (right chart).

Fuzzy reasoning rulesFuzzy reasoning rules

Reformulation

DGN 1 DGN 2 DGN i DGN n

s1j sijsnjs2j

R0: If )0()0()0( 1 Jj s ...s...s then the state of aptitude f0

Rk: If )()()( 11 kJJkjjk Ss...Ss...Ss then the state with fault fk


Rk: If )](...)()]()[( 11 eJbJca ssss[...ss...ss then fault fk

Example of rule isolating fault f1

R1: If )]1()1[()]0[()]1()1[()]0[()]1()1[( 55433211 ssssssss then fault f1

Reference values of diagnostic Reference values of diagnostic signals used for fault reasoningsignals used for fault reasoning


F/ S OK

f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19

s1 0 +1-1

0 0 +1-1

0 0 -1 +1-1

-1 -1 - +1-1

0 - +1-1

-1 0 0 0

s2 0 0 -1 +1 0 -1 +1 +1 0 0 0 - 0 +1-1

- 0 0 0 +1 -1

s3 0 +1-1

-1 +1 +1-1

-1 +1 +1 +1-1

+1 +1 - +1-1

+1-1

- +1-1

+1 0 +1 -1

s4 0 0 -1 +1 0 -1 +1 +1 0 0 0 - 0 +1-1

- 0 0 +1-1

+1 -1

s5 0 +1-1

-1 +1 +1-1

-1 +1 +1 +1-1

+1 +1 - +1-1

+1-1

- +1-1

+1 +1-1

+1 -1

Parallel reasoning schemeParallel reasoning scheme

Fault signatureFault signatureFault signatureFault signature

Actual signals Diagnostic matrix

PA

TT

ER

N

RE

CO

GN

ITIO

N

VKJVkJsJ

...…

VkjSj

...…

Vk1S1

fK...fk...f1F/S

SJ

...

Sj

...

S1

Diagnosticsignals

RulesRulesRulesRuleskkJJkk fthenVsVsVsIf )(...)()( 2211


Fault isolation algorithmFault isolation algorithm

),()(1

jk

J

jk sff

),()(1

jk

J

jMINk sff

Operators

J

jjk

J

jjk

k

sf

sf

f

1

1

),(

),(

)(

DGNR( f )

)( f


}0)(:)(,{ kkk fffDGN

10 Fulfillment degrees of rules’ premises

30 T-norm for fuzzy fk output

40 Diagnosis

)(...)()()(),( jLj2j1jkjjk vvvVssf

)}(),...,(),({),( jkLjk2jk1jk vvvMAXsf

20 k-th fuzzy rule output by fuzzy symptom sj

),(...),(),()( 21 Jkkkk sfsfsff

Industrial benchmark problemIndustrial benchmark problemElementary diagnosisElementary diagnosis


ELEMENTARY DIAGNOSIS DIAGNOSIS MEMBERS

DGN01) OK2), f11, f14

DGN1 f1, f4, f8, f12, f15

DGN2 f1, f4, f8, f9, f10, f12, f15, f16

DGN3 f2, f5, f13, f19

DGN4 f3, f6, f13, f18

DGN5 f7

DGN6 f171)DGN0 denotes undetectable faults and fault free system state2) OK denotes the fault free state (state of full aptitude)3) Theoretical mean diagnosis accuracy dacctm= 0.40

Unisolable faults Unisolable faultsUnisolable faults

Fault free Detectable faultsUndetectable faults

OK f1 f2 f3 f4 f5 f6 f7 f8 f9 f12

Elementary diagnosis:DGN0 = {OK., f1, f2, f3, f4, f5} DGN1 ={f6, f7, f8} DGN2 = {f9, f10, f11}

f10 f11 f19

DGN3 = {f12, ..., f19}

Theoretical diagnosis

accuracy daccti

L - the number of faults

indicated in ist elementary

diagnosis, for DGN0 the fault

free state (OK) is also

included

Ldacci

t

1

1

0

1 N

i

ittm dacc

Ndacc

Theoretical mean diagnosis accuracy

dacctm

N is a number of elementary diagnosis

Industrial benchmark problemIndustrial benchmark problemFault f16 (supply air pressure drop) (OK - state)Fault f16 (supply air pressure drop) (OK - state)

Industrial benchmark problemIndustrial benchmark problemFault f18 (partly opened bypass valve) Fault f18 (partly opened bypass valve)

Industrial benchmark problemIndustrial benchmark problemSummary of experimental FDI performance indices of Summary of experimental FDI performance indices of industrial benchmarkindustrial benchmark


tdt - detection time rfd - false detection rate tdm - detection momenttirt - fault detection recovery time tit - isolation timerfi - false isolation rate rti - true isolation rate tim - isolation momenttirt - fault isolation recovery time

Fault Elementary diagnosis tdt

[s]

rtd rfd tdm

[s]tdrt

[s]tit

[s]rfi rti tim

[s]tirt

[s]

f16 DGN2 3 0.99 0 57283 8 6 0 0.91 57286 3

f18 DGN4 4 0.97 0 58529 3 44 0 0.62 58569 0

f18 DGN4 5 0.95 0 58835 5 27 0 0.68 58857 0

Remarks: 1. detection moment was captured when OK state certainty degree drop down below 0.752. Isolation moment was captured when fault certainty degree rise above 0.25time

Final remarksFinal remarks


Simple and practicable fuzzy fault isolation approach was presented.

The reasoning fuzzy system consists of fuzzyfication and inference procedures. Defuzzyfication is not being applied.

Diagnosis are pointing out particular faults related with the fault certainty degrees.

Improved robustness against measurement noise and model uncertainty.

Applicable for on-line diagnostics of industrial processes

Symptom uncertainty allows to improve the overall tolerance of diagnostic system on the disturbances and.

Fault certainty degree has no direct transformation onto the fault probability. It plays the auxiliary role and serves as an approximate estimation of the fault occurrence degree.

Fault certainty value depends on the selection of parameters of fuzzyfication process, method of fuzzy inferring and modelling quality

Fault certainty degree may be thought as practically acceptable because of intuitive acceptance and easy graphical interpretation.

Documents

Fuzzy Logic Application for Fault Isolation of Actuators Jan Maciej Kościelny Michał Bartyś Paweł Rzepiejewski April 5-7, 2004 DAMADICS 2004 5-th DAMADICS