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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
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
• 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
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
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
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
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
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
Actuator fault detectionActuator fault detection
10
20
50
40
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
)(ˆ1 CVZZr
),(ˆ212 PPZFFr
30 ),(ˆ213 PPCVFFr
)(ˆ4 ZFFr
)(ˆ5 CVFFr
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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)
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
- 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
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
- 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
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
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
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
Setting parameters of membership Setting parameters of membership functionsfunctionsStatistical approach
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
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
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
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
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
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
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
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
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ER
N
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Diagnosticsignals
RulesRulesRulesRuleskkJJkk fthenVsVsVsIf )(...)()( 2211
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
Fault isolation algorithmFault isolation algorithm
),()(1
jk
J
jk sff
),()(1
jk
J
jMINk sff
Operators
J
jjk
J
jjk
k
sf
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DGNR( f )
)( f
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
}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
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
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
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
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
Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems, FP5 DAMADICS Project
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.