Fault Detection In the Electrohydraulic Actuator Using Extended Kalman Filter

272 Pages·2008·11.71 MB·English

Fault Detection
In the Electrohydraulic Actuator
Using Extended Kalman Filter
A Thesis Submitted to
the College ofGraduate Studies and--Research
in Partial Fulfillment ofthe Requirements
for the Degree ofDoctor ofPhilosophy
in the Department ofMechanical Engineering
University ofSaskatchewan, Saskatoon
Canada
By
Yuvin Adnarain Chinniah
© Copyright Yuvin A. Chinniah, March 2004. All rights reserved.
Permission to Use
Inpresentingthis thesis inpartial fulfillment oftherequirements for a Postgraduate
degree from theUniversityofSaskatchewan, I agreethatthe Libraries ofthis University
maymakeitfreely available for inspection. Ifurther agreethat thepermissionfor
copyingthis thesis in anymanner, in wholeorinpartfor scholarlypurposes, maybe
grantedbytheprofessors who supervisedmythesis work or, intheir absence, bythe
Head ofthe DepartmentorDeanofthe Collegeinwhichmythesis workwas
conducted. Itisunderstoodthat anycopyingorpublicationoruse ofthis thesis orparts
thereoffor financial gain shall notbeallowedwithoutmywrittenpermission. Itis also
understoodthatduerecognition shallbe givento me andto the Universityof
Saskatchewan in any scholarlyusewhichmaybemade ofanymaterial inmythesis.
Requests forpermission to copyorto makeotheruse ofmaterial inthis thesis, inwhole
orpart, shouldbeaddressedto:
Head ofthe DepartmentMechanical Engineering
UniversityofSaskatchewan
CollegeofEngineering
57 Campus Drive
sm
Saskatoon, Saskatchewan 5A9
Canada
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Abstract
Inthis thesis a fault detectiontechnique for ahigh perfonnancehydrostatic
actuationsystemwas developed and evaluated. TheExtendedKalmanFilter(EKF)
was used for parameteridentificationandwas appliedto anElectrohydraulicActuator
(ERA) and theperfonnanceofthe technique is discussed. The ERA is ahigh
perfonnance, closedloop actuationsystem consistingofan AC variablespeedelectric
motor, abi-directional gearpump, anaccumulator, checkvalves, a cross-overrelief
valve, connectingtubes anda custommade symmetrical actuator. The ERAhas
potential applications inthe aerospace industryfor flight surface actuation andin
robotics. Failures inthe ERA canposea safetyhazard andunscheduledmaintenance
canresultin costlydowntime. Fault detection inthe ERAwill increaseits safetyand
efficiency.
Theproposedpreventivemaintenance approachinvolvesmonitoringtheERA
byestimatingtwo parametersofinterest, namelythe effectivebulkmodulus and the
viscous dampingcoefficient. Loweringofthe effectivebulkmodulus, as aresult ofair
entrapment, will affecttheresponse ofthe ERA andmay causestabilityissues, by
loweringthebandwidthofthe system. Changes inthe damping coefficientfor the
actuatorcanindicatedeteriorationofthe oil, wearinthe seals orchanges in external
friction characteristics. Thetwo parameterswere estimatedusingtheEKF andchanges
inthe estimatedvalues wererelatedto faults inthe system.
Priorto applyingtheEKF to theERAprototype, an extensivesimulation study
was carriedoutto investigatethefeasibility ofthe approach aswell as the level of
accuracyto be expectedwiththe experimental system. The simulation studywas used
to verifythat changes inthetwo parameters were detected and accuratelyestimated.
In this study, an attemptwas also made to visitsomeoftheproblems reported
withtheuse oftheEKF for fault detectionpurposes, namelythe difficultyinsettingthe
correctvalues inthematrices to initializethe EKF algorithm and thepresenceofbiases
inthe estimates. Theproblem wasbelievedto be linked to systemobservabilitywhich
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was investigated inthis research. Itwas found that using observable statespacemodels
for the EKF improvedthe abilityofthe EKF to estimateparameters, bothinterms of
accuracyofthe estimations and repeatabilityofexperimental results. System
observabilitywas investigatedinthis workbyfirst using simplemechanical systems
andthenusingthemore complex ERA system. Aniterative approachwas presented
wherebyparameters werenot estimated atthe sametimebutiterativelyand using
differentmodels. System observabilitywasmaintainedbyreducingthe numberofstates
andbyusingthe correcttype andnumberofsystemmeasurements. Also, the use of
observable systems eliminatedtheneedto chooseparametervalues, intheinitial state
vectorofthe EKF, closeto the desiredparametervalues, as was very oftendonein
previousresearch. No a-priori knowledge abouttheparameters was assumed inthis
research. Biasesinthe estimates (thishas beenreported inprevious studies) are
believedtobedue to the filter facing alocal minimaproblem. Thisproblemis linkedto
the error covariancematrixnotconvergingto a globalminimum. IntheKalman Filter,
themain objectiveofthe error covariancematrix is to computetheKalman gain, which
is inturnusedto correct an estimatewiththelatest sensormeasurement. Errors inthe
Kalman gainmayleadto biases inthe estimates. Inthis study, itwas also found that
althoughthe systemisnotobservable, it canbedetectable, althoughthe converseis not
true, and as such, changesinparameters canbedetectedbutnotnecessarily accurately
estimated. Observabilityensuresuniqueness ofthe estimate.
The effectivebulkmodulus andviscous damping coefficientwere estimated
successfully, bothinsimulations andusingexperimental data. Faults were introducedin
theEHAprototype and changesintheparameters were detected and estimated.
The friction characteristicofthe actuator for theERA was also investigated. A
novel empirical frictionmodel wasproposed. The EKF wasusedto estimateiteratively
(to maintainsystemobservability), the coefficientsofthat friction function whichwas
believedtobe arealisticrepresentationoffriction effectintheprototype. Simulation
and experimentalresults werepresented. Insummary, the applicationofthe EKF
techniqueto the ERAhas produced verypromisingresults.
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Acknowledgements
The authorexpresseshis gratitudeto his supervisors, Dr. R.T. Burtonand Dr. S. Habibi
for theirguidance and adviceduringthe courseofthis research and thewritingofthis
thesis. Thetechnical assistance ofMr. D.V. Bitneris also gratefullyacknowledged.
Financial support inthe fonn ofgraduate studentmonthlystipend, Universityof
Saskatchewan Graduate Student Scholarship and Canadian Commonwealth Scholarship
is also acknowledged.
Special gratitudemustbe conveyedto mywife, Priscilla, whosepatienceand support
havebeeninvaluableduringmy studies.
I also wishto expressmy gratitudeto myfamily, especiallyto myparents andbrothers
for theirencouragementand support.
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Table ofContents
Permission to Use i
Abstract ii
Acknowledgements iv
Table ofContents v
ListofTables x
· ifD' ..
Llst0 r 19ures Xll
Nomenclature xix
1. Introduction.o. o. o. o. o. o. o. o. o. o. o. o. o. o. o. 1
0 00••• 0 000 0 000 0 0" 0 00••••0 0 000. 0 0•••0" 0•••• 000••00" 0"
1.1. PreliminaryRemar1cs 1
1.2. Techniques Used inHealth Monitoring ofHydraulic Systems 3
1.3. The ExtendedKalman Filterin Condition Monitoring 3
1.4. Parameters ofInterest in theHydrostaticActuationSystem 5
1.5. Research Objectives 7
1.6. Thesis Outline 8
2. Condition Monitoring Strategies in Fluid Power o. o.o.o. 11
00'0•••• 0•••00•••0•••
2.1. Introduction 11
2.2. MonitoringFluid Condition 13
2.3. Vibration Analysis 17
2.4. TemperatureMonitoring 19
2.5. Pressure andFlowMonitoring 20
v
2.6. ExpertSystemsfor Condition Monitoring in FluidPower 21
2.7. NeuralNetworks for Condition Monitoring in FluidPower 22
2.8. FaultDetection usingMathematicalModels ofthe Systems 25
2.9. Condition Monitoring usingthe ExtendedKalman Filter 27
2.10. Condition Monitoringfor the EHA System Using the EKF 28
2.11. Conclusions 30
3. Electrohydraulic Actuator (ERA) 31
3.1. Introduction 31
3.2. Description oftheElectrohydraulicActuator 33
3.2.1 Hydraulic Pump 35
3.2.2 New SymmetricalLinearActuatorfor EHA 37
3.2.3 Accumulator 39
3.2.4 ControlStrategy inEHA 39
3.2.5 ElectricMotor/Pump Subsystem Model 40
3.2.6 LinearizedModel oftheEHA 43
3.3. FailureModes andEffectsAnalysisfortheEHA Components 47
3.3.1 Faults andEffectsAnalysisforthe EHA 50
3.4. Summary 53
4. ERA Instrumentation and Model Validation 54
4.1. ExperimentalDetermination oftheEHA Parameters 54
4.2. ExperimentalDetermination ofthePumpLeakage Coefficient.. 55
4.3. ExperimentalDetermination oftheLeakage Coefficientin theActuator 61
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4.4. SimplifiedModelfor the EHA 64
4.5. Linear Variable Differential Transformer (LVDT) 66
4.6. Measured Outputofthe EHA Prototype Using theLVDT 67
4.7. DifferentialPressure Transducer 69
4.8. LinearOpticalEncoder 70
4.9. ConcludingRemar'ks 73
5. Introduction to the Kalman Filter 74
5.1. Introduction 74
5.2. StatisticalReview 75
5.3. Discrete State SpaceModelofaLinearSystem 75
5.4. The Kalman Filter 76
5.4.1 Derivation oftheKalman FilteringEquations '" 78
5.5. ExtendedKalman Filter 81
5.6. Divergence in the ExtendedKalman Filter 84
5.7. Conclusions 86
6. Parameter Estimation Using Extended Kalman Filter 87
6.1. Importance ofthe Observability Condition 88
6.2. ApplyingtheKalman Filter to the EHA in Simulation 99
6.3. ParameterEstimation in theEHA 104
6.3.1 Discussions 113
6.4. Estimatingthe EffectiveBulkModulus in the EHA 115
6.4.1 Sensitivity Study ofthe Effective BulkModulus 120
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6.4.2 Estimation ofEffectiveBulkModulus (High FrequencyInput) 122
6.5. Estimation ofViscous DampingCoefficientin Simulation 127
6.6. UsingEKFin Estimatingthe Viscous Damping Coefficient Using a Known
EffectiveBulkModulus Value 133
6.7. ConcludingRemarlGs 138
7. Experimental Results: ParameterEstimation in the EHA 141
7.1. Proceduresfor CollectingExperimentalData 141
7.2. Viscous DampingCoefficient Estimation 143
7.3. EffectiveBulkModulus Estimation 148
7.4. Estimation ofViscous Friction Coefficient Using the ComplexModeL 153
7.5. Estimation ofParametersIteratively Using Three EKFs 155
7.6. IntroducingFaults in the EHA Prototype 157
7.7. Conclusions 163
8. Estimation ofNonlinear Friction using the EKF 164
8.1. Friction Nonlinearities in HydraulicActuators 164
8.2. NonlinearFriction Modelfor the ElectrohydraulicActuator 165
8.2.1 Equivalent Viscous Friction 166
8.2.2 QuadraticFrictionModel 170
8.2.3 Summary 182
8.3. Simulation Study Using the QuadraticFrictionModel 183
8.4. Estimation ofthe Effective BulkModulus in Simulation Using the Quadratic
Friction ModeloftheEHA in theEKF 195
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8.4.1Simulation Studies: EffectiveBulkModulus Estimation 197
8.4.2 ExperimentalStudies: EstimatingtheEffectiveBulkModulus 200
8.5. Conclusions 201
9. Conclusions and Recommendations 204
9.1. Summary 204
9.2. Outcomes 205
9.3. Conclusions 207
9.4. Important Contributions 208
9.5. Future Research Recommendations 210
List ofReferences 211
Appendix A: Statistical Review ofRandom (Stochastic) Signals 218
A.1. Expectation (Average) 218
A.2. Variance 218
A.3. Normal or Gaussian Random Variables 218
A.4. Covariance 219
Appendix B: Importance ofObservability Condition to the EKF 220
B.1. Observability Condition andFormula 220
B.2. Mass-Damper System 220
B.3. Applicationofthe EKFto the Mass-Damper System 226
B.4. Mass-Spring-Damper System 232
B.5. ParameterEstimation in the Mass-Spring-Damper System 236
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