MODEL-BASED AND DATA DRIVEN FAULT DIAGNOSIS METHODS WITH APPLICATIONS TO PROCESS MONITORING by Qingsong Yang Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Thesis Advisor: Prof. Kenneth A. Loparo Electrical Engineering and Computer Sciences CASE WESTERN RESERVE UNIVERSITY May 2004 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the dissertation of ______________________________________________________ candidate for the Ph.D. degree *. (signed)_______________________________________________ (chair of the committee) ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ (date) _______________________ *We also certify that written approval has been obtained for any proprietary material contained therein. To my parents Mingai and Shunlan, for everything I am now, and my wife Yunli, for her love, support and understanding. Contents List of Tables iv List of Figures v Acknowledgements vii Abstract ix 1 Introduction 1 1.1 Literature Survey............................. 1 1.1.1 Model-basedFaultDiagnosisApproaches............ 3 1.1.1.1 QuantitativeModel-basedMethods.......... 3 1.1.1.2 QualitativeModel-basedMethods........... 5 1.1.2 Data-drivenFaultDiagnosisApproaches............ 8 1.1.2.1 QuantitativeData-drivenMethods.......... 8 1.1.2.2 QualitativeData-drivenMethods........... 12 1.2 Thesis Summary ............................. 14 1.3 Thesis Organization............................ 16 2 Model-Based Fault Diagnosis Approach: Multiple Model Extended Kalman Filter 18 2.1BasicPrinciplesoftheModel-BasedFaultDiagnosis.......... 19 2.1.1 General Structure of Model-Based Fault Diagnosis Systems . 21 2.1.2 ResidualGenerationTechniques................. 25 2.1.3 FaultDiagnosisforStochasticSystems............. 33 2.1.4 Fault Modelling (Sensor, Actuator & Process Faults) . 35 2.2MultipleModelExtendedKalmanFilter(MMEKF).......... 41 2.2.1 KalmanFilterPreliminaries................... 41 2.2.1.1 OrthogonalProjection................. 41 2.2.1.2 InnovationSequences.................. 44 2.2.1.3 MinimumVarianceEstimates............. 46 2.2.1.4 KalmanFilteringEquations.............. 47 2.2.2 ExtendedKalmanFilterEquations............... 53 2.2.3 MultipleModelEKFFDISystem................ 57 2.3ResidualEvaluationUsingPrincipalComponentAnalysis....... 61 2.3.1 Principal Component Analysis (PCA) Preliminaries . 61 2.3.1.1 Introduction...................... 61 i 2.3.1.2 SingularValueDecomposition(SVD)......... 62 2.3.1.3 GeometricInterpretationofPCA........... 64 2.3.1.4 T 2 and Q statistics................... 65 2.3.2 PCAResidualEvaluation.................... 67 2.3.2.1 PCAFaultEvaluationMechanism.......... 67 2.3.2.2 ImplementationIssues................. 70 2.4 Simulation Study............................. 74 2.4.1 Plant Model ............................ 74 2.4.1.1 ProcessDescription................... 74 2.4.1.2 ControllerLoops.................... 76 2.4.1.3 FaultModes...................... 80 2.4.2 EKFFDISystemSimulation.................. 82 2.4.2.1 Application of EKF to the CSTR Process . 83 2.4.3 SimulationResults........................ 90 2.4.3.1 SimulationSettings................... 90 2.4.3.2 MMEKFFDITestResults.............. 92 2.4.3.3 PCAFaultEvaluationTestResults.......... 102 3 Data Driven Fault Diagnosis Approach: Principal Component Anal- ysis 106 3.1AdaptivePrincipalComponentAnalysis................ 109 3.1.1 Methodology ........................... 110 3.1.1.1 Recursive Update for the Correlation Matrix . 110 3.1.1.2 Recursive Determination of the Number of PCs . 115 3.1.1.3 Adaptation of the Confidence Limits for T 2 and Q scores120 3.1.2 ProcessMonitoringScheme................... 120 3.1.2.1 MissingDataTreatment................ 121 3.1.2.2 OutlierReplacement.................. 122 3.1.2.3 A Complete Adaptive Monitoring Scheme . 123 3.2MovingPrincipalComponentAnalysis................. 124 3.2.1 IndexforMonitoring....................... 125 3.2.2 ProcessMonitoringScheme................... 127 3.3Multi-ScalePrincipalComponentAnalysis............... 129 3.3.1 Wavelets.............................. 131 3.3.2 ProcessMonitoringScheme................... 136 3.3.2.1 Methodology...................... 136 3.3.2.2 DetailedProcedure................... 139 3.4 Illustrative Examples........................... 141 3.4.1 AdaptivePCATest........................ 141 3.4.1.1 PlantDataDescription................. 141 3.4.1.2 TestResultofRun#1................. 142 3.4.1.3 TestResultofRun#4b................ 146 3.4.2 MPCASimulationTests..................... 147 3.4.2.1 SimulationSetup.................... 147 ii 3.4.2.2 MonitoringResultsandDiscussions.......... 149 3.4.3 MSPCASimulationTests.................... 153 3.4.3.1 Mean Shift in Uncorrelated Measurements . 154 3.4.3.2 Monitoring of Auto-correlated Measurements . 162 4 Conclusion 167 4.1Conclusions................................ 167 4.2 Contributions ............................... 170 4.3FutureWork................................ 171 A Recursive Updating of Adaptive PCA 173 A.1UpdatingtheStandardDeviation.................... 173 A.2UpdatingtheCorrelationMatrix.................... 174 B Derivation of the Sliding Window Algorithm 175 Bibliography 177 iii List of Tables 2.1 List of Faults Studied........................... 80 2.2TheAdmissibleFaultMagnitudeRange................ 91 2.3 The Fault Magnitude Used to Set Up Reference PCA Model . 91 2.4TheResidualsCorrelationStructureSimilarityTest.......... 92 3.1TestDataDescription.......................... 142 3.2AdaptivePCAMonitoringResultofRun1............... 144 3.3ConventionalPCAMonitoringResultofRun1 ............ 144 3.4AdaptivePCAMonitoringResultofRun4b.............. 146 3.5ConventionalPCAMonitoringResultofRun4b............ 146 3.6SettingofAbnormalConditions..................... 148 3.7 Reliability (%) of Static CPCA - Applications to the 2 x 2 process . 150 3.8 Reliability (%) of Static MPCA - Applications to the 2 x 2 process . 151 3.9 Reliability (%) of Dynamic CPCA - Applications to the 2 x 2 process 153 3.10 Reliability (%) of Dynamic MPCA - Applications to the 2 x 2 process 154 iv List of Figures 1.1 ClassificationofFaultDiagnosisMethods................ 2 2.1HardwarevsAnalyticalRedundancy.................. 19 2.2 General Structure of Model-Based Fault Diagnosis Systems . 21 2.3RedundantSignalStructureinResidualGeneration.......... 23 2.4FullOrderObserverforResidualGeneration.............. 26 2.5ResidualGenerationviaParallelRedundancy............. 28 2.6FaultDiagnosisandControlLoop.................... 36 2.7 Open-Loop System............................ 37 2.8 Process Fault ............................... 38 2.9SensorFault................................ 40 2.10 Actuator Fault .............................. 40 2.11EKFBlockDiagram........................... 57 2.12MMEKFFDISystemStructure..................... 59 2.13EKFvsRealSystemSchematicDiagram ............... 60 2.14AnExampleoftheGeometricInterpretationofPCA......... 65 2.15ResidualEvaluationProcess....................... 67 2.16ProcessFlowofCSTR(LuybenModel)................. 75 2.17BlockDiagramoftheControlLoop................... 77 2.18 Block Diagram of the fi ControlLoop................. 77 2.19 Block Diagram of the fo ControlLoop................. 78 2.20 Block Diagram of the fj ControlLoop................. 79 2.21 Sensor Fault f1p/1n in fi ControlLoop................. 80 2.22 Actuator Fault f4p/4n in fi ControlLoop................ 81 2.23DetailedBlockDiagramoftheEKFFDISystem........... 83 2.24T2/QStatisticsofNormalProcess(EKFTypen,1p/1n)....... 94 2.25 T2/Q Statistics of Normal Process (EKF Type 4p/4n, 9p/9n) . 95 2.26T2/QStatisticsofSensorFault1p(EKFType1p,n/1n)....... 96 2.27 T2/Q Statistics of Sensor Fault 1p (EKF Type 4p/4n, 9p/9n) . 97 2.28 T2/Q Statistics of Actuator Fault 4n (EKF Type 4n, n/4p) . 98 2.29 T2/Q Statistics of Actuator Fault 4n (EKF Type 1p/1n, 9p/9n) . 99 2.30 T2/Q Statistics of Process Fault 9p (EKF Type 9p, n/9n) . 100 2.31 T2/Q Statistics of Process Fault 9p (EKF Type 1p/1n, 4p/4n) . 101 2.32T2andQStatisticsofProcessFault1p(FaultRatio0.3)....... 105 3.1 Wavelet Decomposition and Separation of Stochastic and Deterministic Components................................ 133 v 3.2 Approximate De-correlation due to Dyadic Wavelet Transform . 135 3.3MSPCAMethodology.......................... 136 3.4 Adaptive PCA Monitoring of Run #1 Using Robust Outlier Replacement144 3.5 Adaptive PCA Monitoring of Run #1 Using Moving Median Filter . 145 3.6ConventionalPCAMonitoringofRun#1............... 145 3.7 CPCA for Detecting Mean Shift of 1 Between Samples [176, 225] in UncorrelatedMeasurements....................... 156 3.8 Multiscale Detection of the Unit Mean Shift at 176 in Uncorrelated MeasurementsforDatainWindow[49,176]............... 157 3.9 Multiscale Detection of the Unit Mean Shift in Uncorrelated Measure- mentsforDatainWindow[53,180]................... 157 3.10 Multiscale Detection of the End of the Unit Mean Shift in Uncorrelated MeasurementsforDatainWindow[103,230].............. 158 3.11 MSPCA Monitoring of the Uncorrelated Measurements with Mean Shiftof1.................................. 160 3.12 MSPCA Monitoring of the Uncorrelated Measurements with Mean Shiftof1.................................. 160 3.13 Features Relevant to Abnormal Operation Extracted from Each Vari- able by MSPCA Signal Reconstruction for 99%