Filter Design for System Modeling, State Estimation and Fault Diagnosis

240 Pages·2022·8.283 MB·English

by  Ziyun Wang, Yan Wang, Zhicheng Ji

Filter Design for
System Modeling,
State Estimation and
Fault Diagnosis
This book analyzes the latest methods in the design of filters for system modeling,
state estimation and fault detection with the intention of providing a new perspec-
tive of both theoretical and practical aspects.
The book also includes fault diagnosis techniques for unknown but bounded sys-
tems, their real applications on modeling and fault diagnosis for lithium battery
systems, DC-DC converters and spring damping systems. It proposes new meth-
ods based on zonotopic Kalman filtering, a variety of state estimation methods of
zonotope and its derived algorithms, a state estimation method based on convex
space, set inversion interval observer filtering-based guaranteed fault estimation
and a novel interval observer filtering-based fault diagnosis.
The methods presented in this text are more practical than the common probabi-
listic-based algorithms, since these can be applied in unknown but bounded noisy
environments. This book will be an essential read for students, scholars and en-
gineering professionals who are interested in filter design, system modeling, state
estimation, fault diagnosis and related fields.
Ziyun Wang is an associate professor at Jiangnan University, China. His research
interests include fault detection, state estimation and filtering methods.
Yan Wang is a professor at Jiangnan University, China. Her research interests in-
clude fault detection and set-membership filtering methods.
Zhicheng Ji is a professor at Jiangnan University, China. His research interests
include state estimation and control theory in practical engineering.

Filter Design for
System Modeling,
State Estimation and
Fault Diagnosis
Ziyun Wang, Yan Wang, Zhicheng Ji
This work is supported in part by the National Key Research and Development Program of China
(2020YFB1710600), the Natural Science Foundation of Jiangsu Province(BK20221533) and the
Jiangsu Science and Technology Association Young Science and Technology Talents Lifting Project
(TJ-2021-006).
This book is published with financial support from National Key Research and Development Pro-
gram of China, the Natural Science Foundation of Jiangsu Province, and the Jiangsu Science and
Technology Association Young Science and Technology Talents Lifting Project.
First edition published 2023
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© 2023 Ziyun Wang, Yan Wang, Zhicheng Ji
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ISBN: 978-1-032-35512-2 (hbk)
ISBN: 978-1-032-35513-9 (pbk)
ISBN: 978-1-003-32721-9 (ebk)
DOI: 10.1201/b23146
Typeset in Nimbus Roman
by KnowledgeWorks Global Ltd.
Publisher’s note: This book has been prepared from camera-ready copy provided by the authors.
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
SymbolDescription . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Systemmodeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Methodsofsystemmodeling . . . . . . . . . . . . . . . . . 2
1.2 Stateestimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Faultdiagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Summaryoffilteringdesignmethods . . . . . . . . . . . . . . . . 7
1.4.1 Traditionalfilteringdesignmethods . . . . . . . . . . . . . 7
1.4.2 Non-probabilisticfilteringdesignmethod . . . . . . . . . . 8
1.5 Motivationandobjective . . . . . . . . . . . . . . . . . . . . . . . 13
1.6 Outlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Parameterestimationalgorithmbasedonzonotope-ellipsoiddouble
filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Problemdescription . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Modelparameterization . . . . . . . . . . . . . . . . . . . 15
2.1.2 Symboldefinitions . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Mainresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 Ellipsoid-filtering-basedestimationalgorithm . . . . . . . . 17
2.2.1.1 Predictionstep . . . . . . . . . . . . . . . . . . . 17
2.2.1.2 Updatestep . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Zonotopicdimensionalreductionfiltering . . . . . . . . . . 19
2.2.3 Discretizationofzonotopeintoconstraintstrips . . . . . . . 21
2.3 Numericalexamples . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
v
vi (cid:4) Contents
3 Stateestimationbasedonzonotope . . . . . . . . . . . . . . . . . . . . 31
3.1 Set-membershipfilteringbasedbi-directionalDC-DCconverter
stateestimationalgorithmforlithiumbatteryformation . . . . . . . 31
3.1.1 Problemdescription . . . . . . . . . . . . . . . . . . . . . 31
3.1.1.1 Buckmode . . . . . . . . . . . . . . . . . . . . . 32
3.1.1.2 Boostmode . . . . . . . . . . . . . . . . . . . . 33
3.1.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.2.1 Definitionofstripandzonotope . . . . . . . . . . 34
3.1.2.2 Properties . . . . . . . . . . . . . . . . . . . . . 34
3.1.3 Mainresults. . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.3.1 Prediction . . . . . . . . . . . . . . . . . . . . . 35
3.1.3.2 Update . . . . . . . . . . . . . . . . . . . . . . . 35
3.1.4 Simulationresults . . . . . . . . . . . . . . . . . . . . . . 37
3.1.4.1 Simulationofbuckmode . . . . . . . . . . . . . 37
3.1.4.2 Simulationofboostmode . . . . . . . . . . . . . 38
3.1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 A novel set-valued observer based state estimation algorithm for
nonlinearsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.1 Systemdescription . . . . . . . . . . . . . . . . . . . . . . 41
3.2.2 Centraldifferencezonotopicset-valuedobserver . . . . . . 41
3.2.2.1 Nonlinearmodellinearization . . . . . . . . . . . 42
3.2.2.2 Boundedlinearizationerror . . . . . . . . . . . . 43
3.2.2.3 Timeupdate . . . . . . . . . . . . . . . . . . . . 44
3.2.2.4 Observationupdate . . . . . . . . . . . . . . . . 44
3.2.3 Numericalexamples . . . . . . . . . . . . . . . . . . . . . 46
3.2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3 Zonotopic particle filtering based state estimation algorithm and its
applicationontemperaturerecognitionforlithiumbattery . . . . . 54
3.3.1 Problemequationandpreliminaries . . . . . . . . . . . . . 54
3.3.1.1 Problemformulation. . . . . . . . . . . . . . . . 54
3.3.1.2 Preliminaries . . . . . . . . . . . . . . . . . . . . 54
3.3.2 Zonotopicparticlefilteringbasedstateestimationalgorithm 55
3.3.2.1 Predictionstep . . . . . . . . . . . . . . . . . . . 55
3.3.2.2 Updatestep . . . . . . . . . . . . . . . . . . . . 56
3.3.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4 Stateestimationbasedonconvexspatialstructure . . . . . . . . . . . 63
4.1 Hyperparallelspaceset-membershipfilteringbasedstateestimation
algorithmfornonlinearsystem . . . . . . . . . . . . . . . . . . . . 63
4.1.1 Problemdescription . . . . . . . . . . . . . . . . . . . . . 63
4.1.2 Preknowledge . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.1.2.1 Parallelotopeandorthotope . . . . . . . . . . . . 64
4.1.2.2 Property . . . . . . . . . . . . . . . . . . . . . . 65
4.1.3 Nonlinearset-membershipfilteringbasedonparallelotope . 65
Contents (cid:4) vii
4.1.3.1 Outerboundoflinearizationerror . . . . . . . . . 65
4.1.3.2 Predictivestep . . . . . . . . . . . . . . . . . . . 67
4.1.3.3 Updatestep . . . . . . . . . . . . . . . . . . . . 69
4.1.4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.2 Nonlinearsystemstateestimationbasedonaxisymmetricboxspace
filterunderuncertainnoise . . . . . . . . . . . . . . . . . . . . . . 82
4.2.1 Relateddefinitionsandproblemdescriptions . . . . . . . . 82
4.2.1.1 Relateddefinitions . . . . . . . . . . . . . . . . . 82
4.2.1.2 Problemdescription . . . . . . . . . . . . . . . . 82
4.2.2 Stateestimationofnonlinearsystembasedonaxisymmetric
boxspacefiltering . . . . . . . . . . . . . . . . . . . . . . 83
4.2.2.1 Linearizationofnonlinearmodels . . . . . . . . . 83
4.2.2.2 Intervalexpressionoflinearizationerror . . . . . 84
4.2.2.3 Stateprediction . . . . . . . . . . . . . . . . . . 86
4.2.2.4 Measurementupdate. . . . . . . . . . . . . . . . 86
4.2.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5 Faultdiagnosisbasedoninterval . . . . . . . . . . . . . . . . . . . . . 95
5.1 Guaranteedfault-estimationalgorithmbasedonintervalsetinversion
observerfiltering . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.1.1 Preliminariesandproblemdescription . . . . . . . . . . . . 95
5.1.2 Mainresults. . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.1.2.1 Minimalconservativeintervalobserver . . . . . . 97
5.1.2.2 Dimensionalvectorsetinversioninterval
contraction . . . . . . . . . . . . . . . . . . . . . 99
5.1.2.3 Algorithmanalysis. . . . . . . . . . . . . . . . . 101
5.1.3 Simulationanalysis . . . . . . . . . . . . . . . . . . . . . . 104
5.1.3.1 Numericalsimulation . . . . . . . . . . . . . . . 104
5.1.3.2 DCmotorsystemsimulation . . . . . . . . . . . 107
5.1.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.2 Interval observer filtering-based fault diagnosis method for linear
discrete-timesystemswithdualuncertainties . . . . . . . . . . . . 112
5.2.1 Problemdescription . . . . . . . . . . . . . . . . . . . . . 112
5.2.2 Mainresults. . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.2.2.1 Stateestimator . . . . . . . . . . . . . . . . . . . 115
5.2.2.2 Faultdiagnosis . . . . . . . . . . . . . . . . . . . 117
5.2.3 Simulationanalysis . . . . . . . . . . . . . . . . . . . . . . 122
5.2.3.1 Numericalexample . . . . . . . . . . . . . . . . 123
5.2.3.2 Fault-freecase . . . . . . . . . . . . . . . . . . . 124
5.2.3.3 Faultdetection,isolationandidentification . . . . 125
5.2.3.4 DCmotorsystemsimulation . . . . . . . . . . . 127
viii (cid:4) Contents
5.2.3.5 DCmotorworkingnormally . . . . . . . . . . . 128
5.2.3.6 DCmotorfails . . . . . . . . . . . . . . . . . . . 129
5.2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.3 Orthometric hyperparallel spatial directional expansion filtering
basedfaultdiagnosismethod . . . . . . . . . . . . . . . . . . . . . 133
5.3.1 Pre-knowledge . . . . . . . . . . . . . . . . . . . . . . . . 133
5.3.2 Problemdescription . . . . . . . . . . . . . . . . . . . . . 133
5.3.3 Orthometrichyperparallelspatialdirectionalexpansion
filteringbasedfaultdiagnosismethod . . . . . . . . . . . . 134
5.3.3.1 Faultdetection . . . . . . . . . . . . . . . . . . . 136
5.3.3.2 Faultisolationandidentification . . . . . . . . . 137
5.3.4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6 FaultdiagnosismethodbasedonzonotopicKalmanfiltering . . . . . 149
6.1 ZonotopicKalmanfiltering-basedfaultdiagnosisalgorithmfor
linearsystemwithstateconstraints . . . . . . . . . . . . . . . . . 149
6.1.1 Problemformulationandpreliminaries . . . . . . . . . . . 149
6.1.1.1 Problemformulation. . . . . . . . . . . . . . . . 149
6.1.1.2 Preliminaries . . . . . . . . . . . . . . . . . . . . 150
6.1.2 Mainresults. . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.1.2.1 Predictionstep . . . . . . . . . . . . . . . . . . . 151
6.1.2.2 Updatestep . . . . . . . . . . . . . . . . . . . . 152
6.1.2.3 Faultdiagnosis . . . . . . . . . . . . . . . . . . . 154
6.1.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.1.3.1 Fault-freesystemsimulation . . . . . . . . . . . 156
6.1.3.2 Faultysystemsimulation . . . . . . . . . . . . . 157
6.1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.2 SensorfaultestimationbasedontheconstrainedzonotopicKalman
filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.2.2 Problemformulation . . . . . . . . . . . . . . . . . . . . . 163
6.2.3 Mainresults. . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.2.3.1 DesignoftheconstrainedzonotopicKalmanfilter 165
6.2.3.2 Faultdetection . . . . . . . . . . . . . . . . . . . 167
6.2.3.3 Design of constrained zonotopic Kalman filter
basedfaultestimator . . . . . . . . . . . . . . . . 168
6.2.4 Simulationanalysis . . . . . . . . . . . . . . . . . . . . . . 175
6.2.4.1 Fault-free . . . . . . . . . . . . . . . . . . . . . 176
6.2.4.2 Additivesensorfault . . . . . . . . . . . . . . . . 177
6.2.4.3 Multiplicativesensorfault . . . . . . . . . . . . . 181
6.2.4.4 Fault-freestate . . . . . . . . . . . . . . . . . . . 184
6.2.4.5 Additivesensorfault . . . . . . . . . . . . . . . . 185
6.2.4.6 Multiplicativesensorfault . . . . . . . . . . . . . 186
6.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Contents (cid:4) ix
6.3 OptimalzonotopicKalmanfilter-basedstateestimationandfault
diagnosisalgorithmforlineardiscrete-timesystemwithtime
delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
6.3.1 Problemformulationandpreliminaries . . . . . . . . . . . 188
6.3.2 DesignoftheoptimalZKFforthesystemwithtimedelay . 190
6.3.3 Faultdiagnosis . . . . . . . . . . . . . . . . . . . . . . . . 197
6.3.3.1 Faultdetection . . . . . . . . . . . . . . . . . . . 197
6.3.3.2 Faultidentification . . . . . . . . . . . . . . . . . 198
6.3.4 Simulationanalysis . . . . . . . . . . . . . . . . . . . . . . 199
6.3.4.1 Fault-free . . . . . . . . . . . . . . . . . . . . . 200
6.3.4.2 Faultinthefaultlibrary . . . . . . . . . . . . . . 200
6.3.4.3 Fault-free . . . . . . . . . . . . . . . . . . . . . 205
6.3.4.4 Faultoutsidethefaultlibrary . . . . . . . . . . . 205
6.3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 209
7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215