Reliability Evaluation of Dynamic Systems Excited in Time Domain: Alternative to Random Vibration and Simulation

305 Pages·2023·9.875 MB·English

by  Achintya Haldar, Hamoon Azizsoltani, J. Ramon Gaxiola-Camacho, Sayyed Mohsen Vazirizade, Jungwon Huh

Reliability Evaluation of
DynamicSystems Excited
in Time Domain

Reliability Evaluation of Dynamic Systems
Excited in Time Domain
Alternative to Random Vibration and Simulation
Achintya Haldar
University of Arizona, Tucson, Arizona, USA
Hamoon Azizsoltani
North Carolina State University, Raleigh, North Carolina, USA
J. Ramon Gaxiola-Camacho
Autonomous University of Sinaloa, Culiacan, Mexico
Sayyed Mohsen Vazirizade
Vanderbilt University, Nashville, Tennessee, USA
Jungwon Huh
Chonnam National University, Gwangju, Korea
Thiseditionfirstpublished2023
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LibraryofCongressCataloging-in-PublicationData
Names:Haldar,Achintya,author.
Title:Reliabilityevaluationofdynamicsystemsexcitedintimedomain:
alternativetorandomvibrationandsimulation/AchintyaHaldar,Hamoon
Azizsoltani,J.RamonGaxiola-Camacho,SayyedMohsenVazirizade,Jungwon
Huh.
Description:Hoboken,NJ,USA:Wiley,[2023]
Identifiers:LCCN2022047650(print)|LCCN2022047651(ebook)|ISBN
9781119901648(hardback)|ISBN9781119901662(adobepdf)|ISBN
9781119901655(epub)
Subjects:LCSH:Reliability(Engineering)–Mathematics.|
Dynamics–Mathematics.|Vibration–Mathematicalmodels.
Classification:LCCTA169.H35232023 (print)|LCCTA169 (ebook)|DDC
620/.004520151–dc23/eng/20221205
LCrecordavailableathttps://lccn.loc.gov/2022047650
LCebookrecordavailableathttps://lccn.loc.gov/2022047651
Coverimage:CourtesyofAchintyaHaldar
CoverdesignbyWiley
Setin9.5/12.5ptSTIXTwoTextbyStraive,Pondicherry,India
v
Contents
1 REDSETandItsNecessity 1
1.1 IntroductoryComments 1
1.2 ReliabilityEvaluationProceduresExistedAround2000 2
1.3 ImprovementsorAlternativetoStochasticFiniteElement
Method(SFEM) 2
1.4 OtherAlternativesBesidesSFEM 4
1.4.1 RandomVibration 4
1.4.2 AlternativetoBasicMonteCarloSimulation 5
1.4.3 AlternativestoRandomVibrationApproachforLargeProblems 5
1.4.4 Physics-BasedDeterministicFEMFormulation 5
1.4.5 MultidisciplinaryActivitiestoStudythePresenceofUncertaintyinLarge
EngineeringSystems 6
1.4.6 LaboratoryTesting 7
1.5 JustificationofaNovelRiskEstimationConceptREDSET
ReplacingSFEM 7
1.6 NotesforInstructors 8
1.7 NotestoStudents 9
Acknowledgments 9
2 FundamentalsofReliabilityAssessment 11
2.1 IntroductoryComments 11
2.2 SetTheory 12
2.3 ModelingofUncertainty 14
2.3.1 ContinuousRandomVariables 15
2.3.2 DiscreteRandomVariables 16
2.3.3 ProbabilityDistributionofaRandomVariable 16
2.3.4 ModelingofUncertaintyforMultipleRandomVariables 17
2.4 CommonlyUsedProbabilityDistributions 19
2.4.1 CommonlyUsedContinuousandDiscreteRandomVariables 19
vi Contents
2.4.2 CombinationofDiscreteandContinuousRandomVariables 20
2.5 ExtremeValueDistributions 20
2.6 OtherUsefulDistributions 21
2.7 Risk-BasedEngineeringDesignConcept 21
2.8 EvolutionofReliabilityEstimationMethods 25
2.8.1 First-OrderSecond-MomentMethod 25
2.8.2 AdvancedFirst-OrderReliabilityMethod(AFOSM) 26
2.8.3 Hasofer-LindMethod 26
2.9 AFOSMforNon-NormalVariables 31
2.9.1 Two-ParameterEquivalentNormalTransformation 31
2.9.2 Three-ParameterEquivalentNormalTransformation 33
2.10 ReliabilityAnalysiswithCorrelatedRandomVariables 33
2.11 First-OrderReliabilityMethod(FORM) 35
2.11.1 FORMMethod1 35
2.11.2 CorrelatedNon-NormalVariables 37
2.12 ProbabilisticSensitivityIndices 39
2.13 FORMMethod2 40
2.14 SystemReliabilityEvaluation 40
2.15 FundamentalsofMonteCarloSimulationTechnique 41
2.15.1 StepsinNumericalExperimentationsUsingSimulation 42
2.15.2 ExtractingProbabilisticInformationfromNDataPoints 43
2.15.3 AccuracyandEfficiencyofSimulation 43
2.16 ConcludingRemarks 44
3 ImplicitPerformanceorLimitStateFunctions 47
3.1 IntroductoryComments 47
3.2 ImplicitLimitStateFunctions–Alternatives 48
3.3 ResponseSurfaceMethod 49
3.4 LimitationsofUsingtheOriginalRSMConceptfortheStructural
ReliabilityEstimation 50
3.5 GenerationofImprovedResponseSurfaces 51
3.5.1 PolynomialRepresentationofanImprovedResponseSurface 52
3.6 ExperimentalRegion,CodedVariables,andCenterPoint 54
3.6.1 ExperimentalRegionandCodedVariables 54
3.6.2 ExperimentalDesign 55
3.6.3 SaturatedDesign 56
3.6.4 CentralCompositeDesign 56
3.7 AnalysisofVariance 56
3.8 ExperimentalDesignforSecond-OrderPolynomial 58
3.8.1 ExperimentalDesign–Model1:SDwithSecond-OrderPolynomial
withoutCrossTerms 58
Contents vii
3.8.2 ExperimentalDesign–Model2:SDwithSecond-OrderPolynomial
withCrossTerms 59
3.8.3 ExperimentalDesign–Model3:CCDwithSecond-OrderPolynomial
withCrossTerms 61
3.9 ComparisonsoftheThreeBasicFactorialDesigns 61
3.10 ExperimentalDesignsforNonlinearDynamicProblemsExcitedinthe
TimeDomain 64
3.11 SelectionoftheMostAppropriateExperimentalDesign 64
3.12 SelectionofCenterPoint 65
3.13 GenerationofLimitStateFunctionsforRoutineDesign 66
3.13.1 ServiceabilityLimitState 66
3.13.2 StrengthLimitStateFunctions 67
3.13.3 InteractionEquationsfortheStrengthLimitStateFunctions 67
3.13.4 DynamicEffectinInteractionEquations 68
3.14 ConcludingRemarks 69
4 UncertaintyQuantificationofDynamicLoadingsAppliedintheTime
Domain 71
4.1 IntroductoryComments 71
4.2 UncertaintyQuantificationinSeismicLoadingsAppliedintheTime
Domain 73
4.2.1 BackgroundInformation 74
4.3 SelectionofaSuiteofAccelerationTimeHistoriesUsingPEER
Database–Alternative1 75
4.3.1 EarthquakeTimeHistorySelectionMethodology 78
4.4 DemonstrationoftheSelectionofaSuiteofGroundMotionTime
Histories–Alternative1 79
4.5 SimulatedGroundMotionsUsingtheBroadbandPlatform
(BBP)–Alternative2 84
4.5.1 BroadbandPlatformDevelopedbySCEC 84
4.6 DemonstrationofSelectionandValidationofaSuiteofGroundMotion
TimeHistoriesUsingBPP 86
4.7 ApplicationsofBBPinSelectingMultipleEarthquakeAccelerationTime
Histories 88
4.8 SummaryofGeneratingMultipleEarthquakeTimeHistories
UsingBPP 91
4.9 UncertaintyQuantificationofWind-InducedWaveLoadingsAppliedin
theTimeDomain 91
4.9.1 IntroductoryComments 91
4.9.2 FundamentalsofWaveLoading 94
4.9.3 MorisonEquation 95
4.10 ModelingofWaveLoading 96
viii Contents
4.10.1 WaveModelingUsingtheNewWaveTheory 97
4.10.2 WheelerStretchingEffect 98
4.10.3 Three-DimensionalDirectionality 98
4.10.4 SummaryofDeterministicModelingofWaveLoading 100
4.11 UncertaintyQuantificationsinWaveLoadingAppliedintheTime
Domain 100
4.11.1 UncertaintyQuantificationinWaveLoading–Three-Dimensional
ConstrainedNewWave(3DCNW)Concept 100
4.11.2 Three-DimensionalConstrainedNewWave(3DCNW)Concept 102
4.11.3 UncertaintyintheWaveHeightEstimation 104
4.11.4 UncertaintyQuantificationofWaveLoading 105
4.11.5 QuantificationofUncertaintyinWaveLoading 106
4.12 WaveandSeismicLoadings–Comparisons 107
4.13 ConcludingRemarks 108
5 ReliabilityAssessmentofDynamicSystemsExcitedinTime
Domain–REDSET 111
5.1 IntroductoryComments 111
5.2 ANovelReliabilityEstimationConcept–REDSET 113
5.2.1 IntegrationofFiniteElementMethod,ImprovedResponseSurface
Method,andFORM 113
5.2.2 IncreaseEfficiencyinGeneratinganIRS 114
5.2.3 OptimumNumberofNDFEARequiredfortheGenerationofanIRS 115
5.2.4 ReductionofRandomVariables 115
5.3 AdvancedSamplingDesignSchemes 116
5.4 AdvancedFactorialDesignSchemes 116
5.5 ModifiedAdvancedFactorialDesignSchemes 119
5.5.1 ModifiedAdvancedFactorialDesignScheme2(MS2) 119
5.5.2 ModifiedAdvancedFactorialDesignScheme3 121
5.6 OptimumNumberofTNDFEARequiredtoImplementREDSET 122
5.7 ImproveAccuracyofSchemeMS3Further–Alternativetothe
RegressionAnalysis 122
5.7.1 MovingLeastSquaresMethod 122
5.7.2 ConceptofMovingLeastSquaresMethod 123
5.7.3 ImproveEfficiencyFurthertotheMovingLeastSquaresMethod 124
5.8 GenerationofanIRSUsingKrigingMethod 126
5.8.1 SimpleKriging 127
5.8.2 OrdinaryKriging 128
5.8.3 UniversalKriging 128
5.8.4 VariogramFunction 131
5.8.5 SchemeS3withUniversalKrigingMethod 133