Uncertainty Analysis by Dimension Reduction Integration and Saddlepoint Approximations.pdf

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1、UncertaintyAnalysisbyDimensionReductionIntegrationandSaddlepointApproximationsBeiqingHuangPh.D.CandidateUncertaintyanalysis,whichassessestheimpactoftheuncertaintyofinputvariablesonGraduateResearchAssistantDepartmentofMechanicalandAerospaceresponses,isanindispensablec

2、omponentinengineeringdesignunderuncertainty,suchEngineering,asreliability-baseddesignandrobustdesign.However,uncertaintyanalysisisanunaf-UniversityofMissouri–Rollafordablecomputationalburdeninmanyengineeringproblems.Inthispaper,anuncer-taintyanalysismethodisproposedw

3、iththepurposeofaccuratelyandefficientlyestimat-XiaopingDu1ingthecumulativedistributionfunction(CDF),probabilitydensityfunction(PDF),andDr.statisticalmomentsofaresponsegiventhedistributionsofinputvariables.ThebivariateAssistantProfessordimensionreductionmethodandnumeri

4、calintegrationareusedtocalculatethemomentsDepartmentofMechanicalandAerospaceoftheresponse;thensaddlepointapproximationsareemployedtoestimatetheCDFandEngineering,PDFoftheresponse.Theproposedmethodrequiresneitherthederivativesofthere-UniversityofMissouri–Rollasponsenor

5、thesearchofthemostprobablepoint,whichisneededinthecommonlyusede-mail:dux@umr.edufirstandsecondorderreliabilitymethods(FORMandSORM)andtherecentlydevelopedfirstordersaddlepointapproximation.Theefficiencyandaccuracyoftheproposedmethodisillustratedwiththreeexampleproblems.W

6、iththesamecomputationalcost,thismethodismoreaccurateforreliabilityassessmentandmuchmoreefficientforestimatingthefullrangeofthedistributionofaresponsethanFORMandSORM.ThismethodprovidesresultsasaccurateasMonteCarlosimulation,withsignificantlyreducedcom-putationaleffort.

7、DOI:10.1115/1.21186671IntroductionTraditionally,commonlyusedmethodscomprisethreemajorcategories:1analyticalmethods,2surrogatemethods,and3Thequantitativeassessmentoftheimpactoftheuncertaintyofsimulationmethods.Typicalanalyticalmethodsincludethefirstinputvariable

8、sonaresponseisnowwidelyrecognizedasanorderreliabilitymethodFORMandthesecondorderreliabilityimportantandindispensablecomponentinen