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1、INTERNATIONALJOURNALFORNUMERICALMETHODSINENGINEERINGInt.J.Numer.Meth.Engng2012;89:354370Publishedonline29July2011inWileyOnlineLibrary(wileyonlinelibrary.com).DOI:10.1002/nme.3248Samplingofclosely-spacedorderedsetofuniformlydistributedrandomvariablesSashiKant
2、hTadinada1,*,andAbhinavGupta21DepartmentofCivil,ConstructionandEnvironmentalEngineering,NorthCarolinaStateUniversity,Box7908,Raleigh,NC27695,U.S.A.2DepartmentofCivilEngineering,NorthCarolinaStateUniversity,Raleigh,NC27695,U.S.A.SUMMARYWhentheindividualPDFsof
3、closely-spacedrandomvariablessuchasnaturalfrequenciesofastructureoverlap,generationofsamplesetsbyassumingthefrequenciestobeindependentrandomvariablescanleadtoincorrectsetsoffrequenciesinthesensethatthefrequenciesdonotremainasorderedsets.Rejectionofsuchdisord
4、eredsamplesetsresultsinindividualdensityfunctionsthataresignificantlydifferentfromthedistributionsinitiallyassumedforsamplingeachrandomvariable.Onewaytoovercomethisconstraintinthesimulationofanorderedsetofrandomvariablesistoconsidertheminanimplicitmannerusing
5、ajointPDF.Inthispaper,wepresentaformulationforajointdensityfunctionthatisdevelopedusingfunda-mentalprobabilityapproaches.Theformulationensuresthatthesampledrandomvariablesalwaysremainasorderedsetsandmaintaintheindividualdensityfunctionsforeachvariable.Applic
6、ationoftheproposedformulationisillustratedforcaseswithnotjusttwoclosely-spacedvariablesbutalsoforacasewithmultipleclosely-spacedvariablessuchthatthePDFsofmorethantworandomvariablesoverlapwitheachother.Anexpressionispresentedtodeterminetheexactnumberoftermsne
7、ededintheformulation.However,itisalsoillustratedthatonlytwotermsaresufficientinmostapplicationsevenwhentheexactnumberoftermsneededisveryhigh.Copyright©2011JohnWiley&Sons,Ltd.Received14May2010;Accepted26May2011KEYWORDS:randomsampling;uniformrandomvariables;joi
8、ntprobabilitydensityfunction;Monte-Carlosimulation;modelinguncertainties1.INTRODUCTIONCertainMonteCarlostudiesincivilengineeringapplicationsrequiresimulationofindependentvari-ablessuchthatallthe
