资源描述：
《A generalized dimension-reduction method for multidimensional.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、INTERNATIONALJOURNALFORNUMERICALMETHODSINENGINEERINGInt.J.Numer.Meth.Engng2004;61:1992–2019Publishedonline11October2004inWileyInterScience(www.interscience.wiley.com).DOI:10.1002/nme.1135Ageneralizeddimension-reductionmethodformultidimensionalintegrationinstochasticmechanicsH.XuandS.Rahman∗,†D
2、epartmentofMechanicalandIndustrialEngineering,TheUniversityofIowa,IowaCity,IA52242,U.S.A.SUMMARYAnew,generalized,multivariatedimension-reductionmethodispresentedforcalculatingstatisticalmomentsoftheresponseofmechanicalsystemssubjecttouncertaintiesinloads,materialproperties,andgeometry.Themetho
3、dinvolvesanadditivedecompositionofanN-dimensionalresponsefunc-tionintoatmostS-dimensionalfunctions,whereS>N;anapproximationofresponsemomentsbymomentsofinputrandomvariables;andamoment-basedquadraturerulefornumericalintegration.Anewtheoremispresented,whichprovidesaconvenientmeanstorepresenttheTa
4、ylorseriesuptoaspecificdimensionwithoutinvolvinganypartialderivatives.Acompleteproofofthetheoremisgivenusingtwolemmas,alsoprovedinthispaper.Theproposedmethodrequiresneitherthecalculationofpartialderivativesofresponse,asincommonlyusedTaylorexpansion/perturbationmethods,northeinversionofrandommat
5、rices,asintheNeumannexpansionmethod.Eightnumericalexamplesinvolv-ingelementarymathematicalfunctionsandsolid-mechanicsproblemsillustratetheproposedmethod.Resultsindicatethatthemultivariatedimension-reductionmethodgeneratesconvergentsolutionsandprovidesmoreaccurateestimatesofstatisticalmomentsor
6、multidimensionalintegrationthanexistingmethods,suchasfirst-andsecond-orderTaylorexpansionmethods,statisticallyequivalentsolutions,quasi-MonteCarlosimulation,andthefullysymmetricinterpolatoryrule.Whiletheaccuracyofthedimension-reductionmethodiscomparabletothatofthefourth-orderNeumannexpansionmet
7、hod,acomparisonofCPUtimesuggeststhattheformeriscomputationallyfarmoreefficientthanthelatter.Copyright2004JohnWiley&Sons,Ltd.KEYWORDS:statisticalmoments;multidimensionalintegration;dimensionreduction;stochasticmechanics;moment-basedquadr
