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1、StructMultidiscOptim(2006)31:134146DOI10.1007/s00158-005-0544-yINDUSTRIALAPPLICATIONSMarcusRedhe·LarsgunnarNilssonAmultipointversionofspacemappingoptimizationappliedtovehiclecrashworthinessdesignReceived:16March2004/Revisedmanuscriptreceived:16May2005/Publishe
2、donline:9December2005©Springer-Verlag2005AbstractInthispaper,spacemapping(SM)techniqueisoftheresponsewillbesmoothedout.Theoptimalsolutioncombinedwithresponsesurfacemethodology(RSM).SMisisthensearchedonthesesmoothsurfaces,ratherthanontheanoptimizationmethodwell
3、suitedforverycostlyproblemsrealresponsesurfaces.ForfurtherreadingaboutRSM,seetofindanimproveddesignwithfulfilledconstraints.TheMyersandMontgomery(1995).SomeattemptshavebeenSMtechniqueuselesscostlymodels,whichcomplementsmadetouseoptimizationmethodsincrashworthine
4、ssde-thecorrectmodels.Thetheoryisestablishedandcomparedsignproblems.Applicationexamplescanbefoundin,e.g.,tothecorrectedRSM.AmultipointversionofSMispre-Etmanetal.(1997)andEtman(1997),whowereamongthesented,whereaseparateevaluationisdoneineachiterationfirsttouseRS
5、Minstructuraloptimization.Forsberg(2002)toimprovethemappingfunction.Usingthisadditionalevalu-hasstudiedaccuracyaspectsofRSMusinglinearpolynomi-ationtoupdatethemappingfunction,generally,thenumberalsandkriging.Marklund(1999)andMarklundandNilssonofiterationstofind
6、theoptimumsolutioncanbereduced.(2001)wereamongthefirsttouseRSMforanindustrialap-Thus,theelapsedtimetosolvetheoptimizationproblemplication.Redhe(2001),RedheandNilsson(2002a,b),andcanbereducedifaparallelcomputerisutilized.Finally,Redheetal.(2002)havecomparedRSMwi
7、thspacemappingoneengineeringoptimizationproblemissolvedtoillustrate(SM)andappliedSMonproblemsinvolvinglargeFEvehicletheapplicationofSMinvehiclecrashworthinessstructuralmodels.SchrammandThomas(1998)andSchramm(2001,optimization.2002)haveappliedRSMinavehicledesig
8、ncontext.Rouxetal.(1998),Standeretal.(2001),StanderandCraig(2002),KeywordsOptimization·Spacemapping·ResponseandCraigetal.(2002)werealsoamongthefirsttouseRSMsurfacemethodology·Crashw
