基于多目标优化策略的结构可靠性稳健设计

第24卷第1期应用力学学报Vol.24No.12007年3月CHINESEJOURNALOFAPPLIEDMECHANICSMar.2007:10004939(2007)01026705*刘仁云1,3张义民2刘巧伶1(130025)1(110004)2(130032)3:应用可靠性稳健优化设计理论和多目标决策方法,将结构可靠性稳健优化设计转化为多目标优化问题运用灰色理论中的关联分析法,选取粒子群算法中的全局极值和个体极值,提出了灰色粒子群算法求解可靠性稳健优化设计问题与传统方法相比,该方法简便易行并能迅速准确地得到结构可靠性稳健优化设计信息:稳健优化设计;灰色粒子群算法;随机摄动法;多目标优化:U463;TH123:A1,,,,[1-6][7],,,(ParticleSwarmOptimization,PSO)KennedyEberhart1995[8],,,,,,221R=g(x)fx(X)dX(1)fx(X)X=(x1,x2,,xn)T,g(X),:g(X)!0,g(X)0g(X)=0Xg(X)X=Xd+Xp(2)g(X)=gd(X)+gp(X)(3),d,p,*:(50535010);(20052034);:20051212:20061120:,,1968,,,;∀∀∀Email:[e-mail],g=E[g(X)]=g=gd(X)(4)2g=Var[g(X)]=(!gd(X)!XT)[2]Var(X)(5)Var(X)g(X)X,!g(X)!XT=!g!x1!g!x2!g!xn(6)(6)(5),!=gg=E[g(X)]Var[g(X)](7)X,R=∀(!)(8)∀(#)22,minf1(X)minf2(X)=|!R!x1|#minfn+1(X)=|!R!xn|st.!∃!T(9)f1(X),X=(x1,x2,,xn)T,R,fi(X)(i=2,3,,n+1),!T:,,(Paretooptimal),(Paretooptimalset),,331(PSO),,,,,()()m,iXi=(xi1,xi2,,xin),Vi=(vi1,vi2,,vin),Pid=(pi1,pi2,,pin),Pgd,vid(k+1)=w%vid(k)+c1%rand()%(pid(k)-xid(k))+c2%rand()%(pgd(k)-xid(k))(10)xid(k+1)=xid(k)+vid(k+1)(11):w;c1c2;rand()(0,1);vid&[-vmax,vmax],vmax,,,,w,w;,,;,,32[9],,,,,,,Y0=(y0(i)i=1,2,,n),Yj=(yi(i)i=1,2,,n),j=1,2,m,mYjY0i0j(i)=minjmini|y0(i)-yj(i)|+∃maxjmaxi|y0(i)-yj(i)||y0(i)-yj(i)|+∃maxjmaxi|y0(i)-yj(i)|(12)26824%=1n∀ni=10j(i)(13)∃,,05,∃=0,;∃=1,33,,PidPgd,PidPgd,:,,;,,,,(13),Pgd,Pid,,,,∋:X;V;mc1c2w;&;Tmaxn(,)While(&&(&)Tmax)∗Fori=1:mForj=1:nX,EndFor/*,,*/EndFor+(13),,PidPgd−(10)(11)XEndWhile441,,,,(1)1,,,,,,s=32DM∋(D4-d4)(14)(=16DT∋(D4-d4)(15)MT;Dd,=s2+3(2=32DM∋(D4-d4)M2+075T2(16),,=MWn(17):M;Wn,2691,:Wn=bh26[1-059d4bh3](18):d;bh,g(X)=r-(19):r;X=(rMTDd)T,X=(rMbhd)TXE(X)Var(X),g(X)X,!g!XT=[!g!r!g!M!g!T!g!D!g!d](20)!g!XT=[!g!r!g!M!g!b!g!h!g!d](21),(7)(8),,!R42:MT(M,M)=(6432658,584729)N#mm,(T,T)=(4472475,362270)N#mm,r(r,r)=(443,275)Mpa!2,dD,∋,Af1(X)=∋4(x22-x21)(22)X=(x1,x2)T=(d,D)T(X=[x1x2]Tf2(X)=!R!x1(23)f3(X)=!R!x2(24),∋!2(:0mm!d!100mm;0mm!D!100mm;D-d∃0,100XV,c1=c2=15;w10123,501:50M(M,M)=(16074212226,9702858912)N#mm,r(r,r)=(443,275)Mpa!3,db,h,∋,Af1(X)=x1x2-∋4x23(25)X=[x1x2x3]T=[bhd]T(X=[x1x2x3]Tf2(X)=!R!x1f3(X)=!R!x2f4(X)=!R!x3(26),∋!3(0mm!b-d!10mm;0mm!h-d!10mm;h-b∃0mm100XV,c1=c2=15;w10123,6011,,,,,,,,27024,,,,50601f1=1089749f2=05670f3=09476d=92801D=99999f1=1300699f2=05878f3=09489d=91329D=99987f1=992254f2=05070f3=09276d=92654D=99239!=3428!=3436!=3467f1=8704437f2=06822f3=08534f4=09548b=123574h=152406d=113569f1=7589666f2=0794f3=08157f4=09432b=122576h=142945d=112464f1=4791840f2=06934f3=07528f4=08960b=120574h=122406d=112663!=4030!=4156!=398785,,,,,pareto,[1],,.[J].,2003,19(3):9598.[2],,,.()[J].,2004,6(4):6771.[3],,,.()[J].,2004,6(5):6165.[4],,,.():[J].,2004,11(5):233237.[5],,,.():[J].,2004,11(5):238242.[6],,,.():[J].,2004,11(6):297300.[7].[M].:,1994:230236.[8]KennedyJ,EberhartRC.Particleswarmoptimization[C]//IEEEIntConfonNeural.Networks,1995:19421948.[9].[M].:,1996:7075.2711,:tude.ThedynamicstressintensityfactoriscalculatedaccordingtotheaboreJintegrals.Keywords:dynamicfracturemechanics,dynamicstressintensityfactor,dynamicJintegral,FEM,fracture.NewRapidAlgorithmforWindinducedRandomVibrationofComplexStructuresXieZhuangning(DepartmentofCivilEngineering,ShantouUniversity,515063,Shantou,China)Abstract:Thetraditionalcompletequadraticcombination(CQC)methodhasnotbeenwidelyusedforrandomvibrationanalysisofcomplexstructuresduetothehugecomputationaltasks.Thepseudoexcitationmethod(PEM)haspartlysolvedthisproblembymeansofaccurateandefficientcomputationtoapplytothefieldsofrandomvibrationanalysisofcomplexstructures.However,ThecalculationanddecompositionoftheexcitationPSDmatrices,isstilltimeconsumingespeciallyforthevibrationanalysisofwindexcitedlargecivilengineeringstructures.Anaccurateandefficientalgorithm,namedasharmonicexcitationmethod(HEM),forwindinducedstructuralrandomresponseanalysisonthebasisoftheperiodicdiagrammethod.TheaccuracyandefficiencyareexaminedbycomparisonwithCQCandPEMmethods.Keywords:randomvibration,complexstructure,multiexcitation,pseudoexcitationmethod,response.StructuralRobustReliabilityDesignforMultiobjectiveOptimizationLiuRenyun1,3ZhangYimin2LiuQiaoling1(CollegeofMechanicalScienceandEngineering,NanlingCampus,JilinUniversity,130025,Changchun,China)1(SchoolofMechanicalEngineeringandAutomation,NortheasternUniversity,110004,Shenyang,China)2(CollegeofMathematics,ChangchunNormalUniversity,130032,Changchun,China)3Abstract:Structuralreliabilitydesignoptimizationistransformedintotheoptimizationwithmultiobjectivedecisionmakingapproach.TheglobaloptimumandpersonaloptimuminPSOalgorithmareselectedwithrelevancyanalysismethodoftheGreyTheory.Thus,aGreySwarmParticleOptimization(GreyPSO)algorithmispresentedfortherobustoptimizationdesignonreliability,andappliedtorearaxlehousingofavehicleasanumericalexample.Keywords:robustdesignoptimization,greyparticleswarmoptimization,probabilisticperturbationmethod,multiobjectiveoptimization.TransientFlowinSealedReservoirsWithWeakCrossflowInterlayerSongFuquan1LiuCiqun2(TheCollegeofMathematicsandPhysics,ZheJiangNormalUniversity,321004,Jinhua,China)1(InstituteofPorousFl