0 INTRODUCTION Under multidiseiPlin娜design叩timization(MDO)environ- ment a eomPlieate system usually 15 eomPosed by various subsys- terns as shown in Fig.1[,,2]:Here 0 15 tne number ofsubsystem;又 15 the eouPledy葫able that 15 inPutto another subsystem’5 analyses; 若15 the set of strietly loeal design~ables without system一level specified targets fromsub斗stem:夕夕are linkillg variables generated as outPuts from subsystem and taken as inPuts to another subsystem (for simPlifieation ofrePresentation,we denote yi二沙ij户1,…,n,j井i as the set of outPut variables of subsystemi,and 丫一{yl,…,共一1,凡1,…,川 as the inPut variables of subsystemi; funetions belonging to subsystemi, belonging to subsystem关,2 15 the set 91 15 5 the set ofobjeetive the set of eonstrain1S rameters(ineluding couPled variable system level. of all the shared design Pa- and linking variables)at Subsystem 1 Fig.l CouPledsystem In above system,there 15 eertain deviation between the sub- system model and actual model,50 uneertainty of any subsystem will inevitab一y influenoe the performanee of出e喃ole system{3,4}. Meanwllile there are eouPling subsystems,ie.the Performanee of one subsystem may be the inPut of another one,and viee versa. Therefore a key Problem of MDO 15 that the uneertainties of one subsystem may be Propagated to another subsystem and the final ou午ut from the integrated systems has an aeculnulation effeet of the uneertainties from the individual subsystem.50 in MDO sys- tem,effeetive uneertainty analysis must take into aeeount the influence of sueh ProPagation ofuneertainty. The source ofuncertainties in MDO systemeanbeelassified as follows:①oimensiona一v丽ation when the芦。面et manufae- tured,ealled input parameter uncertainty.②uneertainty in values ehosen for model Parameters sueh as yield strength, ealled model Parameter uneertainty.③Ineonsisteney between assumed and aetually boundary eonditions,called model strue- ture uneertainty.If the effects of variations are ignored during the design Proeess,this will often lead to a large number of re- jeeted Parts or assemblies,high manufacturing eosts,or failure in serviee[5]. Robust design(RD)has beeome a Powe而1 tool to assist de· signers in making judieious selection and eontrol ofvariation.The fundamental PrinciPle ofRD 15 to imProve the quality ofaProduet by eliminatlngthevariationofeontro1lab1efaetors(i.e.dimension, assemble gaP,material ProPerties,etc)and uneontrollable faetors (1 .e.aPPlied loadings,environment,aging,ete),Consequently,it 15 signifieant to integrate the RD and the MDO for reliable deei- sion一making in designing eomPlex engineering systems. In reeent times,many researehers have exPlored the imPaet of uneertainty within the MDO environment.A muiti·objeetive robust design 15 used to assess tradeoff between the mean and variance ofthere卿nse[61.The斗stemuneertain妙analysis(suA)〔5] and eoncu『rent subsystem uncertainty analysis(ess以)【7〕ean imProve the effieieney of multidiseiPlinary robust design.Auto- matie differentiation 15 used to evaluate the sensitivitV inforroation In rooust OPtltn,Zatlon‘一J.In Pr;nc1Ple,all 01 tne aDoVe aPProacnes belong to the all一in一one tyPe or non一hierarehieal tyPe eonsidering a single Performaneea找ribute.Therefore a hierarehieal aPProaeh to multidiseiPlin卿robust design needs to be develoPed. Both the eoneurrent subsPaee oPtimization(CSSO)and eol- laborative oPtimization(CO)aPProaehes are limited to the aPPli- eation of detellllinistie desi四ootimization and do not allow for alscrete aeslgn Variaoles at tne system levelL”一」.匕esloes,botn ot them are eomPutationally exPensive,and often have diffieulty in eonverg即ee.The objeetive in this work 15 to imProve CSSO framework and CO framework,and ineorporate uneertainty.Con- sequently, a multidiseiPlinary robust design oPtimization frame- work,multidiseiPlinary robust design oPti而zation based on re- sPonse surfaee(MRDO一RS)15 ProPosed in this PaPer. The 519- nifieanti哪rovements of this franlewo改are listed next:①un- der Mno斤amework uncertainty 15 ineo印orated.②The re印onse surfaee aPProximation 15 adopted to Provide information for sys- tem level in order to imProve the eoordination efficieney, and allows eouPling variables to be discrete or diserCte/eontinuous nllXed. CHINESE JOURNAL 0F MECHANICAL ENGINEERING ·47· l MRDo.RS METHoD In MRDO.RS.each subsystem has the function of optimi. zation and uncertainty analysis,and can communicate with sys- tem leveI through network.The basic idea can be described as follows:Each subsystem identifies the controllable factors and uncontrollable ones through uncertainty analysis,and the or. thogonal experiment is adopted to calculate the means and the standard deviations of variables;Each subsystem carries out independent and parallel robust optimization design.the opti. mization purpose of which is to reduce The inconsistency with the variables of other disciplinary;The design information of each subsystem is only propagated to system 1evel but not to other disciplinary;Not only does system