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外文翻译--关于评价特征去除所导致的工程分析错误的规范理论 英文版.pdf

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外文翻译--关于评价特征去除所导致的工程分析错误的规范理论 英文版.pdf

第1页共72页AFORMALTHEORYFORESTIMATINGDEFEATURINGINDUCEDENGINEERINGANALYSISERRORSSANKARAHARIGOPALAKRISHNAN,KRISHNANSURESHDEPARTMENTOFMECHANICALENGINEERING,UNIVERSITYOFWISCONSIN,MADISON,WI53706,UNITEDSTATESRECEIVED13JANUARY2006;ACCEPTED30SEPTEMBER2006ABSTRACTDEFEATURINGISAPOPULARCAD/CAESIMPLIFICATIONTECHNIQUETHATSUPPRESSES‘SMALLORIRRELEVANTFEATURES’WITHINACADMODELTOSPEEDUPDOWNSTREAMPROCESSESSUCHASFINITEELEMENTANALYSISUNFORTUNATELY,DEFEATURINGINEVITABLYLEADSTOANALYSISERRORSTHATARENOTEASILYQUANTIFIABLEWITHINTHECURRENTTHEORETICALFRAMEWORKINTHISPAPER,WEPROVIDEARIGOROUSTHEORYFORSWIFTLYCOMPUTINGSUCHDEFEATURINGINDUCEDENGINEERINGANALYSISERRORSINPARTICULAR,WEFOCUSONPROBLEMSWHERETHEFEATURESBEINGSUPPRESSEDARECUTOUTSOFARBITRARYSHAPEANDSIZEWITHINTHEBODYTHEPROPOSEDTHEORYEXPLOITSTHEADJOINTFORMULATIONOFBOUNDARYVALUEPROBLEMSTOARRIVEATSTRICTBOUNDSONDEFEATURINGINDUCEDANALYSISERRORSTHETHEORYISILLUSTRATEDTHROUGHNUMERICALEXAMPLESKEYWORDSDEFEATURING;ENGINEERINGANALYSIS;ERRORESTIMATION;CAD/CAE1INTRODUCTIONMECHANICALARTIFACTSTYPICALLYCONTAINNUMEROUSGEOMETRICFEATURESHOWEVER,NOTALLFEATURESARECRITICALDURINGENGINEERINGANALYSISIRRELEVANTFEATURESAREOFTENSUPPRESSEDOR‘DEFEATURED’,PRIORTOANALYSIS,LEADINGTOINCREASEDAUTOMATIONANDCOMPUTATIONALSPEEDUPFOREXAMPLE,CONSIDERABRAKEROTORILLUSTRATEDINFIG1ATHEROTORCONTAINSOVER50DISTINCT‘FEATURES’,BUTNOTALLOFTHESEARERELEVANTDURING,SAY,ATHERMALANALYSISADEFEATUREDBRAKEROTORISILLUSTRATEDINFIG1BWHILETHEFINITEELEMENTANALYSISOFTHEFULLFEATUREDMODELINFIG1AREQUIREDOVER150,000DEGREESOFFREEDOM,THEDEFEATUREDMODELINFIG1BREQUIRED25,000DOF,LEADINGTOASIGNIFICANTCOMPUTATIONALSPEEDUP第2页共72页FIG1AABRAKEROTORANDBITSDEFEATUREDVERSIONBESIDESANIMPROVEMENTINSPEED,THEREISUSUALLYANINCREASEDLEVELOFAUTOMATIONINTHATITISEASIERTOAUTOMATEFINITEELEMENTMESHGENERATIONOFADEFEATUREDCOMPONENT1,2MEMORYREQUIREMENTSALSODECREASE,WHILECONDITIONNUMBEROFTHEDISCRETIZEDSYSTEMIMPROVES;THELATTERPLAYSANIMPORTANTROLEINITERATIVELINEARSYSTEMSOLVERS3DEFEATURING,HOWEVER,INVARIABLYRESULTSINANUNKNOWN‘PERTURBATION’OFTHEUNDERLYINGFIELDTHEPERTURBATIONMAYBE‘SMALLANDLOCALIZED’OR‘LARGEANDSPREADOUT’,DEPENDINGONVARIOUSFACTORSFOREXAMPLE,INATHERMALPROBLEM,SUPPOSEONEDELETESAFEATURE;THEPERTURBATIONISLOCALIZEDPROVIDED1THENETHEATFLUXONTHEBOUNDARYOFTHEFEATUREISZERO,AND2NONEWHEATSOURCESARECREATEDWHENTHEFEATUREISSUPPRESSED;SEE4FOREXCEPTIONSTOTHESERULESPHYSICALFEATURESTHATEXHIBITTHISPROPERTYARECALLEDSELFEQUILIBRATING5SIMILARLYRESULTSEXISTFORSTRUCTURALPROBLEMSFROMADEFEATURINGPERSPECTIVE,SUCHSELFEQUILIBRATINGFEATURESARENOTOFCONCERNIFTHEFEATURESAREFARFROMTHEREGIONOFINTERESTHOWEVER,ONEMUSTBECAUTIOUSIFTHEFEATURESARECLOSETOTHEREGIONSOFINTERESTONTHEOTHERHAND,NONSELFEQUILIBRATINGFEATURESAREOFEVENHIGHERCONCERNTHEIRSUPPRESSIONCANTHEORETICALLYBEFELTEVERYWHEREWITHINTHESYSTEM,ANDCANTHUSPOSEAMAJORCHALLENGEDURINGANALYSISCURRENTLY,THEREARENOSYSTEMATICPROCEDURESFORESTIMATINGTHEPOTENTIALIMPACTOFDEFEATURINGINEITHEROFTHEABOVETWOCASESONEMUSTRELYONENGINEERINGJUDGMENTANDEXPERIENCEINTHISPAPER,WEDEVELOPATHEORYTOESTIMATETHEIMPACTOFDEFEATURINGONENGINEERINGANALYSISINANAUTOMATEDFASHIONINPARTICULAR,WEFOCUSONPROBLEMSWHERETHEFEATURESBEINGSUPPRESSEDARECUTOUTSOFARBITRARYSHAPEANDSIZEWITHINTHEBODYTWOMATHEMATICALCONCEPTS,NAMELYADJOINTFORMULATIONANDMONOTONICITYANALYSIS,ARECOMBINEDINTOAUNIFYINGTHEORYTOADDRESSBOTHSELFEQUILIBRATINGANDNONSELFEQUILIBRATINGFEATURESNUMERICALEXAMPLESINVOLVING2NDORDERSCALARPARTIALDIFFERENTIALEQUATIONSAREPROVIDEDTOSUBSTANTIATETHETHEORYTHEREMAINDEROFTHEPAPERISORGANIZEDASFOLLOWSINSECTION2,WESUMMARIZEPRIORWORKONDEFEATURINGINSECTION3,WEADDRESSDEFEATURINGINDUCEDANALYSISERRORS,ANDDISCUSSTHEPROPOSEDMETHODOLOGYRESULTSFROMNUMERICALEXPERIMENTSAREPROVIDEDINSECTION4ABYPRODUCTOFTHEPROPOSEDWORKONRAPIDDESIGNEXPLORATIONISDISCUSSEDINSECTION5FINALLY,CONCLUSIONSANDOPENISSUESAREDISCUSSEDINSECTION6第3页共72页2PRIORWORKTHEDEFEATURINGPROCESSCANBECATEGORIZEDINTOTHREEPHASESIDENTIFICATIONWHATFEATURESSHOULDONESUPPRESSSUPPRESSIONHOWDOESONESUPPRESSTHEFEATUREINANAUTOMATEDANDGEOMETRICALLYCONSISTENTMANNERANALYSISWHATISTHECONSEQUENCEOFTHESUPPRESSIONTHEFIRSTPHASEHASRECEIVEDEXTENSIVEATTENTIONINTHELITERATUREFOREXAMPLE,THESIZEANDRELATIVELOCATIONOFAFEATUREISOFTENUSEDASAMETRICINIDENTIFICATION2,6INADDITION,PHYSICALLYMEANINGFUL‘MECHANICALCRITERION/HEURISTICS’HAVEALSOBEENPROPOSEDFORIDENTIFYINGSUCHFEATURES1,7TOAUTOMATETHEGEOMETRICPROCESSOFDEFEATURING,THEAUTHORSIN8DEVELOPASETOFGEOMETRICRULES,WHILETHEAUTHORSIN9USEFACECLUSTERINGSTRATEGYANDTHEAUTHORSIN10USEPLANESPLITTINGTECHNIQUESINDEED,AUTOMATEDGEOMETRICDEFEATURINGHASMATUREDTOAPOINTWHERECOMMERCIALDEFEATURING/HEALINGPACKAGESARENOWAVAILABLE11,12BUTNOTETHATTHESECOMMERCIALPACKAGESPROVIDEAPURELYGEOMETRICSOLUTIONTOTHEPROBLEMTHEYMUSTBEUSEDWITHCARESINCETHEREARENOGUARANTEESONTHEENSUINGANALYSISERRORSINADDITION,OPENGEOMETRICISSUESREMAINANDAREBEINGADDRESSED13THEFOCUSOFTHISPAPERISONTHETHIRDPHASE,NAMELY,POSTDEFEATURINGANALYSIS,IE,TODEVELOPASYSTEMATICMETHODOLOGYTHROUGHWHICHDEFEATURINGINDUCEDERRORSCANBECOMPUTEDWESHOULDMENTIONHERETHERELATEDWORKONREANALYSISTHEOBJECTIVEOFREANALYSISISTOSWIFTLYCOMPUTETHERESPONSEOFAMODIFIEDSYSTEMBYUSINGPREVIOUSSIMULATIONSONEOFTHEKEYDEVELOPMENTSINREANALYSISISTHEFAMOUSSHERMAN–MORRISONANDWOODBURYFORMULA14THATALLOWSTHESWIFTCOMPUTATIONOFTHEINVERSEOFAPERTURBEDSTIFFNESSMATRIX;OTHERVARIATIONSOFTHISBASEDONKRYLOVSUBSPACETECHNIQUESHAVEBEENPROPOSED15–17SUCHREANALYSISTECHNIQUESAREPARTICULARLYEFFECTIVEWHENTHEOBJECTIVEISTOANALYZETWODESIGNSTHATSHARESIMILARMESHSTRUCTURE,ANDSTIFFNESSMATRICESUNFORTUNATELY,THEPROCESSOF几何分析CANRESULTINADRAMATICCHANGEINTHEMESHSTRUCTUREANDSTIFFNESSMATRICES,MAKINGREANALYSISTECHNIQUESLESSRELEVANTARELATEDPROBLEMTHATISNOTADDRESSEDINTHISPAPERISTHATOFLOCAL–GLOBALANALYSIS13,WHERETHEOBJECTIVEISTOSOLVETHELOCALFIELDAROUNDTHEDEFEATUREDREGIONAFTERTHEGLOBALDEFEATUREDPROBLEMHASBEENSOLVEDANIMPLICITASSUMPTIONINLOCAL–GLOBALANALYSISISTHATTHEFEATUREBEINGSUPPRESSEDISSELFEQUILIBRATING3PROPOSEDMETHODOLOGY31PROBLEMSTATEMENTWERESTRICTOURATTENTIONINTHISPAPERTOENGINEERINGPROBLEMSINVOLVINGASCALARFIELDUGOVERNEDBYAGENERIC2NDORDERPARTIALDIFFERENTIALEQUATIONPDEFAUUCALARGECLASSOFENGINEERINGPROBLEMS,SUCHASTHERMAL,FLUIDANDMAGNETOSTATICPROBLEMS,MAYBEREDUCEDTOTHEABOVEFORMASANILLUSTRATIVEEXAMPLE,CONSIDERATHERMALPROBLEMOVERTHE2DHEATBLOCKASSEMBLYΩILLUSTRATEDINFIG2THEASSEMBLYRECEIVESHEATQFROMACOILPLACEDBENEATHTHEREGIONIDENTIFIEDASΩCOILASEMICONDUCTORDEVICEISSEATEDATΩDEVICETHETWOREGIONSBELONGTOΩANDHAVETHESAME第4页共72页MATERIALPROPERTIESASTHERESTOFΩINTHEENSUINGDISCUSSION,AQUANTITYOFPARTICULARINTERESTWILLBETHEWEIGHTEDTEMPERATURETDEVICEWITHINΩDEVICESEEEQ2BELOWASLOT,IDENTIFIEDASΩSLOTINFIG2,WILLBESUPPRESSED,ANDITSEFFECTONTDEVICEWILLBESTUDIEDTHEBOUNDARYOFTHESLOTWILLBEDENOTEDBYΓSLOTWHILETHERESTOFTHEBOUNDARYWILLBEDENOTEDBYΓTHEBOUNDARYTEMPERATUREONΓISASSUMEDTOBEZEROTWOPOSSIBLEBOUNDARYCONDITIONSONΓSLOTARECONSIDEREDAFIXEDHEATSOURCE,IE,KRTˆNQ,ORBFIXEDTEMPERATURE,IE,TTSLOTTHETWOCASESWILLLEADTOTWODIFFERENTRESULTSFORDEFEATURINGINDUCEDERRORESTIMATIONFIG2A2DHEATBLOCKASSEMBLYFORMALLY,LETTX,YBETHEUNKNOWNTEMPERATUREFIELDANDKTHETHERMALCONDUCTIVITYTHEN,THETHERMALPROBLEMMAYBESTATEDTHROUGHTHEPOISSONEQUATION18100SLCTSLCTSLCTCOILCOILTTBORONQHKAONTINININQTKBCPDEGIVENTHEFIELDTX,Y,THEQUANTITYOFINTERESTIS2,,DEVICEDYCTYXHTCOMPUTEDEVICEWHEREHX,YISSOMEWEIGHTINGKERNELNOWCONSIDERTHEDEFEATUREDPROBLEMWHERETHESLOTISSUPPRESSEDPRIORTOANALYSIS,RESULTINGINTHESIMPLIFIEDGEOMETRYILLUSTRATEDINFIG3FIG3ADEFEATURED2DHEATBLOCKASSEMBLYWENOWHAVEADIFFERENTBOUNDARYVALUEPROBLEM,GOVERNINGADIFFERENTSCALARFIELDTX,Y

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