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首页 四维可视化多目标寻优方法及其在T型滤波器设计中的应用_英文_

四维可视化多目标寻优方法及其在T型滤波器设计中的应用_英文_.pdf

四维可视化多目标寻优方法及其在T型滤波器设计中的应用_英文_

lj100083
2013-05-04 0人阅读 举报 0 0 暂无简介

简介:本文档为《四维可视化多目标寻优方法及其在T型滤波器设计中的应用_英文_pdf》,可适用于IT/计算机领域

第卷第期系统仿真学报©VolNo年月JournalofSystemSimulationOct,••DVisualMultiobjectiveOptimizationMethodandItsEngineeringApplicationonTfilterWUJiaju,WANGWenting,HidehikoSUGIMOTO,LIYuanting(NondestructiveTestKeyLaboratoryofMinistryEducation,NanchangHangkongUniversity,Nanchang,ChinaFukuiUniversity,Japan)Abstract:Tosolvetheproblemofmultiobjectiveoptimizationsuchaslimitedsearchingscope,complicatedcomputation,aDvisualmethodwasproposedColorisintroducedexplicitlyintoconventionalDcoordinatesystemasthethdimensionThreeconventionalcoordinatesstandforthevariables,withcoloredpointsforthevaluesofobjectivefunctionsLinesofthesamecolorarethenintegratedintoisographstoshowtheDvisualeffectsMultiObjectiveoptimizationisconductedbasedontheintersectionsOptimizationofanunsymmetricalpassivelowpassTfilterusedininverterispresentedtodemonstratethemethodindetailIsographsofobjectivefunctiondistributionarevisibleintheenlargedoptimizationscopeAsaresult,stabilityoftheoptimumsolutionissignificantlyimprovedItpointsoutthatsensitivitiesofobjectivefunctionstothevariables,playanimportantroleintheoptimizationMathematicdescription,detaileddesignrules,togetherwithexperimentalresultsforquantitativecomparisonarepresentedKeywords:DvisualizationmultiobjectiveoptimizationcolorgraphTfilter四维可视化多目标寻优方法及其在T型滤波器设计中的应用伍家驹王文婷杉本英彦李园庭(南昌航空大学无损检测技术教育部重点实验室,南昌福井大学,日本)摘要:针对多目标优化设计中存在寻优空间小、计算难度大等问题提出维可视化寻优方法将颜色作为第变量引入维坐标系中分别用三维坐标表示待求自变量用三维空间诸点的颜色表示目标函数的值。视图中多个切片的同色线集成为空间等值域获得清晰的维显性可视化效果并据图中的交域颜色分布实现多目标寻优。以对逆变器的非对称无源T型低通滤波器进行优化设计为例对该方法进行了详细说明和论证在扩大的寻优范围内目标函数的分布状态清晰可见有效地提高了优化解的稳定性。本方法表明:在寻优过程中应充分考虑目标函数对子变量的敏感性。提供了数学证明介绍了使用本方法的设计准则以及用于定量比对的实验数据。关键词:维可视化多目标寻优色图T型滤波器中图分类号:TP文献标识码:A文章编号:X()IntroductionAlmostallmathematicmodelsinengineeringoptimizationarenonlinearhigherpowertranscendentalequationswithoutanalyticalsolutionsResultsobtainedbyconventionaliterationoptimizationrelyonthealgorithmstrongly,aswellasontheinitialsolutionsItoftenleadstoalocaloptimization,insteadoftheglobaloptimizationForexample,theoptimumdesignofTfilterininvertersisatypicalproblemwithhighnonlinearity,nonconvexity,boundaryconstrainedandmultiextremepointsMuchprogresshasbeenmadeinglobaloptimizationalgorithmToobtainalargeroptimizationscope,Receiveddate:Reviseddate:Foundationitem:NationalNaturalScienceFoundationofChina()Biographies:WUJiaju(),PhDProfessor,mainresearchfieldsisPowerElectronicsWANGWenting(),female,master,majoringinPowerElectronicsgeneticalgorithmnonlineartranscendentalequationsareavailablebyWUmethodHowever,itwillbemorepracticalinvisualdataprocessingifthe“discretepoint”solutionsareextendedintoneighborhoodsInRef,onlyasingleparameterisdirectlyavailablebecausethedesigniscarriedoutbymultiobjectivefunctioncrossingmethodinDcoordinatesystemAnumberofDchartsareemployedjointlyinReftosimplifythedesignprocess,whilemultidimensionalvisualizationtechnologymaycontainmoreinformationInRef,aDvisualizationmethodisintroduced,andDvisualizationmethodwillbringmoreconvenienceinmultiobjectivedesignSpecialfunctionsandappliedsoftwareforvisualdesignarealreadyavailableinsomesoftwaretoolkitssuchasMatlabButthecoloredimageisinanimplicitway,orthecolorscanonlybeclearlyseeninspecifiedsliceswhichisindirectthusitcannotbeusedin第卷第期VolNo年月系统仿真学报Oct,··optimaldesignAsshowninFig,itiseitherdifficulttoobservethecolorvariationswithfewerslices,orattheexpenseofreducingviewingscopewithmoreslicesDVisualOptimizationofUnsymmetricalPassiveTfilterPowerfactorofTfilterFigshowsinverter’stopology,Filteristhekeyelementinit,asshownintherightpartCapacity:kVAinputdirectvoltage:Vpowerfrequencyoutputvoltage:V,frequencyofcarrierwave:kHzloadpowerfactor:cosθ∈,|ZL|=ΩR=ΩR=ΩL=mHWhencosθ=,ZL=Rwhencosθ=,ZL=RjωLFigTheimplicitslicesTBCATZLeiTUdLCLiiEFTFigIndirecttestcircuitofpowerfactorEnhancingtheinverter’spowerdensitythroughimprovingsystempowerfactorcosφisaregulardesignobjectiveCorrespondingproblemsare:①φstronglyreliesonthefluctuationofloadpowerfactorcosθ②InputvoltageEifromtheinverterbridgeisaPWMwave,whichoneisofveryrichhighfrequencycomponentsButthepowerfactorcosφcorrespondingtofundamentalωdominatesthepowerdensityoftheinverterConventionaloptimizationThefirststepinconventionaloptimizationistodeterminetheobjectivefunctions,ie,powerfactorunderpureresistiveloadandresistiveinductiveloadconditionsrespectively,shownbyEq()and(),respectivelycosRRTTLωLωRCωLLCωLCωRCLωLLCωφ==−−−()cos()()()()RRTTLωLLωLLLCωLLCωRCLωRCωLLLCωφ==−−−()ThenextstepistoconstructthemodelLetf(L,L,C)standforthefullloadconditionwithunitpowerfactor,Eq(),andf(L,L,C)standforthefullloadconditionwithpowerfactorcosθ=Letf=f∩f,then:minf(L,L,C)()stL>,L>,C>Thelaststepisalgorithmdevelopmentandselectionofinitialconditions,whichareofvitalimportancetotheoptimizationsolutionofEq()anddeterminethesuccessDvisualoptimization①MakethecoloredDgraphslicestransparent②Surfacesareobtainedbasedonsufficientcurves,asshowninFig③IntersectionsareformedbysufficientsurfacesasshowninFig④Tohighlighttheintersectionsthatareveryclosetotheoptimumvaluescosφ,,makeotherintersections∈uncoloredTakethefullloadconditionfandfforexamples,agraphlikeFigcouldbeobtainedNote:(a)Intersectionsforcosφ<arenotshown(b)Variationsofthedependentvariablescanbeobtainedbyrotatingthegrapharbitrarily(c)ZoomisusedtoobservethedetailedtinyfluctuationsFigSurfacesbasedoncurvesLHLHCmFLHLHC×F第卷第期VolNo年月伍家驹,等:四维可视化多目标寻优方法及其在T型滤波器设计中的应用Oct,··FigIntersectionsbasedonsurfacesFigIntersectionsoffandfDistributionofoptimalsolutionsOptimizationaimstofindtheglobaloptimalsolution,butsolutionsobtainedbyconventionaloptimummethodsareoftenlocalonesBecausethedomainofcosφ≥isnotconvex,thenumberofoptimalsolutionandtheoptimalvaluemaynotbeoneLetf=f∩f,FigcouldbeobtainedShrinktheobjectivefunctionvaluewithincosφ,,distributi∈onofcorrespondingoptimalvalueandsolutionsareshowninFigFigIntersectionsoffFigDistributionofoptimumsolutionsAnalysisonOptimumSolutionsStabilityofoptimumsolutionsStabilityoftheoptimalsolutionsisclearlyshowninFigSomesolutionshavelarge∂f∂L,∂f∂L,∂f∂CFollowingexamplesaregivencorrespondingtothethreeindependentvariablesrespectivelyPointUinFig(C=μF,L=mH,L=mH)isverysensitivetoL,thecomputationresultsarelistedinTabPointVinFig(C=μF,L=mH,L=mH)isverysensitivetoL,thecomputationresultsarelistedinTabPointWinFig(C=μF,L=mH,L=mH)isverysensitivetoC,thecomputationresultsarelistedinTabTableSensitivityComputationofcosφtoLatpointUcosθ=Ratedapparentpowercosθ=RatedapparentpowerLmHTableSensitivityComputationofcosφtoLatpointVcosθ=Ratedapparentpowercosθ=RatedapparentpowerLmHTableSensitivityComputationofcosφtoCatpointWcosθ=Ratedapparentpowercosθ=RatedapparentpowerCμFLHLHCmFLHLHC×FboundaryofresistiveinductiveloadboundaryofresistiveloadintersectionLHLHCmFLHLHCmFV第卷第期VolNo年月系统仿真学报Oct,··Abovetablesindicatethatinsomecases,cosφchangessharplyfromto,whileavariableonlychangesItmakestheIGBTloadcurrentincreaserapidlywithinaveryshorttimeValuesofcommerciallyavailablecapacitorCareconstrainedintosomerangewithdiscretechoicesValuesofLandLcannotbeidenticaltotheexpectedinductancesbecauseofthemanufacturedeviationsTherefore,suchsensitivepointsshouldbeavoidedindesignHowever,itisnotsoeasytoselecttheinitialsolutionproperlyinconventionaloptimizationRandomchosenoneswillbeunavoidableplungedintothesesensitivepointsFollowingarethetwoproblemstobesolved:①Therearesofarnogeneralrulesfortheselectionofinitialsolution②ResearchreportsonthesolutionstabilityinmultiobjectiveoptimizationarerarelyseenDesignStrategyInFig,byrotatingthegraphthenmovingawaythepartincosφ∈(,,acompleteconvexisobtainedThenfindtheinscribedsphereofmaximumdiameterBecausethevaluesinsidethesphereareapproximatelyequal,theoptimalsolution(L*,L*,C*)withhighestcosφstabilityshouldbeveryclosetothecenterofthesphereAsaresult,cosφwillberemainedclosetoeventherearefluctuationsofL,LandC(showninFig),becausefL∂∂,,fL∂∂fC∂∂taketheminimumvaluesatthespherecenterTheoptimalsolutionAsthegraphinFigispartlyzoomed,theinscribedsphereofmaximumdiameterisseenwithintheintersectionsCorrespondingoptimumsolutionisC*=μF,L*=mH,L*=mH(showninFig)FigLocationof(L*,L*,C*)DesigneffectcosφunderdifferentloadconditionsTabshowstheresultsforvariousloadsTableComputedresultsofcosφtocosθRatedapparentpowercosθ=cosθ=cosθ=cosθ=cosθ=cosθ=cosθ=(leading)sensitivityofcosφtoL,LandCTab,andshowsensitivityresultsfordifferentL,LandC,respectivelyItcanbeseenfromTab,andthat,①Thelowestvalueofcosφis②Insomecases,powerfactorcosφremains≈,evenavariablehaschangedlargely③Theoptimalsolutionsofhighrobusttovariationsofcosθ,L,LandCTableComputedresultsofcosφtoLcosθ=Ratedapparentpowercosθ=RatedapparentpowerLmHTableComputedresultsofcosφtoLcosθ=Ratedapparentpowercosθ=RatedapparentpowerLmHTableComputedresultsofcosφtoCcosθ=Ratedapparentpowercosθ=RatedapparentpowerCμFComparisonwithotherdesignsTFilterinRefandΓFilterinRefhavegainedgoodoutcomeandtheyareusedincomparisonTabshowstheresultsComparisonresultsshowthatthedesigninthispaperismorerobusttoloadvariationLHLHC×F第卷第期VolNo年月伍家驹,等:四维可视化多目标寻优方法及其在T型滤波器设计中的应用Oct,··TableComparisonresultsRatedapparentpowercosθ=cosφofDmethodcosθ=cosθ=cosφofRefcosθ=cosθ=cosφofRefcosθ=AttenuationcharacteristicsReplacetheoptimalvaluesofL*,L*andC*intoEq(),thenthefollowingtransferfunctionandFigcouldbeobtained()Gssss−−−=×××ItisclearlyseenthatattenuationoftheTFilterisapproximately-dBdecwhichisbetterthantheconventional-dBdecattenuationofΓFilterFigBodeplotoftheTFilterExperimentsTestofpowerfactorTestcircuitTheinputvoltageofTfilterisPWMwave,whiletheinputcurrentisapproximatesinusoidalItisknownthatconventionalpowerfactormeterishelplessinthiscaseTocalculatesystempowerfactorunderrealoutputvoltageandcurrent,FigandFigarethetestcircuitandoutcomewaveform①Inputvoltageeiandcurrentiiarefromtheinverter②Theoscilloscopetype:TDSBwithcurrentprobeAFigTestedwaveformsTestresultPowerfactorisobtainedbyreadingthezerocrossingvaluesofvoltageandcurrentFigshowsthetestedwaveformsoftheinverterSystempowerfactorwithloadvariationLetL=mH,L=mH,C=μFTabshowsthecomparisonofthecomputedvalueswithtesteddataTableThetestedandcomputedofcosφload(W)computedcosφ(cosθ=)testedcomputedcosφ(cosθ=)testedConclusionsByintegratingthecolorgraphsofneighbored①transparentslicesintoisographs,explicitDvisualeffectscouldbeobtainedTakeconventionalcoordinatesstandas②variables,colorasobjectivefunction,multiobjectiveoptimizationisthenavailablebasedontheintersectionsThe③DvisualizationmethodcouldexhibitmultiobjectivefunctioninDcoordinatesquantitativelyTherefore,itiseasytohandletheoveralltrendsandconvenienttogettheglobaloptimaldesignvariableswithpracticalconsiderationTopreventsharpdescendofsystempower④factorwithsmallfilterparameterorloadchanges,itisnecessarytofindthemaximumvolumesatisfyingtheobjectivefunctionandchoosetheoptimalsolution(L*,L*,C*)intheneighborhoodofthecenterofthesphereAcknowledgmentTheauthorswouldliketoexpressthankstoProfChenXuanfromNanchangHangkongUniversityandWuShengyufromTsinghuaUniversityReferences:RenBozhi,LongTengrui,WangKunpingAPragmaticIntellectAlgorithmforOptimizingComplexNonlinearFunctionJJournalofEngineeringMathematics(S),,():(inChinese)ZhangZhansong,CaiXuansanTheprincipleandthedesignofswitchpowersupply(reviseaversion)MBeijing:PublishingHouseofElectronicsIndustry,(inChinese)DuanHaibin,MaGuanjun,WangDaobo,YuXiufenImprovedAntColonyAlgorithmforSolvingContinuousSpaceOptimizationProblemsJJournalofSystemSimulation(SX),,():(inChinese)Frequency(radsec)Phase(deg)Magnitude(dB)VdivAdivmsdiv第卷第期VolNo年月系统仿真学报Oct,··YueYixiang,ZhouLeishan,YueQunxingVisualizedSimulatingandImprovingParticleSwarmOptimizationJJournalofSystemSimulation(SX),,():(inChinese)YangShanlin,KanHongxing,MaXijunAModelofResourceOptimizationandReallocationforSoftwareDevelopmentJJournalofSystemSimulation(SX),,():(inChinese)ZhangFan,ShaoZhijiang,ZhongWeitao,QianJixinDistributedParallelOptimizationComputationEnvironmentBasedonMatlabJJournalofSystemSimulation(SX),,():(inChinese)FengDongqing,ZhangXiping,FeiMinruiOptimizationDesignintegrativeMethodofFuzzyControllerBasedonMATLABJJournalofSystemSimulation(SX),,():(inChinese)WuJiaju,ZhangChaoyan,RenJilin,HidehikoSugimotoAMethodforDesigningNonsymmetryTnetWorkFilterUsedInPWMInvertersJProceedingsoftheCSEE(S),,():(inChinese)MasaakiOhshima,FuminoriNakamuraANovelSinglePhaseUPSInverterbyErrorTrackingModePWMSchemeJTIEEJapan(S),,D():(inJapanese)ZhengChunfang,ZhangBo

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四维可视化多目标寻优方法及其在T型滤波器设计中的应用_英文_

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