电气工程及其自动化毕业设计英语翻译.docx
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电气工程及其自动化毕业设计英语翻译
郑州航空工业管理学院
英文翻译
2011届电气工程及其自动化专业班级
题目遗传算法在非线性模型中的应用
姓名学号
指导教师黄文力职称副教授
二О一一年三月三十日
英语原文:
ApplicationofGeneticProgrammingtoNonlinearModeling
Introduction
Identificationofnonlinearmodelswhicharebasedinpartatleastontheunderlyingphysicsoftherealsystempresentsmanyproblemssinceboththestructureandparametersofthemodelmayneedtobedetermined.Manymethodsexistfortheestimationofparametersfrommeasuresresponsedatabutstructuralidentificationismoredifficult.Oftenatrialanderrorapproachinvolvingacombinationofexpertknowledgeandexperimentalinvestigationisadoptedtochoosebetweenanumberofcandidatemodels.Possiblestructuresarededucedfromengineeringknowledgeofthesystemandtheparametersofthesemodelsareestimatedfromavailableexperimentaldata.Thisprocedureistimeconsumingandsub-optimal.Automationofthisprocesswouldmeanthatamuchlargerrangeofpotentialmodelstructurecouldbeinvestigatedmorequickly.
Geneticprogramming(GP)isanoptimizationmethodwhichcanbeusedtooptimizethenonlinearstructureofadynamicsystembyautomaticallyselectingmodelstructureelementsfromadatabaseandcombiningthemoptimallytoformacompletemathematicalmodel.Geneticprogrammingworksbyemulatingnaturalevolutiontogenerateamodelstructurethatmaximizes(orminimizes)someobjectivefunctioninvolvinganappropriatemeasureofthelevelofagreementbetweenthemodelandsystemresponse.Apopulationofmodelstructuresevolvesthroughmanygenerationstowardsasolutionusingcertainevolutionaryoperatorsanda“survival-of-the-fittest”selectionscheme.Theparametersofthesemodelsmaybeestimatedinaseparateandmoreconventionalphaseofthecompleteidentificationprocess.
Application
Geneticprogrammingisanestablishedtechniquewhichhasbeenappliedtoseveralnonlinearmodelingtasksincludingthedevelopmentofsignalprocessingalgorithmsandtheidentificationofchemicalprocesses.Intheidentificationofcontinuoustimesystemmodels,theapplicationofablockdiagramorientedsimulationapproachtoGPoptimizationisdiscussedbyMarenbach,BettenhausenandGray,andtheissuesinvolvedintheapplicationofGPtononlinearsystemidentificationarediscussedinGray’sanotherpaper.Inthispaper,Geneticprogrammingisappliedtotheidentificationofmodelstructuresfromexperimentaldata.Thesystemsunderinvestigationaretoberepresentedasnonlineartimedomaincontinuousdynamicmodels.
ThemodelstructureevolvesastheGPalgorithmminimizessomeobjectivefunctioninvolvinganappropriatemeasureofthelevelofagreementbetweenthemodelandsystemresponses.Oneexamplesis
(1)
Where
istheerrorbetweenmodeloutputandexperimentaldataforeachofNdatapoints.TheGPalgorithmconstructsandreconstructsmodelstructuresfromthefunctionlibrary.SimplexandsimulatedannealingmethodandthefitnessofthatmodelisevaluatedusingafitnessfunctionsuchasthatinEq.
(1).ThegeneralfitnessofthepopulationimprovesuntiltheGPeventuallyconvergestoamodeldescriptionofthesystem.
TheGeneticprogrammingalgorithm
Forthisresearch,asteady-stateGenetic-programmingalgorithmwasused.Ateachgeneration,twoparentsareselectedfromthepopulationandtheoffspringresultingfromtheircrossoveroperationreplaceanexistingmemberofthesamepopulation.Thenumberofcrossoveroperationsisequaltothesizeofthepopulationi.e.thecrossoverrateis100℅.Thecrossoveralgorithmusedwasasubtreecrossoverwithalimitonthedepthoftheresultingtree.
Geneticprogrammingparameterssuchasmutationrateandpopulationsizevariedaccordingtotheapplication.Moredifficultproblemswheretheexpectedmodelstructureiscomplexorwherethedataarenoisygenerallyrequirelargerpopulationsizes.Mutationratedidnotappeartohaveasignificanteffectforthesystemsinvestigatedduringthisresearch.Typically,avalueofabout2℅waschosen.
Thefunctionlibraryvariedaccordingtoapplicationrateandwhattypeofnonlinearitymightbeexpectedinthesystembeingidentified.Acoreoflinearblockswasalwaysavailable.Itwasfoundthatspecificnonlinearitysuchaslook-uptableswhichrepresentedaphysicalphenomenonwouldonlybeselectedbytheGeneticProgrammingalgorithmifthatnonlinearityactuallyexistedinthedynamicsystem.
Thisallowsthesystemtobetestedforspecificnonlinearities.
Programmingmodelstructureidentification
EachmemberoftheGeneticProgrammingpopulationrepresentsacandidatemodelforthesystem.Itisnecessarytoevaluateeachmodelandassigntoitsomefitnessvalue.Eachcandidateisintegratedusinganumericalintegrationroutinetoproduceatimeresponse.Thissimulationtimeresponseiscomparedwithexperimentaldatatogiveafitnessvalueforthatmodel.Asumofsquarederrorfunction(Eq.
(1))isusedinalltheworkdescribedinthispaper,althoughmanyotherfitnessfunctionscouldbeused.
Thesimulationroutinemustberobust.Inevitably,someofthecandidatemodelswillbeunstableandtherefore,thesimulationprogrammustprotectagainstoverflowerror.Also,allsystemmustreturnafitnessvalueiftheGPalgorithmistoworkproperlyevenifthosesystemsareunstable.
Parameterestimation
ManyofthenodesoftheGPtreescontainnumericalparameters.Thesecouldbethecoefficientsofthetransferfunctions,againvalueorinthecaseofatimedelay,thedelayitself.Itisnecessarytoidentifythenumericalparametersofeachnonlinearmodelbeforeevaluatingitsfitness.Themodelsarerandomlygeneratedandcanthereforecontainlinearlydependentparametersandparameterswhichhavenoeffectontheoutput.Becauseofthis,gradientbasedmethodscannotbeused.GeneticProgrammingcanbeusedtoidentifynumericalparametersbutitislessefficientthanothermethods.TheapproachchoseninvolvesacombinationoftheNelder-Simplexandsimulatedannealingmethods.Simulatedannealingoptimizesbyamethodwhichisanalogoustothecoolingprocessofametal.Asametalcools,theatomsorganizethemselvesintoanorderedminimumenergystructure.Theamountofvibrationormovementintheatomsisdependentontemperature.Asthetemperaturedecreases,themovement,thoughstillrandom,becomesmallerinamplitudeandaslongasthetemperaturedecreasesslowlyenough,theatomsorderthemselvesslowlyenough,theatomsorderthemselvesintotheminimumenergystructure.Insimulatedannealing,theparametersstartoffatsomerandomvalueandtheyareallowedtochangetheirvalueswithinthesearchspacebyanamountrelatedtoaquantitydefinedassystem‘temperature’.Ifaparameterchangeimprovesoverallfitness,itisaccepted,ifitreducesfitnessitisacceptedwithacertainprobability.Thetemperaturedecreasesaccordingtosomepredetermined‘cooling’scheduleandtheparametervaluesshouldconvergetosomesolutionasthetemperaturedrops.Simulatedannealinghasprovedparticularlyeffectivewhencombineswithothernumericaloptimizationtechniques.
OnesuchcombinationissimulatedannealingwithNelder-simplexisan(n+1)dimensionalshapewherenisthenumberofparameters.Thissimplesexploresthesearchspaceslowlybychangingitsshapearoundtheoptimumsolution.Thesimulatedannealingaddsarandomcomponentandthetemperatureschedulingtothesimplexalgorithmthusimprovingtherobustnessofthemethod.
Thishasbeenfoundtobearobustandreasonablyefficientnumericaloptimizationalgorithm.Theparameterestimationphasecanalsobeusedtoidentifyothernumericalparametersinpartofthemodelwherethestructureisknownbutwherethereareuncertaintiesaboutparametervalues.
RepresentationofaGPcandidatemodel
Nonlineartimedomaincontinuousdynamicmodelscantakeanumberofdifferentforms.Twocommonrepresentationsinvolvesetsofdifferentialequationsorblockdiagrams.Boththeseformsofmodelarewellknownandrelativelyeasytosimulate.Eachhasadvantagesanddisadvantagesforsimulation,visualizationandimplementationinaGeneticProgrammingalgorithm.Blockdiagramandequationbasedrepresentationsareconsideredinthispaperalongwithathirdhybridrepresentationincorporatingintegralanddifferentialoperatorsintoanequationbasedrepresentation.
Choiceofexperimentaldataset——experimentaldesign
Theidentificationofnonlinearsystemspresentsparticularproblemsregardingexperimentaldesign.Thesystemmustbeexcitedacrossthefrequencyrangeofinterestaswithalinearsystem,butitmustalsocovertherangeofanynonlinearitiesinthesystem.Thiscouldmeanensuringthattheinputshapeissufficientlyvariedtoexcitedifferentmodesofthesystemandthatthedatacoverstheoperationalrangeofthesystemstatespace.
Alargetrainingdatasetwillberequiredtoidentifyanaccuratemodel.Howeverthesimulationtimewillbeproportionaltothenumberofdatapoints,sooptimizationtimemustbebalancedagainstquantityofdata.ArecommendationonhowtoselectefficientstepandPRBSsignalstocovertheentirefrequencyrageofinterestmaybefoundinGodfreyandLjung’stexts.
Modelvalidation
Animportantpartofanymodelingprocedureismodelvalidation.Thenewmodelstructuremustbevalidatedwithadifferentdatasetfromthatusedfortheoptimization.Therearemanytechniquesforvalidationofnonlinearmodels,thesimplestofwhichisanaloguematchingwherethetimeresponseofthemodeliscomparedwithavailableresponsedatafromtherealsystem.ThemodelvalidationresultscanbeusedtorefinetheGeneticProgrammingalgorithmas