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英文翻译系别专业班级学生姓名学号指导教师报告日期DataCurveFittingBasedonMATLABCurvefittingistheprocessofconstructingacurve,ormathematicalfunction,thathasthebestfittoaseriesofdatapoints,possiblysubjecttoconstraints.Curvefittingcaninvolveeitherinterpolation,whereanexactfittothedataisrequired,orsmoothing,inwhichasmoothfunctionisconstructedthatapproximatelyfitsthedata.Arelatedtopicisregressionanalysis,whichfocusesmoreonquestionsofstatisticalinferencesuchashowmuchuncertaintyispresentinacurvethatisfittodataobservedwithrandomerrors.Fittedcurvescanbeusedasanaidfordatavisualization,toinfervaluesofafunctionwherenodataareavailable,andtosummarizetherelationshipsamongtwoormorevariables.Extrapolationreferstotheuseofafittedcurvebeyondtherangeoftheobserveddata,andissubjecttoadegreeofuncertaintysinceitmayreflectthemethodusedtoconstructthecurveasmuchasitreflectstheobserveddata.ResearchandApplicationofaNewMethodofCurveFitting.Thetechniqueofcurvefittingisusedproverbiallyfortheimageprocessing,reverseengineering,testdataprocessing,etc.Itisinequitabletoprocessphysicalparametersbysomeusualmethodsofcurvefitting.Thosemethodsareperformedonlybyminimizingthefittingerrorofonephysicalparameter,butdonottakeotherparametersintoaccount.ThenewmethodofcurvefittingprocesseseachphysicalparameterequallyThesimulationalsoprovesthatthisnewcurvefittingmethodisrightandeffective.Intheexperimentofsoundvelocity,thevoltammetrytomeasuretheresistanceexperimentandthevolt-amperecharacteristicofdiodeexperimentdataprocessingasanexample,introducedtheexperimentdataprocessingbasedonMATLAB.Withthetraditionalexperimentaldataprocessingmethods,experimentaldataisprocessedbyusingMATLABcaneffectivelyavoidtheerrorcausedbymanualprocessing,butalsocanreducethecomputationalworkload,obtainaccuratecurvefitting,therebyincreasingtheaccuracyofdataprocessingandfast,romgraphicdisplayresultsalsocanbemoreintuitivetojudgethevalidityoftheexperiment.MathematicalexpressionGivensetofdiscretedata(xk,yk)(k=1,2,…,m),(1)Wherexkistheindependentvariablex(scalarorvector,i.e.,amono-orpolyhydricvariable)values;ykof(scalar)correspondingtothevalueofthedependentvariabley.Curvefittingistoseektosolvetheproblemof(1)toadaptthelawsoftheanalyticalexpressionofthebackgroundy=f(x,b),(2)Makingbestapproximationinsomesenseorfit(1),(x,b)iscalledfittingmodel;?Parameterstobedetermined,whenb)onlyappearswhenthelinear,calledalinearmodel?otherwisenon-linear.Amount(k=1,2,…，m)Inxkplacecalledresidualorremainingfit,Thestandardmeasureofgoodnessoffitisusually或Whereωk0asweightcoefficientorweight(Unlessotherwisespecified,generallytakentobetheaverageweight,wk(k=1,2,…,m),Atthistimewithoutmentionweight).Whentheparameterb)makeT(b))orQ(b))toachievethemosthours,Appropriate(2)arereferredto(1)theweightedChebyshevfittingmeaningorweightedleastsquaressense,latterismoresimpleandmostcommonlyusedinthecalculation.Generallinearmodeltodeterminethemodelparametersareparametersb)generalizedpolynomialcoefficients,thatf(x,b)=b0g0(x)+b1g1(x)+…bngn(x)(3)Whereing0,g1,...,gncalledbasisfunctions.Gjonvariousdifferentchoicesmayconstituteavarietyoftypicalandcommonlyusedlinearmodel.Fromthepointofviewoffunctionapproximation,equation(3)canbeapproximatedreflectthenatureofmanyofnonlinearmodels.Intheleastsquaressense(3)fittingalinearmodelwithadiscretesetofpoints(1),parameterbcanbeobtainedbysolvingequations=0(i=0,…,n)todetermine,thatsolutiononb0,b1,…,bnoflinearalgebraicequations(i=0,1,…，n),(4)Formula(i,j＝0,1,…，n),Equations(4)commonlyreferredtoasthenormalequationorthenormalequation,whenmn,generallyhaveauniquesolution.Asforthecaseofnon-linearmodelandtheprincipleofleastsquares,theparameterb)canbedetermined(seenumericalsolutionofnonlinearequations,optimization)nonlinearequationsorcalculationsaboutthemethodoptimization.SelectthemodelForagivendiscretedata(1),theneedtoproperlyselectthegeneralmodel(2)ofthefunctionf(x,b)thetypeandspecificform,whichisthebasisoffittingresults.Ifknown,(1)theactualbackgroundofthelaw,thatisthedependentvariableydependenceoftheempiricalformulaoftheindependentvariablexhasanexpressiondetermineddirectlytakeappropriateempiricalformulaisfittingmodel.Onthecontrary,throughthemodel(3)ofthebasisfunctionsg0,g1,...,gn(numberandtypes)ofdifferentchoices,eachcorrespondingproposedmergerbychoosingthegoodeffect.Functiong0,g1,...,gnadaptationplaysarolethemodelfortesting,itisalsoknowntestfunction.Anotherwayis:thenumberandtypesintoasufficientnumberoftestfunctionsinthemodel(3),bymeansofstatisticalmethodsinmathematicalcorrelationanalysisandtestofsignificanceofthetestfunctioncontainsscreenedindividuallyorsequentiallywithestablishmoreappropriatemodel(seeregressionanalysis).Certainly,theabovemethodmayfitresiduals(asanewdiscretedata)isperformedagaintocompensateforthelackofthefirstfitting.Inconclusion,whentheintrinsiclinkbetweenthevariablesinthedataisnotclear,asthechoicetoadaptthemodeltofitgenerallyrequiresrepeatedtestingandanalysistoidentify.Procedure（一）Drawascatterplot,selecttheappropriatetypeofcurve.Generallybasedonthenatureoftheinformationcanbecombinedwiththeexpertisetodeterminethetypeofcurv