外文翻译-基于MATLAB的数据曲线拟合分析Word格式文档下载.docx
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外文翻译-基于MATLAB的数据曲线拟合分析Word格式文档下载.docx
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DataCurveFittingBasedonMATLAB
Curvefittingistheprocessofconstructingacurve,ormathematicalfunction,thathasthebestfittoaseriesofdatapoints,possiblysubjecttoconstraints.Curvefittingcaninvolveeitherinterpolation,whereanexactfittothedataisrequired,orsmoothing,inwhicha"
smooth"
functionisconstructedthatapproximatelyfitsthedata.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.
Mathematicalexpression
Givensetofdiscretedata(xk,yk)(k=1,2,…,m),
(1)
Wherexkistheindependentvariablex(scalarorvector,i.e.,amono-orpolyhydricvariable)values;
ykof(scalar)correspondingtothevalueofthedependentvariabley.Curvefittingistoseektosolvetheproblemof
(1)toadaptthelawsoftheanalyticalexpressionofthebackground
y=f(x,b),
(2)
Makingbestapproximationinsomesenseorfit
(1),(x,b)iscalledfittingmodel;
?
Parameterstobedetermined,whenb)onlyappearswhenthelinear,calledalinearmodel?
otherwisenon-linear.
Amount
(k=1,2,…,m)
Inxkplacecalledresidualorremainingfit,Thestandardmeasureofgoodnessoffitisusually
或
Whereωk>
0asweightcoefficientorweight(Unlessotherwisespecified,generallytakentobetheaverageweight,wk(k=1,2,…,m),Atthistimewithoutmentionweight).Whentheparameterb)makeT(b))orQ(b))toachievethemosthours,Appropriate
(2)arereferredto
(1)theweightedChebyshevfittingmeaningor
weightedleastsquaressense,latterismoresimpleandmostcommonlyusedinthecalculation.
Generallinearmodeltodeterminethemodelparametersareparametersb)generalizedpolynomialcoefficients,that
f(x,b)=b0g0(x)+b1g1(x)+…bngn(x) (3)
Whereing0,g1,...,gncalledbasisfunctions.Gjonvariousdifferentchoicesmayconstituteavarietyoftypicalandcommonlyusedlinearmodel.Fromthepointofviewoffunctionapproximation,equation(3)canbeapproximatedreflectthenatureofmanyofnonlinearmodels.
Intheleastsquaressense(3)fittingalinearmodelwithadiscretesetofpoints
(1),parameter b can be obtained by solving equations=0(i=0,…,n)todetermine,thatsolutiononb0,b1,…,bnoflinearalgebraicequations
(i=0,1,…,n), (4)
Formula(i,j=0,1,…,n),
Equations(4)commonlyreferredtoasthenormalequationorthenormalequation,whenm>
n,generallyhaveauniquesolution.Asforthecaseofnon-linearmodelandtheprincipleofleastsquares,theparameterb)canbedetermined(seenumericalsolutionofnonlinearequations,optimization)nonlinearequationsorcalculationsaboutthemethodoptimization.
Selectthemodel
Foragivendiscretedata
(1),theneedtoproperlyselectthegeneralmodel
(2)ofthefunctionf(x,b)thetypeandspecificform,whichisthebasisoffittingresults.Ifknown,
(1)theactualbackgroundofthelaw,thatisthedependentvariabley
dependenceoftheempiricalformulaoftheindependentvariablexhasanexpressiondetermineddirectlytakeappropriateempiricalformulaisfittingmodel.Onthecontrary,throughthemodel(3)ofthebasisfunctionsg0,g1,...,gn(number
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