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ID:58615975
大小:226.00 KB
页数:16页
时间:2020-10-22
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1、VibratingBeamModelingResultsPrime(Group7)Abby,Jacob,TJ,LeoThemodelanddataWeareattemptingtousetheordinarydifferentialequationmodel:ThisisassumingthatthebeambehaveslikeanunderdampedharmonicoscillatorC=0.68439333standarderror(C)=0.0089773795%confidenceinterval:(0.66643859,0.70234806)K=1525.693
2、399standarderror(K)=0.35010895%confidenceinterval:(1524.993183,1526.393614)σ2=1.0559e-010noticethemodelonlyappearstoestimateonefrequencyofthethreethatthedataappearstocontain.TheOptimizationAlgorithmThedatavectorismassagedbytruncatingatthemaxandaddingtheaveragebackintoit5000timesAloopusingfm
3、insearchaddsrandomvectorstoCandK.Thevaluesthatproducethelowestleast-squarescostarekept.C1=-0.64450000standarderror(C1)=0.0090848395%confidenceinterval:(-0.66266967,-0.62633033)K1=-1530.600000standarderror(K1)=0.35482595%confidenceinterval:(-1531.309651,-1529.890349)σ12=4.056e-011comparedtoσ
4、2=1.0559e-010cost1=1.9064e-007cost=5.1366e-007NewresidualplotOldresidualplotIdeallytheplotshouldberandomaboutzeroTheoccurrenceofthediagonalpatternimpliesthattheremaybeabetterfitmodelResidualPlotsQQDistributionFirstQQplotSecondQQplotTheQQornormalprobabilityplotshowsthatthefunctiondoesn’thave
5、anormaldistribution.DiagnosticPlotsFirstC,KvaluesSecondC,KvaluesExhibitsnon-constantvarianceTheODEModelThemodelappearstogenerallymimicthebehaviorofthesystemItseemstoonlycaptureoneoutofthreefrequenciesdisplayedItshowsresidualsthatarenotevenlydistributedorrandomaboutzeroAnimprovedmodelshouldb
6、eattemptedPDEModelNext,weattemptedtofitthePDEmodeltothedataThePDEModelInitialparameterguessesPDEModelInitialparameterguessThemodelcatchesthefirsttwo,butmissesthethirdfrequencyPDEModelSecondParameterGuessPDEModelSecondParameterGuessFurtherImprovementsOptimizetheparameterselectionUsestatisti
7、calanalysisforthePDEmodelofourdataAttemptalternatestatisticalanalysistechniquesCollectmultipledatasetsandimprovelaboratorysettingsResearchcurrentliteratureformoreaccuratemodels
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