日》大市回顧及展望.ppt

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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