Determining the Accuracy of Modal Parameter Estimation Methods确定模态参数估计方法的准确性

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1、IMACXFebruary1992DeterminingtheAccuracyofModalParameterEstimationMethodsbyMichaelLeePh.D.,P.E.&MarkRichardsonPh.D.StructuralMeasurementSystemsMilpitas,CAAbstractwhere:{X(w)}=n-vectorofFouriertransformeddisplacementresponsesThemostcommontypeofmodaltestingsystemtodayusesanFFTanalyzertomeasureasetofFr

2、equencyResponse{F(w)}=n-vectorofFouriertransformedforceFunctions(FRFs)fromastructure,andthenusesaparameterinputsestimation(curvefitting)methodtodeterminethestructure’s[H(w)]=(nbyn)matrixofFRFsmodalpropertiesfromtheFRFmeasurements.Thecurven=numberoftestdegrees-of-freedom(DOFs)onfittingmethodtypicall

3、y“fits”ananalyticalmodeltotheFRFthestructuredata,(oritsequivalentImpulseResponsedata)andestimatesw=thefrequencyvariableoftheunknownmodalparametersofthemodelaredeterminedbythisprocess.Theseparameterestimatesarethenassumedtobethecorrectmodalparametersofthestructure.TheFRFmatrixcanbewrittenintermsofmo

4、dalparametersas:Inthispaper,anumberof“standardtestcases”ofsynthesizedFRFsarepresentedfortestingmodalparametermodes[]å[]()[*](*)estimationmethods.TwelvedifferentFRFsarepresented,thatH(w)=Rk2jjw-pk-Rk2jjw-pkaresynthesizedusingtheparametersforthreemodes.k=1Frequencyspacingsbetweenthemodesandmodaldampi

5、ng(2)valuesarevariedtomakeupthedifferentcases,whichrangefromlightmodalcoupling(ormodaldensity)toveryheavywhere:[R]=(nbyn)matrixofresiduesformodekcoupling.RandomnoiseisalsoaddedtothesynthesizedFRFs(k)tosimulatenoisymeasurements,givingatotaloftwenty-fourdifferenttestcases.Theadvantageofthisapproachto

6、curvep=s+jw=complexpolelocationforkkkfittertestingis,ofcourse,thattherightanswers(themodalmode(k)parametersusedtosynthesizetheFRFs)areknown,andcanthereforebeusedasthebasisfordeterminingtheaccuracyofs=modaldampingformode(k)kthefitter.w=modalfrequencyformode(k)kTwodifferentcurvefittingmethods,anSDOF(

7、singlemodes=thenumberofmodesinthemodelmode-at-a-time)andanMDOF(multiplemodes-at-a-time)*-denotesthecomplexconjugaterationalfractionpolynomialfitter,weretriedonthetestcaseFRFs,andtheresultsarepresented.Inpub