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1、SAEPaper2001-01-1471AComparisonofthenewlyProposedGaborOrderTrackingTechniquevs.OtherOrderTrackingMethodsMichaelF.AlbrightGeneralManagerSignal.XTechnologiesLLCShieQianNationalInstrumentsCorporationGaborOrderTrackingSAENoise&VibrationConferenceMay1,2001RoushIndustriesInc.,RoushAnatrolDivisio
2、nWhatisanOrder•AnOrderistheperiodicresponsetoperiodicforcingmodifiedbypathdynamics•Orderisexpressedinmultiplesoftheunderlyingperiodicprocesssuchasshaftrotationspeed,gearmesh,firingfrequency,etc.•Traditionally,OrdermagnitudeisshownagainstacoarseRPMorTimeaxisGaborOrderTrackingSAENoise&Vibrat
3、ionConferenceMay1,2001WhatisOrderTracking•Amethodtoextracttheinstantaneousfrequencyandamplitudemodulationofharmoniccomponentsfromacomplexsignal•Methodsare:⇒Frequencydomain,PowerspectraagainstacoarseRPMaxis⇒TimeDomain,Vold-Kalman⇒Time/Frequencydomain,GaborOrderTracking(GOT)GaborOrderTrackin
4、gSAENoise&VibrationConferenceMay1,2001TheDiscreteGaborExpansion•RepresentsasignalasaweightedSomeGaborAtomssummationoftimeshiftedandfrequencymodulatedelementaryfunctions(GaborAtoms)M−1N−1j2πnk/NS(k)=∑∑Cm,nh(k−m∆M)emn¬GaborCoefficientsGaborSamplingLatticeGaborOrderTrackingSAENoise&VibrationC
5、onferenceMay1,2001TheGaborTransform•AlsoknownastheShortTimeFourierTransform(STFT)orequivalently,theinverseGaborExpansion1L−1*−j2πnk/NCm,n=∑S(k)γ(k−m∆M)ek=0•Therelationshipbetweentheelementaryfunctionh(k)andwhatisknownasitsDualγ(k),isthekeytounderstandingtheGaborTransformanditsinverse,theGa
6、borexpansionM−1N−1j2πnk/NS(k)=∑∑Cm,nh(k−m∆M)emn1Firstpublishedin1980byB.BastiaansGaborOrderTrackingSAENoise&VibrationConferenceMay1,2001TheDualFunctionRelationship•OrthogonalTransformations⇒Asignalisexpressedintermsofitssimilaritytoapre-selectedfamilyoforthogonalbasisfunctions⇒Therefore,re
7、constructionisintermsoftheidenticalfamilyofbasisfunctions−Examples:FourierTransform,WaveletTransformSimple2Dmatrixanalogy⎧S1⎫⎡10⎤⎧C1⎫[]⎧C1⎫⎧C1⎫⎡10⎤⎧S1⎫⎡Ψ1⎤⎧S1⎫⎨S⎬=⎢⎥⎨C⎬=Ψ1
8、Ψ2⎨C⎬⎨⎬=⎢⎥⎨⎬=⎢⎥⎨⎬⎩2⎭⎣01⎦⎩2⎭⎩2⎭⎩C2⎭⎣01⎦⎩S2⎭⎣Ψ2⎦⎩S2⎭GaborOrderTrackingSAENoise&VibrationCo
