Hilbert transform in vibration analysis

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1、MechanicalSystemsandSignalProcessing25(2011)735–802ContentslistsavailableatScienceDirectMechanicalSystemsandSignalProcessingjournalhomepage:www.elsevier.com/locate/jnlabr/ymsspTutorialReviewHilberttransforminvibrationanalysisnMichaelFeldmanFacultyofMec

2、hanicalEngineering,Technion—IsraelInstituteofTechnology,IsraelarticleinfoabstractArticlehistory:ThispaperisatutorialonHilberttransformapplicationstomechanicalvibration.TheReceived18July2010approachisaccessibletonon-stationaryandnonlinearvibrationapplic

3、ationinthetimeAccepted29July2010domain.ItthrivesonalargenumberofexamplesdevotedtoillustratingkeyconceptsonactualmechanicalsignalsanddemonstratinghowtheHilberttransformcanbetakenKeywords:advantageofinmachinediagnostics,identificationofmechanicalsystemsan

4、dHilberttransformdecompositionofsignalcomponents.Envelope&2010ElsevierLtd.Allrightsreserved.InstantaneousfrequencyNonlinearsystemidentificationNon-stationarysignaldecompositionContents1.Introduction.......................................................

5、...................................7371.1.BriefhistoryoftheHilberttransform................................................................7371.2.Hilberttransformapplicationinvibration............................................................7382.Not

6、ationandmainpropertiesoftheHilberttransform........................................................7382.1.Localvs.globalestimations........................................................................7382.2.TheHilberttransformnotation...............

7、......................................................7392.3.MainpropertiesoftheHilberttransform.............................................................7392.4.TheHilberttransformofmultiplication.....................................................

8、.........7393.Analyticsignal........................................................................................7403.1.Polarnotation..................................................................................7413.2.Angularposi