altobedecomposed.SuchreplacementwilleffectivelyreducethenumberofensembletrialsrequiredtoobtainmeaningfulIMFs.Technically,band-limitednoisecanbeobtainedbylow-passfilteringthewhitenoise,withthecut-offfrequencybeingtheupperlimitofthesignalcomponentofinterest.ToevaluatetheeffectivenessofthemodifiedEEMD(MEEMD)method,Fouriertransformisfirstperformedonthesignaltogainanoverviewofitsfrequencyspectrum.Asshong[].Essentially,EEMDrepeatedlydecomposestheoriginalsignalwithaddedwhitenoiseintoaseriesofIMFs,byapplyingtheoriginalEMDprocess,andtreatsthe(ensemble)meansofthecorrespondingIMFsduringtherepetitiveprocessasthefinalEEMDdecompositionresult.Thispaperinvestigatestheeffectoftwoparameters–theamplitudeofaddednoiseandthenumberofensembletrials–ontheperformanceoftheEEMDmethod.AfterintroducingthetheoreticalbackgroundoftheEEMDprocess,asimulatedsignalthatpresentsthemodemixingphenomenonisdevelopedtofacilitatequantitativeevaluationofthetwoparameters.Furthermore,itisproposedtoreplacewhitenoisewithnoiseoffinitebandwidthfortheEEMDprocesstoimprovecomputationalefficiency.Subsequently,bothnumericalevaluationsonatestsignalthatmimicrealisticbearingvibrationsignalandexperimentalstudyonvibrationsignalsmeasuredonabearingtestbedhaveverifiedtheeffectivenessoftheimprovedEEMDmethodforbearingdefectdiagnosis.ComparisonwiththeoriginalEMDandEEMDmethodshasdemonstratedthatthemodifiedEEMD(MEEMD)methodismoreeffectiveandcomputationallyefficient,andiswellsuitedforapplicationsinvolvingrotarymachinehealthdiagnosis..ModifiedEEMDmethodWhiletheEEMDmethodsolvestheproblemofmodemixing,thelargenumberofensembletrailspresentsahighcomputationalload.ImprovingthecomputationalefficiencyofEEMDisthusdesired.Thepurposeofaddingwhitenoiseistofacilitatethatcomponentsindifferentscalesofthesignalareproperlyprojectedontoscalesofreferenceestablishedbythewhitenoise[].ThismeansthelowfrequencypartoftheaddedwhitenoisewillaffectthedecompositionresultsoftheEEMDprocess(i.e.reducingmodemixinginthedecomposedIMFs),aslongasitcoversthefrequencyrangeofthesignalofinterest.Incomparison,thehigh-frequencysectionoftheaddedwhitenoisehasnoeffect.ThisindicatesthatimprovementontheComputationalefficiencyoftheEEMDprocesscanbeachievedbyreplacingwhitenoisewithaband-limitednoisetobeaddedtothesignaltobedecomposed.SuchreplacementwilleffectivelyreducethenumberofensembletrialsrequiredtoobtainmeaningfulIMFs.Technically,band-limitednoisecanbeobtainedbylow-passfilteringthewhitenoise,withthecut-offfrequencybeingtheupperlimitofthesignalcomponentofinterest.ToevaluatetheeffectivenessofthemodifiedEEMD(MEEMD)method,Fouriertransformisfirstperformedonthesignaltogainanoverviewofitsfrequencyspectrum.Assho结果,只要它涵盖了感兴趣信号频率范围。在分解过程中,所加白噪声信号高频部分对结果无影响。这就意味着可以通过将白噪声替换为被分解带限噪声来提高EEMD计算效率。这种替换将会有效减少需要用来获得有意义本证模式分量整体实验次数。技术上来讲,带限噪声信号可通过低通滤波白噪声信号来获取,伴随着将感兴趣信号截止频率作为上限。要评估改良EEMD(MEEMD)方法有效性,傅立叶变换是首先被用来推荐作为获得信号频谱概述方法。正如图所示,信号高频成分坐落在约-赫兹地区。因此,-赫兹有限带宽信号被选择添加到作为EEMD分解用信号。图说明,随着整体实验次数不同,分解结果是怎样变化。图显示了IMF和分量x(t)在信号上相关性。相比而言,使用原来EEMD方法取得图所示结果,图是使用修改后EEMD方法获得结果,可以看出,使用修改后方法,高频分量可以很容易地在整体试验后在IMF中确定,而不是以前需要试验。这意味着节省了计算量。图显示结果看出,对于次整体实验,提取IMF和高频分量之间相关系数达到了.。第章试验评价为了评估修改后EEMD方法分析非平稳信号有效性,于轴承测试系统采集振动信号(图)。该系统由直流电动机((LessonCDFT),两个支撑枕块(SKF-),液压缸(米勒ZB),液压泵(ENERPACP),用于轴承转速测量光电编码器。在径向,液压缸为轴承提供了变载荷。加速度计(带宽Hz到kHz)从两个测试轴承测量振动,其中一个种子缺陷轴承带有缺陷(整个外圈滚道有.毫米沟)。设置采样频率为千赫,试验轴承转速为每分,径向预紧力为磅每平方英寸。图显示了俩个相同轴承振动信号::一个没有任何种子缺陷(即轴承是“健康”),一个有缺陷(即轴承是“不健康”)。传统EMD方法首次应用于两个振动信号,结果如图所示,将健康轴承和有缺陷轴承本征模式分量进行了对比,其相应HHT频谱在图显示。可以看出,健康轴承(图(a)),没有明显周期信号被识别,而在缺陷轴承HHT频谱中,一个时间间隔为毫秒周期信号明显显示出来。这样结果来源于滚动体和滚到缺陷定期相互作用结果。可以看出,在图HHT光谱中,高频率分量和中频分量没有明确相互分离,低频分量混合在一起,这就表明混合模式是存在。然后将EEMD原始方法应用到相同振动信号,提取本征分量示于图(左为健康轴承,右为有缺陷轴承),其相应HHT谱如图所示。比较图(b)所示结果,可以看出,在图(b)中,中、高频率成分清楚分开。对于有缺陷轴承,毫秒周期信号被识别。此外,低频成分不再混在一起。当将MEEMD方法应用于振动信号,振动信号频率范围第一次被估计用来确定被添加用来促进EEMD过程噪声信号合适带宽。随后,这样带限噪声(可达千赫)被添加到被分析振动信号。在以分解MEEMD信号(健康和有缺陷轴承)HHT光谱图(图)中,可以明显看出,MEEMD方法表现优于EMD方法,其结果显示在图。。此外,与原EEMD方法相比,MEED方法在降低低频范围内模式混合现象表现更好,如图b所示。为了评估计算成本,原EEMD和修改后EEMD方法在同一台拥有.GHz双核CPU和GBRAM笔记本电脑MATLAB环境下运行,对于原始EEMD方法,花费了约秒来完成全部工作,而对于MEEMD,才花费约秒。这表明,MEEMD方法不仅能有效地消除模式混合,也比原来EEMD方法更高效。要系统评估MEEMD方法计算效率,将从内部和外部滚道缺陷分别为、.、.英寸轴承上获得数据进行了分析。轴承在不同旋转速度(,和RPM)下进行测试测试。传统EEMD和改进后EEMD计算时间对比在图和图中已显示,更进一步数据列于表格和中。可以看出,基于运行环境,计算效率提高了到。这就意味着改进后EEMD方法可以广泛应用于原EEMD检测轴承故障领域来提高效率。第章结论整体经验模式分解信号方法已被研究用于信号分解,两个参数影响EEMD方法性能:噪声增加幅度和整体实验数量,这已经用模拟信号进行了系统研究。根据分析,修改后EEMD方法,即MEEMD,已经被提出来了。这种方法使用带限噪声来代替白噪声使得EEMD计算过程简便,从而大幅提高其计算效率。比较研究使用从滚动轴承获得模拟信号和振动信号证明,EEMD方法在消除模式混合上是优于传统EMD方法,而修改后EEMD即MEEMD,不仅仅计算更高效,而且算法更有效。EEMD和MEEMD数据驱动性质使得他们能够潜在适应于应用,当算法可重构性被需要来更好地适应变化环境情况。ng[].Essentially,EEMDrepeatedlydcomposestheoriginalsignalwithaddedwhitenoiseintoaseriesofIMFs,byapplyingtheoriginalEMDprocess,andtreatsthe(ensemble)meansofthecorrespondingIMFsduringtherepetitiveprocessasthefinalEEMDdecompositionresult.Thispaperinvestigatestheeffectoftwoparameters–theamplitudeofaddednoiseandthenumberofensembletrials–ontheperformanceoftheEEMDmethod.Afterintroducingthetheoreticalbac中文字附录附录A外文资料翻译MachanicalSystermsandSignalProcessing()PerformanceenhancementofensembleempiricalmodedecompositionAbstractEnsembleempiricalmodedecomposition(EEMD)isanewlydevelopedmethodaimedateliminatingmodemixingpresentintheoriginalempiricalmodedecomposition(EMD).Toevaluatetheperformanceofthisnewmethod,thispaperinvestigatestheeffectoftwoparameterspertinenttoEEMD:theamplitudeofaddedwhitenoiseandthenumberofensembletrials.AtestsignalwithmodemixingthatmimicsrealisticbearingvibrationsignalsmeasuredonabearingtestbedwasdevelopedtoenablequantitativeevaluationoftheEEMDandprovideguidanceonhowtochoosethetwoparametersappropriatelyforbearingsignaldecomposition.Subsequently,amodifiedEEMD(MEEMD)methodisproposedtoreducethecomputationalcostoftheoriginalEEMDmethodaswellasimprovingitsperformance.NumericalevaluationandsystematicstudyusingvibrationdatameasuredonanexperimentalbearingtestbedverifiedtheeffectivenessandcomputationalefficiencyoftheproposedMEEMDmethodforbearingdefectdiagnosis..IntroductionInrecentyears,time–frequencyandtime-scaleanalysistechniquessuchasshorttimeFouriertransform(STFT)[]andwavelettransform[,]havebeenincreasinglyinvestigatedfornon-stationaryand/ornonlinearsignalprocessinginmachinehealthdiagnosis.Thesetechniques,whilehavingshowntobesuccessfulinvariousapplications,arenon-adaptiveinnature.Asaresult,oncethewindowtypeorabasewavelethasbeenchosen,theanalysisfunctionremainsthesameduringthesubsequentsignaldecompositionprocess.Incomparison,theHilbert–Huangtransform(HHT)[,]decomposesasignalintoasetofintrinsicmodefunctions(IMFs)throughtheempiricalmodedecomposition(EMD)process,thusonlyinvolvingthesignalbeinganalyzeditselfinsteadofrequiringananalysisfunctiontobeconvolutedwith.Asaresult,itpresentsadata-drivenapproachtodealingwithnon-stationarityand/ornonlinearityinthesignal.WhiletheHHTtechniquehasbeenappliedtovariousfields,suchasmachinehealthmonitoringandstructuraldamagedetection[–],filteringanddenoising[,],andbioscience[–],aproblemthathasremainedexistingintheEMDprocessisthemodemixing,whichresultsfromsignalintermittency[–].ToimprovetheEMDmethod,theensembleempiricalmodedecomposition(EEMD)methodhasbeenrecentlyproposedtoeliminatemodemixing[].Essentially,EEMDrepeatedlydecomposestheoriginalsignalwithaddedwhitenoiseintoaseriesofIMFs,byapplyingtheoriginalEMDprocess,andtreatsthe(ensemble)meansofthecorrespondingIMFsduringtherepetitiveprocessasthefinalEEMDdecompositionresult.Thispaperinvestigatestheeffectoftwoparameters–theamplitudeofaddednoiseandthenumberofensembletrials–ontheperformanceoftheEEMDmethod.AfterintroducingthetheoreticalbackgroundoftheEEMDprocess,asimulatedsignalthatpresentsthemodemixingphenomenonisdevelopedtofacilitatequantitativeevaluationofthetwoparameters.Furthermore,itisproposedtoreplacewhitenoisewithnoiseoffinitebandwidthfortheEEMDprocesstoimprovecomputationalefficiency.Subsequently,bothnumericalevaluationsonatestsignalthatmimicrealisticbearingvibrationsignalandexperimentalstudyonvibrationsignalsmeasuredonabearingtestbedhaveverifiedtheeffectivenessoftheimprovedEEMDmethodforbearingdefectdiagnosis.ComparisonwiththeoriginalEMDandEEMDmethodshasdemonstratedthatthemodifiedEEMD(MEEMD)methodismoreeffectiveandcomputationallyefficient,andiswellsuitedforapplicationsinvolvingrotarymachinehealthdiagnosis..ModifiedEEMDmethodWhiletheEEMDmethodsolvestheproblemofmodemixing,thelargenumberofensembletrailspresentsahighcomputationalload.ImprovingthecomputationalefficiencyofEEMDisthusdesired.Thepurposeofaddingwhitenoiseistofacilitatethatcomponentsindifferentscalesofthesignalareproperlyprojectedontoscalesofreferenceestablishedbythewhitenoise[].ThismeansthelowfrequencypartoftheaddedwhitenoisewillaffectthedecompositionresultsoftheEEMDprocess(i.e.reducingmodemixinginthedecomposedIMFs),aslongasitc 中文2930字附录附录A外文资料翻译MachanicalSystermsandSignalProcessing13(2010)PerformanceenhancementofensembleempiricalmodedecompositionAbstractEnsembleempiricalmodedecomposition(EEMD)isanewlydevelopedmethodaimedateliminatingmodemixingpresentintheoriginalempiricalmodedecomposition(EMD).Toevaluatetheperformanceofthisnewmethod,thispaperinvestigatestheeffectoftwoparam