基于EMD的滚动轴承故障诊断方法的研究
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摘要
滚动轴承是工业生产中使用最广泛的机械零件，也是机械设备的重要故障源之一。准确判断轴承工作状态直接关系到整台机组乃至整条生产线的生产质量和安全。研究滚动轴承的监测和诊断技术，对于避免重大事故及变革维修体制等具有重要的理论研究价值和实际应用意义。
本文首先对滚动轴承的振动特性进行了研究，得到滚动轴承分别在内圈、外圈以及滚动体存在缺陷时的时频特性。对所采集的振动信号中的若干问题，如存在奇异点、趋势项和较强的噪声，进行了研究，提出了冗余二代小波去噪法，有效地去除了信号中的噪声成分，提高了信号的信噪比。同时利用EMD去趋势项法消除了采集信号中的趋势项。
其次，在对EMD基本理论、算法及其特性进行研究的基础上，针对EMD在实际运用中存在的端点效应、模态混合及虚假模式等问题进行了研究，提出了有效解决这些问题的方法：把支持向量机和窗函数有机结合起来，消除了EMD的端点效应；利用EEMD法解决了模态混合问题；根据滚动轴承的振动特性，以峭度为参数，很好地提取出含有故障信息的固有模态函数，使EMD具有更大的实用价值。
最后，在此基础上，提出了IEEMD-SK滚动轴承故障诊断法。仿真与实验证明，该方法可以有效提取出滚动轴承的故障特征频率，使故障诊断结果更准确。
Rolling element bearing is one of the most widely used components for industrialproduction as well as one is easily damaged in an mechanical equipment.Its workingcondition has influence on product quality and working safety in industry directly.So itis very significant to research on bearing condition monitoring and fault diagnosistechniques,especially for bearing early fault.
In this paper,first study on vibration characteristics of the rolling element bearingand time-frequency characteristics of bearing when there is an defect in the inner ring,outer ring or rolling element is gained. Then, a certain number of problems in the actualacquisition vibration signals, such as the existence of singular points, the trend and thestrong noise, are studied. EMD is used to eliminate the trend of the acquisition signal,and The Second generation redundant wavelet denoising method are adopted toeliminate the noise components in the signal, and improves the signal-to-noise ratioeffectively.
Then, on the basis of EMD basic theory, algorithm and its characteristics,study onend effect,mode mixture and false modes of EMD, and put forward the effectivesolutions to these problems: the support vector machine and window function werecombined to eliminate EMD end effect; the problem of mode mixing was solvedby using the EEMD method; according to the vibration characteristics of rolling bearing,kurtosis was used to chose the intrinsic mode functions containing faultinformation. Through these improvements make EMD a more practical tool.
Finally, IEEMD-SK rolling bearings fault diagnosis method was put forward on thebase of these improvements, and prove that this method can extract the frequency ofrolling bearing fault quickly and accurately through the experiment.
本文首先对滚动轴承的振动特性进行了研究，得到滚动轴承分别在内圈、外圈以及滚动体存在缺陷时的时频特性。对所采集的振动信号中的若干问题，如存在奇异点、趋势项和较强的噪声，进行了研究，提出了冗余二代小波去噪法，有效地去除了信号中的噪声成分，提高了信号的信噪比。同时利用EMD去趋势项法消除了采集信号中的趋势项。
其次，在对EMD基本理论、算法及其特性进行研究的基础上，针对EMD在实际运用中存在的端点效应、模态混合及虚假模式等问题进行了研究，提出了有效解决这些问题的方法：把支持向量机和窗函数有机结合起来，消除了EMD的端点效应；利用EEMD法解决了模态混合问题；根据滚动轴承的振动特性，以峭度为参数，很好地提取出含有故障信息的固有模态函数，使EMD具有更大的实用价值。
最后，在此基础上，提出了IEEMD-SK滚动轴承故障诊断法。仿真与实验证明，该方法可以有效提取出滚动轴承的故障特征频率，使故障诊断结果更准确。
Rolling element bearing is one of the most widely used components for industrialproduction as well as one is easily damaged in an mechanical equipment.Its workingcondition has influence on product quality and working safety in industry directly.So itis very significant to research on bearing condition monitoring and fault diagnosistechniques,especially for bearing early fault.
In this paper,first study on vibration characteristics of the rolling element bearingand time-frequency characteristics of bearing when there is an defect in the inner ring,outer ring or rolling element is gained. Then, a certain number of problems in the actualacquisition vibration signals, such as the existence of singular points, the trend and thestrong noise, are studied. EMD is used to eliminate the trend of the acquisition signal,and The Second generation redundant wavelet denoising method are adopted toeliminate the noise components in the signal, and improves the signal-to-noise ratioeffectively.
Then, on the basis of EMD basic theory, algorithm and its characteristics,study onend effect,mode mixture and false modes of EMD, and put forward the effectivesolutions to these problems: the support vector machine and window function werecombined to eliminate EMD end effect; the problem of mode mixing was solvedby using the EEMD method; according to the vibration characteristics of rolling bearing,kurtosis was used to chose the intrinsic mode functions containing faultinformation. Through these improvements make EMD a more practical tool.
Finally, IEEMD-SK rolling bearings fault diagnosis method was put forward on thebase of these improvements, and prove that this method can extract the frequency ofrolling bearing fault quickly and accurately through the experiment.
引文
[1]陈进主编.机械设备振动监测与故障诊断，上海交通大学出版社，1999
[2]黄文虎,夏松波.刘瑞岩等编著.设备故障诊断原理、技术及应用，科学出版社，1996
[3]徐敏等编著.设备故障诊断手册，西安交通大学出版社，1998
[4]菜进.大型设备状态监测与故障诊断-现状与发展.动态分析与测试技术.1996,23:26~31
[5]佟德纯,李华彪编著.上海科学技术文献出版社，1997
[6]梅宏斌．滚动轴承诊断监测与诊断-理论、方法、系统．北京：机械工业出版社，1995
[7]周福昌．基于循环平稳信号处理的滚动轴承故障诊断方法研究：(博士学位论文)．上海：上海交通大学，2006
[8] N.E.Huang,S.Zheng,R.L.Steven, The empirical mode decomposition and the Hilbertspectrum for nonlinear and non-stationary time series analysis, Proceedings of theRoyal Society of London454(1998)903~995
[9] Gravier B.M.，N.N.J.，Pelstring J.A. An assessment of the application of the Hilbertspectrum to the fatigue analysis of marine risers.Proceedings of the Internationaloffshore and Polar Engineering Conference，2001:P268～275
[10]程军戴,于德介.基于EMD的信号瞬时特征的小波分析方法.地震工程与工程振动.2004,24(2):182~184
[11] Parey,A.,etal.Dynamic modeling of spur gear pair and application of empiricalmode decomposition-based statistiecal analysis for early detection of localizedtooth defect Journal of Sound and Vibration，2006,294(3):547～561
[12]杨世锡，胡劲松，吴昭同.旋转机械振动信号基于EMD的希尔伯特变换和小波变换时频分析比较.中国电机工程学报，2003.23(6):102～107
[13] Ding， H.， et al. Hilbert-Huang transform based signal analysis for thecharacterization of gas-liquid two-phase flow. Flow Measurement andInstrumentation，2007.18(l):37～46
[14] Blaneo-Velaseo，M.，B.Weng，K.E.Barner. ECG signal denoising and baselinewander correction based on the empirical mode decomposition.Computers inBiology and Medicine，2008.38(l):l～13.
[15] V.K. Rai,A.R.M.Bearing fault diagnosis using FFT of intrinsic mode functions inHilbert-Huang Transform. Mechanical Systems and Signal Processing，2007.21:P2607～2615.
[16] Kamath，V.，et al. Empirical Mode Decomposition and Blind Source SeparationMethods for Antijamming with GPS Signals.in Position，Location，And Navigationsymposium，2006IEEE/ION.2006.
[17]雷亚国，何正嘉，瞥艳阳.基于特征评估和神经网络的机械故障诊断模型.西安交通大学学报，200640(5):558～562.
[18]杨建文，贾民平.希尔伯特—黄谱的端点效应分析及处理方法研究.振动工程学报，2006.19(2):283～288.
[19] Deng YJ，W.W.，QIAN C C.Boundary-proeessing-technique in EMD method andHilbert transform. Chinese Science bulletin,2001.46(11):954～961.
[20]胡爱军.Hilbert-Huang变换在旋转机械振动信号分析中的应用研究.华北电力大学博士学位论文，2008
[21] G.G.S.PEGRAM，M.C.P. Empirical mode decomposition using rational splines:anapplication to rainfall time series.Proe.R.Soc.A.2007:pl-20.
[22] Flandrin，P.，P. Goncalves，G Rilling. EMD equivalent filter banks，frominterpretation to applications Hilbert-Huang Transform: Introduction andApplications，2005.
[23]田海泉，基于GA-ANN的滚动轴承诊断研究.江苏大学学位论文,2006
[24] Z.S.Chan,Y.M.Yang,X.S.Wen.Early diagnosis of helicopter gearboxes based onindependent component analysis.Processing of IMS2003:International Conferenceon Intelligent Maintenance Systems.2003:291~295
[25]张永强.软件数值积分误差原因分析及改进办法.机械强度，2006
[26] Sweldens W. The lifting scheme: a custom-design construction of biorthogonalwavelets.Appl Comput Harmon Anal.1996，3(2).186～200
[27]于明月.第二代小波变换在旋转机械故障诊断中的应用研究.南京航空航天大学学位论文，2008
[28]段晨东.基于第二代小波变换的故障诊断技术研究[D].博士学位论文，西安交通大学，2005
[29]崔玲丽，高立新，殷海晨，张建宇.基于第二代小波和EMD的解调方法及其应用研究[J].振动与冲击，2008，27（6）：1～4
[30] Xiaoming Lu,Jine Wang. Bearing fault diagnosis based on redundant secondgeneration wavelet denoising and EEMD.Consumer Electronics, Communicationsand Networks (CECNet),2011International Conference on XianNing.2011
[31] Donoho D L. Denoising by soft-thresholding[J]. IEEE Transaction on InformationTheory,1995,41(3):613~627
[32] Donoho D L,Johnstone I M. Ideal spatial adaptation by wavelet shrinkage.Biometrika[J].1994,81(3).425~455
[33] Pan Quan,Zhang Lei,Dai Guanzhou.Two de-noising methods by wavelettransform.IEEE Transactions on Signal Processing.1999,47(12).3401~3406
[34]何正嘉，訾艳阳，孟庆丰等.机械设备非平稳信号的故障诊断原理及应用[M].北京：高等教育出版社，2001：1～51
[35] N.E.Huang,A New Method For Nonlinear And Non-Stationary Time SeriesAnalysis And Its Application For Civil Infrastructure Health Monitoring,NASAGoddard Space Flight Center,Greenbelt,Maryl and20771,USA
[36]曹冲锋.基于EMD的机械振动分析与诊断方法研究[D].博士学位论文，浙江大学，2009，06
[37] N.E.Huang,Shen Z,Long S R.A new view of nonlinear water waves: the Hilbertspectrum.annu.Rev.Fluid Mech.1999,31:417～457
[38]余波.自适应时频分析方法的理论研究与用应研究.大连：大连理工大学博士论文，1998
[39]于德介,杨宇.机械故障诊断的Hilbert-Huang变换方法.科学出版社
[40]杜陈艳,经验模态分解边缘效应抑制方法综述.仪器仪表学报,2009
[41] ZHAOJP，HUANG D J.Mirror extending and circular spline function for empiricalmode decomposition method [J].Journal of Zhejiang University(SCIENCE)，2001，2:247～252
[42]舒忠平杨智春抑制经验模分解边缘效应的极值点对称延拓法[J].西北工业大学学报，2006,24(5):639～643
[43]张郁山，梁建文，胡幸贤.应用自回归模型处理EMD方法中的边界问题[J].自然科学进展，2003，13(10):1054～1059
[44] CHENG J S,YU D J,YANG Y. Application of support vector regression machinesto the recessing of end effects of Hilbert-Huang transform[J].Mechanical systemsand Signal Processing,2007(21):1197～1211
[45] QI K Y,HE Z J,ZI Y Y. Cosine window-based boundary processing method forEMD and its application in rubbing fault diagnosis[J].Mechanical Systems andSignal Processing,2007(21):2750～2760
[46] Wu, Z., and N.E. Huang.Ensemble Empirical Mode Decomposition: anoise-assisted data analysis methodⅡ. Advances in Adaptive Data Analysis, Vol.1,No.1,2009, pp.23~27
[47] Du,S.Yang,Application of the EMD method in the vibration analysis of ballbearing,Mechanical Systems and Signal Processing21(2007)2634~2644
[48]红英，马孝江．基于局域波分解的信号降噪算法[J]．农业机械学报，2006，37(1)：118~120
[49] Roberto Ricci, Paolo Pennacchi. Diagnostics of gear faults based on EMD andautomatic selection of intrinsic mode functions. Mechanical Systems and SignalProcessing25(2011)821~838
[50]谭冬梅，姚三，瞿伟廉.振动模态的参数识别综述.华中科技大学学报，2002.19（3）：73~78
[51] Roberto Ricci, Paolo Pennacchi.Diagnostics of gear faults based on EMD andautomatic selection of intrinsic mode functions. Mechanical Systems and SignalProcessing25(2011)821~838
[52]苏文胜，王奉涛，张志新，郭正刚，李宏坤.EMD降噪和谱峭度法在滚动轴承早期故障诊断中的应用振动与冲击，2010第29卷第3期
[53] Sawalhi N，Randall R B，Endo H．The enhancement of fault detection anddiagnosis in rolling element beatings using minimum entropy deconvolutinncombined with spectral kurtosis[J]． Mechanical Systems and SignalProcessing.2007，21：2616~2633
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[57] Antoni J. Fast computation of the kurtogram for the detection of transient faults.Mechanical Systems and Signal Processing.2007,21(1):108~124
[58] Antoni J，Randall R B，The spectral kurtosis：Application to the vibratorysurveillance and diagnostics of rotating machines[J]．Mechanical Systems andSignal Processing，2006，20：308~331
[59] N.H. Abu-Zahra, G. Yu, Gradual wear monitoring of turning inserts using waveletanalysis of ultrasound waves, International Journal of Machine Tools andManufacture43(2003)337~343.
[2]黄文虎,夏松波.刘瑞岩等编著.设备故障诊断原理、技术及应用，科学出版社，1996
[3]徐敏等编著.设备故障诊断手册，西安交通大学出版社，1998
[4]菜进.大型设备状态监测与故障诊断-现状与发展.动态分析与测试技术.1996,23:26~31
[5]佟德纯,李华彪编著.上海科学技术文献出版社，1997
[6]梅宏斌．滚动轴承诊断监测与诊断-理论、方法、系统．北京：机械工业出版社，1995
[7]周福昌．基于循环平稳信号处理的滚动轴承故障诊断方法研究：(博士学位论文)．上海：上海交通大学，2006
[8] N.E.Huang,S.Zheng,R.L.Steven, The empirical mode decomposition and the Hilbertspectrum for nonlinear and non-stationary time series analysis, Proceedings of theRoyal Society of London454(1998)903~995
[9] Gravier B.M.，N.N.J.，Pelstring J.A. An assessment of the application of the Hilbertspectrum to the fatigue analysis of marine risers.Proceedings of the Internationaloffshore and Polar Engineering Conference，2001:P268～275
[10]程军戴,于德介.基于EMD的信号瞬时特征的小波分析方法.地震工程与工程振动.2004,24(2):182~184
[11] Parey,A.,etal.Dynamic modeling of spur gear pair and application of empiricalmode decomposition-based statistiecal analysis for early detection of localizedtooth defect Journal of Sound and Vibration，2006,294(3):547～561
[12]杨世锡，胡劲松，吴昭同.旋转机械振动信号基于EMD的希尔伯特变换和小波变换时频分析比较.中国电机工程学报，2003.23(6):102～107
[13] Ding， H.， et al. Hilbert-Huang transform based signal analysis for thecharacterization of gas-liquid two-phase flow. Flow Measurement andInstrumentation，2007.18(l):37～46
[14] Blaneo-Velaseo，M.，B.Weng，K.E.Barner. ECG signal denoising and baselinewander correction based on the empirical mode decomposition.Computers inBiology and Medicine，2008.38(l):l～13.
[15] V.K. Rai,A.R.M.Bearing fault diagnosis using FFT of intrinsic mode functions inHilbert-Huang Transform. Mechanical Systems and Signal Processing，2007.21:P2607～2615.
[16] Kamath，V.，et al. Empirical Mode Decomposition and Blind Source SeparationMethods for Antijamming with GPS Signals.in Position，Location，And Navigationsymposium，2006IEEE/ION.2006.
[17]雷亚国，何正嘉，瞥艳阳.基于特征评估和神经网络的机械故障诊断模型.西安交通大学学报，200640(5):558～562.
[18]杨建文，贾民平.希尔伯特—黄谱的端点效应分析及处理方法研究.振动工程学报，2006.19(2):283～288.
[19] Deng YJ，W.W.，QIAN C C.Boundary-proeessing-technique in EMD method andHilbert transform. Chinese Science bulletin,2001.46(11):954～961.
[20]胡爱军.Hilbert-Huang变换在旋转机械振动信号分析中的应用研究.华北电力大学博士学位论文，2008
[21] G.G.S.PEGRAM，M.C.P. Empirical mode decomposition using rational splines:anapplication to rainfall time series.Proe.R.Soc.A.2007:pl-20.
[22] Flandrin，P.，P. Goncalves，G Rilling. EMD equivalent filter banks，frominterpretation to applications Hilbert-Huang Transform: Introduction andApplications，2005.
[23]田海泉，基于GA-ANN的滚动轴承诊断研究.江苏大学学位论文,2006
[24] Z.S.Chan,Y.M.Yang,X.S.Wen.Early diagnosis of helicopter gearboxes based onindependent component analysis.Processing of IMS2003:International Conferenceon Intelligent Maintenance Systems.2003:291~295
[25]张永强.软件数值积分误差原因分析及改进办法.机械强度，2006
[26] Sweldens W. The lifting scheme: a custom-design construction of biorthogonalwavelets.Appl Comput Harmon Anal.1996，3(2).186～200
[27]于明月.第二代小波变换在旋转机械故障诊断中的应用研究.南京航空航天大学学位论文，2008
[28]段晨东.基于第二代小波变换的故障诊断技术研究[D].博士学位论文，西安交通大学，2005
[29]崔玲丽，高立新，殷海晨，张建宇.基于第二代小波和EMD的解调方法及其应用研究[J].振动与冲击，2008，27（6）：1～4
[30] Xiaoming Lu,Jine Wang. Bearing fault diagnosis based on redundant secondgeneration wavelet denoising and EEMD.Consumer Electronics, Communicationsand Networks (CECNet),2011International Conference on XianNing.2011
[31] Donoho D L. Denoising by soft-thresholding[J]. IEEE Transaction on InformationTheory,1995,41(3):613~627
[32] Donoho D L,Johnstone I M. Ideal spatial adaptation by wavelet shrinkage.Biometrika[J].1994,81(3).425~455
[33] Pan Quan,Zhang Lei,Dai Guanzhou.Two de-noising methods by wavelettransform.IEEE Transactions on Signal Processing.1999,47(12).3401~3406
[34]何正嘉，訾艳阳，孟庆丰等.机械设备非平稳信号的故障诊断原理及应用[M].北京：高等教育出版社，2001：1～51
[35] N.E.Huang,A New Method For Nonlinear And Non-Stationary Time SeriesAnalysis And Its Application For Civil Infrastructure Health Monitoring,NASAGoddard Space Flight Center,Greenbelt,Maryl and20771,USA
[36]曹冲锋.基于EMD的机械振动分析与诊断方法研究[D].博士学位论文，浙江大学，2009，06
[37] N.E.Huang,Shen Z,Long S R.A new view of nonlinear water waves: the Hilbertspectrum.annu.Rev.Fluid Mech.1999,31:417～457
[38]余波.自适应时频分析方法的理论研究与用应研究.大连：大连理工大学博士论文，1998
[39]于德介,杨宇.机械故障诊断的Hilbert-Huang变换方法.科学出版社
[40]杜陈艳,经验模态分解边缘效应抑制方法综述.仪器仪表学报,2009
[41] ZHAOJP，HUANG D J.Mirror extending and circular spline function for empiricalmode decomposition method [J].Journal of Zhejiang University(SCIENCE)，2001，2:247～252
[42]舒忠平杨智春抑制经验模分解边缘效应的极值点对称延拓法[J].西北工业大学学报，2006,24(5):639～643
[43]张郁山，梁建文，胡幸贤.应用自回归模型处理EMD方法中的边界问题[J].自然科学进展，2003，13(10):1054～1059
[44] CHENG J S,YU D J,YANG Y. Application of support vector regression machinesto the recessing of end effects of Hilbert-Huang transform[J].Mechanical systemsand Signal Processing,2007(21):1197～1211
[45] QI K Y,HE Z J,ZI Y Y. Cosine window-based boundary processing method forEMD and its application in rubbing fault diagnosis[J].Mechanical Systems andSignal Processing,2007(21):2750～2760
[46] Wu, Z., and N.E. Huang.Ensemble Empirical Mode Decomposition: anoise-assisted data analysis methodⅡ. Advances in Adaptive Data Analysis, Vol.1,No.1,2009, pp.23~27
[47] Du,S.Yang,Application of the EMD method in the vibration analysis of ballbearing,Mechanical Systems and Signal Processing21(2007)2634~2644
[48]红英，马孝江．基于局域波分解的信号降噪算法[J]．农业机械学报，2006，37(1)：118~120
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[50]谭冬梅，姚三，瞿伟廉.振动模态的参数识别综述.华中科技大学学报，2002.19（3）：73~78
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