基于均生函数周期叠加外推法的EMD端点问题的研究
|
摘要
HHT过程存在端点效应问题,针对端点效应的产生机理,并在研究现有端点效应处理方法的基础上,提出一种基于均生函数周期叠加外推法的端点延拓方法。通过构造信号序列的均生函数延拓矩阵,从中提取优势周期,将各周期叠加并作外延,来对信号端点外的数据进行预测。该方法克服了现有各种极值延拓方法仅参考两端点附近的有限个极值点的缺陷,并且相比其它数据预测延拓方法精度更高、算法简便且计算时间大大缩短。仿真和实例信号证明,该方法能够有效抑制端点效应。
The end effect exists in HHT.According to the generation mechanism and the results in existing literatures,a method based on MGF period superposition extrapolation was proposed for dealing with the end effect.Through the construction of MGF matrix about the signal as well as the extraction,superposition and extension of advantage cycles the data were forecasted beyond the ends of the signal.The method can overcome the defect that only finite extremes near the ends are taken in use in the existing extreme extension methods.Compared with other prediction methods,it is more accurate and easy,and can save more time consuming in calculation.Simulations and real signals processing verify that the method can effectively inhibit the end effect.
The end effect exists in HHT.According to the generation mechanism and the results in existing literatures,a method based on MGF period superposition extrapolation was proposed for dealing with the end effect.Through the construction of MGF matrix about the signal as well as the extraction,superposition and extension of advantage cycles the data were forecasted beyond the ends of the signal.The method can overcome the defect that only finite extremes near the ends are taken in use in the existing extreme extension methods.Compared with other prediction methods,it is more accurate and easy,and can save more time consuming in calculation.Simulations and real signals processing verify that the method can effectively inhibit the end effect.
引文
[1]Huang N E,Shen Z,Long S R,et al.The empirical modedecomposition and the Hilbert spectrum for non linear non-stationary time series analysis[J].Proc.R.Soc,London,1998,A 454:903-955.
[2]钟佑明,秦树人,汤宝平.Hilbert-Huang变换中的理论研究[J].振动与冲击,2002,21(4):13-17.ZHONG You-min,QIN Shu-ren,TANG Bao-ping.Researchon the theory of the Hilbert-Huang transform[J].Journal ofVibration and Shock:2002,21(4):13-17.
[3]陈隽,徐幼麟.HHT方法在结构模态参数识别中的应用[J].振动工程学报,2003,16(3):383-388.CHEN Jun,XU You-lin.Application of HHT for modalparameter identification to civil structures[J].Journal ofVibration Engineering,2003,16(3):383-388.
[4]张义平,李夕兵,赵国彦.基于HHT方法的爆破地震信号分析[J].工程爆破,2005,11(1):1-7.ZHANG Yi-ping,LI Xi-bing,ZHAO Guo-yan.Analysis ofblasting vibration signal based on HHT method[J].Engineering Blasting,2005.11(1):1-7.
[5]杨宇,于德介,程军圣.基于Hilbert边际谱的滚动轴承故障诊断方法[J].振动与冲击,2005,24(1):70-72.YANG Yu,YU Dei-jie,CHENG Jun-sheng.Roller bearingfault diagnosis based on hilbert marginal spectrum[J].Journal of Vibration and Shock,2005,24(1):70-72.
[6]Huang N E,Wu Z H.A review on Hilbert-Huang transform:method and its applications to geophysical studies[J].Reviews of Geophysics,2008,46:1-23.
[7]沈路,周晓军,张志刚,等.Hilbert-Huang变换中的一种端点延拓方法[J].振动与冲击,2009,28(8):168-171.SHEN Lu,ZHOU Xiao-jun,ZHANG Zhi-gang,et al.Boundary-extension method in hilbert-huang transform[J].Journal of vibration and shock,2009,28(8):168-171.
[8]Marcus D,Torsten S.Performance and limitations of theHilbert-Huang transform(HHT)with an application toirregular water waves[J].Ocean Engineering,2004,31:1783-1834.
[9]Rilling G,FlandrinP,Goncalves P.On empirical modedecomposition and its algorithms[R].IEEE-EURASIPWorkshop on Nonlinear Signal andI mage Processing,NSIP-03,2003:1.
[10]刘慧婷,张旻,程家兴.基于多项式拟合算法的EMD端点问题的处理[J].计算机工程与应用,2004,16:83-86.LIU Hui-ting,ZHANG Min,CHENG Jia-xing.Dealing withthe End Issue of EMD based on polynomial fitting alogrithm[J].Computer Engineering and Applications,2004,16:83-86.
[11]蔡艳平,李艾华,石林锁,等.EMD端点效应的改进型混沌延拓方法及其在机械故障诊断中的应用[J],振动与冲击,2011,30(11):46-52.CAI Yan-ping,LI Ai-hua,SHI Lin-suo,et al.Processingmethod for end effects of EMD based on improved chaosforecasting model and its application in machinery faultdiagnosis[J].Journal of Vibration and Shock,2011,30(11):46-52.
[12]周龙宝,马景辉,李强.GA和BEF神经网络的Hilbert.Huang变换端点问题研究[J].计算机测量与控制,2012,20(2):447-450.ZHOU Long-bao,MA Jing-hui,LI Qiang.Research of endeffects in hilbert.huang transform based on genetic algorithmand RBF neural network[J].Computer Measurement andControl,20(2):447-450.
[13]Feldman M.Theoretical analysis and comparison of theHilbert transform decomposition method[J].Mechanicalsystem and Signal Processing,2008.22(3):509-519.
[14]魏凤英,曹鸿兴.长期预测的数学模型及其应用[M].北京:气象出版社,1990:9-5.
[2]钟佑明,秦树人,汤宝平.Hilbert-Huang变换中的理论研究[J].振动与冲击,2002,21(4):13-17.ZHONG You-min,QIN Shu-ren,TANG Bao-ping.Researchon the theory of the Hilbert-Huang transform[J].Journal ofVibration and Shock:2002,21(4):13-17.
[3]陈隽,徐幼麟.HHT方法在结构模态参数识别中的应用[J].振动工程学报,2003,16(3):383-388.CHEN Jun,XU You-lin.Application of HHT for modalparameter identification to civil structures[J].Journal ofVibration Engineering,2003,16(3):383-388.
[4]张义平,李夕兵,赵国彦.基于HHT方法的爆破地震信号分析[J].工程爆破,2005,11(1):1-7.ZHANG Yi-ping,LI Xi-bing,ZHAO Guo-yan.Analysis ofblasting vibration signal based on HHT method[J].Engineering Blasting,2005.11(1):1-7.
[5]杨宇,于德介,程军圣.基于Hilbert边际谱的滚动轴承故障诊断方法[J].振动与冲击,2005,24(1):70-72.YANG Yu,YU Dei-jie,CHENG Jun-sheng.Roller bearingfault diagnosis based on hilbert marginal spectrum[J].Journal of Vibration and Shock,2005,24(1):70-72.
[6]Huang N E,Wu Z H.A review on Hilbert-Huang transform:method and its applications to geophysical studies[J].Reviews of Geophysics,2008,46:1-23.
[7]沈路,周晓军,张志刚,等.Hilbert-Huang变换中的一种端点延拓方法[J].振动与冲击,2009,28(8):168-171.SHEN Lu,ZHOU Xiao-jun,ZHANG Zhi-gang,et al.Boundary-extension method in hilbert-huang transform[J].Journal of vibration and shock,2009,28(8):168-171.
[8]Marcus D,Torsten S.Performance and limitations of theHilbert-Huang transform(HHT)with an application toirregular water waves[J].Ocean Engineering,2004,31:1783-1834.
[9]Rilling G,FlandrinP,Goncalves P.On empirical modedecomposition and its algorithms[R].IEEE-EURASIPWorkshop on Nonlinear Signal andI mage Processing,NSIP-03,2003:1.
[10]刘慧婷,张旻,程家兴.基于多项式拟合算法的EMD端点问题的处理[J].计算机工程与应用,2004,16:83-86.LIU Hui-ting,ZHANG Min,CHENG Jia-xing.Dealing withthe End Issue of EMD based on polynomial fitting alogrithm[J].Computer Engineering and Applications,2004,16:83-86.
[11]蔡艳平,李艾华,石林锁,等.EMD端点效应的改进型混沌延拓方法及其在机械故障诊断中的应用[J],振动与冲击,2011,30(11):46-52.CAI Yan-ping,LI Ai-hua,SHI Lin-suo,et al.Processingmethod for end effects of EMD based on improved chaosforecasting model and its application in machinery faultdiagnosis[J].Journal of Vibration and Shock,2011,30(11):46-52.
[12]周龙宝,马景辉,李强.GA和BEF神经网络的Hilbert.Huang变换端点问题研究[J].计算机测量与控制,2012,20(2):447-450.ZHOU Long-bao,MA Jing-hui,LI Qiang.Research of endeffects in hilbert.huang transform based on genetic algorithmand RBF neural network[J].Computer Measurement andControl,20(2):447-450.
[13]Feldman M.Theoretical analysis and comparison of theHilbert transform decomposition method[J].Mechanicalsystem and Signal Processing,2008.22(3):509-519.
[14]魏凤英,曹鸿兴.长期预测的数学模型及其应用[M].北京:气象出版社,1990:9-5.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心