经验模态分解中多种边界处理方法的比较研究
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摘要
经验模态分解(EMD)的一个关键问题是处理边界效应。尽管目前除了Huang申请了NASA专利的边界处理方法,仍没有一个最终的解决方案,但工程上已经提出了多种处理方法。本文实现了工程上常用的5种EMD边界处理方法:线性外延,多项式拟合,镜像法,径向基(RBF)神经网络预测和AR预测方法,设计了一套消除了EMD处理中信号的相互作用及模式混淆影响的测试方法,并利用准周期信号和随机信号对它们的边界效应处理结果进行了定量测试。结果表明镜像法是目前相对最优的EMD边界处理方法。
One of the most important problems in Empirical Mode Decomposition (EMD) applications is mitigation of the end effect. Except Huang's patented approach several methods have been proposed. However, a final solution for this problem is yet to be found. In this paper five common end effect mitigation methods of EMD have been investigated, including linear extending method, polynomial fitting extending method, mirror extrema extending method, RBF neural network prediction method and AR prediction method. With a quasi-periodical signal and a stochastic signal as the test bed a quantitative test method was proposed for elimination of the mode confusion effect of EMD. The five end effect mitigation methods were quantitatively evaluated and the comparison shows that mirror extrema extending method is the best option among the five methods.
One of the most important problems in Empirical Mode Decomposition (EMD) applications is mitigation of the end effect. Except Huang's patented approach several methods have been proposed. However, a final solution for this problem is yet to be found. In this paper five common end effect mitigation methods of EMD have been investigated, including linear extending method, polynomial fitting extending method, mirror extrema extending method, RBF neural network prediction method and AR prediction method. With a quasi-periodical signal and a stochastic signal as the test bed a quantitative test method was proposed for elimination of the mode confusion effect of EMD. The five end effect mitigation methods were quantitatively evaluated and the comparison shows that mirror extrema extending method is the best option among the five methods.
引文
[1]Huang N E,Shen Z,and Long S R.The empirical modedecomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis[J].Proc.R.Soc.Lond.A,1998,454:903-995.
[2]Huang N E.Computer implicated empirical mode decomposition method,apparatus,and article of manufacture[P].U.S.Patent Pending1996.
[3]黄大吉,赵进平,苏纪兰等.希尔伯特-黄变换的端点延拓.海洋学报[J],2003,25(1):1-11.
[4]邓拥军,王伟,钱成春等.EMD方法及Hilbert变换中边界问题的处理[J].科学通报,2001,46(3):257-263.
[5]张郁山,梁建文,胡垏贤.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.
[6]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.2004,40(16):84-86.
[7]Flandrin P,Gabriel Rilling G,and Goncalves P.Empirical mode decompositon as a filter bank.IEEE Signal Processing Letters,2004,11(2):112-114.
[8]Wu Z and Huang N E.A study of the characteristics of white noise using the empirical mode decomposition method.Proc.R.Soc.London A,2002,submitted for publication.
[9]Chen Qiu-hui,Huang Norden,Riemenschneider S,and Xu Yuesheng.A B-spline approach for empirical mode decompositions.Advances in Computational Mathematics,2006,24(1-4):171-195.
[10]陈忠,郑时雄.EMD信号分析方法边缘效应的分析[J].数据采集与处理.2003,18(3):114-118.
[11]Deering R and Kaiser J F.The use of a masking signal to improve empirical mode decomposition.IEEE International Conference on Acoustics,Speedh,and Signal Processing(ICASSP-05).Philadelphia,Pennsylvania,USA,March2005,Vol.4:485-488.
[12]程军圣,于德介,杨宇.基于EMD的信号瞬时特征的小波分析方法[J].地震工程与工程振动,2004,24(2):181-186.
[2]Huang N E.Computer implicated empirical mode decomposition method,apparatus,and article of manufacture[P].U.S.Patent Pending1996.
[3]黄大吉,赵进平,苏纪兰等.希尔伯特-黄变换的端点延拓.海洋学报[J],2003,25(1):1-11.
[4]邓拥军,王伟,钱成春等.EMD方法及Hilbert变换中边界问题的处理[J].科学通报,2001,46(3):257-263.
[5]张郁山,梁建文,胡垏贤.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.
[6]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.2004,40(16):84-86.
[7]Flandrin P,Gabriel Rilling G,and Goncalves P.Empirical mode decompositon as a filter bank.IEEE Signal Processing Letters,2004,11(2):112-114.
[8]Wu Z and Huang N E.A study of the characteristics of white noise using the empirical mode decomposition method.Proc.R.Soc.London A,2002,submitted for publication.
[9]Chen Qiu-hui,Huang Norden,Riemenschneider S,and Xu Yuesheng.A B-spline approach for empirical mode decompositions.Advances in Computational Mathematics,2006,24(1-4):171-195.
[10]陈忠,郑时雄.EMD信号分析方法边缘效应的分析[J].数据采集与处理.2003,18(3):114-118.
[11]Deering R and Kaiser J F.The use of a masking signal to improve empirical mode decomposition.IEEE International Conference on Acoustics,Speedh,and Signal Processing(ICASSP-05).Philadelphia,Pennsylvania,USA,March2005,Vol.4:485-488.
[12]程军圣,于德介,杨宇.基于EMD的信号瞬时特征的小波分析方法[J].地震工程与工程振动,2004,24(2):181-186.
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