Hilbert-Huang变换中的一种端点延拓方法
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摘要
经验模式分解是Hilbert-Huang变换中的关键一步,但其在构造极值点上下包络线的过程中存在着严重的端点效应问题。在现有解决该问题方法的基础上提出了一种相似极值延拓方法。该方法将数据两端相邻极值点的横坐标差值作为极值形状特征,再利用该形状特征和已知极值点的均值对信号进行延拓。克服了现有延拓方法仅参照数据端点处极值点进行延拓的缺陷,综合考虑了数据序列两端极值点变化与其它极值点信息对信号进行延拓。仿真和实例证明,相似极值延拓方法能够有效的抑制端点效应,而且算法简单且易于实现。
Serious end effect will be produced when the upper and lower envelopes are constructed in the process of EMD. Similar extrema extension method was proposed to overcome the problem. Abscissa difference of adjacent extrema at both ends of data was considered as the shape characteristic, then the shape characteristic and the average of extrema were used to extend signal. Both the trend of extrema variation near boundary and the rest of extrema were considered in similar extrema extension, while only the extrema near boundary are taken to extend signal in current methods. The simulation and experiment results show the method is effective in restraining end effect, furthermore it is simple and easy to realize.
Serious end effect will be produced when the upper and lower envelopes are constructed in the process of EMD. Similar extrema extension method was proposed to overcome the problem. Abscissa difference of adjacent extrema at both ends of data was considered as the shape characteristic, then the shape characteristic and the average of extrema were used to extend signal. Both the trend of extrema variation near boundary and the rest of extrema were considered in similar extrema extension, while only the extrema near boundary are taken to extend signal in current methods. The simulation and experiment results show the method is effective in restraining end effect, furthermore it is simple and easy to realize.
引文
[1]Huang N E,et al.The empirical mode decomposition and theHilbert spectrum for nonlinear and non-stationary time series a-nalysis[J].Proc R Soc Lond A,1998,454:903-995.
[2]Vincent HT,Hu S L J,Hou Z.Damage detection using em-pirical mode decomposition method and a comparison withwavelet analysis[J].Signal Processing and Diagnostic Meth-ods,1999:891-900.
[3]希尔波特-黄变换地震信号时频分析与属性提取[J].地球物理学进展.2007,22(10):1585-1590.
[4]Yu Dejie,Cheng Junsheng,et al.Application of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearings[J].Mechanical Systems and Signal Processing,2005,19:259-270.
[5]邵晨曦,王剑.一种自适应的EMD端点延拓方法[J].电子学报,2007,35(10):1944-1948.
[6]Rilling G,Flandrin P,Goncalves P.On empirical mode de-composition and its algorithms[R].IEEE-EURASIP Workshopon Nonlinear Signal and Image Processing,NSIP-03,2003:1-5.
[7]Marcus D,Torsten S.Performance and limitations of the Hil-bert-Huang transform(HHT)with an application to irregularwater waves[J].Ocean Engineering,2004,31:1783-1834.
[8]刘慧婷,张昱,等.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.
[2]Vincent HT,Hu S L J,Hou Z.Damage detection using em-pirical mode decomposition method and a comparison withwavelet analysis[J].Signal Processing and Diagnostic Meth-ods,1999:891-900.
[3]希尔波特-黄变换地震信号时频分析与属性提取[J].地球物理学进展.2007,22(10):1585-1590.
[4]Yu Dejie,Cheng Junsheng,et al.Application of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearings[J].Mechanical Systems and Signal Processing,2005,19:259-270.
[5]邵晨曦,王剑.一种自适应的EMD端点延拓方法[J].电子学报,2007,35(10):1944-1948.
[6]Rilling G,Flandrin P,Goncalves P.On empirical mode de-composition and its algorithms[R].IEEE-EURASIP Workshopon Nonlinear Signal and Image Processing,NSIP-03,2003:1-5.
[7]Marcus D,Torsten S.Performance and limitations of the Hil-bert-Huang transform(HHT)with an application to irregularwater waves[J].Ocean Engineering,2004,31:1783-1834.
[8]刘慧婷,张昱,等.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.
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