综合斜率和三次样条的EMD端点效应抑制方法

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (14) : 70-76.

论文

梁黎明1,2，王茂芝1,2，徐文皙1,2，谭梦婷1,2，张明月1,2，王尚坤1,2

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Restriction of the end effect of EMD by utilizing slope and cubic spline based methods

LIANG Liming1,2，WANG Maozhi1,2，XU Wenxi1,2，TAN Mengting1,2，ZHANG Mingyue1,2，WANG Shangkun1,2

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摘要

端点效应会严重影响经验模态分解(empirical mode decomposition, EMD) 提取本征模态函数(intrinsic mode function，IMF) 的效果。针对基于三次样条端点延拓算法(cubic spline based method, CSBM) 在设置延拓点坐标位置时缺乏对信号趋势进行考量的缺陷，结合改进斜率延拓方法( improved slope based method, ISBM) 的设计思想，提出一种综合斜率变化率和三次样条的EMD端点延拓方法。新方法的主要创新点在于利用斜率变化率度量信号变化趋势，并基于信号和包络趋势来设置延拓点坐标信息。通过选取四组不同类型模拟信号以及两组实际工程应用信号，利用正交指数、均方误差和能量误差三个度量指标对算法性能进行评价，实验结果表明，所提方法的性能在整体上优于CSBM和ISBM方法。
关键词：经验模态分解；端点效应；斜率；三次样条；延拓

Abstract

The end effect will influence the results of empirical mode decomposition (EMD) during the processing of intrinsic mode function (IMF) extraction. In this paper, a new end condition method combined with the idea of improved slope based method (ISBM) and cubic spline based method (CSBM) is proposed. The novelty of this new method lies in that the slope ratio is defined as the tendency of the signal, further to set the coordinates of the extended points combined with the tendency of the signal and its envelope, which can overcome the deficiency of CSBM when setting the values of the extended points. Four different analog signals, two signals from engineering applications, and three performance criteria, i.e., orthogonal index, mean square error and energy error, are selected to evaluate the new method compared with ISBM and CSBM. Experimental results indicate that, overall, the performance of the proposed method is better than that of CSBM and ISBM.
Key words: empirical mode decomposition; the end effect; slope; cubic spline; extension

导出引用

梁黎明1,2，王茂芝1,2，徐文皙1,2，谭梦婷1,2，张明月1,2，王尚坤1,2. 综合斜率和三次样条的EMD端点效应抑制方法[J]. 振动与冲击, 2022, 41(14): 70-76

LIANG Liming1,2，WANG Maozhi1,2，XU Wenxi1,2，TAN Mengting1,2，ZHANG Mingyue1,2，WANG Shangkun1,2. Restriction of the end effect of EMD by utilizing slope and cubic spline based methods[J]. Journal of Vibration and Shock, 2022, 41(14): 70-76

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