基于最大相关波形延拓的经验模式分解端点效应抑制方法

针对端点效应使经验模式分解（Empirical Mode Decomposition，EMD）结果出现畸变，严重影响算法精度的现象，提出了一种新的抑制经验模式分解端点效应的方法：最大相关波形延拓法。该方法借鉴匹配追踪算法思想，将信号端点处波形向信号内部平移，以找出与之最相似的波形，然后以最相似波形外侧的一段数据作为信号端点外数据的估计。利用仿真数据和某炼油厂风机轴瓦振动数据对最大相关波形延拓法进行了验证，结果表明该方法能够明显减小经验模式分解的端点效应，特别对周期信号和循环平稳信号有很好效果。同时，所提出的方法具通用性，能够减小数字滤波、小波分析等信号分析方法中端点效应对算法精度的影响，具有较大的理论意义和实用价值。

A maximal correlation waveform extension method for end effects reduction of empirical mode decomposition

Empirical mode decomposition (EMD) is an adaptive time-frequency analysis method, which is widely used in non-stationary and non-linear signal analyzing. However, end effects reduce the precision of empirical mode decomposition greatly. In this paper, a new method, maximal correlation waveform extension (MCWE), is proposed to decrease the end effects of empirical mode decomposition. In MCWE an end waveform including some data is shifted to the other end of the signal waveform to seek the most similar waveform whose correlation coefficient with the former is maximal, then the outboard waveform of the found one is regarded as the estimation of the outboard waveform of this end. A simulation signal and a practical vibration signal of an air compressor from a petroleum refinery are applied to test the performance of MCWE. The results show that the proposed new method can reduce end effects of empirical mode decomposition and improve its precision significantly, especially for period signals and cyclostationary signals. Moreover, the MCWE can be applied to diminish end effects of other signal processing methods, such as digital filtering and wavelet analysis, therefore it is universal and useful for engineering applications.