经验模态分解边缘效应抑制方法综述

Approaches for the end effect restraint of empirical mode decomposition algorithm

由Huang提出的经验模态分解(empirical mode decomposition,EMD)算法,在对非线性、非平稳信号进行平稳化处理时表现出了它特有的分析能力。但是它本身也存在不足之处,在利用三次样条插值求上下包络时,由于不能确定两端点处的极值,使得拟合出的包络线有可能偏离实际的包络线,这种现象将严重影响EMD分解的质量。针对这个问题,许多抑制边缘效应(有的文献也称:端点效应)的方法已被提出。本文对其中主要几种方法:镜像闭合延拓法、极值点对称延拓法、自回归模型(AR模型)延拓法、时变参数ARMA模型延拓法、正交多项式拟合法、神经网络的数据序列延拓法、支持矢量回归机法及窗函数法等作了一个归纳总结,阐述了各种方法的原理、抑制效果及存在的局限性。

The empirical mode decomposition （EMD） method proposed by Huang presents its own ability for processing nonlinear and non-stationary signals. However, this method also has limitation when the upper and lower envelopes, which are constructed from given signals using a cubic spline function, deviate from the true ones because of the unknown accurate data at the end of the signal. This defect influences the signal decomposition quality of the EMD algorithm seriously. In order to solve this problem, many approaches for restraining the end effect were proposed. This paper presents a review of the main approaches, including mirror extending, symmetrical extending, auto-regressive model, ARMA with time-varying parameters, orthogonal polynomial fitting, support vector regression machine and window function methods, and discusses their principles, restraint effects and limitations.