基于标准互相关函数的经验模态分解端点效应处理方法

Method of Empirical Mode Decomposition End Effect Based on Standardized Cross-correlation Function

在经验模态分解(Empirical mode decomposition,EMD)过程中由于信号端点处极值点的不确定,导致信号上下包络线拟合过程中存在端点效应,使得EMD的分解结果严重失真。在分析现有处理方法的基础上,提出一种基于标准互相关函数的包络线拟合法。该方法以标准互相关函数为判定依据,每次分解时在信号上下包络线内部分别寻找一段与端点处包络线波形最相似、幅值差异最小的波形,用此段波形代替产生端点效应的包络线进行迭代,实现端点处包络线与原信号包络线边界处的光滑过度,减小端点处包络线的拟合误差。通过仿真和油膜涡动试验表明该算法可以有效解决端点效应问题,具有较高的分解精度,同时对模态混叠现象也有一定的抑制作用,与其他几种常见算法相比具有算法简单、易于实现的特点。

In the empirical mode decomposition method （EMD）, as a result of the uncertainty of the signal at both ends of the border, the end effect exists in the course of getting envelop of data. The emergence of the effect makes the results of EMD have a serious distortion. On the basis of the existing algorithm, an improved method for EMD based on standardized cross-correlation function is proposed. The standardized cross-correlation function is used for the similarity criterion of the internal signal to fred the endpoint waveform which is the smallest amplitude difference waveforms for data extension, instead of this segment waveform to produce the end effect of the envelope. The method not only realizes the smooth transition between extending envelope and original envelope but also reduces the error of envelope near the ends of data. Simulation and experiment prove that the algorithm can effectively solve the end effect, and can restrain mode mixing. The algorithm is simple and easy to implement compared with several other common algorithm.