基于B样条插值的局部均值分解方法研究

Local mean decomposition method based on B-spline interpolation

局部均值分解(Local Mean Decomposition,LMD)方法是一种较新的自适应信号分析方法。LMD算法的核心思想是将原始信号分解为多个乘积函数(Production Function,PF),其中每个PF都是一个包络函数和一个纯调频函数的乘积。在LMD算法中需要提取信号的局部均值函数和包络估计,然而常规的提取方法会带来局部误差且分解速度慢。为了解决此问题,提出了利用三次B样条对信号上、下极值点进行插值得到上、下包络线,进而获取信号局部均值和包络估计的新方法。对仿真信号和机械振动信号的对比实验验证了该方法的优越性。

The local mean decomposition (LMD) is a relatively new approach of adaptive signal analysis.The core of LMD is to decompose an original signal into several production functions (PF),and each of which is a product of an envelope function and a pure frequency-modulated one.Both the local mean function and the envelope estimation of the signal need to be extracted in the LMD algorithm,while the conventional extraction approach brings the local error and a slow rate of decomposition.To solve these problems,a new approach for extracting the local mean and the envelope estimation using the cubic B-spline interpolation (CBI) was proposed.The upper envelope and the lower envelope were obtained by using the CBI firstly,and then the local mean and the envelope estimation were extracted from these two envelopes.The comparative experiments between the simulated signals and the mechanical vibration signals verified the superiority of this new approach.