基于ESN延拓与HMM修正的端点效应处理及其应用

An Improved Method for Mitigating the End Effects in EMD by ESN Extension Coupled with HMM Correction

近来年,经验模态分解(Empirical Mode Decomposition,EMD)以其优异的自适应性获得广泛关注,但端点效应影响了信号分解的性能并使结果失真。针对现有的抑制算法受限于延拓准确性或运算效率,难以快速给原序列添加更符合内部信息和端点特征的极值点的问题,提出了基于回声状态网络(Echo State Network,ESN)延拓与隐马尔科夫模型(Hidden Markov Model,HMM)修正的端点效应处理方法(ESN-HMM)。首先借用复杂度较小、训练简单且准确性较高的ESN网络对原序列进行初步预测,然后通过经典的统计方法HMM对误差序列进行建模和估计,最后将初步预测值与估计误差相结合得到校正后的延拓序列。仿真和实验结果表明,经过ESN-HMM处理的EMD方法能够有效提取出信号幅值和频率的时变特征,为旋转机械的信号处理和故障诊断提供了前提条件。

Empirical mode decomposition has lately received great attention due to its excellent adaptability.However,the end effect problem has made it challenging to the performance of the signal decomposition and distorts the results.Existing suppression algorithms are limited by continuation accuracy or computational efficiency.In order to quickly add extreme points which are more in line with the internal information and endpoint characteristics,an unconventional end effect processing method on the basis of echo state network(ESN)extension technique coupled with Hidden Markov Model(HMM)is proposed.Firstly,the initial sequence is predicted by the ESN network with less complexity and simple training but high precision.Then the error sequence is modeled and estimated by the classical statistical method HMM.Finally,the preliminary prediction value is combined with the estimation error to obtain the corrected extension sequence.The simulation and experiment results demonstrate that the ESN-HMM can effectively extract the time-varying characteristics of signal amplitude and frequency.It makes the EMD decomposition result more exact and provides a prerequisite for the signal processing and fault diagnosis of rotating machinery.