振动信号包络线的稀疏重构最优化算法研究与应用

Sparse recovery optimizing Algorithm for vibration signal envelopes

经验模态分解是处理非线性、非平稳信号的有效方法,其核心关键是包络线的提取。针对目前提出的包络拟合算法所存在的端点效应、拟合误差大、抗噪性低等问题,在文献[9]的基础上,提出一种基于稀疏复原最优化算法提取信号包络线的方法。首先利用外罚函数将包络线稀疏优化模型的凹问题转换为凸二次规划问题;其次采用混合变异粒子群算法对改变稀疏基频带宽度的变化因子m进行全局寻优,利用最优变化因子构建适合包络线变化趋势的最佳稀疏基,然后将采集信号的所有极值点作为稀疏重构过程中的观测值,利用最佳稀疏基与观测值建立稀疏重构模型,使用内点法对该模型进行处理,最终自适应地得到了全局最优的包络线信号。结果表明,该方法可以有效抑制端点飞翼问题,粒子群算法的引入可以自适应地匹配最优的稀疏基映射带宽,在拟合精度和抗噪声等性能方面获得了比文献[9]更好的效果,有效提高了包络线拟合精度和抗噪性。

Empirical mode decomposition(EMD)is one of effective methods to process nonlinear and non-stationary signals,its key is to extract signals’envelope curve.A method based on the sparse recovery optimizing algorithm was proposed to overcome defects of the envelope fitting algorithm,such as,end effect,bigger fitting error and low anti-noise ability,etc.Firstly,the concave problem of envelope sparse optimal model was converted into a convex quadratic programming problem by using exterior penalty functions.Secondly,the mixed variant particle swarm optimization(PSO)algorithm was used to solve the global optimization of the variant factor m which changes the sparse base’s frequency band width.This m was employed to build the optimal sparse bases being suitable for envelope variation trend.All extreme value points of the collected signal were taken as observed values in the process of sparse recovery.The optimal sparse bases and observed values were used to establish the sparse recovery model.The interior-point method was adopted to process the built model.Finally,the globally optimal envelope signal was gained adaptively.The results showed that this method can effectively suppress the end effect;PSO introduced here can adaptively match the mapping band width of the optimal spare bases,it improves the signal envelope fitting precision and noise immunity.