基于稀疏指标的优化变分模态分解方法  

An optimal variational mode decomposition method based on sparse index

作　　者：张露 理华[1] 崔杰[1] 王晓东[1] 肖灵[1] ZHANG Lu;LI Hua;CUI Jie;WANG Xiaodong;XIAO Ling(Institute of Acoustics,Chinese Academy of Sciences,Beijing 100190,China;School of Electronic,Electrical and Communication Engineering,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院声学研究所,北京100190 [2]中国科学院大学电子电气与通信工程学院,北京100049

出　　处：《振动与冲击》2023年第8期234-250,共17页Journal of Vibration and Shock

基　　金：国家重点研发计划(2020YFC2004003-03);国家自然基金重大仪器(32127802)。

摘　　要：针对复合信号源信号数目未知,无法正确预设分解模态数K值而不能对信号进行有效变分模态(variational mode decomposition,VMD)的问题,提出了一种基于稀疏指标的优化VMD法。该方法基于VMD所构建变分模型中各个分量的稀疏先验知识,实现了VMD自适应寻优K值,其将最佳K值确定为稀疏指标由上升至下降的转折点;在计算VMD各个分量的稀疏度时,考虑到不同分量间的能量差异加入了能量权值因子,最后将稀疏指标确定为分解后各分量边际谱稀疏度的平均值。仿真信号与实际信号分解试验验证表明:相较于其他两种VMD的K值确定方法,该方法确定的K值结果更为准确,实现的优化VMD自适应性更强,较其他信号分解法如经验模态分解(empirical mode decomposition,EMD)有更好的分解效果,为源信号数目未知的复合信号VMD提供了新思路;此外,噪声的鲁棒性试验证明所提基于稀疏指标的优化VMD法还具有一定的抗噪能力,较稳健,可开发应用于实际工程。A sparse index-based variational mode decomposition(VMD)method was presented in this work to deal with the challenge of determining the decomposition mode number K when the number of composite signal sources is unknown.Based on the sparse prior theory of each component in the VMD decomposition,the adaptive optimal K value of VMD was discovered as the turning point of the sparse index from rising to falling.Considering the energy difference between different components,the energy weight factor was added in the computation of sparsity index.Finally,the sparsity index was determined as the average value of the marginal spectral sparsity of each component after decomposition.The results of simulations and real-world signal decomposition experiments prove the superiority of the method.Compared with another two modified VMD methods,the proposed method determines a more accurate K value and is more adaptive.Moreover,the results of experiment show that the method has a better decomposition effect than other signal decomposition methods like empirical mode decomposition(EMD).The proposed method introduces a novel concept for adaptive and efficient VMD decomposition of composite signals with unknown source numbers.To the next level,the robust noise experiment demonstrates that the suggested sparse index approach has a certain anti-noise ability.It shows that the method is relatively robust and can be developed and applied to practical engineering.

关 键 词：复合信号分解 变分模态分解(VMD) 分解模态数 稀疏指标 自适应寻优 

分 类 号：TN911.72[电子电信—通信与信息系统]