中值互补集合经验模态分解  

Median Complementary Ensemble Empirical Mode Decomposition

作　　者：刘淞华 何冰冰 郎恂 陈启明 张榆锋[1] 苏宏业[2] LIU Song-Hua;HE Bing-Bing;LANG Xun;CHEN Qi-Ming;ZHANG Yu-Feng;SU Hong-Ye(School of Information,Yunnan University,Kunming 650504;State Key Laboratory of Industrial Control Technology,Zhejiang University,Hangzhou 310027)

机构地区：[1]云南大学信息学院,昆明650504 [2]浙江大学工业控制技术国家重点实验室,杭州310027

出　　处：《自动化学报》2023年第12期2544-2556,共13页Acta Automatica Sinica

基　　金：国家自然科学基金(81771928,62003298);云南省基础研究计划重点项目(202101AS070031);中国博士后科学基金资助项目(2020M683389)资助。

摘　　要：针对经验模态分解(Empirical mode decomposition,EMD)系列方法存在的模态分裂(Mode splitting,MS)问题,提出中值互补集合经验模态分解(Median complementary ensemble EMD,MCEEMD)算法.通过概率模型量化互补集合经验模态分解(Complementary ensemble EMD,CEEMD)的MS问题,证明了使用中值算子替代算术平均算子对抑制MS的有效性.为了兼具抑制MS和残留噪声的性能,MCEEMD算法首次在集合过程中结合了中值和平均算子.具体地,所提方法首先添加N对互补的白噪声至原信号中,并经过EMD分解得到2N组固有模态函数(Intrinsic mode functions,IMFs),然后分别对其中互补相关的IMFs两两取平均得到N组IMFs,最后使用中值算子处理上述N组IMFs得到输出结果.对仿真信号与两个真实案例的分析结果表明,本文提出的MCEEMD方法不仅有效抑制了CEEMD的MS问题,而且避免了单一使用中值算子的两个缺点:分解完备性差和IMFs中存在的毛刺现象.In order to restrain the mode splitting(MS)problem of the empirical mode decomposition(EMD)series methods,a median complementary ensemble EMD(MCEEMD)algorithm is proposed in this paper.We first present novel probabilistic tools to quantify the MS phenomenon of complementary ensemble EMD(CEEMD),which aims at demonstrating the effectiveness of using the median operator to replace the mean operator during the ensemble process.To combine the advantages of suppressing MS and residual noise,the MCEEMD algorithm integrates both median and mean operators within the ensemble process for the first time.Specifically,the MCEEMD algorithm is enlightened and featured by following procedures:1)Add N pairs of complementary white noise to the original signal to obtain 2N groups of intrinsic mode functions(IMFs)by EMD decomposition;2)By averaging each pair of the complementary IMFs,the 2N groups of IMFs are computed into N IMF groups;3)Assemble same-index components across the N groups of IMFs using the median operator to obtain the final IMFs within MCEEMD.Through typical simulations as well as two real-world cases,we show that the present work not only effectively alleviates the MS problem,but also avoids two shortcomings of using a single median operator,i.e.,the poor decomposition completeness and the presence of burr in IMFs.

关 键 词：模态分裂 中值算子 互补白噪声 互补集合经验模式分解 

分 类 号：TN911.7[电子电信—通信与信息系统]