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集成经验模态分解（EEMD）在一定程度上减轻了经验模态分解（EMD）中的模态混叠，但集成平均会带来新的模态混叠、频谱丢失和运算量增大等问题，影响到对信号物理特征的分析与提取. 因此，本文提出一种基于复数据经验模态分解（CEMD）的噪声辅助信号分解方法，在CEMD中以白噪声分解的内禀模态函数（IMF）在指定方向上的投影为基函数来辅助观测信号分解过程中的极值选取，从而减小模态混叠，同时利用噪声投影的影响在求包络质心时被消除的特性，减小EEMD因集成平均带来的相关问题. 仿真结果表明，本文方法在进一步降低模态混叠效应的同时，明显提高了运算速度，并且在一定程度上减轻了频谱丢失问题.The ensemble empirical mode decomposition has been proposed in order to alleviate mode mixing in empirical mode decomposition, but the ensemble average in it can always result in new mode mixing, spectrum losing, and computational cost increasing, which can affect the analysis and extraction of signal physical characteristics. To tackle these problems, a noise-assisted signal decomposition method based on complex empirical mode decomposition is proposed, in which the mode mixing is reduced by taking the projection of intrinsic mode functions decomposed from white noise as basis functions for signal extrema extraction. While the problems result from ensemble average are reduced because the effects of noise projection are eliminated in the process of calculating the envelope barycenter. Simulation results show that our method has further reduced mode mixing, and speeded up the operation rate visibly and alleviated spectrum losing to a certain degree.
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Keywords:
- ensemble empirical mode decomposition /
- complex empirical mode decomposition /
- noise-assisted signal decomposition
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[26] Lin W T, Chen L H, Ouyang C 2012 Acta Phys. Sin. 61 080204 (in Chinese)[林万涛, 陈丽华, 欧阳成 2012 物理学报 61 080204]
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[1] Nathaniel E U, Beloff N, George N J 2013 Chin. Phys. B 22 084701
[2] Yang Y F, Wu Y F, Ren X M 2010 Acta Phys. Sin. 59 3778 (in Chinese) [杨永锋, 吴亚锋, 任兴民 2010 物理学报 59 3778]
[3] Hou W B, Liu T Q, Li X Y 2010 Acta Phys. Sin. 59 3531 (in Chinese) [侯王宾, 刘天琪, 李兴源 2010 物理学报 59 3531]
[4] Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 069701 (in Chinese) [王文波, 张晓东, 汪祥莉 2013 物理学报 62 069701]
[5] Zou M W, Feng G L, Gao X Q 2006 Chin. Phys. B 15 1384
[6] Wang W B, Wang X L 2013 Acta Phys. Sin. 62 209701 (in Chinese)[王文波, 汪祥莉 2013 物理学报 62 209701]
[7] Sweeney K T, McLoone S F 2013 IEEE Trans. Biomed. Eng. 60 97
[8] Huang N E, Shen Z, Long S R 1999 Ann. Rev. Fluid Mech 31 417
[9] Wu Z H, Huang N E 2009 Advances in Adaptive Data Analysis 1 1
[10] Fu M J, Zhuang J J, Hou F Z 2010 Chin. Phys. B 19 058701
[11] Tang J 2013 Acta Phys. Sin. 62 129701 (in Chinese)[唐洁 2013 物理学报 62 129701]
[12] Xue C F, Hou W, Zhao J H 2013 Acta Phys. Sin. 62 109203 (in Chinese) [薛春芳, 侯威, 赵俊虎 2013 物理学报 62 109203]
[13] Tang J 2014 Acta Phys. Sin. 63 049701 (in Chinese) [唐洁 2014 物理学报 63 049701]
[14] Torres M E, Colominas M A, Schlotthauer G 2011 IEEE ICASSP Prague, May22-27, 2011 p4144
[15] Tanaka T, Mandic D P 2006 IEEE Signal Process Lett. 14 101
[16] Altaf M U B, Gautama T, Tanaka T 2007 IEEE ICASSP 3 1009
[17] Rilling G, Flandrin P, Gonalves P 2007 IEEE Signal Process Lett. 14 936
[18] Yang W X, Court T, Tavner P 2011 J. Sound Vib. 330 3766
[19] Ahrabian A, Rehman A U, Mandic D 2013 IEEE Signal Process Lett. 20 245
[20] Gao Y C, Sang E F, Shen Z Y 2008 CISP'08. Congress on Image and Signal Processing Sanya Hainan, May 27-30, 2008 p141
[21] Rilling G, Flandrin P, Gonçalves P 2003 Proceedings of IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing Grado (I), June 2003 p1
[22] Li X J 2008 Acta Phys. Sin. 57 5366 (in Chinese) [李晓静 2008 物理学报 57 5366]
[23] Cao X Q, Song J Q, Zhu X Q 2012 Chin. Phys. B 21 020203
[24] Zhang W F, Zhao Q 2013 Chin. Phys. B 22 120201
[25] Wang W, Xu Y, Lu S P 2011 Acta Phys. Sin. 60 030205 (in Chinese) [王雯, 徐燕, 鲁世平 2011 物理学报 60 030205]
[26] Lin W T, Chen L H, Ouyang C 2012 Acta Phys. Sin. 61 080204 (in Chinese)[林万涛, 陈丽华, 欧阳成 2012 物理学报 61 080204]
[27] Du Z J, Lin W T, Mo J Q 2012 Chin Phys. B 21 090201
[28] Newman M, Compo G P, Alexander M A 2003 J. Clim. 16 3853
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