基于独立成分分析和经验模态分解的混沌信号降噪

王文波; 张晓东; 汪祥莉

doi:10.7498/aps.62.050201

摘要

基于经验模态分解和独立成分分析去噪的特点,提出了一种联合独立成分分析和经验模态分解的混沌信号降噪方法. 利用经验模态分解对混沌信号进行分解,根据平移不变经验模态分解的思想构造多维输入向量, 通过所构造的多维输入向量和独立成分分析对混沌信号的各层内蕴模态函数进行自适应去噪处理; 将处理后的所有内蕴模态函数进行累加重构,从而得到降噪后的混沌信号. 仿真实验中分别对叠加不同强度高斯噪声的Lorenz混沌信号及实际观测的月太阳黑子混沌序列进行了研究, 结果表明本文方法能够对混沌信号进行有效的降噪,而且能够较好地校正相空间中点的位置, 逼近真实的混沌吸引子轨迹.

关键词:

Abstract

According to the characteristics of empirical mode decomposition and denoise of independent component analysis, an adaptive denoising method of chaotic signal is proposed based on independent component analysis and empirical mode decomposition. First, the chaotic signal is decomposed into a set of intrinsic mode functions by empirical mode decomposition; then, the multi-dimensional input vectors are constructed based on the translation invariant empirical mode decomposition, and the noise of each intrinsic mode function is removed through the constructed multi-dimensional input vectors and the independent component analysis; finally, the denoisied chaotic signal is obtained by accumulating and reconstructing all the processed intrinsic mode functions. Both the chaotic signal generated by Lorenz map with different level Gaussian noises, and the observed monthly series of sunspots are respectively used for noise reduction using the proposed method. The results of numerical experiments show that the proposed method is efficient. It can better correct the positions of data points in phase space and approximate the real chaotic attractor trajectories more closely．

Keywords:

作者及机构信息

1.
武汉科技大学信息与计算科学系, 武汉 430065;

2.
遥感科学国家重点实验室, 北京 100101;

3.
武汉大学测绘遥感信息工程国家重点实验室, 武汉 430079;

4.
国家海洋局第二研究所,卫星海洋环境动力学国家重点实验室, 杭州 310012;

5.
武汉理工大学计算机科学与计算学院, 武汉 430063

基金项目: 国家自然科学基金(批准号: 41071270, 11201354)、测绘遥感信息工程国家重点实验室开放基金 (批准号: 11R01)、遥感科学国家重点实验室开放基金(批准号: OFSLRSS201209)、卫星海洋环境动力学国家重点实验室开放基金(批准号: SOED1102)、湖北省自然科学基金(批准号: 2010CDB03305)、武汉市晨光计划(批准号: 201150431096)和中央高校基本科研业务费专项资金(批准号: 2012-IV-043)资助的课题.

Authors and contacts

1.
School of Science, Wuhan University of Science and Technology, Wuhan 430065, China;

2.
State Key Laboratory of Remote Sensing Science, Beijing 100101, China;

3.
State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China;

4.
State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012, China;

5.
School of Computer Science and Technology, Wuhan University of Technology, Wuhan 430063,China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 41071270, 11201354), the Open Fund of State Key Laboratory of Information Engineering in Suiveying Mapping and Remote Sensing (Grant No. 11R01), the Open Fund of State Key Laboratory of Remate Sensing Science (Grant No. OFSLRSS201209), the State Key Laboratory of Satellite Ocean Environment Dynamics Research Funding (Grant No. SOED1102), the Natural Science Foundation of Hunan Province, China (Grant No. 2010CDB03305), the Chenguang Foundation of Wuhan City (Grant No. 201150431096), and the Central University Basic Research Fund (Grant No. 2012-IV-043).

参考文献

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[2]	Vicha T, Dohnal M 2008 Chaos, Solitons & Fractals 38 70
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[4]	Jako Z, Kis G 2000 IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 47 1720
[5]	Schreiber T 1993 Physical Review E 47 2401
[6]	Han M, Liu Y H, Shi Z W, Xiang M 2007 Journal of System Simulation 19 364 (in Chinese) [韩敏, 刘玉花, 史志伟, 项牧 2007 系统仿真学报 19 364]
[7]	Leontitsis A, Bountis T, Pagge J 2004 Chaos 14 106
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[9]	Murguia J S, Campos C E 2006 Revista Mexicana De Fisica 52 155
[10]	Liu Y X, Yang G S, Jia Q 2011 Acta Electronica Sinica 39 13 (in Chinese) [刘云侠, 杨国诗, 贾群 2011 电子学报 39 13]
[11]	Zhang L, Bao P, Wu X 2005 IEEE Transactions on Circuits and Systems for Video Technology 15 469
[12]	Zhang H, Chen X H, Yang H Y 2011 Oil Geophysical Prospecting 46 70 (in Chinese) [张华, 陈小宏, 杨海燕 2011 石油地球物理勘探 46 70]
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[14]	Yang Y F, Ren X M, Qin W Y, Wu Y F, Zhi X Z 2008 Acta Phys. Sin. 57 6139 (in Chinese) [杨永锋, 任兴民, 秦卫阳, 吴亚锋, 支希哲 2008 57 6139]
[15]	An X L, Jiang D X, Zhao M H, Liu C 2011 Communications in Nonlinear Science and Numerical Simulation 17 1036
[16]	Boudraa A, Cexus J 2007 IEEE Transaction on Instrumentation and Measurement 56 2196
[17]	Olufemi A, Vladimir A, Auroop R 2011 IEEE Sensors Journal 11 2565
[18]	Kopsinis Y, Mclaughli S 2009 IEEE Transactions on Signal Processing 57 1351
[19]	Hyvarinen A, Oja E 2000 Neural Networks 13 411
[20]	Li P J, Jin H R, Song B Q 2008 Acta Scientiarum Naturalium Universitatis Pekinensis 4 45(in Chinese) [李培军, 金慧然, 宋本钦 2008 北京大学学报(自然科学版) 4 45]
[21]	Zhang Z S, Yu J, Yan Q, Meng Y S, Zhao Z 2011 Acta Geodaetica et Cartographica Sinica 40 289 (in Chinese) [张中山, 余洁, 燕琴, 孟云闪, 赵争 2011 测绘学报 40 289]
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[23]	Aapo H 1999 IEEE Transactions on Neural Networks 10 626
[24]	Zhao H W, Norden E H 2004 Proc. R. Soc. Lond. A8 460 1597
[25]	Schlotthauer G, Torres M E, Rufiner H L, Flandrin P 2009 Advances in Adaptive Data Analysis 1 11

施引文献

[1]	Li G L, Chen X Y 2008 Acta Electronica Sinica 36 1814 (in Chinese) [李冠林, 陈希有 2008 电子学报 36 1814]
[2]	Vicha T, Dohnal M 2008 Chaos, Solitons & Fractals 38 70
[3]	Dedieu H, Kisel A 1999 International Journal of Circuit Theory and Applications 27 577
[4]	Jako Z, Kis G 2000 IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 47 1720
[5]	Schreiber T 1993 Physical Review E 47 2401
[6]	Han M, Liu Y H, Shi Z W, Xiang M 2007 Journal of System Simulation 19 364 (in Chinese) [韩敏, 刘玉花, 史志伟, 项牧 2007 系统仿真学报 19 364]
[7]	Leontitsis A, Bountis T, Pagge J 2004 Chaos 14 106
[8]	Huang X G, Xu J X, He D H 1999 Acta Phys. Sin. 48 1810 (in Chinese) [黄显高, 徐健学, 何岱海, 夏军利 1999 48 1810]
[9]	Murguia J S, Campos C E 2006 Revista Mexicana De Fisica 52 155
[10]	Liu Y X, Yang G S, Jia Q 2011 Acta Electronica Sinica 39 13 (in Chinese) [刘云侠, 杨国诗, 贾群 2011 电子学报 39 13]
[11]	Zhang L, Bao P, Wu X 2005 IEEE Transactions on Circuits and Systems for Video Technology 15 469
[12]	Zhang H, Chen X H, Yang H Y 2011 Oil Geophysical Prospecting 46 70 (in Chinese) [张华, 陈小宏, 杨海燕 2011 石油地球物理勘探 46 70]
[13]	Huang N E, Shen Z, Long S R 1998 Proc. of the Royal Society of London A454 903
[14]	Yang Y F, Ren X M, Qin W Y, Wu Y F, Zhi X Z 2008 Acta Phys. Sin. 57 6139 (in Chinese) [杨永锋, 任兴民, 秦卫阳, 吴亚锋, 支希哲 2008 57 6139]
[15]	An X L, Jiang D X, Zhao M H, Liu C 2011 Communications in Nonlinear Science and Numerical Simulation 17 1036
[16]	Boudraa A, Cexus J 2007 IEEE Transaction on Instrumentation and Measurement 56 2196
[17]	Olufemi A, Vladimir A, Auroop R 2011 IEEE Sensors Journal 11 2565
[18]	Kopsinis Y, Mclaughli S 2009 IEEE Transactions on Signal Processing 57 1351
[19]	Hyvarinen A, Oja E 2000 Neural Networks 13 411
[20]	Li P J, Jin H R, Song B Q 2008 Acta Scientiarum Naturalium Universitatis Pekinensis 4 45(in Chinese) [李培军, 金慧然, 宋本钦 2008 北京大学学报(自然科学版) 4 45]
[21]	Zhang Z S, Yu J, Yan Q, Meng Y S, Zhao Z 2011 Acta Geodaetica et Cartographica Sinica 40 289 (in Chinese) [张中山, 余洁, 燕琴, 孟云闪, 赵争 2011 测绘学报 40 289]
[22]	Li H, Sun Y L 2007 Journal of Beijing University of Posts andTelecommunicatios 30 33 (in Chinese) [李洪, 孙云莲 2007 北京邮电大学学报 30 33]
[23]	Aapo H 1999 IEEE Transactions on Neural Networks 10 626
[24]	Zhao H W, Norden E H 2004 Proc. R. Soc. Lond. A8 460 1597
[25]	Schlotthauer G, Torres M E, Rufiner H L, Flandrin P 2009 Advances in Adaptive Data Analysis 1 11

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