混沌背景下非平稳谐波信号的自适应同步挤压小波变换提取

汪祥莉; 王斌; 王文波; 喻敏

doi:10.7498/aps.65.200202

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摘要

针对同步挤压小波变换（SST）在提取混沌背景下非平稳谐波信号时的不足，提出一种改进的自适应最优累加频率范围的SST非平稳谐波信号提取方法.首先根据非平稳谐波信号小波系数与小波基支撑区间的关系，推导非平稳谐波SST提取时自适应累加频率范围的计算公式；然后，利用最小能量误差准则确定自适应累加频率范围公式中参数的最优值，从而实现非平稳谐波信号的SST自适应提取.分别在Lorenz混沌背景和Duffing混沌背景下对不同类型的非平稳谐波信号进行了实验分析，实验结果表明，该方法能有效地从含噪混沌背景中提取非平稳谐波信号，与经典的单一累加频率范围的SST方法相比，提取结果在均方误差和相关系数两方面都有较好的提高.

关键词:

作者及机构信息

1.
武汉理工大学, 交通物联网技术湖北省重点实验室, 武汉 430063;

2.
武汉科技大学信息科学与工程学院, 武汉 430081;

3.
武汉科技大学理学院, 武汉 430065

通信作者: 汪祥莉, wwb0178@163.com

基金项目: 国家自然科学基金（批准号：61473213）、湖北省自然科学基金（批准号：2015CFB424，2015CFB602）和武汉理工大学交通物联网技术湖北省重点实验室开放基金（批准号：2015Ⅲ015-B02）资助的课题.

参考文献

[1]	Aghababa M P 2012 Chin. Phys. B 21 100505
[2]	Hu J F, Zhang Y X, Li H Y, Yang M, Xia W, Li J 2015 Acta Phys. Sin. 64 220504 (in Chinese)[胡进峰, 张亚璇, 李会勇, 杨淼, 夏威, 李军2015物理学报64 220504]
[3]	Arunprakash J, Reddy G R, Prasad N S S R K 2016 Procedia Technology 24 988
[4]	Xing H Y, Zhang Q, Xu W 2015 Acta Phys. Sin. 64 040506 (in Chinese)[行鸿彦, 张强, 徐伟2015物理学报64 040506]
[5]	Wang E F, Wang D Q, Ding Q 2011 J. Commun. 32 60 (in Chinese)[王尔馥, 王冬青, 丁群2011通信学报32 60]
[6]	Li H T, Zhu S L, Qi C H, Gao M X, Wang G Z 2013 Adv. Mater. Res. 73 4 3145
[7]	Leung H, Huang X P 1996 IEEE Trans. Signal Process. 44 2456
[8]	He G T, Luo M K 2012 Chin. Phys. Lett. 29 060204
[9]	Guan J, Liu N B, Huang Y, He Y 2012 IET Radar Sonar Nav. 6 293
[10]	Li H C, Zhang J S 2005 Chin. Phys. Lett. 22 2776
[11]	Xu Y C, Qu X D, Li Z X 2015 Chin. Phys. B 24 034301
[12]	Huang X G, Xu J X 2001 Int. J. Bifurcation Chaos 11 561
[13]	Wang G G, Wang S X 2006 J. Jilin Univ. (Sci. Ed.) 44 439(in Chinese)[王国光, 王树勋2006吉林大学学报(理学版) 44 439]
[14]	Wang X L, Wang B, Wang W B, Y M, Wang Z, Chang Y C 2015 Acta Phys. Sin. 64 100201 (in Chinese)[汪祥莉, 王斌, 王文波, 喻敏, 王震, 常毓禅2015物理学报64 100201]
[15]	Huang N E, Shen Z, Long S R 1998 Proc. R. Soc. London, Ser. A 454 903
[16]	Daubechies I, Lu J F, Wu H T 2011 Appl. Comput. Harmon. Anal. 2 243
[17]	Gaurav T, Eugene B, Neven S F, Wu H T 2012 Sign. Process. 93 1079
[18]	Sylvain M, Thomas O, Stephen M 2012 IEEE Trans. Signal. Process. 60 5787
[19]	Wang Z C, Ren W X, Liu J L 2013 J. Sound Vib. 332 6016

施引文献

[1]	Aghababa M P 2012 Chin. Phys. B 21 100505
[2]	Hu J F, Zhang Y X, Li H Y, Yang M, Xia W, Li J 2015 Acta Phys. Sin. 64 220504 (in Chinese)[胡进峰, 张亚璇, 李会勇, 杨淼, 夏威, 李军2015物理学报64 220504]
[3]	Arunprakash J, Reddy G R, Prasad N S S R K 2016 Procedia Technology 24 988
[4]	Xing H Y, Zhang Q, Xu W 2015 Acta Phys. Sin. 64 040506 (in Chinese)[行鸿彦, 张强, 徐伟2015物理学报64 040506]
[5]	Wang E F, Wang D Q, Ding Q 2011 J. Commun. 32 60 (in Chinese)[王尔馥, 王冬青, 丁群2011通信学报32 60]
[6]	Li H T, Zhu S L, Qi C H, Gao M X, Wang G Z 2013 Adv. Mater. Res. 73 4 3145
[7]	Leung H, Huang X P 1996 IEEE Trans. Signal Process. 44 2456
[8]	He G T, Luo M K 2012 Chin. Phys. Lett. 29 060204
[9]	Guan J, Liu N B, Huang Y, He Y 2012 IET Radar Sonar Nav. 6 293
[10]	Li H C, Zhang J S 2005 Chin. Phys. Lett. 22 2776
[11]	Xu Y C, Qu X D, Li Z X 2015 Chin. Phys. B 24 034301
[12]	Huang X G, Xu J X 2001 Int. J. Bifurcation Chaos 11 561
[13]	Wang G G, Wang S X 2006 J. Jilin Univ. (Sci. Ed.) 44 439(in Chinese)[王国光, 王树勋2006吉林大学学报(理学版) 44 439]
[14]	Wang X L, Wang B, Wang W B, Y M, Wang Z, Chang Y C 2015 Acta Phys. Sin. 64 100201 (in Chinese)[汪祥莉, 王斌, 王文波, 喻敏, 王震, 常毓禅2015物理学报64 100201]
[15]	Huang N E, Shen Z, Long S R 1998 Proc. R. Soc. London, Ser. A 454 903
[16]	Daubechies I, Lu J F, Wu H T 2011 Appl. Comput. Harmon. Anal. 2 243
[17]	Gaurav T, Eugene B, Neven S F, Wu H T 2012 Sign. Process. 93 1079
[18]	Sylvain M, Thomas O, Stephen M 2012 IEEE Trans. Signal. Process. 60 5787
[19]	Wang Z C, Ren W X, Liu J L 2013 J. Sound Vib. 332 6016

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混沌背景下非平稳谐波信号的自适应同步挤压小波变换提取

1. 武汉理工大学, 交通物联网技术湖北省重点实验室, 武汉 430063;

2. 武汉科技大学信息科学与工程学院, 武汉 430081;

3. 武汉科技大学理学院, 武汉 430065

通信作者: 汪祥莉, wwb0178@163.com

基金项目:

国家自然科学基金（批准号：61473213）、湖北省自然科学基金（批准号：2015CFB424，2015CFB602）和武汉理工大学交通物联网技术湖北省重点实验室开放基金（批准号：2015Ⅲ015-B02）资助的课题.

收稿日期: 2016-05-26

修回日期: 2016-06-25

刊出日期: 2016-10-20

摘要: 针对同步挤压小波变换（SST）在提取混沌背景下非平稳谐波信号时的不足，提出一种改进的自适应最优累加频率范围的SST非平稳谐波信号提取方法.首先根据非平稳谐波信号小波系数与小波基支撑区间的关系，推导非平稳谐波SST提取时自适应累加频率范围的计算公式；然后，利用最小能量误差准则确定自适应累加频率范围公式中参数的最优值，从而实现非平稳谐波信号的SST自适应提取.分别在Lorenz混沌背景和Duffing混沌背景下对不同类型的非平稳谐波信号进行了实验分析，实验结果表明，该方法能有效地从含噪混沌背景中提取非平稳谐波信号，与经典的单一累加频率范围的SST方法相比，提取结果在均方误差和相关系数两方面都有较好的提高.

关键词:

Extractraction of non-stationary harmonic from chaotic background based on synchrosqueezed wavelet transform

1.
Hubei Key Laboratory of Transportation Internet of Things, Wuhan University of Technology, Wuhan 430063, China;

2.
School of Information Science and Engineering, Wuhan University of Science and Technology, Wuhan 430081, China;

3.
College of Science, Wuhan University of Science and Technology, Wuhan 430065, China

Fund Project:

Project supported by the National Natural Science Fund of China (Grant No. 61473213), the Natural Science Foundation of Hubei Province, China (Grant Nos. 2015CFB424, 2015CFB602), and the Hubei Key Laboratory of Transportation Internet of Things Foundation, China (Grant No. 2015III015-B02).

Received Date: 26 May 2016

Accepted Date: 25 June 2016

Published Online: 20 October 2016

Abstract: The signal detection in chaotic background has gradually become one of the research focuses in recent years. Previous research showed that the measured signals were often unavoidable to be contaminated by the chaotic noise, such as the radar signal detection from sea clutter wave,signal source extraction from chaotic secure communication and ECG/EEG abnormal signal detection,etc.At present,there are two methods to detect the target signal from the chaotic background.One is to detect the target signals by using the difference in geometric structure between the chaotic signal and the target signal,and the other is to regard the chaotic signal as the noise,and the target signal is extracted from the chaotic background by the time frequency analysis method,such as wavelet transform and empirical mode decomposition. The first kind of method can detect the target signal well,but it needs to characterize the chaotic system and reconstruct the phase space,which is difficult in the practical applications.The second kind of method does not need to reconstruct the chaotic phase space and can effectively extract the target signal from the chaotic background.However,the wavelet transform lacks adaption and how to select the optimal wavelet basis and decomposition layers is a difficult problem.In the empirical mode decomposition there exists the mode mixing that is very sensitive to the noise.The synchrosqueezed wavelet transform (SST) effectively improves the mixing of mode by compressing the continuous wavelet coefficients in the frequency direction,but also it has good robustness to noise.Therefore,the SST can extract the harmonic signal well from the chaotic background.In the present algorithm of abstracting harmonic signal from chaotic background by SST,the harmonic signals are extracted by using single accumulation frequency range SST (SAFR-SST) based on wavelet ridge detection.If the target signal is stable harmonic signal,whose frequency does not change with time,the SAFR-SST method can have a high abstraction precision.But if the target signal is the non-stable harmonic signal whose frequency changes with time,the SAFR-SST method is not enough nor can obtain high abstraction precision.In order to overcome the shortcomings of the SST in extracting the non-stationary harmonic signal from the chaotic background, an improved SST extracting method is proposed which is based on the adaptive optimal cumulative frequency range. Firstly,the formulas of calculating the adaptive cumulative frequency range in SST extraction are deduced according to the relationship between the wavelet coefficient of non-stationary harmonic and the interval of supporting wavelet bases.Then,the optimal values of the parameters in the adaptive cumulative frequency range formula are calculated by the minimum energy error criterion according to the integrity and orthogonality of the intrinsic mode types function.Finally,the SST adaptive extraction of the non-stationary harmonic signal is realized according to the SST inverse transform.In experiment,the different types of non-stationary harmonics are extracted from the Lorenz and Duffing chaotic background.The experimental results show that the proposed method can effectively extract the non-stationary harmonic from the noisy chaotic background.Compared with the classical SST method with single cumulative frequency range,the proposed method has good performance in both mean square error and correlation coefficient.And when the chaotic background contains different-intenity Gauss white noises,the proposed method can also effectively abstract the non-stationary harmonic from the chaos and noise interference.So,the proposed method has a good practice value.

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