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The chaos detection method based on Holmes Duffing equation is studied. Since this method is suitable only for the detection of a single signal frequency, the selection of the equation parameters is inconvenient, and the noise may affect the detection results, we propose a new method of detecting weak characteristic signals based on the scale transformation of Duffing oscillator. The numerical simulation shows that the proposed method can be used to detect harmonic signal with any frequency and phase by only a set of determined parameters.
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Keywords:
- Duffing oscillator /
- weak characteristic signal /
- Gaussian white noise /
- scale transformation
[1] Gao J Z 2005 Detection of Weak Signals (Beijing: Tsinghua University Press) pp19-24 (in Chinese) [高晋占 2005 微弱信号检测(北京:清华大学出版社) 第19-24页]
[2] Zhou K B, Dou C Q, Chen T 2007 J. Wuhan Univ. Technol. 4 53 (in Chinese) [周凯波, 豆成权, 陈涛 2007 武汉理工大学学报 4 53]
[3] Nie C Y 2009 Chaotic Systems and Weak Signal Detection (Beijing: Tsinghua University Press) pp5-6 (in Chinese) [聂春燕 2009 混沌系统与弱信号检测(北京:清华大学出版社) 第5-6页]
[4] Belhaq M, Houssni M 2000 Chaos, Solitons and Fractals 11 1237
[5] Zhai D Q, Liu C X, Liu Y 2010 Acta Phys. Sin. 59 816 (in Chinese) [翟笃庆, 刘崇新, 刘尧 2010 59 816]
[6] Zhang G J, Xu J X, Yao H 2006 Acta Mech. Sin. 38 283 (in Chinese) [张广军, 徐健学, 姚宏 2006 力学学报 38 283]
[7] Li Y, Yang B J 2007 Chaotic Oscillator Systems (L-Y) and Detection (Beijing: Science Press) p20 (in Chinese) [李月, 杨宝俊 2007 混沌振子系统(L-Y)与检测(北京:科学出版社) 第20页]
[8] Liu B Z, Peng J H 2004 Nonlinear Dynamics (Beijing: High Education Press) pp132-135 (in Chinese) [刘秉正, 彭建华 2004 非线性动力学(北京:高等教育出版社) 第132-135页]
[9] JiangWL, Zhang S Q,Wang Y Q 2005 Chaos and Wavelet Based Fault Information Diagnosis (Beijing: National Defence Industry Press) pp84-85 (in Chinese) [姜万录, 张淑清, 王益群 2005 基于混沌和小波的故障信息诊断(北京:国防工业出版社) 第84-85页]
[10] Liu Z R, He B L 1994 Perturbation Criteria of Chaos (Shanghai: Shanghai Science and Technology Press) p10 (in Chinese) [刘曾荣, 赫伯林 1994 混沌的微扰判据(上海:上海科技教育出版社) 第10页]
[11] Yi W S, Shi Y W, Nie C Y 2006 Acta Metrologica Sin. 27 156 (in Chinese) [衣文索, 石要武, 聂春燕 2006 计量学报 27 156]
[12] Leng Y G, Leng Y S, Guo Y 2006 J. Sound Vibrat. 292 788
[13] Leng Y G, Wang T Y, Qin X D 2004 Acta Phys. Sin. 53 717 (in Chinese) [冷永刚, 王太勇, 秦旭达 2004 53 717]
[14] Leng Y G, Wang T Y 2007 Mech. Syst. Sign. Proces. 21 138
[15] Leng Y G 2009 Acta Phys. Sin. 58 5196 (in Chinese) [冷永刚 2009 58 5196]
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[1] Gao J Z 2005 Detection of Weak Signals (Beijing: Tsinghua University Press) pp19-24 (in Chinese) [高晋占 2005 微弱信号检测(北京:清华大学出版社) 第19-24页]
[2] Zhou K B, Dou C Q, Chen T 2007 J. Wuhan Univ. Technol. 4 53 (in Chinese) [周凯波, 豆成权, 陈涛 2007 武汉理工大学学报 4 53]
[3] Nie C Y 2009 Chaotic Systems and Weak Signal Detection (Beijing: Tsinghua University Press) pp5-6 (in Chinese) [聂春燕 2009 混沌系统与弱信号检测(北京:清华大学出版社) 第5-6页]
[4] Belhaq M, Houssni M 2000 Chaos, Solitons and Fractals 11 1237
[5] Zhai D Q, Liu C X, Liu Y 2010 Acta Phys. Sin. 59 816 (in Chinese) [翟笃庆, 刘崇新, 刘尧 2010 59 816]
[6] Zhang G J, Xu J X, Yao H 2006 Acta Mech. Sin. 38 283 (in Chinese) [张广军, 徐健学, 姚宏 2006 力学学报 38 283]
[7] Li Y, Yang B J 2007 Chaotic Oscillator Systems (L-Y) and Detection (Beijing: Science Press) p20 (in Chinese) [李月, 杨宝俊 2007 混沌振子系统(L-Y)与检测(北京:科学出版社) 第20页]
[8] Liu B Z, Peng J H 2004 Nonlinear Dynamics (Beijing: High Education Press) pp132-135 (in Chinese) [刘秉正, 彭建华 2004 非线性动力学(北京:高等教育出版社) 第132-135页]
[9] JiangWL, Zhang S Q,Wang Y Q 2005 Chaos and Wavelet Based Fault Information Diagnosis (Beijing: National Defence Industry Press) pp84-85 (in Chinese) [姜万录, 张淑清, 王益群 2005 基于混沌和小波的故障信息诊断(北京:国防工业出版社) 第84-85页]
[10] Liu Z R, He B L 1994 Perturbation Criteria of Chaos (Shanghai: Shanghai Science and Technology Press) p10 (in Chinese) [刘曾荣, 赫伯林 1994 混沌的微扰判据(上海:上海科技教育出版社) 第10页]
[11] Yi W S, Shi Y W, Nie C Y 2006 Acta Metrologica Sin. 27 156 (in Chinese) [衣文索, 石要武, 聂春燕 2006 计量学报 27 156]
[12] Leng Y G, Leng Y S, Guo Y 2006 J. Sound Vibrat. 292 788
[13] Leng Y G, Wang T Y, Qin X D 2004 Acta Phys. Sin. 53 717 (in Chinese) [冷永刚, 王太勇, 秦旭达 2004 53 717]
[14] Leng Y G, Wang T Y 2007 Mech. Syst. Sign. Proces. 21 138
[15] Leng Y G 2009 Acta Phys. Sin. 58 5196 (in Chinese) [冷永刚 2009 58 5196]
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