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In the paper, we analyse the basic dynamical model of the chaotic oscillator by using the theory of intermittent chaos to construct the column of the intermittent chaos, and present an effective method to detect the weak underwater acoustic signal with an unknown frequency. Duffing oscillator is sensitive to phase transformation from chaos to intermittent chaos, whose frequency difference is slightly different from that between the driving force signal and the signal to be detected. By employing this theory, we detect the frequency of the ship signal in ocean background noise. For the detection by using the intermittent chaos, there exists no effective way to estimate the frequency of the signal to be detected, which can only be judged by empirical methods and therefore the man-made error will exist. All of these will affect the consequence of the intermittent chaos and make the practical application difficult. To solve this problem, in this paper, we first study the basic theory of the chaotic system, then construct the simulated signal to examine the system, and finally detect the ship signal. To make the detection feasible, a chaotic oscillator column is considered to sweep through the unknown frequency of the signal. By using this method, we can obtain the frequency range. Finally Hilbert transform is used to detect the envelope of the intermittent chaos followed by measuring the frequency of the envelope through using Fourier spectrum. Thus the frequency of the signal can be calculated by using the function describing the relationship among the driving force signal, ship signal and the envelope. The simulations and the detection processing of the measured acoustic signal are carried out by using the proposed method, which can effectively detect the frequency of the ship signal embedded within strong background noise and also the frequency of the signal to be detected can be calculated, which is conducive to solving the presently existing problem about frequency estimation. Signal-to-noise ratio can be enhanced by 4.4 dB based on the method by using the Hilbert transform compared with by using the method just through using an intermittent chaotic oscillator column, which verifies the effectiveness of the method in this paper.
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Keywords:
- Duffing oscillator /
- intermittent chaos /
- Hilbert transform /
- envelope detection
[1] Xia J Z, Liu Y H, Leng Y G, Ge J T 2011 Noise and Vibration Control 31 156 (in Chinese) [夏均忠, 刘远宏, 冷永刚, 葛纪桃 2011噪声与振动控制 31 156]
[2] Li Y, Yang B J 2004 Chaotic Oscillator Detection Introduction (Beijing: Publishing House of Electronics Industy) p29 (in Chinese) [李月, 杨宝俊 2004 混沌振子检测引论 (北京: 电子工业出版社) 第29页]
[3] Gao J Z 2005 Weak Signal Detection (Beijing: Tsinghua University Press) p2 (in Chinese) [高晋占 2005 微弱信号检测 (北京: 清华大学出版社)第2页]
[4] Zhou K B, Dou C Q, Chen T 2007 J. Wuhan Univ. Technol. 29 53 (in Chinese) [周凯波, 豆成权, 陈涛 2007 武汉理工大学学报 29 53]
[5] Nie C Y 2009 Chaotic Systems with Weak Signal Detection (Beijing: Tsinghua University Press) p38 (in Chinese) [聂春燕 2009 混沌系统与微弱信号检测(北京: 清华大学出版社) 第38页]
[6] Birx D L 1992 IEEE International Joint Conference on Neural Networks Baltimore, MD, USA, June 7-11, 1992 881
[7] Qin H L, Sun X L, Jin T 2010 10th International Conference on Signal Processing Beijing, China, October 24-28, 2010 p2501
[8] Li Y, Shi Y W, Ma H T, Yang B J 2004 Acta Electron. Sin. 32 87 (in Chinese) [李月, 石要武, 马海涛, 杨宝俊 2004 电子学报 32 87]
[9] Lai Z H, Leng Y G, Sun J Q, Feng S B 2012 Acta Phys. Sin. 61 050503 (in Chinese) [赖志慧, 冷永刚, 孙建桥, 范胜波 2012 物理学报 61 050503]
[10] Fan J, Zhao W L, Wang W Q 2013 Acta Phys. Sin. 62 180502 (in Chinese) [范剑, 赵文礼, 王万强 2013 物理学报 62 180502]
[11] Cong C, Li X K, Song Y 2014 Acta Phys. Sin. 63 064301 (in Chinese) [丛超, 李秀坤, 宋扬 2014 物理学报 63 064301]
[12] Li Y, Yang B J 2007 Chaotic Vibration Subsystem (L-Y) and Detection (Beijing: Science Press) p57 (in Chinese) [李月, 杨宝俊 2007 混沌阵子系统(L-Y)与检测 (北京: 科学出版社) p57]
[13] Liu B Z, Peng J H 2004 Nonlinear Dynamics (Beijing: Higher Education Press) p143 (in Chinese) [刘秉正, 彭建华 2004 非线性动力学 (北京: 高等教育出版社) p143]
[14] Zhu L P, Zhang L Y, Xie W F, Li N 2012 Radio Engineering 42 17 (in Chinese) [朱来普, 张陆勇, 谢文凤, 李楠 2012 无线电工程 42 17]
[15] Wang Y, Chen D J 1999 Trans. Industrial. Electron. 46 440
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[1] Xia J Z, Liu Y H, Leng Y G, Ge J T 2011 Noise and Vibration Control 31 156 (in Chinese) [夏均忠, 刘远宏, 冷永刚, 葛纪桃 2011噪声与振动控制 31 156]
[2] Li Y, Yang B J 2004 Chaotic Oscillator Detection Introduction (Beijing: Publishing House of Electronics Industy) p29 (in Chinese) [李月, 杨宝俊 2004 混沌振子检测引论 (北京: 电子工业出版社) 第29页]
[3] Gao J Z 2005 Weak Signal Detection (Beijing: Tsinghua University Press) p2 (in Chinese) [高晋占 2005 微弱信号检测 (北京: 清华大学出版社)第2页]
[4] Zhou K B, Dou C Q, Chen T 2007 J. Wuhan Univ. Technol. 29 53 (in Chinese) [周凯波, 豆成权, 陈涛 2007 武汉理工大学学报 29 53]
[5] Nie C Y 2009 Chaotic Systems with Weak Signal Detection (Beijing: Tsinghua University Press) p38 (in Chinese) [聂春燕 2009 混沌系统与微弱信号检测(北京: 清华大学出版社) 第38页]
[6] Birx D L 1992 IEEE International Joint Conference on Neural Networks Baltimore, MD, USA, June 7-11, 1992 881
[7] Qin H L, Sun X L, Jin T 2010 10th International Conference on Signal Processing Beijing, China, October 24-28, 2010 p2501
[8] Li Y, Shi Y W, Ma H T, Yang B J 2004 Acta Electron. Sin. 32 87 (in Chinese) [李月, 石要武, 马海涛, 杨宝俊 2004 电子学报 32 87]
[9] Lai Z H, Leng Y G, Sun J Q, Feng S B 2012 Acta Phys. Sin. 61 050503 (in Chinese) [赖志慧, 冷永刚, 孙建桥, 范胜波 2012 物理学报 61 050503]
[10] Fan J, Zhao W L, Wang W Q 2013 Acta Phys. Sin. 62 180502 (in Chinese) [范剑, 赵文礼, 王万强 2013 物理学报 62 180502]
[11] Cong C, Li X K, Song Y 2014 Acta Phys. Sin. 63 064301 (in Chinese) [丛超, 李秀坤, 宋扬 2014 物理学报 63 064301]
[12] Li Y, Yang B J 2007 Chaotic Vibration Subsystem (L-Y) and Detection (Beijing: Science Press) p57 (in Chinese) [李月, 杨宝俊 2007 混沌阵子系统(L-Y)与检测 (北京: 科学出版社) p57]
[13] Liu B Z, Peng J H 2004 Nonlinear Dynamics (Beijing: Higher Education Press) p143 (in Chinese) [刘秉正, 彭建华 2004 非线性动力学 (北京: 高等教育出版社) p143]
[14] Zhu L P, Zhang L Y, Xie W F, Li N 2012 Radio Engineering 42 17 (in Chinese) [朱来普, 张陆勇, 谢文凤, 李楠 2012 无线电工程 42 17]
[15] Wang Y, Chen D J 1999 Trans. Industrial. Electron. 46 440
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