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Aiming at the blind angle in detecting weak signals of the same frequency by Duffing oscillator, a novel method of dephasing for the driving signals is proposed to eliminate the blind angle. According to the characteristic of weak signals, expression of blind angle is analyzed, and then the range of blind angle is found out, which corresponds to the amplitude of a new driven signal synthesized from the original driven signals and the unknown one. By making the original driven signal phase shift a degree of π, detection for the same frequency signal can be realized when the synthesized signal is located in the blind angle region, whose feasibility is proven by an experiment that it remains in chaotic status in the case of blind angle but becomes a great period status after the original driven signal's phase is dephased by π. To overcome the drawbacks of qualitative analysis and distinguish effectively different status in signal detection course, a detection statistics based on likelihood-Halmiton system is constructed. On the basis of it, a diagram of detection for any frequency signal is drawn. The key point is to make it as an unknown signal's frequency range where there are two adjacent frequency values whose corresponding detection statistics both located in the range of intermittent chaotic status, while one of them is just corresponding to the maximum value of the detection statistics. By simulations of different circumstances, detection statistics for numerical ranges of chaos, intermittent chaos, and great period is summarized. Furthermore, detection for any frequency signal may be realized by use of the numerical range. It is shown that the proposed method could not only provide quantitative judgment for the system status, but improve the signal detection performance. Also, it could be combined well with the traditional oscillator array method or adaptive step intermittent chaotic oscillator method, which further can improve some existing signal detection methods with Duffing oscillator.
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Keywords:
- Duffing oscillator /
- weak signal /
- blind angle /
- detection statistic
[1] Xu Y C, Yang C L 2010 J. Harbin Institute Technol. 42 446
[2] Chen M J, Ling H L, Liu Y H, Qu S X, Ren W 2014 Chin. Phys. B 23 028701
[3] Birx D I 1992 IEEE Int. Joint Conf. Neural Networks 22 881
[4] Zhang X Y, Guo H X, Wang B H 2007 Chin. Sci. Bull. 52 1906
[5] Shi S H, Yuan Y, Wang H Q, Luo M K 2011 Chin. Phys. Lett. 28 040502
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[9] 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]
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[11] Yang M, An J P, Chen N, Wei J C 2011 Trans. Beijing Institute Technol. 31 329 (in Chinese) [杨淼, 安建平, 陈宁, 卫景宠 2011 北京理工大学学报 31 329]
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[13] Wang Y S, Jiang W Z, Zhao J J, Fan H D 2008 Acta Phys. Sin. 57 2053 (in Chinese) [王永生, 姜文志, 赵建军, 范洪达 2008 物理学报 57 2053]
[14] Jiang W L, Wu S Q, Zhang J C 2002 J. Yanshan Univ. 26 114 (in Chinese) [姜万录, 吴胜强, 张建成 2002 燕山大学学报 26 114]
[15] 15Xu Y C 2010 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese) [徐艳春 2010 博士学位论文 (哈尔滨:哈尔滨工业大学)]
[16] Wang G Y, Chen D J, Lin J Y, Chen X 1999 IEEE Trans. Industr. Electron. 46 440
[17] Vahedi H, Gharehpetian G B, Karrari M 2012 IEEE Trans. Power Delivery 27 1973
[18] Fan J, Zhao W L, Zhang M L, Tan R H, Wang W Q 2014 Acta Phys. Sin. 63 110506 (in Chinese) [范剑, 赵文礼, 张明路, 檀润华, 王万强 2014 物理学报 63 110506]
[19] Wei H D, Gan L, Li L P 2012 J. Univ. Electron. Sci. Technol. China 41 203 (in Chinese) [魏恒东, 甘露, 李立萍 2012 电子科技大学学报 41 203]
[20] Jin T, Zhang H 2011 Sci. China: Inform. Sci. 41 1184 (in Chinese) [金天, 张骅 2011 中国科学: 信息科学 41 1184]
[21] Yuan R S, Ma Y A, Yuan B, Ao P 2014 Chin. Phys. B 23 010505
[22] Lu P, Li Y 2005 Acta Electron. Sin. 33 527 (in Chinese) [路鹏, 李月 2005 电子学报 33 527]
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[1] Xu Y C, Yang C L 2010 J. Harbin Institute Technol. 42 446
[2] Chen M J, Ling H L, Liu Y H, Qu S X, Ren W 2014 Chin. Phys. B 23 028701
[3] Birx D I 1992 IEEE Int. Joint Conf. Neural Networks 22 881
[4] Zhang X Y, Guo H X, Wang B H 2007 Chin. Sci. Bull. 52 1906
[5] Shi S H, Yuan Y, Wang H Q, Luo M K 2011 Chin. Phys. Lett. 28 040502
[6] Wang Y C, Zhao Q C, Wang A B 2008 Chin. Phys. B 17 2373
[7] Wen Z, Li L P 2007 Acta Automat. Sin. 33 536 (in Chinese) [文忠, 李立萍 2007 自动化学报 33 536]
[8] Liu H B, Wu D W, Dai C J, Mao H 2013 Acta Electron. Sin. 41 8 (in Chinese) [刘海波, 吴德伟, 戴传金, 毛虎 2013 电子学报 41 8]
[9] 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]
[10] Rui G S, Zhang Y, Miao J, Zhang S, Shi T 2012 Acta Electron. Sin. 40 1269 (in Chinese) [芮国胜, 张洋, 苗俊, 张嵩, 史特 2012 电子学报 40 1269]
[11] Yang M, An J P, Chen N, Wei J C 2011 Trans. Beijing Institute Technol. 31 329 (in Chinese) [杨淼, 安建平, 陈宁, 卫景宠 2011 北京理工大学学报 31 329]
[12] Jimenez-Triana A, Tang K S W, Chen G R 2010 IEEE Trans. Circ. Syst.-II: EXPRESS BRIEFS 57 305
[13] Wang Y S, Jiang W Z, Zhao J J, Fan H D 2008 Acta Phys. Sin. 57 2053 (in Chinese) [王永生, 姜文志, 赵建军, 范洪达 2008 物理学报 57 2053]
[14] Jiang W L, Wu S Q, Zhang J C 2002 J. Yanshan Univ. 26 114 (in Chinese) [姜万录, 吴胜强, 张建成 2002 燕山大学学报 26 114]
[15] 15Xu Y C 2010 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese) [徐艳春 2010 博士学位论文 (哈尔滨:哈尔滨工业大学)]
[16] Wang G Y, Chen D J, Lin J Y, Chen X 1999 IEEE Trans. Industr. Electron. 46 440
[17] Vahedi H, Gharehpetian G B, Karrari M 2012 IEEE Trans. Power Delivery 27 1973
[18] Fan J, Zhao W L, Zhang M L, Tan R H, Wang W Q 2014 Acta Phys. Sin. 63 110506 (in Chinese) [范剑, 赵文礼, 张明路, 檀润华, 王万强 2014 物理学报 63 110506]
[19] Wei H D, Gan L, Li L P 2012 J. Univ. Electron. Sci. Technol. China 41 203 (in Chinese) [魏恒东, 甘露, 李立萍 2012 电子科技大学学报 41 203]
[20] Jin T, Zhang H 2011 Sci. China: Inform. Sci. 41 1184 (in Chinese) [金天, 张骅 2011 中国科学: 信息科学 41 1184]
[21] Yuan R S, Ma Y A, Yuan B, Ao P 2014 Chin. Phys. B 23 010505
[22] Lu P, Li Y 2005 Acta Electron. Sin. 33 527 (in Chinese) [路鹏, 李月 2005 电子学报 33 527]
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