随机共振动力学机理及其微弱信号检测方法的研究

范剑; 赵文礼; 张明路; 檀润华; 王万强

doi:10.7498/aps.63.110506

摘要

目前已有的随机共振理论对于随机共振系统的非线性动力学行为及其发生机理阐释得不够具体和明晰，本文从分析一阶非线性Duffing方程的动力学特性入手，推导得到非自治Duffing方程的吸引子曲线，基于该曲线和输入信号之间的映射关系分析了系统输出的动力学行为，并由此进一步定性分析了随机共振现象发生的动力学机理；研究表明：作用于系统的内禀信号能推动系统动点沿吸引子曲线移动，它对系统的输出起内在的和本质的作用，而噪声在一定条件下能够诱发系统产生跃迁行为；文章最后利用该动力学机理对已有的调参数和调阻尼等基于随机共振的微弱信号检测方法作了统一和延拓.

关键词:

Abstract

According to the exited stochastic resonance theory, we cannot obtain the dynamic behavior of a stochastic resonance (SR) system intuitively. In order to reveal the dynamic mechanism of SR, a kind of first-order Duffing equation attractor is analyzed at first, and then the property of nonlinear Duffing equation is studied, based on which the nonautonomous Duffing equation attractor curve is deduced. The output of SR system can be obtained by mapping the input signal on the attractor curve, and the dynamic mechanism of SR is explained by using the mapping method. Analysis of the result indicates that the intrinsic signal can push the system to move along the attractor curve, and the noise can evoke a transition response of the system under the given conditions. Some exited SR weak signal detection methods, such as the parameter-adjustment and damping-adjustment are extended by the proposed dynamic mechanism.

Keywords:

作者及机构信息

1.
河北工业大学机械工程学院, 天津 300401;

2.
杭州电子科技大学机械工程学院, 杭州 310018;

3.
台州学院机电工程系, 台州 318000

基金项目: 国家自然科学基金（批准号：50875070）和浙江省教育厅科研项目（批准号：Y201326915）资助的课题.

Authors and contacts

1.
School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, China;

2.
School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China;

3.
Department of Mechanical & Electrical Engineering, Taizhou University, Taizhou 318000, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 50875070), the Scientific Research Fund of Zhejiang Provincial Education Department and the Technology Research of China (Grant No. Y201326915).

参考文献

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[2]	Hu G, Qing G R, Gong D C 1991 Phys. Rev. A 44 6414
[3]	McNamara B, Wiesenfeld K 1989 Phys. Rev. A 39 4854
[4]	Dykman M I 1990 Phys. Rev. Lett. 65 2606
[5]	Gammaitoni L, Marchesoni F 1989 Phys. Rev. Lett. 62 349
[6]	Dykman M I, Haken H, Hu G 1993 Phys. Lett. A 180 332
[7]	Dykman M I, Luchinsky D G, Mannella R 1994 Phys. Lett. A 193 61
[8]	Zhou T, Moss F 1990 Phys. Rev. A 41 4255
[9]	Choi M H, Fox R F, Jung P 1998 Phys. Rev. E 57 6335
[10]	Giacomelli G, Marin F, Rabbiosi I 1999 Phys. Rev. Lett. 82 675
[11]	Jung P, P Hänggi 1989 Euro. phys. Lett. 8 505
[12]	Hu G, Nicolis G, Nicolis C 1990 Phys. Rev. A 42 2030
[13]	Lu Z H, Lin J H, Hu G 1993 Acta Phys. Sin. 42 1556 (in Chinese)[卢志恒, 林建恒, 胡岗 1993 42 1556]
[14]	Li X L, Leng Y G, Fan S B, Shi P 2011 J. Vibration and Shock. 30 78 (in Chinese) [李晓龙, 冷永刚, 范胜波, 石鹏 2011 振动与冲击 30 78]
[15]	Peng H, Zhong S C, Ma H 2013 Acta Phys. Sin. 62 080501 (in Chinese)[彭皓, 钟苏川, 马洪 2013 62 080501]
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[17]	Lin M, Fang L M, Zheng Y J 2009 Chin. Phys. B 18 1725
[18]	Li J L, Zeng L Z 2011 Chin. Phys. B 20 010503
[19]	Zhang L Y, Jin G X, Cao L, Wang Z Y 2012 Chin. Phys. B 21 120502
[20]	Jiang S Q, Hou M J, Jia C H, He J R, Gu T X 2009 Chin. Phys. B 18 2667
[21]	Leng Y G, Wang T Y, Guo Y 2007 Acta Phys. Sin. 56 30 (in Chinese)[冷永刚, 王太勇, 郭焱 2007 56 30]
[22]	Leng Y G 2011 Acta Phys. Sin. 60 020503 (in Chinese)[冷永刚 2011 60 020503]
[23]	Wang G F, Ouyang S, Zhang H R 2010 J. Guilin Univ. Elec. Tec. 30 396 (in Chinese) [王国富, 欧阳缮, 张海如 2010 桂林电子科技大学学报 30 396]
[24]	Qu Y, Wang F Z, Sun J J 2011 Sci. sin. 41 1190 (in Chinese) [曲媛, 王辅忠, 孙静静 2011 中国科学 41 1190]
[25]	Zhao W L, Wang J, Wang L Z 2013 Chaos 23 033117
[26]	Fan Y Y, Li L P, Dang R R 2013 Chin. J. Scie. Ins. 34 566 (in Chinese) [樊养余, 李利品, 党瑞荣 2013 仪器仪表学报 34 566]
[27]	Zhao W L, Liu J, Yin Y P 2011 Chin. J. Scie. Ins. 32 721 (in Chinese) [赵文礼, 刘进, 殷园平 2011 仪器仪表学报 32 721]
[28]	Leng Y G, Wang T Y 2003 Acta Phys. Sin. 52 2431 (in Chinese)[冷永刚, 王太勇 2003 52 2431]
[29]	Wang L Z, Zhao W L, Chen X 2012 Acta Phys. Sin. 61 160501 (in Chinese)[王林泽, 赵文礼, 陈旋 2012 61 160501]

施引文献

[1]	Benzi R, Parisi G, Sutera A, Vulpiana A 1981 J. Phys. A: Math. Gen. 14 453
[2]	Hu G, Qing G R, Gong D C 1991 Phys. Rev. A 44 6414
[3]	McNamara B, Wiesenfeld K 1989 Phys. Rev. A 39 4854
[4]	Dykman M I 1990 Phys. Rev. Lett. 65 2606
[5]	Gammaitoni L, Marchesoni F 1989 Phys. Rev. Lett. 62 349
[6]	Dykman M I, Haken H, Hu G 1993 Phys. Lett. A 180 332
[7]	Dykman M I, Luchinsky D G, Mannella R 1994 Phys. Lett. A 193 61
[8]	Zhou T, Moss F 1990 Phys. Rev. A 41 4255
[9]	Choi M H, Fox R F, Jung P 1998 Phys. Rev. E 57 6335
[10]	Giacomelli G, Marin F, Rabbiosi I 1999 Phys. Rev. Lett. 82 675
[11]	Jung P, P Hänggi 1989 Euro. phys. Lett. 8 505
[12]	Hu G, Nicolis G, Nicolis C 1990 Phys. Rev. A 42 2030
[13]	Lu Z H, Lin J H, Hu G 1993 Acta Phys. Sin. 42 1556 (in Chinese)[卢志恒, 林建恒, 胡岗 1993 42 1556]
[14]	Li X L, Leng Y G, Fan S B, Shi P 2011 J. Vibration and Shock. 30 78 (in Chinese) [李晓龙, 冷永刚, 范胜波, 石鹏 2011 振动与冲击 30 78]
[15]	Peng H, Zhong S C, Ma H 2013 Acta Phys. Sin. 62 080501 (in Chinese)[彭皓, 钟苏川, 马洪 2013 62 080501]
[16]	Guo F, Luo X D, Li S F, Zhou Y R 2010 Chin. Phys. B 19 080502
[17]	Lin M, Fang L M, Zheng Y J 2009 Chin. Phys. B 18 1725
[18]	Li J L, Zeng L Z 2011 Chin. Phys. B 20 010503
[19]	Zhang L Y, Jin G X, Cao L, Wang Z Y 2012 Chin. Phys. B 21 120502
[20]	Jiang S Q, Hou M J, Jia C H, He J R, Gu T X 2009 Chin. Phys. B 18 2667
[21]	Leng Y G, Wang T Y, Guo Y 2007 Acta Phys. Sin. 56 30 (in Chinese)[冷永刚, 王太勇, 郭焱 2007 56 30]
[22]	Leng Y G 2011 Acta Phys. Sin. 60 020503 (in Chinese)[冷永刚 2011 60 020503]
[23]	Wang G F, Ouyang S, Zhang H R 2010 J. Guilin Univ. Elec. Tec. 30 396 (in Chinese) [王国富, 欧阳缮, 张海如 2010 桂林电子科技大学学报 30 396]
[24]	Qu Y, Wang F Z, Sun J J 2011 Sci. sin. 41 1190 (in Chinese) [曲媛, 王辅忠, 孙静静 2011 中国科学 41 1190]
[25]	Zhao W L, Wang J, Wang L Z 2013 Chaos 23 033117
[26]	Fan Y Y, Li L P, Dang R R 2013 Chin. J. Scie. Ins. 34 566 (in Chinese) [樊养余, 李利品, 党瑞荣 2013 仪器仪表学报 34 566]
[27]	Zhao W L, Liu J, Yin Y P 2011 Chin. J. Scie. Ins. 32 721 (in Chinese) [赵文礼, 刘进, 殷园平 2011 仪器仪表学报 32 721]
[28]	Leng Y G, Wang T Y 2003 Acta Phys. Sin. 52 2431 (in Chinese)[冷永刚, 王太勇 2003 52 2431]
[29]	Wang L Z, Zhao W L, Chen X 2012 Acta Phys. Sin. 61 160501 (in Chinese)[王林泽, 赵文礼, 陈旋 2012 61 160501]

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