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将Levy噪声与幂函数型单稳随机共振系统相结合, 为确保实验数据的可靠性, 以平均信噪比增益为衡量指标, 针对Levy噪声激励下的随机共振现象进行了研究. 详细介绍了单稳系统势函数形式及Levy噪声的产生原理, 深入探究了不同特征指数 和不同对称参数 取值条件下, 单稳系统参数a和b、Levy噪声强度放大系数D对幂函数型单稳系统共振输出的作用规律. 研究结果表明, 在任意Levy噪声分布条件下, 通过对系统参数a和b的适当调整均能诱导随机共振, 完成微弱信号检测, 且有多个随机共振区间与之对应, 同时这些区间不随 或 的改变而改变; 此外, 在研究噪声诱导的随机共振时也发现了同样的规律, 通过调节噪声强度放大系数D也能产生随机共振, 且随机共振区间也不随 或 的改变而改变; 最后, 在研究系统参数a和b之间的相互作用关系时发现, 一个系统参数的随机共振取值区间会随着另一个系统参数的改变而改变. 所获得的研究结果有效解决了Levy噪声激励下幂函数型单稳随机共振系统的系统参数、噪声强度放大系数的选择问题, 为其应用于工程实践提供了可靠的理论依据.In this paper, the Levy noise is combined with a power function type monostable stochastic resonance system for the first time. In order to ensure the reliability of the experimental data, the average signal-to-noise ratio gain is regarded as an index to investigate the stochastic resonance phenomenon stimulated by Levy noise. Potential function form of the monostable system and the method of generating Levy noise are presented in detail. The pulse characteristic and smear characteristic of Levy noise are also presented in detail. The laws for the resonant output of monostable system, governed by parameters a and b, the intensity amplification factor D of Levy noise, are explored under different values of characteristic index and symmetry parameter of Levy noise. Results show that no matter whether it is under any different characteristic index or symmetry parameter of Levy noise, the weak signal can be detected by adjusting the system parameters a and b. The intervals of a and b which can induce stochastic resonances are multiple, and do not change with nor . Moreover, the same rule is founded which by adjusting the intensity amplification factor D of Levy noise can also realize synergistic effect when studying the noise-induced stochastic resonance, and the interval of D does not change with nor ; the best value of characteristic index is =1 under any system parameter, and the best value of symmetry parameter is =1 under any system parameter. So, the system performance is best when =1 and =1. Finally, the interaction relationship between system parameters a and b is investigated, and it is found that the interval of a or b will change with b or a when characteristic index , symmetry parameter and the intensity amplification factor D of Levy noise are fixed. These results will contribute to reasonably choosing the system parameters and intensity amplification factor of power function type monostable stochastic resonance system under Levy noise, and provide a reliable basis for practical engineering application of weak signal detection by stochastic resonance.
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Keywords:
- Levy noise /
- power function type monostable system /
- stochastic resonance /
- average signal-to-noise ratio gain
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[22] Gitterman M 2005 Physica A 352 309
[23] Gilbarg D, Trudinger N 2001 Elliptic Partial Differential Equations of Second Order (Berlin: Springer) pp149, 152
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[26] Chambers J M 1976 J. Am. Stat. Assoc. 71 340
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[30] Wan P, Zhan Y J, Li X C, Wang Y H 2011 Acta Phys. Sin. 60 040502 (in Chinese) [万频, 詹宜巨, 李学聪, 王永华 2011 物理学报 60 040502]
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[1] Beniz R, Sutera A, Vulplana A 1981 Physica A 14 453
[2] Beniz R, Parisi G, Srutera A, Vulplana A 1982 Tellus 34 11
[3] Leng Y G, Leng Y S, Wang T Y, Guo Y 2006 J. Sound Vib. 292 788
[4] Lin L F, Tian Y, Ma H 2014 Chin. Phys. B 23 080503
[5] Lemarchand A, Gorecki J, Gorecki A, Nowakowski B 2014 Phys. Rev. E 89 022916
[6] Tang Y, Gao H J, Zou W, Kurths J 2013 Phys. Rev. E 87 062920
[7] Wang K K, Liu X B 2014 Chin. Phys. B 23 010502
[8] Liu H B, Wu D W, Dai C J, Mao H 2013 Acta Elec. Sin. 41 9 (in Chinese) [刘海波, 吴德伟, 戴传金, 毛虎 2013 电子学报 41 9]
[9] Zhang L Y, Jin G X, Cao L, Wang Z Y 2012 Chin. Phys. B 21 120502
[10] Yang J H, Liu X B 2010 Chin. Phys. B 19 050504
[11] Zhao L, Luo X Q, Wu D, Zhu S Q, Gu J H 2010 Chin. Phys. Lett. 27 040503
[12] Jiao S B, Ren C, Li P H, Zhang Q, Xie G 2014 Acta Phys. Sin. 63 070501 (in Chinese) [焦尚彬, 任超, 李鹏华, 张青, 谢国 2014 物理学报 63 070501]
[13] Zhang W Y, Wang Z L, Zhang W D 2009 Cont. Eng. Chin. 16 639 (in Chinese) [张文英, 王自力, 张卫东 2009 控制工程 16 639]
[14] Li P, Nie L R, Huang Q R, Sun X X 2012 Chin. Phys. B 21 050503
[15] Leng Y G, Leng Y S, Guo Y 2006 J. Sound Vib. 292 788
[16] Leng Y G, Wang T Y 2007 Mech. Sys. Signal Process. 21 138
[17] Zhu W N, Lin M 2014 J. Vib. Shock 33 143 (in Chinese) [朱维娜, 林敏 2014 振动与冲击 33 143]
[18] Lei Y G, Han D, Lin J, He Z J, Tan J Y 2012 J. Mech. Eng. 48 63 (in Chinese) [雷亚国, 韩冬, 林京, 何正嘉, 谭继勇 2012 机械工程学报 48 63]
[19] Li J M, Chen X F, He Z J 2011 J. Mech. Eng. 47 58 (in Chinese) [李继猛, 陈雪峰, 何正嘉 2011 机械工程学报 47 58]
[20] Ji Y D, Zhang L, Luo M K 2014 Acta Phys. Sin. 63 164302 (in Chinese) [季袁冬, 张路, 罗懋康 2014 物理学报 63 164302]
[21] Doiron B, Lindner B, Longtin A, Maler L, Bastian J 2004 Phys. Rev. Lett. 93 048101
[22] Gitterman M 2005 Physica A 352 309
[23] Gilbarg D, Trudinger N 2001 Elliptic Partial Differential Equations of Second Order (Berlin: Springer) pp149, 152
[24] Xu B H, Zeng L Z, Li J L 2007 Sound Vib. 303 255
[25] Dybiec B, Gudowska-Nowak E 2006 Acta Phys. Polo. B 37 1479
[26] Chambers J M 1976 J. Am. Stat. Assoc. 71 340
[27] Weron A, Weron R 1995 Lec. Notes Phys. 457 379
[28] Weron R 1996 Statist. Prob. Lett. 28 165
[29] Gong C, Wang Z L 2008 MATLAB Language Commonly Used Algorithm for Assembly (Beijing: Publishing House of Electronics Industry) (in Chinese) [龚纯, 王正林2008 MATLAB语言常用算法程序集 (北京: 电子工业出版社) ]
[30] Wan P, Zhan Y J, Li X C, Wang Y H 2011 Acta Phys. Sin. 60 040502 (in Chinese) [万频, 詹宜巨, 李学聪, 王永华 2011 物理学报 60 040502]
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