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通过调节双稳系统参数实现大参数频率范围内周期信号的随机共振, 在工程上具有重要意义. 推导了双稳系统参数的归一化变换, 利用归一化变换原理对大参数周期信号的随机共振进行了数值仿真, 阐明该原理适用于任意频率周期信号. 对大参数随机共振用电路模拟进行了实验验证, 揭示了通过调节双稳系统参数可以实现大参数频率范围内的随机共振. 分析了二次采样实现大参数周期信号随机共振的机理, 通过数值仿真与参数归一化变换方法进行了比较. 仿真结果表明, 在输入信号幅度变化的情况下, 二次采样方法易出现发散现象, 而归一化变换具有更好的稳定性与适应性.It is of significance in engineering to achieve stochastic resonance of periodic signal with large frequency by turning the parameters of a bistable system. The normalization transform of bistable system parameter is deduced. Stochastic resonance of periodic signal with large parameters is exhibited by numerical simulation based on the proposed normalization transform, by which an arbitrary high frequency periodic signal can be processed. Analog circuit is used to verify the stochastic resonance happening in the bistable system with large parameters. The mechanism of realizing a periodic signal with large parameters by twice sampling stochastic resonance is analyzed, which is compared with normalization transform method through numerical simulation. The simulation results show that the numerical solution of twice sampling stochastic resonance is prone to being unstable with the variation of mixed input signal amplitude, while the normalization transform method possesses more stability and adaptability.
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Keywords:
- bistable system /
- stochastic resonance with large parameters /
- detection of weak periodic signal /
- numerical simulation
[1] Benzi R, Sutera A, Vulpiana A 1981 Physica A 14 L453
[2] Benzi R, Parisi G, Sutera A, Vulpiana A 1982 Tellus 34 11
[3] Bulsara A R, Gammaitoni L 1996 Phys. Today 49 39
[4] Chen H, Varshney P K 2008 IEEE Trans. Signal Process. 56 5031
[5] Liu Z Q, Zhang H M, Li Y Y, Hua C C, Gu H G 2010 Physica A 389 2642
[6] Sasaki H, Sakane S, Saito H, Todorokihara M, Aoki R 2010 J. Physiol. Sci. 60 138
[7] Zhang H Q, Xu W, Sun C Y, Xu Y 2011 Int. J. Mod. Phys. B 25 1775
[8] Lin M, Huang Y M, Fang L M 2008 Acta Phys. Sin. 57 2041 (in Chinese) [林敏, 黄咏梅, 方利民 2008 物理学报 57 2041]
[9] Leng Y G, Wang T Y 2003 Acta Phys. Sin. 52 2432 (in Chinese) [冷永刚, 王太勇 2003 物理学报 52 2432]
[10] Leng Y G, Wang T Y, Qin X D, Li R X, Guo Y 2004 Acta Phys. Sin. 53 717 (in Chinese) [冷永刚, 王太勇, 秦旭达, 李瑞欣, 郭焱 2004 物理学报 53 717]
[11] Leng Y G, Leng Y S, Wang T Y, Guo Y 2006 J. Sound Vib. 292 788
[12] Leng Y G, Wang T Y, Guo Y, Wu Z Y 2007 Acta Phys. Sin. 56 30 (in Chinese) [冷永刚, 王太勇, 郭焱, 吴振勇 2007 物理学报 56 30]
[13] Leng Y G 2009 Acta Phys. Sin. 58 5196 (in Chinese) [冷永刚 2009 物理学报 58 5196]
[14] Zhu G Q, Ding K, Zhang Y, Zhao Y 2010 Acta Phys. Sin. 59 3001 (in Chinese) [朱光起, 丁珂, 张宇, 赵远 2010 物理学报 59 3001]
[15] Chen M, Hu N Q, Qin G J, An M C 2009 Chin. J. Mech. Eng. 45 131 (in Chinese) [陈敏, 胡茑庆, 秦国军, 安茂春 2009 机械工程学报 45 131]
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[1] Benzi R, Sutera A, Vulpiana A 1981 Physica A 14 L453
[2] Benzi R, Parisi G, Sutera A, Vulpiana A 1982 Tellus 34 11
[3] Bulsara A R, Gammaitoni L 1996 Phys. Today 49 39
[4] Chen H, Varshney P K 2008 IEEE Trans. Signal Process. 56 5031
[5] Liu Z Q, Zhang H M, Li Y Y, Hua C C, Gu H G 2010 Physica A 389 2642
[6] Sasaki H, Sakane S, Saito H, Todorokihara M, Aoki R 2010 J. Physiol. Sci. 60 138
[7] Zhang H Q, Xu W, Sun C Y, Xu Y 2011 Int. J. Mod. Phys. B 25 1775
[8] Lin M, Huang Y M, Fang L M 2008 Acta Phys. Sin. 57 2041 (in Chinese) [林敏, 黄咏梅, 方利民 2008 物理学报 57 2041]
[9] Leng Y G, Wang T Y 2003 Acta Phys. Sin. 52 2432 (in Chinese) [冷永刚, 王太勇 2003 物理学报 52 2432]
[10] Leng Y G, Wang T Y, Qin X D, Li R X, Guo Y 2004 Acta Phys. Sin. 53 717 (in Chinese) [冷永刚, 王太勇, 秦旭达, 李瑞欣, 郭焱 2004 物理学报 53 717]
[11] Leng Y G, Leng Y S, Wang T Y, Guo Y 2006 J. Sound Vib. 292 788
[12] Leng Y G, Wang T Y, Guo Y, Wu Z Y 2007 Acta Phys. Sin. 56 30 (in Chinese) [冷永刚, 王太勇, 郭焱, 吴振勇 2007 物理学报 56 30]
[13] Leng Y G 2009 Acta Phys. Sin. 58 5196 (in Chinese) [冷永刚 2009 物理学报 58 5196]
[14] Zhu G Q, Ding K, Zhang Y, Zhao Y 2010 Acta Phys. Sin. 59 3001 (in Chinese) [朱光起, 丁珂, 张宇, 赵远 2010 物理学报 59 3001]
[15] Chen M, Hu N Q, Qin G J, An M C 2009 Chin. J. Mech. Eng. 45 131 (in Chinese) [陈敏, 胡茑庆, 秦国军, 安茂春 2009 机械工程学报 45 131]
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