Levy噪声驱动下的三稳态随机共振特性分析
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摘要
将Levy噪声与三稳态随机共振系统相结合,以平均信噪比增益为衡量指标,针对Levy噪声驱动下的三稳态系统的随机共振特性进行深入研究。探究了当Levy噪声特征指数与对称参数取不同值时,三稳态系统参数w,a和b,Levy噪声强度放大系数D对系统共振输出的影响。研究结果表明,在不同Levy噪声分布作用下,通过调节系统参数均可诱导随机共振,并且产生随机共振的参数区间大致相同;另外,调节噪声强度放大系数同样使系统产生随机共振。本研究结果为Levy噪声环境下参数诱导的三稳态随机共振现象系统参数的合理选取提供了依据。
The characteristic analysis of tri-stable stochastic resonance with Levy noise is analyzed deeply with Levy noise being combined with a tri-stable stochastic resonance system and average signal-to-noise ratio gain being used as index. The effect of tri-stable system parameters w, a, b and Levy noise intensity amplification factor D on the resonant output is explored with different Levy noise. Results show that for different distribution of Levy noise, the stochastic resonance phenomenon can be induced by tuning the system parameters. The parameter intervals which can induce stochastic resonances are approximately equal. Moreover, by adjusting the intensity amplification factor D of Levy noise, the stochastic resonances can happen similarly. These results will provide a basis for the reasonable selection of system parameters of parameter-induced tri-stable stochastic resonance under Levy noise.
The characteristic analysis of tri-stable stochastic resonance with Levy noise is analyzed deeply with Levy noise being combined with a tri-stable stochastic resonance system and average signal-to-noise ratio gain being used as index. The effect of tri-stable system parameters w, a, b and Levy noise intensity amplification factor D on the resonant output is explored with different Levy noise. Results show that for different distribution of Levy noise, the stochastic resonance phenomenon can be induced by tuning the system parameters. The parameter intervals which can induce stochastic resonances are approximately equal. Moreover, by adjusting the intensity amplification factor D of Levy noise, the stochastic resonances can happen similarly. These results will provide a basis for the reasonable selection of system parameters of parameter-induced tri-stable stochastic resonance under Levy noise.
引文
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[15]Xu B H,Zeng L Z,Li J L.Application of stochastic resonance in target detection in shallow-water reverberation[J].Journal of Sound and Vibration(S0022-460X),2007,303(1):255-263.
[16]焦尚彬,杨蓉,张青,等.α稳定噪声驱动的非对称双稳随机共振现象[J].物理学报,2015,64(2):020502.Jiao S B,Yang R,Zhang Q,et al.Stochastic resonance of asymmetric bistable system withαstable noise[J].Acta Physica Sinica,2015,64(2):020502.
[2]陈仲生,杨拥民.悬臂梁压电振子宽带低频振动能量俘获的随机共振机理研究[J].物理学报,2011,7(7):430-436.Chen Z S,Yang Y M.Stochastic resonance mechanism for wideband and low frequency vibration energy harvesting based on piezoelectric cantilever beams[J].Acta Phys.Sin.,2011,7(7):430-436.
[3]Gao Z B,Liu X Z,Zheng N.Study on the method of chaotic oscillator in weak signal detection[J].Chongqing Univ.Posts and Telecommunications(S1673-825X),2013,25(4):440-444.
[4]Lindner J F,Breen B J,Wills M E,et al.Mono stable array-enhanced stochastic resonance[J].Phys.Rev.E(S1539-3755),2001,63(5):051107.
[5]Wang K K,Liu X B.Stochastic resonance for a metapopulation system driven by multiplicative and additive colored noises[J].Chin.Phys.B(S1674-1056),2014,23(1):010502.
[6]刘海波,吴德伟,戴传金,等.基于Duffing振子的弱正弦信号检测方法研究[J].电子学报,2013,41(1):8-12.Liu H B,Wu D W,Dai C J,et al.A new weak sinusoidal signal detection method based on duffing oscillators[J].Acta Electronica Sinica,2013,41(1):8-12.
[7]Lu S L,He Q B,Zhang H B,et al.Signal amplification and filtering with a tri stable stochastic resonance cantilever[J].Review of Scientific Instruments(S0034-6748),2013(2):026110.
[8]Li J M,Chen X F,He Z J.Multi-stable stochastic resonance and its application research on mechanical fault diagnosis[J].Journal of Sound and Vibration(S0022-460X),2013,33(22):5999-6015.
[9]Zhang H Q,Xu Y,Xu W,et al.Logical stochastic resonance in triple-well potential systems driven by colored noise[J].Chaos(S1054-1500),2012,22(4):043130.
[10]Arathi S,Rajasekar S.Impact of the depth of the wells and multiracial analysis on stochastic resonance in a triple-well system[J].Phys.Scr.(S1402-4896),2011,84,065011.
[11]赖志慧,冷永刚.三稳系统的动态响应及随机共振[J].物理学报,2015,64(20):200503-200503.Lai Z H,Leng Y G.Dynamic Response and Stochastic Resonance of a Tri-stable System[J].Acta Phys.Sin.,2015,64(20):200503-200503.
[12]张广丽,吕希路,康艳梅.α稳定噪声环境下过阻尼系统中的参数诱导随机共振现象[J].物理学报,2012,61(4):040501.Zhang G L,Lv X L,Kang Y M.Lparameter-induced stochastic resonance in overdamped system withαstable Noise[J].Acta Phys.Sin.,2012,61(4):040501.
[13]张刚,胡韬,张天骐.Levy噪声激励下的幂函数型单稳随机共振特性分析[J].物理学报,2015,64(22):72-81.Zhang G,Hu T,Zhang T Q.Characteristic analysis of power function type monostable stochastic resonance with Levy noise[J].Acta Physica Sinica,2015,64(22):72-81.
[14]焦尚彬,任超,黄伟超,等.α稳定噪声环境下多频微弱信号检测的参数诱导随机共振现象[J].物理学报,2013,62(21):26-35.Jiao S B,Ren C,Huang W C,et al.Parameter-induced stochastic resonance in multi-frequency weak signal detection withαstable noise[J].Acta Physica Sinica,2013,62(21):26-35.
[15]Xu B H,Zeng L Z,Li J L.Application of stochastic resonance in target detection in shallow-water reverberation[J].Journal of Sound and Vibration(S0022-460X),2007,303(1):255-263.
[16]焦尚彬,杨蓉,张青,等.α稳定噪声驱动的非对称双稳随机共振现象[J].物理学报,2015,64(2):020502.Jiao S B,Yang R,Zhang Q,et al.Stochastic resonance of asymmetric bistable system withαstable noise[J].Acta Physica Sinica,2015,64(2):020502.