Levy噪声驱动下指数型单稳系统的随机共振特性分析

Characteristic Analysis of Exponential Type Monostable Stochastic Resonance under Levy Noise

该文基于绝对值型和指数型势函数,构建了更一般的指数型单稳势函数,深入研究了Levy噪声驱动的指数型单稳系统,并总结出不同特征指数a和不同对称参数b下,指数型系统参数l和b,Levy噪声强度系数D对指数系统共振输出的作用规律。研究表明:在不同Levy噪声驱动下,通过调节参数l和b均可诱导随机共振(SR),且当b(或l)的取值越大时,产生较好随机共振效果l(或b)的区间越大,从而改善传统SR系统由于参数选择不当造成随机共振效果不佳的问题。此外,通过调节噪声强度系数D也能产生随机共振,且较好随机共振区间不随a或b变化;最后将指数型单稳系统应用于轴承故障检测,效果明显优于传统双稳系统。

Based on the absolute and exponential monostable potential, a generalized exponential type single-well potential function is constructed. The laws for the resonant output of monostable system governed by l and b, D of Levy noise are explored under different characteristic index a and symmetry parameter of Levy noise. The results show that the stochastic resonance phenomenon can be induced by adjusting the exponential type parameters l and b under any a or β of Levy noise. The larger b （or l） is, the wider parameter interval of 1 （or b） can induce SR （Stochastic Resonance）. The ESR （Exponential SR） system can solve the problem that the traditional system can not achieve SR due to the improper selection of parameters. The interval of D of Levy noise which induces good stochastic resonance, does not change with a or β. At last, the proposed exponential type monostable is applicated to detect bearing fault signals, which achieves better performance compared with the traditional bisabled system.