Levy噪声下新型势函数的随机共振特性分析及轴承故障检测

Stochastic resonance characteristic analysis of the new potential function under Levy noise and bearing fault detection

针对经典双稳随机共振(Classical Bistablestochastic Resonance,CBSR)系统的输出饱和性问题,构建了一种新型的分段非线性双稳随机共振(Piecewise Nonlinear Bistable Stochastic Resonance,PNBSR)系统,用所提的PNBSR系统在理论上和CBSR系统作了对比;然后以平均信噪比增益(MSNRI)为衡量指标,用量子粒子群算法进行参数寻优,深入的探究了在Levy噪声不同特征指数与对称参数情况下,PNBSR系统参数l,c,a,b和Levy噪声强度放大系数D对共振输出的规律。研究表明:相对于CBSR系统的输出信噪比,PNBSR系统的输出信噪比有4dB的提高;并且发现在不同的Levy噪声分布作用下,通过调节系统参数l,c,a,b和噪声强度系数D均可诱导随机共振,且系统较好的随机共振区间不随α或β变化;最后将PNBSR系统应用于轴承故障检测,效果明显优于CBSR系统。

Based on the output saturation of classical bistable stochastic resonance,a new type of piecewise nonlinear bistable potential stochastic resonance(PNBSR)system was constructed.Firstly,the PNBSR system was compared with the CBSR systems in theory.Then,the mean signal-to-noise ratio gain was treated as an index to measure the stochastic resonance phenomenon.The quantum particle swarm algorithm was used to seek optimal parameters.The laws for the resonant output of piecewise nonlinear bistable system governed by l,c,a,b,and D of Levy noise were explored under different characteristic indexαand symmetry parameterβof Levy noise.The results show that the output of the PNBSR system has increased 4dB compared with the output signal-to-noise ratio of a classical bistable stochastic resonance(CBSR)system.And the stochastic resonance phenomenon can be induced by adjusting the piecewise nonlinear system's parameters under anyαorβof Levy noise and D of Levy noise,and the best interval does not change withαorβ.At last,the piecewise nonlinear bistable stochastic resonance system was applied to detect bearing fault signals,which achieves better performance compared with the classical bistable stochastic resonance system.