Stochastic resonance in a single-well system with exponential potential driven by Levy noise

Noise and potential function are vital to stochastic resonance (SR). This paper attempts to broaden the research of the SR and explore a better potential function. Based on the absolute and exponential potentials, a generalized exponential type single-well potential function is constructed. Then the characteristics of the corresponding exponential type single-well SR (ESR) system driven by Levy noise is analyzed numerically. Firstly, the effects of the characteristic index α, symmetric parameter β and noise intensity D of Levy noise on the input signal to noise ratio (SNRi) are investigated. Then, the effects of system parameters a, b, r and noise intensity D on the resonant output is explored. Finally, the ESR system is applied to the fault characteristic extraction of rolling element bearings. The simulation results show that the SR phenomenon is able to be excited by tuning the parameters a, b, r and D under different values of α and β. The larger b (or a) widens the parameter interval of a (or b) which can induce SR. The ESR system is able to solve the problem that the traditional systems fail to achieve SR due to the improper selection of parameters. In bearing fault detection, the detection effect of the ESR system is superior to the bistable SR system.