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 α and symmetry parameter β 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 α or β of Levy noise. The larger b (or l) is, the wider parameter interval of l (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 α 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.
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