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Stochastic Resonance in Unsaturated Piecewise Nonlinear Bistable System Under Multiplicative and Additive Noise for Bearing Fault Diagnosis

With regard to the fault diagnosis, the stochastic resonance (SR) method takes advantage of noise imbedded in vibration signals while most traditional methods suppress or eliminate noise to enhance weak fault characteristics. In this paper, a novel piecewise nonlinear bistable SR (PNBSR) is proposed and its corresponding potential function called piecewise nonlinear bistable system (PNBS) overcomes the output saturation disadvantage which bothers the classical bistable system (CBS). The output saturation limits the enhancement capability for extracting fault characteristics of classical bistable SR (CBSR). Satisfying the adiabatic condition, the expression of the output signal-to-noise (SNR) of PNBSR is derived and compared with the output SNR of CBSR. Considered the multiplicative and additive noise, two methods are applied to extract characteristic frequency from simulated harmonic vibration signal and actual bearing fault signals. The SNR increase (SNRI) is chosen as the index for evaluating the performance of CBSR and PNBSR in experimental simulations. The diagnosis results indicate that the proposed PNBSR method is superior to the CBSR by analyzing SNRI and the effect of extracting fault characteristics.