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The classical bistable stochastic resonance (CBSR) has the disadvantage of output saturation, which limits the enhancement capability for weak signal detection. To break the limitation of output saturation, a novel unsaturated piecewise non-linear bistable stochastic resonance (PNBSR) method is proposed. Because the trichotomous noise exists in practical engineering, the PNBSR under trichotomous noise is explored in this paper. The performance of PNBSR is evaluated by the index, i.e., the mean of M times signal-to-noise ratio increase (MSNRI). The double-peak phenomenon of SR is observed under trichotomous noise. Experiments reveal that the proposed PNBSR method performs best on extracting characteristic components from a strong noise background, compared with the CBSR method and the traditional digital filter. Then, the PNBSR is applied to the fault diagnosis of rolling element bearings. The paper focuses on solving practical engineering problems with mathematical methods. [ABSTRACT FROM AUTHOR]

The asymmetric bistable system with time delays in the feedback force and random force under multiplicative and additive Gaussian noise is studied. Using the small time delay approximation approach and time-delayed Fokker–Planck equations (FPE), the signal-to-noise ratio (SNR) of the proposed stochastic system is obtained. The stochastic resonance (SR) phenomena influenced by parameters — including system parameters a , b , asymmetry parameter r , time delay τ , strength 𝜀 of the time-delayed feedback, noise intensities D and Q of multiplicative and additive noise, and correlation strength λ between two noises, are also analyzed by numerical simulations. Results demonstrate that the SR performance of the asymmetric bistable system is superior to one symmetric bistable system. Besides, both time delay and strength of time-delayed feedback could enhance the SR to some extent. Then, the asymmetric time-delayed bistable SR (ATDBSR) method is used to the bearing fault diagnosis. The engineering applications of the ATDBSR method are realized and the value of the method is verified by effective experimental results. [ABSTRACT FROM AUTHOR]