A study of stochastic resonance in tri-stable generalized Langevin system

In this work, the phenomenon of stochastic resonance is studied in the tri-stable generalized Langevin system with nonlinear dissipation, which is forced by correlated noises and weak periodic signal. Analytical expression for the spectral amplification is derived in the presence of internal colored noise. The results suggest that memory effects in the tri-stable potential enhance signal amplification. There is appropriate asymmetric tri-stable potential for which stochastic resonance is optimum. Moreover, as the internal and external noises are correlated, the stochastic multi-resonance is found by simulating signal-to-noise ratio. The effect of stochastic resonance is enlarged in low-temperature domain. Specifically, the suitable choice of cross-correlation strength and nonlinear stiffness coefficients can substantially improve the response of the system to an external periodic signal. Finally, the proposed method is applied to bearing fault detection by using frequency-shifted and re-scaling transformation. It is demonstrated that the performance of extracting fault characteristics can be extremely enhanced thanks to the stochastic resonance system with memory and noise correlation. (c) 2023 Elsevier B.V. All rights reserved.