Non-Markovian effects on stochastic resonance in a nonlinear dissipative system with biharmonic signal

This paper investigates stochastic resonance in a generalized Langevin system with nonlinear dissipation, driven by a biharmonic signal and coexisting colored and white noises. General expressions for the response of the non-Markovian system to an external biharmonic excitation are obtained. Results suggest that the stochastic resonance effect can be improved by increasing memory time. The appropriate choice of memory damping can substantially improve the system response. Moreover, the numerical results of signal-to-noise ratio demonstrate that the noise correlation time and the memory time play opposite roles in the onset and enhancement of stochastic resonance and antiresonance if the memory of the model is independent of its noise spectrum. The friction-induced resonance is found in the regime of long memory time. Interestingly, the nonlinear dissipation amplifies system output in the absence of instantaneous friction, while its presence induces output attenuation. Also, the observation of resonant behavior depends strongly on the asymmetry of potential and the ratio of subharmonic frequency to main frequency. Finally, the proposed stochastic resonance model is applied to bearing fault diagnosis based on quantum particle swarm optimization algorithm. Compared with the classical memoryless Langevin framework, the inclusion of memory effects and nonlinear dissipation significantly improves the performance of inner and outer race fault detection. Specifically, the generalized Langevin model with nonlinear dissipation accurately identifies the fault frequency of bearing rolling element, whereas both linear dissipative models and variational mode decomposition are ineffective for this case.