Piecewise unsaturated multi-stable stochastic resonance under trichotomous noise and its application in bearing fault diagnosis

The classical tri-stable stochastic resonance (CTSR) has the weakness of output saturation, which restricts the ability to enhance weak signal detection. To overcome the limitation of output saturation, a piecewise unsaturated multi-stable stochastic resonance (PUMSR) method is proposed. Due to the presence of trichotomous noise in practical application, this paper explores the PUMSR under a trichotomous noise environment. The performance of PUMSR is evaluated by means of an index, mean signal-to-noise ratio increase (MSNRI). In order to meet the adiabatic approximation conditions, the signal is secondary sampled and a genetic algorithm (GA) is implemented to optimize the system parameters. Simulation experiments demonstrate that the proposed PUMSR system is superior to the CTSR system in terms of its ability to extract signals at multi-frequency. The PUMSR is then applied to the diagnosis of bearing faults. It is further proved that the PUMSR system has good performance in bearing fault diagnosis and has great feasibility in real engineering application.