Research on stochastic resonance method in fractional-order tristable systems

We introduce an innovative approach to fractional-order tristable stochastic resonance (SR), utilising the advantages of temporal memory and spatial correlation inherent in fractional-order systems while harnessing the non-saturating properties of tristable SR mechanisms. First, we derived the fractional-order tristable Langevin equation and studied the SR phenomenon within this system across key parameters, such as the fractional-order α, system parameters and external periodic force, within the α range of (0,2]. We identified the optimal resonance region through this analysis. Second, to achieve adaptive fractional-order SR and effectively handle high-frequency and experimental signals, we introduced a standard scale transformation method along with the butterfly optimisation algorithm. Finally, through verification with simulation signals, laboratory data and experimental data from the outer race fault of an aircraft engine’s intermediate shaft bearing, we demonstrated that our proposed method could efficiently extract weak fault characteristic signals from environments with strong noise. Comparative analysis with traditional tristable SR methods and the empirical mode decomposition algorithm showed that signals extracted using our method exhibited larger characteristic frequency amplitudes and higher signal-to-noise ratios (SNR).