Application of a piecewise unsaturated tri-stable stochastic resonance system based on CEEMDAN in bearing fault diagnosis

Abstract This paper proposes a novel bearing fault signal detection method that integrates Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and a two-dimensional linearly coupled piecewise unsaturated tri-stable stochastic resonance (LCPUTSR) system. First, a piecewise unsaturated tri-stable stochastic resonance (PUTSR) model is designed to overcome the output saturation limitations of conventional stochastic resonance systems. Subsequently, a linear coupling mechanism is introduced to construct the LCPUTSR system. Based on adiabatic approximation theory, the equivalent potential function, stationary probability density (SPD), mean first-passage time (MFPT), and spectral amplification factor (SA) of the system are analytically derived, and the influence of key parameters on system performance is systematically analyzed. Numerical simulations are then conducted to compare the response characteristics of the classical tri-stable stochastic resonance (CTSR), PUTSR, and LCPUTSR models. The results demonstrate that the LCPUTSR system exhibits superior performance in both spectral amplification and signal-to-noise ratio improvement (SNRI). Furthermore, the QGA-optimized LCPUTSR model, validated on the Paderborn and Case Western Reserve University (CWRU) bearing datasets, shows enhanced performance compared with the other two systems. The final QGA–CEEMDAN–LCPUTSR framework further improves the SNRI, confirming the proposed method’s remarkable engineering applicability and superiority.