A novel piecewise unsaturated asymmetric coupled tri-stable stochastic resonance method and its application in enhanced detection

Abstract

Stochastic resonance (SR) has been extensively explored as an effective technique for weak signal detection, relying on the principle of enhancing weak signal components through the introduction of an appropriate amount of noise to improve signal detectability. To address the output saturation issue of classical tri-stable stochastic resonance (CTSR) system, we introduce a novel piecewise unsaturated asymmetric coupled tri-stable stochastic resonance (PUACTSR) system, incorporating three improvements: unsaturation, asymmetry and coupling. First, the steady-state probability density (SPD) and the power spectral amplification factor (SA) are derived using adiabatic approximation theory, and the effects of system parameters on performance are analyzed. Second, the signal-to-noise ratio gain (SNRG) is utilized as an index to assess the system’s enhancement. Numerical simulations and detection of simulated periodic signals demonstrate that the PUACTSR system outperforms both the CTSR and piecewise unsaturated asymmetric time-delayed tri-stable stochastic resonance (PUATDTSR) systems. Finally, the proposed method employs a quantum genetic algorithm (QGA) for parameter optimization, effectively eliminating the randomness and low accuracy associated with manual tuning in computational settings. The results show that for detecting outer-ring fault signals, the PUACTSR system achieves a 0.14 dB improvement over the PUATDTSR system, a 2.31 dB improvement over the symmetric case, and a 4.76 dB improvement over the CTSR system. Furthermore, the power spectral curves show reduced noise interference, demonstrating superior detection performance compared to the other systems. This study highlights the theoretical significance of the PUACTSR system for bearing fault diagnosis and its potential for practical engineering applications.