Enhanced weak signal detection via synchronization of symmetrically coupled fractional-order stochastic resonance systems

Abstract

Existing studies on coupled fractional-order stochastic resonance (SR) systems have predominantly focused on implicit linear or weakly nonlinear restoring terms, leaving the synchronization mechanisms, stability conditions, and weak signal enhancement capabilities of systems driven by explicit nonlinear potential functions insufficiently explored. This paper proposes a symmetric coupled bistable fractional-order stochastic resonance (SCBFSR) system and systematically analyzes the dynamical behavior of coupled particles under explicit potential fields. First, based on mean dynamics and synchronization error dynamics, the existence of synchronized motion among coupled particles is theoretically demonstrated. The stability boundary of the synchronization manifold is then derived, yielding explicit analytical relationships between the coupling coefficient, the curvature of the potential function, and system parameters, which delineate the necessary parameter region for the emergence of collective stochastic resonance. Subsequently, statistical linearization theory combined with the Gaussian closure method is employed to resolve the moment non-closure problem induced by nonlinear potential functions. An analytical expression for the amplitude gain of the SCBFSR system is obtained, and the effects of system parameters on the amplitude gain are systematically investigated. Finally, the butterfly optimization algorithm (BOA) is employed to optimize the system parameters and the effectiveness and practical applicability of the SCBFSR system are validated through real bearing fault frequency detection experiments. Comparative results against four benchmark systems, including single-particle fractional-order, integer-order coupled, and improved potential function models, demonstrate that the proposed SCBFSR system achieves at least 10 dB improvement in signal-to-noise ratio gain, with the performance improvement primarily attributed to the cooperative noise-averaging effect of the symmetric coupling structure and the memory accumulation property of the fractional-order operator.