Research and application of Gaussian coupled control bistable stochastic resonance system with independent parameter regulation

• Constructed a GBCSR system with individually adjustable potential well characteristics. • The nonlinear dynamic characteristics of the system is analyzed based on derived the SPD and MFPT. • The BSO algorithm is used to simultaneously optimize the system parameters. • The application of GBCSR system in the detection of four types of bearing fault signals has shown superior performance. The theory of Stochastic Resonance (SR) has drawn significant attention due to its exceptional ability to detect faint signals. Despite this, research to date indicates that for SR systems, whether they are monostable, bistable, or multi-stable, modifications to the system parameters lead to concurrent alterations in the depth and breadth of the potential wells when analyzing engineering signals, which results in suboptimal detection outcomes. To address these issues, a two-dimensional Gaussian bistable coupled SR (GBCSR) system has been proposed that can individually adjust the potential well characteristics. This innovative system facilitates the separate adjustment of shape characteristics of potential, allowing for more precise manipulation of the system’s dynamic response. The system’s non-linear dynamic traits are explicated through an analysis of the steady-state probability density (SPD) function and the mean first passage time (MFPT), substantiating the effectiveness of the new model. In practical scenarios, a variety of bearing defect signals serve as the objects of detection. The structural parameters of the GBCSR system are co-optimized using the Brain Storm Optimization (BSO) algorithm. This optimization approach leverages the algorithm’s ability to enhance population diversity and improve convergence accuracy, thereby optimizing the system’s performance. The experimental outcome results show that the proposed system can accurately detect the frequency of bearing fault signals. When compared with traditional SR systems such as the traditional bistable stochastic SR (TBSR), the traditional Gaussian SR system (TGSR), and the cascade stochastic resonance system, the proposed coupled system demonstrates superior performance. This is achieved through the transfer of energy or information between subsystems, which enables more efficient utilization of noise energy. The system can trigger the resonance effect over a broader range of noise intensities and significantly enhance the signal-to-noise ratio (SNR) of weak signals under the same noise intensity.