Adaptive two-dimensional coupled unsaturated asymmetric combined Gaussian potential stochastic resonance energy gain model and application of bearing fault diagnosis

Fault diagnosis of mechanical equipment is critical to energy storage, and stochastic resonance shows great potential in the field of diagnosing weak fault signals. To enhance the detection capabilities, a new system called adaptive TCUACGSR (two-dimensional coupled unsaturated asymmetric combined Gaussian potential stochastic resonance) has been proposed. Firstly, based on the two-state theory, the steady-state probability density (SPD), the mean first passage time (MFPT), and the signal-to-noise ratio (SNR) of the TCUACGSR system are derived. Then, the mean signal-to-noise gain (MSNRG) is used to further analyze the performance improvement of the system, and the mean energy gain (MEG) is used to measure the energy conversion of the system. Finally, it is combined with the Adaptive Genetic Algorithm (AGA) for practical bearing fault diagnosis. Experimental results show that compared with the UACGSR and TCBSR systems, the MSNRG of the TCUACGSR system is 0.112 dB and 6.647 dB higher, and the MEG is 22.63 dB and 1.881 dB higher, with amplitude ranges 183.28 and 1.54 times higher than theirs, respectively. This highlights the theoretical importance and practical value of the system in identifying the characteristic frequencies of faults and improving noise immunity and energy gain.