Coupled piecewise tri-stable stochastic resonance system driven by dual inputs and joint EMD/VMD analysis

Abstract A novel piecewise tri-stable stochastic resonance (NPTSR) system is proposed to address the issue of output saturation caused by high-order terms limitation in this paper. Building upon this, the exploration is extended to a coupled piecewise tri-stable stochastic resonance system driven by dual inputs (DCPTSR). First, we uncover the influence of dual input interaction on output quality, finding that when the fRequencies of the two input signals are consistent, varying the amplitude of the driving signal can effectively enhance the output performance of the target signal. Secondly, by utilizing the adiabatic approximation theory, the steady-state probability density (SPD) and signal-to-noise ratio (SNR) of the DCPTSR system are derived, which allows us to analyze the effects of various parameters on both SPD and SNR. Next, three combined denoising systems, namely EMD-DCPTSR, VMD-DCPTSR, and SDCPTSR, are constructed by utilizing empirical mode decomposition (EMD), variational mode decomposition (VMD), and the stochastic resonance (SR). Through numerical simulations, we demonstrate that the combined denoising system outperforms the stand-alone SR system, and we analyze the stochastic resonance phenomenon of the DCPTSR system using the spectral amplification (SA) coefficient as an evaluation index. Finally, to assess practical applicability, these systems are deployed for bearing fault detection. The experimental results exhibit notable signal-to-noise gain improvements for the DCPTSR system compared to standalone SR systems by 0.7699 ∼ 9.4541 dB. The EMD-DCPTSR system shows signal-to-noise gain improvements of 0.3245 ∼ 1.1709 dB compared to the VMD-DCPTSR and SDCPTSR systems. Moreover, all three combined denoising systems outperform the standalone SR system in terms of signal processing capabilities. In conclusion, this paper extensively investigates the interaction between the two input signals in a dual-input system and studies the output performance of using EMD, VMD, and SR as preprocessing methods for the SR system. Through numerical simulations and practical engineering applications, we highlight the substantial advantages of combined denoising systems. These findings offer essential theoretical insights and promising prospects for engineering applications.