Committed to solving the output saturation problem of the classical quad-stable stochastic resonance (CQSR) system, a new type of piecewise unsaturated quad-stable stochastic resonance (PUQSR) system is constructed. Firstly, the anti-saturation characteristic of PUQSR is verified by simulation of experimental signals. Then, the potential function structure variation of the PUQSR system is studied. According to adiabatic approximation theory, the steady-state probability density (SPD) and power spectrum amplification (SA) coefficient of the PUQSR system are deduced theoretically, and the influence of system parameters on them is analyzed in detail. Further, the signal-to-noise ratio improvement (SNRI) and SA are used as indicators to measure system performance, and numerical simulation verifies that the PUQSR system is better at amplifying signals and converting noise energy. At the same time, to extract the target signal more effectively in the context of strong noise, a new MOMEDA-PUQSR system is proposed by combining the multi-point optimal minimum entropy deconvolution (MOMEDA) method and the SR system. Finally, the optimal parameters of the MOMEDA-PUQSR system are found through the autocorrelation function and quantum genetic algorithm and successfully applied to the actual fault signal. The experimental results show that the increased fault signal envelope exhibits more obvious pulse characteristics, and the SNR is increased by 15.404 2~26.077 8 dB compared to the original signal. At the same time, compared with the MOMEDA-CQSR system, the output SNR of the increased signal through the MOMEDA-PUQSR system has been increased by 0.281 5~1.406 3 dB, and the spectral peak has been increased by 480.144~4 314.187 3.