Periodic modulation enhanced multistable stochastic resonance with power spectral entropy for unknown weak signal detection

Multi-stable stochastic resonance (MSR) systems have been widely used for weak signal detection owing to their superior noise-to-signal energy transfer capabilities. However, traditional parameter-induced MSR systems still exhibit some residual noise when detecting strong noisy background signals, resulting in their incapacity to identify weak signals. Moreover, existing stochastic resonance (SR) metrics typically rely on prior information, limiting their applicability in real-world engineering scenarios involving unknown signals. In this paper, a periodically modulated two-dimensional multi-stable stochastic resonance system (PTMSR) is proposed derived from the Maclaurin expansion of periodic functions. The system can be modified by introducing a periodic weighting factor to facilitate the transition between steady states and improve its performance. Additionally, power spectral entropy (PSE) is introduced as a prior-free metric for evaluating SR effects for the first time. The quantitative study found that PSE follows an inverted bell-shaped trend as noise intensity increases, in contrast to the classical signal-to-noise ratio (SNR). Accordingly, PSE does not rely on specific signal characteristics but provides equivalent sensitivity and discrimination performance to that of SNR. Building upon these findings, an innovative SR method for detecting unknown weak signals is proposed. Simulations and experiments demonstrate that this approach significantly enhances and reliably extracts unknown bearing fault features under strong noise background. Validating the effectiveness of periodic modulation and PSE. This work provides a novel technical pathway and theoretical foundation for applying SR to unknown signals detection.