## 5 Conclusions  
The classic bistable stochastic resonance algorithm has inherent output saturation defects. This paper introduces a non-saturated bistable stochastic resonance signal detection algorithm and an accelerated stochastic resonance signal detection algorithm based on the segmented potential function to address this issue. The output signal of the classic algorithm is limited by the quadratic term in its potential function, which impacts the detection performance. To overcome this limitation, the proposed algorithms are based on the segmented potential function without higher-order terms, optimizing the algorithm structure. The paper also derives the Kramers escape rate and output signal-to-noise ratio expressions of the algorithms theoretically to ensure their feasibility. Simulation experiments demonstrate that the proposed algorithm exhibits better weak-signal enhancement capability and faster detection speed compared to the classic bistable stochastic resonance algorithm. Furthermore, it significantly improves the detection accuracy of power system harmonics and various types of periodic characteristic signals compared to traditional time-frequency domain detection methods.  
In future research, the single-trap approximation model for unsaturated stochastic resonance detection system and accelerated stochastic resonance detection system is investigated, and the model performance of the single traps of UBSR, as well as ASR, is analyzed with reference to the stochastic resonance single-trap approximation model proposed by us in the literature [20], which extends the detection object to non-periodic signals.  
Conceptualization, S.S. and X.Q.; methodology, X.Q.; software, X.Q.; validation, Z.Y. and Z.L.; formal analysis, Z.Y.; investigation, X.T.; resources, X.T. and Z.L.; data curation, Z.Y. and X.T.; writing--original draft preparation, X.Q., S.S., and Z.Y.; writing--review and editing, X.Q., S.S. and Z.L.; visualization, X.Q. and S.S.; supervision X.T. and Z.L.; project administration, S.S.; funding acquisition S.S. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the National Natural Science Foundation of China: A Novel Power System Inertia Power Frequency Multi spatiotemporal Coupling Mechanism and Wide Area Coordinated Control (U22B20109); State Grid Corporation Science and Technology Project: Research on DC Control Optimization to Improve the Dynamic and Transient Performance of AC/DC Hybrid Power Grid (5100-202124011A-0-0-00).  
Not applicable.  
**Data Availability Statement:** Sharing of the data used in this study is limited due to the privacy restrictions of the project. If necessary, the data can be obtained by contacting the corresponding author.  
The authors declare no conflicts of interest.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Methodologies**} & \multicolumn{2}{c}{\
\begin{tabular}{c} **Plus Window** \\ **Interpolation** \\ **FFT** \\ \end{tabular} } & \multirow{2}{*}{**VMD**} & \multirow{2}{*}{**EEMD**} & \multicolumn{2}{c}{
\begin{tabular}{c} **Empirical** \\ **Wavelet** \\ **Tranform** \\ \end{tabular} } & \multirow{2}{*}{**SR**} & \multirow{2}{*}{**UBSR**} & \multirow{2}{*}{**ASR**} \\  & & & & & **Tranform** & & & \\ \hline time- & \multirow{2}{*}{1.032} & \multirow{2}{*}{2.3814} & \multirow{2}{*}{7.5216} & \multirow{2}{*}{2.0105} & \multirow{2}{*}{0.8123} & \multirow{2}{*}{1.0117} & \multirow{2}{*}{1.2361} \\ consuming/s & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of real-time performance of different detection methods.