## 4 Result and Discussion
### Discussion  
The results of this study demonstrate that the FA-PSOBP model exhibits superior performance in predicting acoustic emission (AE) parameters compared to traditional BP and LSTM models. This improvement can be attributed to the effective integration of factor analysis (FA) and Particle Swarm Optimization (PSO), which enhances the model's ability to handle high-dimensional data and avoid local optima. Compared to previous studies, our model achieves a higher R\({}^{2}\) value (0.86409) and a lower mean relative error (13.653%), indicating better predictive accuracy.  
Notably, prior research employing machine learning for AE-based rockburst prediction has predominantly focused on classification tasks (e.g., severity levels) rather than regression-based time series forecasting. For instance:  
[PERSON] et al. [24] compared 10 machine learning methods (including SVM, BP, and RF) for microseismic event identification, achieving classification accuracies of 75-85% but did not report R\({}^{2}\) values for regression tasks. [PERSON] et al. [26] utilized a CNN with dynamic moving windows to predict microseismic parameter trends, reporting an R\({}^{2}\) of 0.79-0.82, which is lower than our model's 0.864. [PERSON] et al. [29] applied LSTM to predict microseismic information, achieving an R\({}^{2}\) of 0.83, slightly below the FA-PSOBP's performance. [PERSON] et al. [23] employed a Random Gradient Boosting model for rockburst classification using AE data but focused on accuracy metrics rather than regression scores.  
These comparisons highlight that, while existing studies often prioritize classification, our work advances the regression-based prediction of AE parameters, offering a more granular tool for early warning systems. The FA-PSOBP's R\({}^{2}\) surpasses both conventional models (e.g., BP neural networks at 0.714) and hybrid approaches like GA-BP (0.824), as shown in Table 6. This underscores the efficacy of factor analysis in reducing dimensionality and PSO in optimizing neural network weights, addressing key limitations in prior AE signal processing.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Title 1** & **R\({}^{2}\)** & **Mean Relative Error** \\ \hline FA-PSOBP & 0.864 & 13.65\% \\ BP & 0.714 & 22.27\% \\ GA-BP & 0.824 & 19.18\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Performance comparison between FA-PSOBP and benchmark models in rockburst prediction.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Title 1** & **R\({}^{2}\)** & **Mean Relative Error** \\ \hline FA-PSOBP & 0.864 & 13.65\% \\ LSTM & 0.845 & 18.76\% \\ CNN & 0.744 & 21.44\% \\ SVM & 0.782 & 19.88\% \\ Random Forest & 0.721 & 23.12\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Performance Comparison of different machine learning models in rockburst prediction.  
The implications of this research are significant for the field of rockburst early warning systems. By accurately predicting AE parameters, the FA-PSOBP model can provide timely warnings for potential rockburst events, thereby improving safety in deep underground engineering projects. This is particularly relevant in mining and tunneling operations, where rockbursts pose serious risks to personnel and equipment.  
Future research could focus on further optimizing the FA-PSOBP model by incorporating additional data sources, such as microseismic monitoring or electromagnetic radiation signals. Additionally, the model could be tested on larger datasets from different geological conditions to validate its generalizability. Exploring other optimization algorithms, such as genetic algorithms or simulated annealing, may also yield further improvements in prediction accuracy.