## 4 Result and Discussion  
### Prediction Performance Comparison  
To validate the performance of the FA-PSOBP prediction model proposed by the author, simulations of the prediction model were conducted using Matlab functions and the Neural Network Toolbox. The parameter settings are as follows: the prediction time horizon length was set to 1, indicating a single-step prediction; the time step, number of iterations, population size, and learning factor were set to 10, 5, 30, and 20, respectively. The reduced dimensional acoustic emission signals collected in Section 2 were used as input samples for the acoustic emission time series prediction model. Among these, 190 sets of data were selected as training data for the prediction model, while the remaining 10 sets were used as test samples for the training, learning, and predictive analysis of the acoustic emission time series. The results are presented in Table 4 and Figure 8.  
The experiment utilized 200 sets of acoustic emission data which were divided into a training set (140 sets) and a test set (60 sets) in a 7:3 ratio. This division follows conventional practices in time series prediction, ensuring that the training set covers complete evolutionary cycles, while the test set focuses on the critical failure stage (the last 60 sets of data corresponding to rockburst precursors). The model was optimized for hyperparameters through 5-fold cross-validation within the training set to avoid overfitting. The prediction errors for samples 197, 198, and 199 in Figure 8 are relatively high (27.35%, 25.80%, and 20.37%, respectively). Possible reasons for this include the following:  
Data noise interference: During the stage approaching rockburst, acoustic emission signals are susceptible to interference from equipment vibration or ambient noise, leading to abnormal parameter measurements (such as sudden changes in d7-RMS voltage). Model sensitivity: The PSO-BP model has limited capability in capturing high-frequency transient signals. Further optimization is needed, potentially through the integration of wavelet denoising techniques. Heterogeneity of rock mass: The uneven distribution of microcracks within the samples may cause the acoustic emission response of local failure events to deviate from statistical laws. These factors could collectively contribute to the higher prediction errors observed for these specific samples. Simultaneously, we need to evaluate the predictive performance of the FA-PSOBP model from both vertical and horizontal perspectives. Firstly, by comparing the average accuracy of the model before and after optimization, we must analyze the impact of the PSO process on the original model to determine whether it has a positive or negative effect. To assess the optimization capability of PSO compared to other algorithms, it is necessary to conduct a comprehensive comparison of the performance of FA-PSOBP with common optimization models. As shown in Table 5, the FA-PSOBP model outperforms the comparison models in terms of both R\({}^{2}\) and error indicators. Although LSTM and CNN perform well due to their inherent advantages in processing time series, they still suffer from relatively high errors. By utilizing factor analysis for dimensionality reduction and PSO for optimizing weights, FA-PSOBP effectively balances accuracy and efficiency, verifying its reliability as a tool for rockburst prediction.