## 3 Model Development
### Rockburst Prediction Model  
To improve the accuracy of rockburst prediction, the PSO-BPNN-AdaBoost and PSO-BPNN-XGBoost models were constructed by integrating PSO-optimized BPNN with the AdaBoost and XGBoost algorithms. To improve the generalization ability and reduce the overfitting of the model, a stratified sampling strategy was used to divide the 266 sets of original rockburst data and 488 sets of preprocessed rockburst data before the model  
Figure 10: Structure of the XGBoost algorithm. training stage. Three-quarters of the data were used as the training dataset, and the remaining one-quarter was used as the test dataset to assess the generalization ability and reliability of the model. During the model training phase, the grid search and five-fold cross-validation methods were applied to find the best parameters. The former helped in selecting the ideal model parameters, while the latter was used to assess the model performance. Moreover, the grid search method can be embedded with the five-fold cross-validation method to assess the performance of each set of model parameters. By combining five-fold cross-validation with the grid search method, the performance of the model can be more accurately evaluated, and the best combination of model parameters can be obtained. The schematic of five-fold cross-validation is shown in Figure 11.  
Specifically, the dataset was split into five parts, each of which was used as a separate validation set, while the remaining parts served as the training set. Five performance indicators of the models can be generated through the above process. Subsequently, each parameter combination was treated as an input by the grid search approach, and then the average performance indicators of each combination were calculated after five-fold cross-validation. Finally, the parameter combination with the highest performance was used in model training. (1) Model construction  
Since the efficiency of the entire prediction model can be directly influenced by the generalizability and accuracy of the weak predictor, the effectiveness of the BPNN was first confirmed by using the aforementioned data. The input layer was the influencing factor with six nodes, and the output layer was the rockburst level with four nodes. In addition, the sigmoid function was used as the excitation function. According to [PERSON]'s theorem, the range of the number of nodes in the hidden layer is 4 to 13-. After repeated tests, the results showed that the best fitting effect was achieved under the combination of the population size of 50, the number of evolutions of 300, the learning factor of two, the inertia weight of [0.5, 1] with gradient descent, and the number of nodes in the hidden layer of six. To avoid overfitting, a dropout function with a probability of 0.25 was used. It was found that the error rate was significantly lower when the maximum number of iterations exceeded 25. Therefore, a default value of 50 was used for the maximum number of iterations, and a default value of 0.1 was used for the learning rate to determine the best number of iterations for boosting. The process of rockburst prediction based on AdaBoost/XGBoost integrated learning is shown in Figure 9, and the detailed steps are listed as follows:  
Figure 11: Schematic of five-fold cross-validation. Step 1: The weak learner for AdaBoost/XGBoost integrated learning in an optimized BPNN model was determined by finding the PSO parameters. Step 2: The ideal iteration count and the learning rate for AdaBoost/XGBoost integrated learning were chosen as the model hyperparameters. Step 3: The classifier was trained using the obtained AdaBoost/XGBoost integrated learning parameters. Step 4: The trained AdaBoost/XGBoost classifier was tested with the test set, and the classification results were output.