## 5 Discussion
### Validation of Data Preprocessing  
To further illustrate the necessity of data balancing and to verify the capability of the SMOTE algorithm, eighteen different prediction models were deployed to the original rockburst dataset. The prediction results were compared with the corresponding results obtained from the dataset preprocessed by SMOTE, as shown in Figure 15.  
The accuracy of different models was improved after the dataset was balanced by the SMOTE algorithm, which showed that SMOTE could be used well to improve the ability of the model to learn from the minority class samples in the unbalanced dataset. Moreover, the accuracy of GP, BagGP, KNN, BagKNN, and NBM models showed the most significant improvement. It is revealed that the SMOTE algorithm produces a more significant bias for models sensitive to noise, such as BPNN and decision trees. Further, the response of different models to the imbalance in the original dataset was investigated. For the KNN model, the data around particular samples must be considered so that the imbalance may lead to insufficient neighbor data and, thus, poor performance. Nevertheless, the accuracy of the RF model is less affected by imbalanced datasets because it adapts to differences between sample sizes and exhibits more randomness in the dataset-dividing process. For the decision tree model, changes in sample size can improve the model's ability to fit the data and reduce the risk of overfitting. As for the BPNN model, the minority class samples in the unbalanced data are easily ignored, which leads to low accuracy. There could be many reasons for this behavior. The first one is unbalanced sample distribution. The network tends to concentrate on the class \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**NO.**} & \multirow{2}{*}{**Provenance**} & \multirow{2}{*}{**UCS**} & \multirow{2}{*}{**UTS**} & \multirow{2}{*}{**MTS**} & \multirow{2}{*}{**MTS/UCS**} & \multirow{2}{*}{**UCS/UTS**} & \multirow{2}{*}{**\(W_{et}\)**} & \multicolumn{3}{c}{**Rockburst Hazard**} \\ \cline{5-10}  & & & & & & & & & **Engineering** & **PSO-BPNN-** & **PSO-BPNN-** \\  & & & & & & & & & **AcdaBoost** & **XGBoost** \\ \hline
1 & Zhonganshan Tunnel & 122 & 5.38 & 43.1 & 0.35 & 22.68 & 3.31 & II & II & II \\
2 & Zhonganshan Tunnel & 121 & 8.73 & 87.5 & 0.72 & 13.36 & 9.05 & IV & IV & IV \\
3 & Zhonganshan Tunnel & 124 & 8.64 & 79.1 & 0.64 & 14.35 & 7.74 & IV & IV & IV \\
4 & Zhonganshan Tunnel & 119 & 7.21 & 56.2 & 0.47 & 16.50 & 5.52 & III & III & III \\
5 & Zhonganshan Tunnel & 120 & 6.45 & 62.8 & 0.52 & 18.60 & 4.16 & III & III & II\({}^{*}\) \\
6 & Daxangling Tunnel & 59.7 & 1.3 & 25.67 & 0.43 & 45.9 & 1.7 & I & I & I \\
7 & Daxangling Tunnel & 62.8 & 2.1 & 26.36 & 0.42 & 29.9 & 2.4 & II & II & II \\
8 & Daxangling Tunnel & 90 & 2.1 & 27.9 & 0.31 & 42.8 & 1.8 & I & I & I \\
9 & Daxangling Tunnel & 88 & 3.1 & 29.32 & 0.34 & 28.3 & 3 & II & II & II \\
10 & Daxangling Tunnel & 114 & 2.3 & 55.86 & 0.49 & 49.5 & 4.7 & III & II\({}^{*}\) & II\({}^{*}\) \\
11 & Cangling Tunnel & 160 & 6.6 & 32.8 & 0.21 & 24.24 & 4.6 & II & II & II \\
12 & Cangling Tunnel & 160 & 6.8 & 44.8 & 0.28 & 23.53 & 4.9 & II & II & II \\
13 & Cangling Tunnel & 160 & 7.5 & 50.9 & 0.32 & 21.33 & 5.3 & III & III & II\({}^{*}\) \\
14 & Cangling Tunnel & 160 & 6.7 & 44.8 & 0.28 & 23.88 & 4.8 & II & II & II \\ \hline \hline \end{tabular} * The flag of prediction error.  
\end{table} 
Table 1: Prediction results obtained by the proposed models. with a larger sample size and ignore the information from the minority class. The second is due to the loss function. BPNN commonly uses cross-entropy as the loss function, which may cause the model to overprioritize the majority class when working with imbalanced data. The third is the hidden layer node issue. In BPNN, the number of hidden layer nodes is often fixed. When the number of samples from the minority class is relatively low, the network cannot learn from the group and build a model accordingly, which leads to poor prediction performance.