## 4 Result and Analysis
### Comparative Analysis of Models  
Three indicators were used to evaluate these models to determine their predictive accuracy. A comparison of the three models was made to determine the best model for predicting the safety risk factors in the Xiaonan coal mine. The _MSE_, _MAPE_, and \(R^{2}\) values were used to compare the performance of the optimized models with that of the BP neural network, as shown in Table 3.  
Comparing the GA-BP neural network with the BP neural network, it can be seen that the _MSE_ and _MAPE_ values for the tests of the GA-BP neural network were 4.2 \(\times\)\(10^{-4}\) and 5.1, respectively, compared to the testing of the BP neural network, which achieved 1.5 \(\times\)\(10^{-3}\) and 9.7, respectively, as shown in Table 3. Lower _MSE_ and _MAPE_ values show more efficient prediction accuracy of the models, so the GA-BP neural network had better prediction accuracy than the BP neural network. More importantly, the \(R^{2}\) value of the model GA-BP for the tests was 0.78 compared to the BP neural network model, which was 0.50. This shows that the predicted values of the GA-BP neural network model had a good correlation with the actual values compared to the BP neural network model. This makes the GA-BP neural network model more favorable and reliable than the BP neural network model [81]. Furthermore, comparing the PSO-BP neural network model with the BP neural network model, the PSO-BP neural network model turns out to be better. For example, the _MSE_ and _MAPE_ values for testing the PSO-BP neural network model were 2.0 \(\times\)\(10^{-4}\) and 4.3, respectively. The testing values of the _MSE_ and _MAPE_ for the BP neural network model were 1.5 \(\times\)\(10^{-3}\) and 9.7, respectively. In comparison, the PSO-BP neural network model had lower _MSE_ and _MAPE_ values, indicating improved prediction accuracy. In addition, the \(R^{2}\) value of the PSO-BP neural network model for the testing was 0.92 compared with the BP neural network model, which had 0.50. Higher \(R^{2}\) values indicate that the predictive accuracy of the PSO-BP neural network model had a good correlation with the actual values compared to the BP neural network model [82; 83]. This shows that the PSO-BP neural network model is more favorable and reliable than the BP neural network model. Figure 7 shows the error comparison of the three models for training and testing data sets. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & \multicolumn{2}{c}{_MSE_} & \multicolumn{2}{c}{_MAPE (\%)_} & \multicolumn{2}{c}{\(R^{2}\)} \\ \hline  & Train & Test & Train & Test & Train & Test \\ BPNN & 1.3 \(\times\)\(10^{-3}\) & 1.5 \(\times\)\(10^{-3}\) & 6 & 9.7 & 0.64 & 0.50 \\ GA-BPNN & 3.2 \(\times\)\(10^{-4}\) & 4.2 \(\times\)\(10^{-4}\) & 4.2 & 5.1 & 0.82 & 0.78 \\ PSO-BPNN & 1.1 \(\times\)\(10^{-4}\) & 2.0 \(\times\)\(10^{-4}\) & 3.1 & 4.3 & 0.94 & 0.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance of each of the models. Figure 7: Error comparison between the predicted values of the BP neural network, the GA-BP neural, and the PSO-BP neural network. (**a**) Training data sets (**b**) Testing data sets. Again, a comparison was made between the GA-BP neural network model and the PSO-BP neural network model to determine the most efficient and reliable model. The _MSE_ of the testing for the GA-BP neural network model was \(4.2\times 10^{-4}\), whereas the PSO-BP neural network model was \(2.0\times 10^{-4}\). The _MAPE_ value of the testing for the GA-BP neural network model was \(5.1\), whereas the PSO-BP neural network model was \(4.3\%\). Smaller _MSE_ and _MAPE_ values indicate a better-performing model, so the PSO-BP neural network model has higher prediction accuracy than the GA-BP neural network model. In addition, the \(R^{2}\) value of the testing for the GA-BP neural network model reached a value of \(0.78\) compared to the PSO-BP neural network, which was \(0.92\).