## 4 Result and Analysis
### Results Analysis  
Predictive accuracy ensures timely intervention and the possible prevention of accidents. Therefore, developing precision models is paramount to promoting miner and equipment safety in underground coal mines worldwide. As mentioned earlier, the BP neural network can get stuck at a local minimum when trying to find the global minimum during training. This happens because the gradient descent algorithm used in training the BP neural network tries to find the direction of the steepest descent to minimize the error function. However, it may get stuck at a local minimum instead of reaching the global minimum. In addition, the convergence speed of BPNN decreases with large data, and the real-time performance of its inhibition becomes poor. In this research, the BP neural network was used and then optimized to build a more efficient and accurate prediction model for the prediction of safety risk factors in the Xiaonan coal mine. The BP neural network was optimized with the GA neural network to form the GA-BP neural network. The BP neural network was also optimized with the PSO neural network to form the PSO-BP neural network. Therefore, the particle swarm optimization (PSO) algorithm, with its simple implementation and high convergence speed, was investigated to optimize the BP neural network. The PSO technique does not require complex encoding and decoding processes like genetic algorithms do. The real number denotes a particle whose internal velocity is updated for the optimal solution [79]. Therefore, the PSO algorithm was combined with the BP neural network to build an efficient model for predicting safety risk factors in underground coal mines. The assessment indicators for the PSO-BP neural network are shown in Table 2.  
Ten repeated optimization models were run for the PSO-BP neural network to determine the best fitness (see Table 2). In each iteration, a new population was continuously generated, and the optimal weights and biases of the BP neural network were determined. Figure 5 shows the best global fitness of the ten models. _MSE_, _MAPE_, and \(R^{2}\) were used as the main evaluation indicators, as shown in Table 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & _MSE_ [\(\times\)**10\({}^{-4}\)]** & \multicolumn{2}{c}{_MAPE (\%)_} & \multicolumn{2}{c}{\(R^{2}\)} \\ \hline  & Train & Test & Train & Test & Train & Test \\
1 & 2.9 & 3.7 & 4.1 & 4.7 & 0.84 & 0.83 \\
2 & 5.4 & 5.5 & 5.0 & 5.1 & 0.83 & 0.80 \\
3 & 3.5 & 2.6 & 3.6 & 4.9 & 0.86 & 0.84 \\
4 & 3.5 & 3.0 & 4.3 & 4.2 & 0.85 & 0.86 \\
5 & 1.1 & 2.0 & 1.2 & 2.6 & 0.94 & 0.92 \\
6 & 3.7 & 3.8 & 3.6 & 4.8 & 0.87 & 0.91 \\
7 & 3.5 & 4.3 & 4.3 & 4.2 & 0.88 & 0.87 \\
8 & 2.1 & 2.3 & 4.0 & 3.7 & 0.85 & 0.81 \\
9 & 2.4 & 3.9 & 3.7 & 4.1 & 0.87 & 0.83 \\
10 & 2.2 & 2.3 & 3.7 & 4.7 & 0.83 & 0.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Assessment indicators of the PSO-BP neural network. Figure 5: The evolution of the global best’s fitness. Best and average fitness based on the error (MSE) of the BP neural network models 1–10. It can be seen that the fifth model had the lowest value of 2.5 \(\times\) 10\({}^{-4}\), while the second model had the highest value of 4.0 \(\times\) 10\({}^{-4}\) among all the ten models. This shows that the 5 th model had the best predictive accuracy compared to the 2 nd model, which had the highest global fitness value. This is because a lower global fitness value indicates that the model has the best prediction accuracy. In addition, it can be seen from Table 2 that the error values when testing the 5 th model were 2.0 \(\times\) 10\({}^{-4}\). Additionally, the mean absolute percentage value of the fifth model for testing was 2.6, which is the lowest value compared to the results obtained by the other models. On the other hand, the second model, which had the worst values for prediction accuracy, achieved an error value of 5.5 \(\times\) 10\({}^{-4}\) and a mean absolute percentage value of 5.1 for the testing of the data sets.