## 4 Prediction Model of WCFZ Height Based on DEWGO-BPNN
### Comparative Analysis  
To highlight the superiority of DEGWO-BPNN prediction performance, we compare the prediction performance of other methods, such as 'Mining Code', multiple linear regression (MLR), BPNN, and GWO-BPNN. 'Building, water, railway and main roadway pillar setting and coal mining code' is referred to as 'Mining Code', which was released by four National Administrations, including the State Administration of Safety Supervision, the National Coal Mine Safety Administration, the National Energy Administration, and the National Railway Administration of the People's Republic of China in 2007. MAE, MAPE, RMSE, and R\({}^{2}\) are used to evaluate the prediction performance of these models. The prediction results of five models on 25 testing samples are shown in Table 1.  
It can be seen from Table 1 that the BPNN optimized by the DEGWO hybrid algorithm has significantly improved the prediction accuracy compared with the prediction results of the BPNN model. To be specific, the prediction accuracy of the DEGWO-BPNN model is close to 10% greater than that of the BPNN model, while the prediction accuracy of the GWO-BPNN model is between the DEGWO-BPNN model and the BPNN model. In five of the prediction models, the prediction performance of WCFZ height calculated by 'Mining Code' is the worst, followed by MLR. Their prediction accuracies are 59.37% and 77.45%, respectively.  
Furthermore, the quantitative evaluation indexes also show a certain change characteristic; MAE, RMSE, and MAPE show a downward trend from the conventional 'Mining Code' prediction method to DEGWO-BPNN, while R\({}^{2}\) and prediction precision increase, as shown in Figure 7. Using the machine learning method, such as BPNN and improved BPNN, the model prediction performance is effectively improved. In particular, when the BPNN is optimized, the expected values of each evaluation index are ideal. The prediction accuracy of the GWO-BPNN model and DEGWO-BPNN model is better than the other three models. To obtain the optimal prediction performance, differential evolution is introduced to optimize the GWO algorithm for the search for the best weights and threshold in the BPNN model. Compared with the GWO-BPNN model, the prediction accuracy of the DEGWO-BPNN model is improved by 6.11%. MAE, MAPE, RMSE, and R\({}^{2}\) of the DEGWO-BPNN model are also better than those of the GWO-BPNN model.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Prediction** & **MAE** & **MAPE** & **RMSE** & **R\({}^{2}\)** & **Prediction Accuracy** \\ \hline Mining Code & 27.69 & 40.63\% & 40.38 & 0.2332 & 59.37\% \\ MLR & 13.64 & 22.55\% & 19.06 & 0.7631 & 77.45\% \\ BPNN & 11.39 & 18.68\% & 16.06 & 0.8211 & 81.32\% \\ GWO-BPNN & 8.53 & 15.41\% & 11.14 & 0.9625 & 84.59\% \\ DEGWO-BPNN & 5.44 & 9.30\% & 7.089 & 0.9779 & 90.70\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Evaluation indicators and prediction accuracy of five models.  
Figure 7: Comparison of evaluation indicators in five prediction models. (**a**) is the comparison of MAE, RMSE and MAPE in five prediction models; (**b**) is the comparison of R2 and Prediction accuracy in five prediction models.