## 6 Conclusions  
In this study, we consider the advantages of the differential evolution and the grey wolf optimization, and a hybrid optimization algorithm of DEGWO is proposed. Through the powerful search ability of DEGWO, the optimal weight and threshold of BPNN are extracted to improve the prediction accuracy. The prediction performance of DEGWO-BPNN is discussed by taking the development height of WCFZ threatening the mine safety as the prediction object and compared with other prediction models using several evaluation indexes. The primary conclusions are made as follows:  
(1) Based on systematic analysis, five main factors affecting the height development of WCFZ are determined, namely mining height, mining depth, coal seam dip, panel width, and ratio of hard rock. The topology structure of the DEGWO-BPNN model is preliminarily determined as '5-12-1'. (2) The prediction model is preliminarily identified by training 104 samples. The deviation between the prediction value and the actual value of the training sample is smaller with an average error of 2.39. Testing samples further validate the reliability of \begin{table}
\begin{tabular}{c c c c c c} \hline
**Borehole** & **Mining** & **Mining** & **Coal Seam** & **Panel Width/m** & **Ratio of Hard** & **Measured Height** \\
**ID** & **Height/m** & **Depth/m** & **Dip/\({}^{\circ}\)** & **Rock** & **of WCFZ/m** \\ \hline DS1 & 3.20 & 173.13 & 5.0 & 220 & 0.49 & 52.50 \\ \hline \end{tabular}
\end{table} 
Table 2: The relevant parameters and measured height of WCFZ. \begin{table}
\begin{tabular}{c c c c} \hline
**Prediction Models** & **Prediction Height/m** & **Absolute Error/m** & **Relative Error/\%** \\ \hline Mining Code & 36.70 & 15.80 & 30.10 \\ MLR & 38.64 & 13.86 & 26.40 \\ BPNN & 44.87 & 7.63 & 14.53 \\ GWO-BPNN & 57.44 & 4.94 & 9.41 \\ DEGWO-BPNN & 53.03 & 0.53 & 1.01 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of prediction models for WCFZ in the 11601 panel. the prediction model through four evaluation indexes consisting of MAE, RMSE, MAPE, and R2. Their values are 2.3952, 3.4674, 5.3148%, and 0.99077, respectively. The prediction accuracy of the model is 94.6852%. (3) 'Mining Code', MLR, BPNN, and GWO-BPNN are considered as the comparison models. The comparative analysis shows that the prediction performance of the WCFZ height calculated by 'Mining Code' is the worst, followed by MLR, while the prediction accuracy of the DEGWO-BPNN model is the best. Compared with the GWO-BPNN model, the prediction accuracy of the DEGWO-BPNN model is improved by 6.11%. It outperforms other algorithms and statistical approaches. (4) BPNN optimized by the DEGWO algorithm is applied to predict the WCFZ height of the 11601 panel in the Dananhu No.7 Coal Mine. The prediction error of the DEGWO-BPNN model is lower compared with other prediction models. The relative error is 4.53%, and the prediction precision is higher. As such, the DEGWO-BPNN model can be well applied to the prediction of WCFZ height. This method is suitable for coal mines with different regional geological conditions. It can provide a valuable reference for mine safety production because of its wider application range and higher prediction performance. Conceptualization, H.W. ; Methodology, H.W. ; Software, J.Z. ; Validation, J.Z. ; Formal analysis, J.Z. ; Writing--original draft, H.W. ; Writing--review and editing, J.Z. ; Visualization, J.Z. ; Supervision, W.L. All authors have read and agreed to the published version of the manuscript. This work was financially supported by the National Natural Science Foundation of China (No. 42372316), the project of \"Enlisting and Leading\" of China Coal (No. 2022 JB01), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX23_2760), the Fundamental Research Funds for the Central Universities (No. 2023 XSCX003), and the Graduate Innovation Program of China University of Mining and Technology (No. 2023 WLKXJ003). Not applicable.