## 2 Working Resistance Prediction Model for Supports in Ultra-Long Mining Faces
### Results and Analysis
#### 2.3.2 Performance Comparison and Analysis  
(1) Selection of supports for prediction  
As shown in Figure 6, the supports in the fully mechanized mining face were divided into three groups, i.e., upper, middle, and lower measurement areas, along the strike. During the advancement of the mining face, the end-of-loop resistances of the adjacent supports exhibited similar characteristics, and the amplitude and range were highly coupled. Therefore, it was necessary to perform the prediction based on the working resistance of the highly correlated adjacent supports [22]. Compared with the Pearson correlation coefficient, the maximum information coefficient (MIC) [23] can better characterize the degree of correlation between two sequences. Therefore, the MIC was utilized to measure the correlation between the working resistances \begin{table}
\begin{tabular}{c c c} \hline \hline
**Time Window (Days)** & **MAE** & **MAPE** \\ \hline
8 & 1497.31 & 13.05\% \\ \hline
16 & 1351.47 & 11.68\% \\ \hline
32 & 1948.21 & 15.86\% \\ \hline
64 & 2663.28 & 20.49\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Model performance under varying time windows. Figure 6: Classification of supports in the #202 fully- mechanized mining face. of the supports in the mining face, and the support with the greatest correlation with the remaining supports in each measurement area was used as the predictive support. The work resistance time series of two supports, \(X_{i}\) and \(X_{j}\), were divided into \(x\times y\) segments. MIC(\(X_{i}\); \(X_{j}\)) was calculated as follows:  
\[mic\left(X_{i};X_{j}\right) =\underset{x*y<B}{max}\frac{\int P(x,y)log_{2}\frac{P(x,y)}{P(x)P( y)}dxdy}{log_{2}min(x,y)} \tag{14}\]  
where \(P(x\),\(y)\) is the joint probability distribution of \(x\) and \(y\). \(P(x)\) and \(P(y)\) are the probability distributions of \(x\) and \(y\), respectively. \(B\) is the maximum resolution. The sum of the MICs of the working resistance of support \(i\) and those of the other supports was calculated as follows:  
\[mic^{i}(x;y)=\sum_{j=1}^{N}mic\left(X_{i};X_{j}\right) \tag{15}\]  
The support with the maximum MIC \(mic_{\max}^{i}(x;y)\) in each measurement area was selected as the predictive support. Due to space limitations, only the details for the support in the lower measurement area are presented (Table 3). Among the supports in the lower measurement area, support #60 had the largest MIC value (6.6877), indicating that the correlation between support #60 and the other supports in the lower measurement area was the highest. Thus, support #60 was selected in the testing set as the representative support of the lower measurement area and was employed to compare the performance of the AGCRN model and the reference models, thereby verifying the performance of the AGCRN model. (2) Performance comparison  
Figure 7 and Table 4 present a comparison of the original value and the results for support #60 predicted using four different models. The \(x\)-axis is the samples in the testing set, and the \(y\)-axis is the time-weighted average end-of-loop resistance. As shown in Table 4, the MAE values of the BP model, GRU model, and DCRNN model were 797.34-1322.78, and the MAPE values were 6.47-10.69%. In comparison, the MAE of the AGCRN model was 585.15, and the MAPE was 6.19%. The errors of the DCRNN and AGCRN models were significantly lower than those of the other single-sequence prediction models, and the AGCRN had the smallest prediction error, demonstrating the effectiveness of the proposed AGCRN model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Models** & **MAE** & **MAPE** \\ \hline BP & 1322.78 & 10.69\% \\ GRU & 1116.42 & 9.02\% \\ DCRNN & 797.34 & 6.47\% \\ AGCRN & 585.15 & 6.19\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performances of the four reference models in pressure prediction of the #60 support in the lower measurement area.