## 4 Experimental Results
### Simulation Result  
Except for the typical PIM parameters and mining parameters (e.g., mining depth, mining thickness), the mesh size and the number of generated random points within the extraction element also need to be set before the prediction for the proposed method. In order to evaluate the impact of these two parameters on the accuracy of ground subsidence prediction, a rectangular mining area is simulated. As shown in Figure 9, the lengths of the mining area in the \(x\) direction and \(y\) direction are 600 m and 300 m, respectively. The dip angle of the coal seam, mining depth and mining thickness are set as 0\({}^{\circ}\), -700 m and 300 cm, respectively. Typical PIM parameters of the YanZhou coalfield, China, are used to calculate ground subsidence. The PIM parameters and simulated mining area parameters are listed in Table 1. The ground subsidence predictions obtained by the traditional PIM described in Section 2 are treated as the in-situ ones. The contours of the in-situ ground subsidence are shown in Figure 9. The proposed method-based subsidence predictions on 402 ground points, which are within the subsidence contour of 1 cm, are selected to compare with the in-situ subsidence; the distribution of these ground points is also shown in Figure 9. The minimum and maximum in-situ subsidence of these selected ground points are 1.0 cm and 233.4 cm, respectively. Figure 9: Simulated mining area and traditional PIM predicted subsidence contours. The approximation degree between the proposed method-based calculation area and the in-situ one is related to the ratio of mesh size to the minimum deviation of the inflection point of the mining area; the smaller ratio would produce a higher approximation between the two calculation areas, and thus more accurate subsidence predictions. Figure 10 shows a scatterplot of the RMS of the proposed method-based subsidence prediction errors versus the ratios of mesh size to deviation of the inflection point of the simulated mining area. The number of generated random points within an auxiliary domain is set as 1000 times the area of the corresponding extraction element. Note that, as the number of generated random points within the auxiliary domain is large enough, the Monte Carlo integration-induced subsidence prediction error could be ignored. It can be seen from Figure 10 that, before the ratio reaches 0.5, the RMS (root-mean-square) values of the proposed method-based subsidence prediction errors are very small, and slowly increase with the increase of the ratio. When the ratio is in the range of 0.5 to 3, the RMSE (root-mean-square error) values linearly increase with the increase of the ratio. With the increase of the ratio, the area of the extraction element and the BDs of the element also increase; once each BD of the element is greater than the corresponding deviation of the inflection point (which case corresponds to the ratio greater than 3 in Figure 10), all extraction elements would be treated as the elements within the calculation area, resulting in an overestimation of subsidence predictions for the proposed method. This could also be seen clearly in Table 2, which shows the Mean, STD (standard deviation) and RMS of the proposed method-based subsidence prediction errors under different ratios. When the ratio is greater than 3, the RMS of the proposed method-based subsidence prediction error reaches its maximum (about 8 cm) for the simulated mining area, and the RMSE tends towards stability as the calculation area does not change any more with the increase of the ratio. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Length on \(x\)** & **Length on \(y\)** & **\(\alpha\) (\({}^{\circ}\))** & **\(H\) (m)** & **\(M\) (cm)** & **\(q\)** & **tan\(\beta\)** & **\(k\)** \\ \hline
600 & 300 & 0 & –700 & 300 & 0.85 & 2.2 & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PIM parameters and simulated mining area parameters.