## 3 Simulated Experiment
### Simulation Application Experiment and Results  
To ensure the stability of parameter inversion and reduce the impact of accidental errors, 50 inversion experiments were performed in each plan, and the inversion values (IVs) of the probability integral parameters were averaged. Table 1 shows the average value, relative error (RE), and fitting RMSE of the parameters in the simulation experiments.  
From Table 1, it can be seen that when there are gross errors at three different positions on the subsidence curve, the RMSE (GA) parameter inversion results are 22.5 mm, 33.8 mm, and 28.7 mm, respectively. The relative error of the parameter is 11.43%, 23.73%, and 10.66%. The RMSE of the proposed parameter inversion method is 2.8 mm, 1.7 mm, and 1.4 mm, respectively, and the maximum RE is 4.61%, 1.24%, and 2.67%, respectively. The RMSE and maximum RE of the parameter inversion proposed method are significantly smaller than for the GA. Moreover, the RMSE of the proposed parameter inversion method is reduced by 19.7 mm, 32.1 mm, and 27.3 mm, respectively, compared with the GA. The result of the parameter inversion using this method is closer to the actual value. This  
Figure 2: Distribution of working faces and observation points.  
indicates that this method is resistant to errors and can reduce the effects of gross errors, ensuring stability and reliability.  
In order to verify the accuracy of the probability integral parameters obtained from the inversion of the three schemes for predicting the subsidence of the basin, the parameters of the three experimental schemes and PIM model were used and the subsidence prediction values were obtained. The subsidence predicted by the three schemes was compared with the actual subsidence, as shown in Figures 3-5.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{\
\begin{tabular}{c} **Design** \\ **Value** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Plan 1** \\ **Method** \\ \end{tabular} } & \multicolumn{2}{c}{**Plan 2**} & \multicolumn{2}{c}{**Plan 3**} \\ \cline{3-8}  & & & **GA** & **Proposed** & **GA** & **Proposed** & **GA** & **Proposed** \\  & & & **Method** & **Method** & **Method** & **Method** & **Method** \\ \hline \multirow{2}{*}{\(q\)} & IV & \multirow{2}{*}{0.64} & 0.6395 & 0.6405 & 0.6417 & 0.6400 & 0.6600 & 0.6403 \\  & RE & & 0.08\% & 0.09\% & 0.26\% & 0.00\% & 3.12\% & 0.04\% \\  & IV & & 1.5322 & 1.4804 & 1.5339 & 1.5000 & 1.4171 & 1.5013 \\  & RE & & 2.15\% & 1.31\% & 2.26\% & 0.00\% & 5.52\% & 0.09\% \\  & IV & & 1.5322 & 85.5932 & 85.2471 & 85.9763 & 85.5607 & 85.6825 \\  & RE & & 2.15\% & 1.05\% & 1.45\% & 0.61\% & 1.09\% & 0.95\% \\  & IV & & 49.9317 & 45.2301 & 39.7648 & 44.8008 & 47.2286 & 45.1187 \\  & RE & 45 & 10.96\% & 0.51\% & 11.63\% & 0.44\% & 4.95\% & 0.26\% \\  & IV & & 50.1448 & 44.8294 & 34.3203 & 45.1991 & 47.0186 & 45.5513 \\  & RE & & 11.43\% & 0.38\% & 23.73\% & 0.44\% & 4.49\% & 1.23\% \\  & IV & & 44.3203 & 44.9174 & 45.2729 & 45.5575 & 46.5879 & 46.2037 \\  & RE & & 1.51\% & 0.18\% & 1.62\% & 1.24\% & 3.53\% & 2.67\% \\  & IV & & 44.3203 & 47.0725 & 47.1754 & 45.4753 & 49.7983 & 45.3857 \\  & RE & 45 & 1.51\% & 4.61\% & 4.83\% & 1.06\% & 10.66\% & 0.86\% \\  & RMSE/mm & & & 22.5 & 2.8 & 33.8 & 1.7 & 28.7 & 1.4 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results and accuracy of inversion probability integral parameters.  
Figure 3: Comparison of fitted subsidence values between proposed method and GA (Plan 1).  
length and width of the working surface of \(D_{3}=620\) m and \(D_{1}=205\) m. The main body of the observation line is arranged in the strike direction, with the observation points being spaced at 30 m. The main body of the inclination observation line is located 310 m away from the start-mining line and 205 m away from the stop-mining line. Taking into account the terrain conditions above the working surface, the inclination observation line is set as a half observation line. Figure 6 shows the study area and the observation points.