## 3 Simulated Experiment
### Engineering Application Experiments and Results  
The measured subsidence of 24 points (ML01-ML24) and 12 observation points (MS25-MS36) were selected as the experimental data. Two plans were used to invert the parameters of 13121(1). In the first plan, the PIM parameter inversion is performed using the GA and the measured data without adding coarse errors, and the result is used as the reference value. Three points are selected near the inflection point in the measured subsidence curve data and gross errors are added (two points are selected on the strike observation line; one point is selected on the inclination observation line; and a gross error of 500 mm is added for each point), and then the GA is used to invert the parameters. In the second engineering application plan, three points are selected at \(W_{max}\) in the measured subsidence curve data and gross errors are added (a gross error of 500 mm is added for each point), and then the GA and the proposed method are used to invert the parameters of the PIM. To ensure that the inversion results are not affected by accidental errors, both schemes perform 50 inversions, and the average value is selected as the result. Table 2 shows the mean and fitting RMSE of the result. Figure 6: Study area and observation points. From Table 2, we can see that when gross errors are added near the inflection point and \(W_{max}\), the RMSE values of the PIM parameters inverted using the traditional GA are 101.2 mm and 107.3 mm, respectively, while the RMSE values of the parameters inverted using the proposed method are 76.8 mm and 69.8 mm, respectively. In the experiments involving the introduction of two sets of gross errors, the RMSE of the proposed method is reduced by 24.4 mm and 37.5 mm, respectively, compared to that of the traditional genetic algorithm. The proposed method demonstrates better resistance to gross errors compared to the traditional genetic algorithm. To verify the precision of the parameters obtained from the inversion of the two plans for predicting the subsidence of the basin, the parameters from both plans and the PIM were used. The subsidence values predicted by the two plans were compared with the actual subsidence values, and the results are shown in Figures 7 and 8. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Parameter**} & \multicolumn{1}{c}{**Reference Value**} & \multicolumn{2}{c}{**Engineering Application Plan 1**} & \multicolumn{2}{c}{**Engineering Application Plan 2**} \\  & & **GA Method** & **Proposed Method** & **GA Method** & **Proposed Method** \\ \hline \multirow{2}{*}{\(q\)} & IV & \multirow{2}{*}{1.2672} & 1.5533 & 1.2404 & 1.3798 & 1.2889 \\  & RE & & 17.94\% & 34.47\% & 27.10\% & 31.91\% \\  & IV & \multirow{2}{*}{1.8928} & 1.6547 & 1.8700 & 1.9113 & 1.8721 \\  & RE & & 12.58\% & 1.20\% & 0.98\% & 1.09\% \\  & IV & & 87.4652 & 85.3094 & 86.8843 & 85.5449 \\  & RE & & 1.08\% & 1.41\% & 0.41\% & 1.13\% \\  & IV & & 36.5795 & 17.0370 & 43.2282 & 23.7842 \\  & RE & & 161.17\% & 21.64\% & 208.64\% & 69.81\% \\  & IV & & 52.0727 & 42.7824 & 26.5384 & 34.7214 \\  & RE & & 16.86\% & 3.99\% & 40.44\% & 22.08\% \\  & IV & & 10.6886 & 15.6669 & \(-\)11.2751 & 9.6938 \\  & RE & \(-\)2.9398 & 463.58\% & 632.92\% & 283.53\% & 429.74\% \\  & IV & & 3.3455 & \(-\)21.3161 & 21.0065 & \(-\)4.0305 \\  & RE & & 46.87\% & 438.54\% & 233.63\% & 164.01\% \\  & RMSE/mm & & 69.7 & 101.2 & 76.8 & 107.3 & 69.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental results of the two plans. Figure 7: Comparison of fitted subsidence between proposed method and GA (Plan 1). According to Tables 3-5, the parameter inversion results for introducing gross errors at three different positions are as follows: when k = 10, the maximum RE values of the parameter inversion results are 6.74%, 8.45%, and 5.57%, respectively, and the RMSE values are 15.2 mm, 18.8 mm, and 25.8 mm, respectively.