## 4 Experimental Results and Analysis
When combining the Weibull time function model, which had the highest RMSE among the four individual models, with the MMF time function model, which had the lowest RMSE, the resulting model outperformed these two individual models. Relative to the relatively poor-fitting Weibull individual model, the Weibull-MMF combined model experienced a greater improvement in MAPE, approximately 22.99%. Its RMSE increased by 59.41%, and MAE increased by 61.89%. Additionally, when combining two individual time function models with similar accuracies, such as the [PERSON] and Richards models, the increase in MAPE for the Usher model was relatively small, around 1.60%. The RMSE increased by 9.00%, and MAE increased by 13.70%. Among the six combined models, the Weibull-MMF model exhibited the smallest RMSE, MAE, and MAPE, as well as the largest R\({}^{2}\), indicating the highest prediction accuracy for this model. In addition, since the four models in Figure 14 \begin{table}
\begin{tabular}{c c c} \hline \hline
**Evaluation Indicator** & **Entropy Weighting** & \
\begin{tabular}{c} **Improved Coefficient of** \\ **Variation Weighting** \\ \end{tabular} &
\begin{tabular}{c} **Optimization Empowerment** \\ \end{tabular} \\ \hline RMSE & 65.36 & 55.64 & 42.98 \\ MAE & 52.80 & 45.17 & 34.21 \\ MAPE & 0.0870 & 0.0759 & 0.0778 \\ R\({}^{2}\) & 0.99754 & 0.99821 & 0.99894 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the prediction accuracy of three weighting methods of Usher-Weibull. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Entropy Weighting**} & \multicolumn{3}{c}{**Improved Coefficient of**} & \multicolumn{3}{c}{**Optimization**} \\  & **d\({}_{1}\)** & **d\({}_{2}\)** & **Q\({}_{1}\)** & **Q\({}_{2}\)** & **d\({}_{1}\)** & **d\({}_{2}\  
were the same as those in Figure 15, and they were all derived from the TRF algorithm, their RMSEs were the same. To further illustrate the applicability of the variable-weight combined model, the ten different time function models were used to predict subsidence at point C16. The resulting residual values between the predicted and measured values are shown in Figure 16. Among the ten prediction models, the Weibull time function model had the largest residual values over the entire ground movement observation period, indicating lower prediction accuracy for this model. From the 4 th to the 14 th day of observation, the residual values for all prediction models were relatively larger. This was because this period corresponded to the active phase of surface deformation, characterized by intense overburden movement. Additionally, due to the comprehensive effects of geological factors, mining activities, and other uncertainties during overlying rock subsidence, this phase tended to exhibit larger residuals compared to other phases. After the 14 th day, surface subsidence had entered a decline phase, with smaller surface subsidence. During this stage, the predictions from these models were more accurate, with smaller residual values for all time function models except for the Weibull prediction model. Among these ten prediction models, the combined model's prediction residuals were smaller compared to the corresponding residuals of  
Figure 15: Evaluation of prediction effects of individual and combined models: (**a**) comparison of RMSE for individual and combined model predictions; (**b**) comparison of MAE for individual and combined model predictions; (**c**) comparison of MAPE for individual and combined model predictions; (**d**) comparison of R2 for individual and combined model predictions. the two individual prediction models. This indicated that the combined model provided more accurate predictions, further demonstrating the suitability of the variable-weight combined model.