# Dynamic Prediction Model for Progressive Surface Subsidence Based on MMF Time Function
## 4 Conclusions  
An accurate and effective dynamic prediction of progressive surface subsidence is important and indispensable for mine production and planning and for the protection of surface structures. To this end, this paper investigates the dynamic prediction model based on MMF time function and the conclusions are summarized here.  
The MMF time function for progressive prediction was proposed based on the model assumption and formula derivation, and the characteristics of the MMF time function parameters for describing surface dynamic subsidence were clarified. Subsequently, the variation relationship between the MMF time function parameters and the geological mining technical conditions was analyzed and fitting formulas were given. The MMF time function was then combined with the probability integral method (PIM), which is applied for predicting the final state surface subsidence to develop a dynamic progressive prediction model.  
For the proposed model validation, the measured data of working panel 22101 were used as an engineering example. The average RMSE and average RRMSE, which used the MMF time function, were 46.65 mm and 4.63%, respectively. Compared with Logistic time function, Gompertz time function and Weibull time function, the accuracy of RMSE is improved by 33.92 mm, 33.12 mm, 43.96 mm, respectively, and the accuracy of RRMSE is improved by 3.03%, 3.10%, 3.99%, respectively. The MMF time function outperforms other time functions in terms of prediction accuracy at all time periods.  
The results show that the accuracy of the model proposed in this paper can meet the requirements of practical engineering applications. This model can assess surface building damage and determine repair time so that appropriate repair measures can be given to reduce economic losses and alleviate the conflict between mining companies and residents. Therefore, the method is expected to be widely used.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Time** & **Advance** & \multicolumn{4}{c}{**RMSE/mm**} & \multicolumn{4}{c}{**RRMSE**} \\ \cline{2-10}
**Period/d** & **Distance/m** & **Logistic** & **Gompertz** & **Weibull** & **MMF** & **Logistic** & **Gompertz** & **Weibull** & **MMF** \\ \hline
52 & 100 & 3.55 & 4.73 & 3.76 & 2.79 & 7.25\% & 9.66\% & 7.67\% & 5.70\% \\
84 & 150 & 92.40 & 57.38 & 107.75 & 36.10 & 8.83\% & 5.48\% & 10.29\% & 3.45\% \\
114 & 190 & 114.58 & 85.10 & 150.42 & 67.16 & 8.32\% & 6.18\% & 10.92\% & 4.88\% \\
178 & 410 & 111.75 & 171.88 & 100.49 & 80.53 & 6.24\% & 9.59\% & 5.61\% & 4.49\% \\ Average & 80.57 & 79.77 & 90.61 & 46.65 & 7.66\% & 7.73\% & 8.62\% & 4.63\% \\ Increased accuracy & 33.92 & 33.12 & 43.96 & & 3.03\% & 3.10\% & 3.99\% & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Accuracy comparison for prediction results among four time functions.  
Nevertheless, it should be pointed out that the prediction model mentioned in this paper only considers the mining case of a single coal seam and does not consider the mining case of multiple coal seams. However, this is a common case in actual production and will affect dynamic surface subsidence prediction. Therefore, predicting progressive subsidence under multiple coal seams is a future endeavor for our country.  
Conceptualization, Y.Y.; methodology, B.Z.; software, J.K.; validation, B.Z.; formal analysis, B.Z.; investigation, J.K.; resources, Y.Y.; data curation, B.Z.; writing--original draft preparation, B.Z.; writing--review and editing, Y.Y.; visualization, B.Z.; supervision, Y.Y.; project administration, Y.Y.; funding acquisition, J.K. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China grant number [52074133, 51574242], the Fundamental Research Funds for the Central Universities grant number [2022Y]SDC19, 2022Y]SDC20]. The APC was funded by [2022Y]SDC19].  
Not applicable.  
The authors declare no conflict of interest.