## 5 Discussion and Conclusions  
### Discussion  
Although the variable weight time function combined model achieved reasonably good predictive results, it also exhibited some shortcomings. In the model, different parameters had varying impacts on the accuracy of prediction results, and the model was sensitive to parameter adjustments. Extensive data was required for the training and validation of this model, especially when dealing with complex problems. Insufficient data may lead to less accurate predictions. Due to various constraints such as geological conditions and mining methods, the results of this prediction method may be less accurate in extremely complex scenarios.  
In addition, the TRF algorithm had some potential limitations. Compared to DE, GA, and PSO algorithms, the TRF algorithm demonstrated superior stability and convergence. However, this algorithm involved a complex computational process, requiring the solution of an optimization subproblem in each iteration step, which entailed intricate calculations. Additionally, the algorithm typically relied on the second derivative or an approximation of the second derivative of the objective function. In certain situations, obtaining this information may pose challenges due to difficulty or high computational costs. Furthermore,  
Figure 16: Comparison of residual plots for each individual model and the combined model: (**a**) comparison of residual values of Usher, Weibull, and Usher-Weibull models; (**b**) comparison of residual values of Usher, Richards, and Usher-Richards models; (**c**) comparison of residual values of Usher, MMF, and Usher-MMF models; (**d**) comparison of residual values of Weibull, Richards, and Weibull-Richards models; (**e**) comparison of residual values of Weibull, MMF, and Weibull-MMF models; (**f**) comparison of residual values of Richards, MMF, and Richards-MMF models.  
the performance of the TRF algorithm was often highly dependent on parameter selection, which demanded considerable expertise.  
The prediction process may involve uncertainties and could potentially incur certain errors. During the data collection process, measured data may be subject to measurement errors influenced by human factors and instrument characteristics. Additionally, due to inherent limitations such as overfitting or underfitting, the time function model may not be able to accurately depict the entire process of surface subsidence. In the coal mining process, uncertainties such as sudden increases or decreases in extraction speed, changes in mining methods, and pauses in the extraction process can impact the accuracy of predictive results.  
We still have a lot of work to do in future research. The variable weight time function combined model primarily employs mathematical computation methods and falls short in fully analyzing the stress changes in overlying rocks and the surface during the mining process. Therefore, future predictive models should comprehensively consider the mechanical mechanisms of overlying rock and surface subsidence during the extraction process. The model faces challenges in applicability when lacking actual measurement data. Subsequent research can explore the suitability of different temporal functions in various mining areas and propose methods to determine the parameters of temporal functions based on geological conditions in mining areas. Even after the subsidence of the mining area stabilizes, the surface continues to undergo minor deformations. Hence, further monitoring and research are necessary for the long-term surface deformations after the stability of surface subsidence.