## 4 Experimental Results and Analysis
To assess the feasibility of using the TRF algorithm for parameter estimation, this study employed the optimal parameters corresponding to the minimum RMSE value obtained from the 50 runs as previously mentioned. Combined with the prediction formula of the individual time function model, the obtained correlation coefficient R\({}^{2}\) between the predicted and measured values at point C22 served as the evaluation metric. As shown in Table 1, it was evident that the R\({}^{2}\) values obtained using the TRF algorithm for all four time function models were greater than those obtained using the other three algorithms. Notably, the MMF time function model, when employing the TRF algorithm, yielded the highest R\({}^{2}\) value of 0.99926. This suggested that using this algorithm for parameter estimation in time function models resulted in greater accuracy and improved model fit. After determining the parameter estimation algorithm, the optimal window size was calculated using the entropy method. Table 2 provides the entropy values for window sizes ranging \(V=2\sim 7\). From the table, it was apparent that the entropy value was greatest when \(V=3\). This indicated that at this window size, the degree of variation of prediction errors within the window was minimized, making it the optimal window size. In the case of a window size of 3, we calculated the coefficient of variation and weight for each window using the entropy weighting method, improved coefficient of variation weighting method, and optimization empowerment method. By assigning the weight of the \(k\)-th window to the combined model at time \(t_{k+V-1}\), we calculated the predictions of the variable-weight combined model. Taking the [PERSON] combined model as an example, this paper provided the coefficient of variation and weights for the three distinct weighting methods, as shown in Figure 13.0 \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{4}{c}{**R\({}^{2}\)**} \\ \cline{2-5}  & **[PERSON]** & **[PERSON]** & **[PERSON]** & **MMF** \\ \hline DE & 0.99882 & 0.99617 & 0.99846 & 0.99925 \\ GA & 0.99887 & 0.99600 & 0.99856 & 0.99925 \\ PSO & 0.99887 & 0.99619 & 0.99856 & 0.99925 \\ TRF & 0.99888 & 0.99620 & 0.99864 & 0.99926 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of R\({}^{2}\) obtained using different models and algorithms. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Window Size/V** & **2** & **3** & **4** & **5** & **6** & **7** \\ \hline
**Entropy** & 0.7422 & 0.9490 & 0.8992 & 0.8410 & 0.6977 & 0.6975 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Window size and corresponding entropy values. Based on the weights determined in Table 3, predictions for the Usher-Weibull combined model were calculated using the three different weighting methods. Subsequently, weight calculations were performed for other combined models of individual time function in a similar manner to the Usher-Weibull combined model. Upon comparison of the four evaluation indicators in Table 4, it was observed that the optimization empowerment method outperformed both the entropy weighting method and the improved coefficient of variation weighting method. Therefore, this paper adopted the optimization empowerment method to determine the weights for the combined models. After determining the weights, to better illustrate the superiority of the variable weight combined prediction model over individual time function model, we evaluated and compared the predictions obtained via the combined model and the four individual models for the C22 point, using the four evaluation criteria from Section 3.5. This comparison is presented in Figure 15.  
From the graph, it was obvious that all models exhibited good fitting performance, with R\({}^{2}\) values exceeding 0.99. The four evaluation metrics for the combined prediction models were superior to their corresponding individual prediction models.