## 4 Results  
Figure 5 shows the relationship between static stiffness and dynamic stiffness for the three types of rail pads studied. The graph reveals a positive and mostly linear correlation between the two variables, with some scatter and outliers that will be analyzed later. Type A rail pads, marked with red circles, show a more concentrated distribution, with static stiffness values ranging from 15 to 70 kN/mm and dynamic stiffness between 15 and 130 kN/mm. The relationship between the two stiffnesses is primarily linear under all conditions. Type B rail pads (green triangles) show greater dispersion, with static stiffness ranging from 20 to 165 kN/mm and dynamic stiffness values reaching up to nearly 500 kN/mm. Although a linear trend is also observed, the variability in the relationship between static and dynamic stiffnesses is more pronounced, indicating less predictable behavior compared to Type A rail pads. Finally, the Type C rail pads (blue squares) exhibit the widest range in both static stiffness (75 to nearly 300 kN/mm) and dynamic stiffness (125 to 925 kN/mm). For this type of rail pad, an increasing trend in dynamic stiffness with static stiffness is observed. However, unlike Type A and B pads, the relationship appears to follow a non-linear pattern and shows significant dispersion under certain conditions. The results suggest that Type C rail pads, which is the stiffest family, exhibit greater variability and non-linear behavior in the relationship between static and dynamic stiffnesses, in contrast to Type A pads, the least stiff, where dynamic stiffness depends almost exclusively on static stiffness, showing a linear relationship with low variability. Type B pads, with intermediate stiffness, display predominantly linear behavior and greater dispersion than Type A pads, although without reaching the non-linearity and variability observed in Type C pads. These results indicate that additional variables beyond static stiffness influence the dynamic stiffness of all rail pads, with their impact varying depending on the pad type. This suggests that the effects of mechanical and environmental conditionsdiffer depending on the geometry and material of the rail pad. Based on the observations and previous discussions, different ML models have been trained and evaluated to predict dynamic stiffness. In the initial analysis, only the operating conditions were used as input variables, which include frequency (Hz), toe load (kN), and amplitude (kN), along with static stiffness (kN/mm). Information regarding the test conditions listed in Table 1 and the type of rail pad was excluded from this initial analysis. Table 2 collects the mean squared error, mean absolute error, coefficient of determination, and root mean squared error. These metrics were applied to the following models: linear regression, Lasso, Ridge, RF, KNN, and GB. Subsequently, an independent model was created for each type of rail pad, using the same input variables as in the previous model. The objective was to evaluate the model's ability to generalize. The results are presented in Table 3.  
The results indicate that the decision-tree-based models (RF and GB) and KNN achieved the best performances, prompting the exclusion of linear models from further analysis. To enhance performance, the hyperparameters of RF, GB, and KNN were optimized using a grid search (GridSearchCV), revealing that GB outperformed the others. Consequently, GB was selected for subsequent analyses. Finally, Table 4 summarizes the obtained hyperparameters, and Table 5 presents the metrics. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **LR** & **Lasso** & **Ridge** & **RF** & **KNN** & **GB** \\ \hline MSE (kN\({}^{2}\)/mm\({}^{2}\)) & 4392.75 & 4388.43 & 4389.19 & 1848.43 & 4594.29 & 2388.02 \\ MAE (kN/mm) & 45.74 & 45.43 & 45.72 & 21.73 & 37.37 & 26.45 \\ R\({}^{2}\) & 0.8702 & 0.8703 & 0.8704 & 0.9454 & 0.8643 & 0.9294 \\ RMSE (kN/mm) & 66.27 & 66.24 & 66.25 & 42.99 & 67.78 & 48.86 \\ \hline \end{tabular}
\end{table}