## 4 Results and Discussion
### Test Results and Comparison  
Figure 6 compares the responses for the test results, the proposed equation by [PERSON] et al. [10], and the three different models. The 250 and 500 N loading plates were applied to the specimens. Figure 4 of the Appendix shows additional comparison plots under (40 and 80) N loadings. The \(x\)- and \(y\)-axes represent the deflection of the specimens and the dynamic stiffness, respectively. The solid curves with markers (blue) and the solid curves (red) indicate the test results and the dynamic stiffness calculated using the equation, respectively. The three different types of dashed curves represent the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Correlation Coefficient** & **Root Mean Square Error** & **Relative Absolute Error (\%)** & **Root Relative Square Error (\%)** \\ \hline k-nn regression & 0.9864 & 1.5221 & 12.2242 & 16.5721 \\ Regression tree & 0.9817 & 1.7481 & 16.0049 & 19.0322 \\ MLP Regression & 0.9848 & 1.9931 & 13.9954 & 17.3445 \\ [PERSON] et al. [10] & 0.8992 & 3.5529 & 195.5806 & 198.8626 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Error comparison between the ANN algorithms.  
Figure 5: RMSE comparison of the three algorithms.  
dynamic stiffness predicted using the three ANN algorithms. The vertical line in the plots represents the maximum deflection of the resilient materials under each loading. The deflection was measured for more than 500 days and the load-deflection responses of the specimens were reported by [PERSON] et al. [10]. The vertical line implies the practical maximum deflection of each material.  
In most cases, the regression data using the algorithms predicts well the test results. Reasonable data regression among the actual test data was observed in the ANN system using the k-nn regression and regression tree algorithms. However, the regression models could not predict the dynamic stiffness-deflection responses outside of the actual data range. These algorithms were effective only within the actual test data range. MLP Regression more reasonably predicted the test data than the proposed equation in most cases and could predict the deflection dependent dynamic stiffness outside the measured test data. The data regression tendency of these ANN systems was similar in all the specimens.  
For example, in the case of EPS(2)-15-C (Figure 5c), the maximum deflection of specimens under (250 and 500) N loading was (10.34 and 17.21) mm, respectively. The three ANN models well predicted the dynamic stiffness prior to reaching the maximum deflection. However, k-nn regression and regression tree algorithms could not track the dynamic stiffness trend after the final deflection, and tended to converge to the final recorded dynamic stiffness. Regardless of the deflection increase, the predicted dynamic stiffness was about (8.34 and 8.10) MN/m\({}^{3}\) under (250 and 500) N loading, respectively. On the other hand, MLP regression well inferred the trend of data and showed a similar tendency to the proposed equation. The step-wise prediction responses were monitored in PE-24-F (Figure 6e) when k-nn and regression tree algorithms were applied. This shape is due to the sparsely measured test data in which caused by a significant increase of deflection during the test. However, the continuous curve response was obtained when MLP regression was used.  
Figure 6: \(Cont\).  
Figure 6: Dynamic stiffness comparisons between the test results and the equation for 250 N and 500 N.