## 3 Results and Discussion
### Test Results by ANN Structure  
For the ANN trained with eight different structures having various numbers of hidden layers and nodes, testing was performed using data that were not used for training. The purpose of the test is to determine whether overfitting has occurred during the training process. Overfitting refers to situations in which the ANN is trained well, but the trained ANN do not predict data well. This means that the ANN simply memorized the correlation between the input and output values of the training data rather than defining it well ([PERSON] et al., 2018). This is an important process because in order to be practically applicable, an ANN must be able to produce accurate predictions for untrained data. The test procedure was as follows. The strain obtained from the analysis of a load scenario that was not used for training was input to the ANN trained as described in Section 3.1. The trained ANN can predict displacement (output) immediately, which is one of the advantages of ANN. Then, the displacement predicted by the ANN was compared with the displacement obtained from the analysis. The data used in this test were those for the one load scenario for each of the three velocities (40 km/h, 60 km/h, and 80 km/h) that were not used for training, as mentioned in Section 2.2.3. All ANN architectures trained as described in Section 3.1 were tested, and the test results were reviewed. For testing, as the output value is immediately predicted after the input is entered into the trained neural network, the training time is not indicated separately. The test results are shown in Table 6, and the error for the load scenario at 40 km/h is shown in Figure 10. From the results for 40 km/h, when there was one hidden layer, the minimum and maximum MSE values were \(0.67\times 10^{-3}\) (case 4) and \(0.70\times 10^{-3}\) (case 1), respectively. The minimum and maximum \(R\) values were 0.995533 (case 1) and 0.995705 (case 4), respectively. When there were two hidden layers, the minimum and maximum MSE values were \(0.70\times 10^{-3}\) (case 8) and \(0.77\times 10^{-3}\) (case 5), respectively. The minimum and maximum \(R\) values were 0.995058 (case 5) and 0.995519 (case 8), respectively. Compared to the training results, the accuracy rankings for the structures with 110 and 111 hidden layers differed. However, as the difference is very small, it is considered that the test results are similar to the training results. Similar results were obtained for 60 km/h and 80 km/h. The test MSE values for 40 km/h and 60 km/h are smaller than the training MSE values, and the test MSE values for 80 km/h are larger than the training MSE values. This is because the MSE is affected by the magnitude of the absolute value. In addition, a comparison of the \(R\) values shows that the \(R\) value in testing was smaller than that for training for all velocities. Therefore, it is considered that the test results are slightly reduced in accuracy compared to the training results. However, we can see fairly good test results for MSE and \(R\) overall. Particularly in the cases with one hidden layer, a higher accuracy is shown. Therefore, it can be confirmed that the ANN was not overfitting, indicating that training and testing progressed very well. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multicolumn{2}{c}{**No. of**} & \multirow{2}{*}{**ANN Structure**} & \multicolumn{2}{c}{**Training Performance**} & \multirow{2}{*}{**Training Time (s)**} \\ \cline{3-3} \cline{5-6}  & \multicolumn{1}{c}{**Hidden Layers**} & & & **MSE (\(\times\)10\({}^{-3}\))** & \multicolumn{1}{c}{**\(R\)**} \\ \hline
1 & & 55-28-55 & 1.31 & 0.998728 & 840.30 \\
2 & & 55-55-55 & 1.20 & 0.998829 & 1566.92 \\
3 & & 55-110-55 & 1.10 & 0.998927 & 3403.87 \\
4 & & 55-111-55 & 1.10 & 0.998928 & 3440.74 \\ \hline
5 & & 55-The test results for the case of 55-111-55 (case 4), which showed the highest accuracy among the various ANN architectures, are shown in Figures 11-14.