## 4 Application to a Plate Girder Bridge under Vehicle Load
### Optimization Results  
According to the proposed method in Section 2.2., the locations of \(\mathrm{n_{s}}\) strain-measurement points per girder as optimization variables were optimized in the order of four, three, and two. Since the bridge model has five girders, the total number of strain-measurement points was \(5\times\mathrm{n_{s}}\). Additionally, it was assumed that the location of \(\mathrm{n_{s}}\) strain-measurement points were all the same for five girders. Fifty populations per generation were evaluated based on the objective function (= MSE). Additionally, the optimization was set to end when the minimum fitness value had not changed in more than 50 iterations. In Figure 11, the change in fitness value according to generation is shown. In Figure 11, the MSE gradually decreases with the generations even though there are differences depending on the number of strain measurements. Table 6 and Figure 12 show the optimized locations of strain-measurement points and the training MSE and R for the optimized locations. The training results for arbitrary locations are also presented in Table 6. Using eleven strains and using two strains, the MSE (\(\times 10^{-3}\)) was 1.2007 and 2.5370, respectively. Although the number of strain-measurement points decreased by more than five times, there was no significant difference in MSE values. When comparing the R-values using eleven strains and two strains, the R-values were 0.9988 and 0.9975, respectively. It is also considered that there was no significant difference in the R-value. In the case of four strains for arbitrary and optimized locations, the training MSE (\(\times 10^{-3}\)) was 5.4946 and 1.4268, respectively. In other words, when the strains at the optimized locations were used as the ANN input, the training accuracy was much higher. The same result occurred even when three and two strains were used. In the case of the optimized locations, the number of strains was four, three, and two, and the training MSE (\(\times 10^{-3}\)) tended to increase slightly to1.4268, 1.7511, and 2.5370, respectively. However, since the values were all very close to zero, even when two strains at the optimized locations were used as ANN input, very high training accuracy can be expected. In addition, the R-value was close to 1 for all optimized positions. From the training results, the effectiveness of the GA for the location optimization of strains required for displacement prediction could be confirmed. To test for overfitting and prediction accuracy of the trained ANN, three test datasets (40 km/h, 60 km/h, and  
Figure 11: The best fitness value changes in generations by GA. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Training Data**} & \multicolumn{3}{c}{**Test Data**} \\ \hline
**Velocity (km/h)** & 40 & 60 & 80 & 40 & 60 & 80 \\
**Number of load scenarios** & 24 & 24 & 24 & 1 & 1 & 1 \\
**Number of datasets per scenario** & 800 & 800 & 800 & 800 & 800 & 800 \\
**Total number of datasets** & & 57,600 & & & 2400 & \\ \hline \hline \end{tabular}  
One dataset consists of 55 strains (input) and 55 displacements (output).  
\end{table} 
Table 5: The number of training and test datasets. 80 km/h) that were not used for training were utilized. Table 7 shows the test results for the test dataset. When the strains at the optimized locations obtained from numerical analysis were input into the trained ANN, the trained ANN predicted displacements from the strains. In the case of using four strains at arbitrary locations, the MSE (\(\times 10^{-3}\)) was 1.7815, 1.7924, and 7.6117 for 40 km/h, 60 km/h, and 80 km/h, respectively. Additionally, using four strains at the optimized locations, the MSE (\(\times 10^{-3}\)) was 0.7987, 0.4805, and 4.7009 for 40 km/h, 60 km/h, and 80 km/h, respectively. Comparing the two cases, it could be seen that the displacement prediction accuracy was very high when the strains at the optimized locations were used. Similar results were obtained for three and two strains.