## 4 Model Verification
In the first case study, for example, as the number of training data increased by 10 times, from 400 to 4400, the computational time increased by 88 times, from 5 s to 445 s.  
The present study adopted 10-fold cross validation (K = 10) as recommended by [PERSON] et al. 's study [18] for all 11 sizes of training dataset. Table 3 presents the average validation accuracies of each experiment \(A\) obtained via Equation (8) and 10-fold cross-validation for the proposed model with a training dataset of 4400 samples. Specifically, with 11 building characteristics as the inputs for \(S_{dy}\) and \(S_{ay}\), these average validation accuracies were 0.666 and 0.648, respectively; and with 20 building characteristics as the inputs for \(S_{dy}\) and \(S_{ay}\), they were 0.709 and 0.695, respectively. As noted in Table 1, such validation accuracies indicate that both the 11-characteristic and 20-characteristic models are reasonably accurate at predicting \(S_{dy}\) and \(S_{ay}\) when 4400 training samples are used. The experiment with the highest validation accuracies out of all 10 experiments, which are those ones with the maximum values in validation accuracies in Table 4, was selected as the optimal model for further model testing. Finally, for the sake of maximum predictive accuracy, as recommended by [PERSON] et al. 's study [26], the present study adopted a proportion of 5:1 between the sizes of the training dataset and the testing dataset  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Experiment**} & \multicolumn{6}{c}{**11 Building Characteristics**} & \multicolumn{6}{c}{**20 Building Characteristics**} \\ \cline{2-10}  & \multicolumn{2}{c}{**Spectral-Yield**} & \multicolumn{2}{c}{**Spectral-Yield**} & \multicolumn{2}{c}{**Spectral-Yield**} & \multicolumn{2}{c}{**Spectral-Yield**} & \multicolumn{2}{c}{**Spectral-Yield**} \\  & \multicolumn{2}{c}{**Displacement, \(S_{dy}\)**} & \multicolumn{2}{c}{**Acceleration, \(S_{ay}\)**} & \multicolumn{2}{c}{**Displacement, \(S_{dy}\)**} & \multicolumn{2}{c}{**Acceleration, \(S_{ay}\)**} \\ \cline{2-10}  & **Training** & **Validating** & **Training** & **Validating** & **Training** & **Validating** & **Training** & **Validating** \\ \hline
1 & 0.689 & 0.557 & 0.675 & 0.537 & 0.761 & 0.712 & 0.764 & 0.698 \\
2 & 0.686 & 0.697 & 0.671 & 0.691 & 0.764 & 0.747 & 0.763 & 0.697 \\
3 & 0.681 & 0.649 & 0.690 & 0.715 & 0.765 & 0.659  
In the first case study, the first 11 building characteristics in Table 2 were used as the model inputs, and \(P_{Y}(S_{dy},S_{ay})\) and \(P_{U}(S_{du},S_{au})\) as outputs. First, we tested the influence of all 11 sizes of training dataset on the model's prediction accuracy (Table 4), with 30 trials run for each training size using samples randomly selected from among the NCREE's 5400 buildings. The resulting accuracies \(A\) of the output \(S_{dy}\) are presented in Figure 4 and Table 5, which show that such accuracies increased slightly as the size of the training dataset increased: from 0.51 with a training dataset of 400 samples, to 0.54 at 4400 samples. This implies that when only 11 building characteristics were used as model inputs, the proposed SVM model could only achieve an accuracy of 0.52 in the prediction of \(S_{dy}\), even when its training sample was as large as 4400; and that improvements in accuracy based solely on further increases in the size of the training dataset (as opposed to the number of building characteristics) are unlikely to be dramatic. We also observed that the standard deviation (SD) of our SVM models' prediction accuracy over 30 trials decreased as the size of the training dataset increased: from 0.12 with a training dataset size of 400 is 0.12, to 0.04 at a size of 4400 samples, with a maximum value of 0.63 and a minimum of 0.03 (Table 5). These results indicate that the reliability of the proposed model can be increased by enlarging the training dataset, at least up to a point.