## 3 Numerical Validation
### Training Results and Discussion  
For demonstration of training results, classification accuracy of each validation datasets is shown in Table 5. According to classification results, Case 1 shows better classification capability in both cases. These results can lead us to the fact that training with longer data, which represents higher degree of excitation can provide more information to train the model. However, the longer the data, the longer the model takes to learn and harder to use for real world applications. For example, training a 60-s-long raw data with an input size of 9 \(\times\) 6000 takes 34 s per epoch, whereas normalized 81 \(\times\) 1024 takes 13 s. Thus, to secure learning efficiency in time-series deep learning model for structural damage detection, the proposed data normalization step is essential. A comparison was made between the proposed method and the model proposed by [PERSON] et al. (2010). Since the existing model was originally proposed to train with raw acceleration data, 10.24 s of raw acceleration data of which the size is 9 \(\times\) 1024 was used for training. Furthermore, for demonstration of proposed data normalization, Case 1 dataset was used with the existing model. As shown in Table 6, classification accuracy is 99.90% and 81.20% under random excitation for the proposed method and the existing model, respectively. The proposed method showed 18.70% better performance in damage classification compared to existing model. It is noteworthy that the accuracy of the models using traffic loading clearly show excellence of the proposed model. The proposed method showed 99.20% of accuracy while the existing model exhibited 59.80% of classification accuracy. The difference is resulted from the use of the proposed data normalization that allows to aggregate frequency-domain information compared to instant time-domain information presented in the existing model. As a result of applying the data normalization method to existing model, the classification accuracy was significantly improved. However, in the existing model, the accuracy in the training process reached 100% at 98 th epoch, but the validation accuracy did not \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Network Architecture**} & \multicolumn{2}{c}{**Validation Accuracy on Different Loading Cases (\%)**} \\ \cline{2-3}  & **Random Excitation** & **Traffic Loading** \\ \hline Proposed model (Data & 99.90 & 99.20 \\ Normalization + CNN) & & \\ [PERSON] et al. (2010) (CNN) & 81.20 & 59.80 \\ [PERSON] et al. (2010) (Data & 97.30 & 89.60 \\ Normalization + CNN) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance comparison of proposed model. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Name**} & **Value** & **Description** \\ \hline Batch size & 128 & Size of data used in training step \\ Steps per epoch & 8 & Number of steps per epoch \\ Total epochs & 1000 & Number of training epochs \\ Initial learning rate & \(1\times 10^{-5}\) & Initial learning rate of Adam optimizer \\ \(\beta_{1}\) & 0.9 & Parameter of Adam optimizer, weight of the momentum term \\ \(\beta_{2}\) & 0.999 & Parameter of Adam optimizer, controlling the decay of learning rate \\ Epsilon & \(1\times 10^{-7}\) & Parameter of Adam optimizer, constant for numerical stability \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Training case of random excitation. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Case 1: 60 s of Data**} & \multicolumn{2}{c}{**Case 2: 20-60 s of Data**} \\ \cline{2-4}  & **Random Excitation** & **Traffic Loading** & **Random Excitation** & **Traffic Loading** \\ \hline Validation accuracy (\%) & 99.90 & 99.20 & 99.30 & 97.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Classification results of training cases. exceed 93%. Since the existing model used max-pooling layers after convolutional layers, the overfitting issue was presented.