## 3 Numerical Example
### Model Training and Hyperparameter Optimization  
This study is based on the deep learning framework Pytorch and the programming language Python to complete the model compilation work. A computer with an Intel Core i5-9300H CPU, GeForce GTX 1650 GPU, and RAM 16.00 GBs was used. Additionally, Windows 10, Pytorch 1.4.0, and Python 3.8.2 operating systems were used, as well as CUDA 10.2 software. For deep learning algorithms, hyperparameters are critical for model performance; therefore, the model parameters need to be adjusted and optimized. The following hyperparameters were optimized and adjusted by the control variable method: learning rate, rate of dropout, mini-batch, and BN layer. The specific parameters to be adjusted are shown in Table 3. The epoch was set to 50, and the average epoch duration was 9720 s. The damage recognition results of the CNN-LSTM model with different learning rates are plotted in  
Figure 7: Architecture of the proposed CNN-LSTM. Figure 8. It should be noted that the accuracy is the ratio of the number of samples correctly localized in the validation set. Val-Mse is the mean square error between the prediction vector of the damage severity and the target vector. Figure 8 indicates that under different learning rates, the loss of CNN-LSTM used for damage localization and severity prediction, respectively, shows a short horizontal segment in the second to eighth epoch, and then, it continues decreasing until the value stabilizes. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Layer** & & **Size/No.** & **Stride** & **Padding** & **Input/Output** & **Activation** \\ \hline \multirow{3}{*}{Convolutional block 1} & Conv1 & \(64\times 1/32\) & 2 & SAME & \(31\times 1024/32\times 512\) & ReLU \\  & BN layer & - & - & - & - & - \\  & Pool1 & \(3\times 1/32\) & 2 & SAME & \(32\times 512/32\times 256\) & - \\ \hline \multirow{3}{*}{Convolutional block 2} & Conv2 & \(3\times 1/64\) & 2 & SAME & \(32\times 256/64\times 128\) & ReLU \\  & BN layer & - & - & - & - & - \\  & Pool2 & - & - & - & - \\ \hline \multirow{3}{*}{Convolutional block 3} & Conv3 & \(3\times 1/128\) & 2 & SAME & \(64\times 64/128\times 32\) & ReLU \\  & BN layer & - & - & - & - & - \\  & Pool3 & \(3\times 1/128\) & 2 & SAME & \(128\times 32/128\times 16\) & - \\ \hline \multirow{3}{*}{Convolutional block 4} & Conv4 & \(3\times 1/256\) & 2 & SAME & \(128\times 16/256\times 8\) & ReLU \\  & BN layer & - & - & - & - & - \\  & Pool4 & \(3\times 1/256\) & 2 & SAME & \(256\times 8/256\times 4\) & - \\ \hline LSTM layer & & - & - & - & \(64\times 496/64\times 256\) & - \\ \hline \multirow{3}{*}{Fully connected block 1} & Fc1 & - & - & - & \(1280/1280\) & - \\  & BN layer & - & - & - & \(256/256\) & ReLU \\ \hline Fully connected block 2 & Fc2 & - & - & - & \(256/31(62)\) & - \\ \hline \multirow{3}{*}{Fully connected block 3} & Fc3 & - & - & - & \(31(62)\) & Sigmoid (-) \\ \hline \end{tabular} Note. The size of the parameter used for damage localization is in brackets, and the size of the parameter used for damage severity prediction is outside the brackets.  
\end{table} 
Table 2: Parameters of CNN-LSTM. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters to Be Adjusted** & **Value** & **Parameters to Be Adjusted** & **Value** \\ \hline \multirow{4}{*}{Learning rate} & 0.01 & 32 \\  & 0.005 & Mini-batch & 64 \\  & 0.001 & 128 \\ \cline{1-1}  & 0.0005 & 0 \\  & 0.0001 & Rate of dropout & 0.3 \\ \hline \multirow{2}{*}{BN layer} & Setting & 0.5 \\  & Not Setting & 0.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hyperparameters optimization of CNN-LSTM model. Figure 8: Influence of different learning rate on CNN-LSTM: (**a**) Localization; (**b**) Severity prediction. As shown in Figure 8a, the training speed of the damage localization is the fastest when the learning rate is 0.0001 and 0.0005, and the accuracy is higher under the same epoch, but the accuracy curve with a learning rate of 0.0005 is more volatile.