## 3 Case Study
### Results  
In this paper, the structural damage identification experiment can be regarded as a multi-label classification of multivariate time series. The reference criteria for evaluating the model effect are accuracy of validation set, loss value, F1 score, precision and recall. The accuracy rate is the average of the K validation sets obtained by K-fold cross-validation value and variance, F1 score, accuracy rate, and recall rate are the mean of the K validation sets obtained by K-fold cross-validation, The loss function adopts the cross entropy loss function. For the three experimental schemes, the comprehensive recognition accuracy and loss values of each comparison model were compared horizontally, as shown in Table 7. F-1 value, accuracy rate and recall rate are shown in Table 8. The running time of each comparison model is shown in Table 9. The confusion matrix generated by the three experimental schemes is shown in Figure 11.  
Under the condition of keeping the hyperparameters such as epoch and learning rate consistent among all the compared models, the VMD-CSANN combined model demonstrates superior performance in terms of accuracy, loss value, F1 score, precision, and recall metrics compared to other models. This is attributed to the ability of variational mode decomposition to decompose the original signal, including noisy and non-smooth segments, into several relatively smooth segments. This substantiates that augmenting the VMD-CSANN model with both VMD and self-attention mechanisms leads to improved recognition capabilities, whether for specific working conditions or across the board. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**WC1, 3, 5, 7, 9**} & \multicolumn{3}{c}{**WC2, 4, 6, 8, 10**} & \multicolumn{3}{c}{**All**} \\ \cline{2-10}
**Compared** & **Accuracy** & **Precision** & **Accuracy** & **Precision** & **Accuracy** & **Precision** & \\
**Model** & **Rate** & **Rate** & **Loss** & **Rate** & **Rate** & **Loss** & **Rate** & **Loss** \\
**(Average)** & **(Variance)** & **(Variance)** & **(Variance)** & **(Variance)** & **(Variance)** & **(Variance)** & **(Variance)** & **(Variance)** & **(Variance)** \\ \hline
**CNN** & 91.87\% & 94.48\% & 0.1315 & 91.87\% & 94.48\% & 0.4865 & 87.80\% & 89.77\% & 0.4865 \\
**LSTM** & 77.24\% & 83.76\% & 0.7594 & 80.36\% & 87.32\% & 0.6194 & 88.62\% & 90.74\% & 0.3504 \\
**GRU** & 78.86\% & 79.87\% & 0.6716 & 84.82\% & 86.43\% & 0.5141 & 90.24\% & 91.88\% & 0.3157 \\
**VMD-CSANN** & **95.12\%** & **93.99\%** & **0.1291** & **93.75\%** & **94.46\%** & **0.1993** & **93.90\%** & **94.00\%** & **0.3014** \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Accuracy and loss of each model verification set. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**WC1, 3, 5, 7, 9**} & \multicolumn{3}{c}{**WC2, 4, 6, 8, 10**} & \multicolumn{3}{c}{**All**} \\ \cline{2-10}
**Compared** & **Precision** & **Recall** & **Precision** & **Recall** & **Precision** & **Recall** & **Precision** & **Recall** \\
**Model** & **(Average)** & **Rate** & **Rate** & **(Average)** & **Rate** & **Rate** & **(Average)** & **Rate** & **Rate** \\ \hline
**CNN** & 0.9284 & 0.9321 & 0.9306 & 0.9310 & 0.9281 & 0.9218 & 0.8791 & 0.8842 & 0.8769 \\
**LSTM** & 0.7815 & 0.7865 & 0.7892 & 0.8231 & 0.8219 & 0.8291 & 0.8814 & 0.8852 & 0.8783 \\
**GRU** & 0.7882 & 0.7931 & 0.7872 & 0.8452 & 0.8523 & 0.8493 & 0.9051 & 0.9101 & 0.9089 \\
**VMD-CSANN** & **0.9412** & **0.9459** & **0.9482** & **0.9381** & **0.9421** & **0.9401** & **0.9317** & **0.9391** & **0.9401** \\ \hline \hline \end{tabular}
\end{table} 
Table 8: F1 score, accuracy rate and recall rate of each model validation set.