# Structural Damage Detection through Dual-Channel Pseudo-Supervised Learning
## 3 Validation by a Numerical Model
### Comparative Experimental Results  
The testing results in the \(x\) direction on the initial floor of simulated data from the IASC-ASCE SHM benchmark structure were utilized for a comparative analysis, and classification accuracy (ACC) was used as an indicator to measure the performance of each model. The training set experienced 5% and 20% noise augmentations. This involves directing the training data into two distinct channels within the DCPS architecture, facilitating the acquisition of noise-robust features by the proposed model. Table 2 presents the accuracy performance and inference time of different models on the IASC-ASCE SHM benchmark dataset. Table 2 shows that the CNN-LSTM and Conformer models, which extracted both local and global features, achieved higher accuracy than the CNN and multi-head CNN models, which only extracted local features, and the LSTM model, which only extracted global features. Since the Conformer model has the local information representation ability of CNNs and also inherits the long-sequence temporal modeling ability of Transformers, it achieved the best classification accuracy, reaching 95.19%. The classification performance of the Conformer was 2.64% higher than  
that of CNN-LSTM, which considers both local and global features; 6.09% higher than that of 1D CNN, which only considers local features; and 6.97% higher than that of LSTM, which only considers global features. The Conformer model achieves the highest prediction performance among the compared models. Moreover, it has a very low computational cost, requiring only about three times the computational resources of the fastest CNN model, which has the lowest accuracy. This indicates that the proposed model effectively balances performance and computational efficiency. To verify the effectiveness of the DCPS learning strategy, Table 3 presents the gains achieved using the different network combinations (i.e., CNN+CNN, CNN+Conformer, and Conformer+Conformer). These tests were conducted on the IASC-ASCE SHM benchmark simulated dataset. In Table 3, \"+\" means the network architecture of each branch of the DCPS. Figure 6 intuitively shows the different network combinations used in the DCPS learning strategy. From Table 3, it can be seen that the performances of the single CNN model and the Conformer model are 89.1% and 95.19%, respectively. The models utilizing DCPS learning generally exhibited superior performance compared to those without it. In particular, the performances of CNN+CNN and Conformer+Conformer were 5.13% and 1.77% higher than those of the single CNN and Conformer model, respectively. Since the DCPS learning strategy took different levels of noise signals as the input, the classification results of the same network architecture with different initialization weights \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **1D CNN** & **LSTM** & **Multi-Head CNN** & **CNN-LSTM** & **Transformer** & **Conformer** \\ \hline ACC & 89.10 & 88.22 & 92.39 & 92.55 & 94.07 & 95.19 \\ \hline Time(s) & \(0.57\times 10^{-3}\) & \(3.2\times 10^{-3}\) & \(1.0\times 10^{-3}\) & \(2.9\times 10^{-3}\) & \(1.0\times 10^{-3}\) & \(1.6\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Detection accuracy (%) results and inference time (s) of baseline models for tests conducted on the IASC-ASCE SHM benchmark simulated dataset. Figure 6: Three combinations were used to verify the effectiveness of DCPS learning. were used as the target to perform cross-channel learning. Driven by a DCPS learning strategy, this network was robust to different levels of noise signals. Finally, a more accurate classification performance was obtained. In addition, we used a different network architecture (i.e., CNN+Conformer) for DCPS learning and also achieved performance improvements relative to the single CNN or Conformer model. This means that this DCPS learning strategy can generalize to different models.