# Structural Damage Detection through Dual-Channel Pseudo-Supervised Learning
## 3 Validation by a Numerical Model
### Comparative Analysis at Different Noise Levels  
Lastly, the accuracy results of different models were compared using the complete IASC-ASCE SHM benchmark simulated data for in-depth research and a comprehensive analysis. This evaluation encompassed the entire dataset across different noise levels. Through this study, the aim is to demonstrate the exceptional capabilities of the proposed model in environments characterized by high levels of noise, thereby reaffirming its noise robustness. Table 5 provides the detailed results. Some conclusions were obtained. First, the single CNN, the Conformer, or the multi-head CNN model had a higher classification accuracy in low-noise signals. As the noise level increases, the classification accuracy also dropped significantly. Secondly, it can be seen that there was a smaller gap in the performance of the different noise levels when using a DCPS training model (i.e., CNN+Conformer and Conformer+Conformer). This means that the noise robustness of the model is improved after DCPS training. Note that DCPS learning was of great significance in practical applications for the noise robustness brought by the model, since the noise in the acceleration response \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **CNN+CNN** & **CNN+Conformer** & **Conformer+Conformer** \\ \hline Noise handling of the training set & Noisy & Noiseless & Noisy & Noiseless & Noisy & Noiseless \\ ACC & 94.23 & 93.43 & 95.99 & 95.91 & 96.96 & 96.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Detection accuracy (%) with and without noise augmentation using the DCPS learning strategy. ’Noisy’ indicates that the noise augmentation step of the training set is used, and ’Noiseless’ means that the noise augmentation step is omitted. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **1D CNN** & **Conformer** & **CNN+CNN** & **CNN+Conformer** & **Conformer+Conformer** \\ \hline ACC & 89.10 & 95.19 & 94.23 & 95.99 & 96.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Detection accuracy (%) of different network combinations for tests conducted on the IASC-ASCE SHM benchmark simulated data. signal was more complex. Finally, the proposed models (i.e., CNN+Conformer and Conformer+Conformer) achieved an average accuracy of 95.42% and 96.15%, respectively, surpassing all existing traditional models. To intuitively demonstrate the classification accuracy of the Conformer+Conformer model under different noise levels, the confusion matrices of the Conformer+Conformer model under two high-noise-level conditions are presented in Figure 7. As can be seen from Figure 7, D.P.0 and D.P.4 are occasionally confused. This phenomenon was mainly attributed to intra-class differences in D.P.4 (or D.P.0), which led to the collected training data not fully covering all instances of damage in this pattern. But overall, the classification accuracy of Conformer+Conformer was close to 1. These aforementioned results unequivocally showcase the effectiveness of the proposed model in the field of structural damage detection. The model exhibited remarkable performance improvements across various noise levels for the IASC-ASCE SHM benchmark simulated dataset. Furthermore, the compatibility and transferability of the DCPS strategy were evident, as networks with both identical and distinct structures consistently achieved superior performance. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Noise Level** & & & & & & \\
**(\%)** & **Direction** & **Floor** & **CNN** & **Multi-Head** & & & \\
**(\%)** & **Direction** & **Floor** & **CNN** & **Conformer** & **CNN+Conformer *** & **Conformer+Conformer *** \\ \hline  
*Average ACC at 50\% noise level** & **67.51** & **90.42** & **92.32** & **93.45** & **94.29** \\ \hline
**Average** & & **74.31** & **92.81** & **94.58** & **95.42** & **96.15** \\ \hline \hline \end{tabular}  
* represents structural damage identification methods that combine the conformer model and the DCPS learning strategy.  
\end{table}