# Deep Autoencoder Framework for Classifying Damage Mechanisms in Repaired CFRP
## 3 Results and Discussions
### Results of Deep Autoencoder Training
Singular value decomposition (SVD) is employed to select the most significant latent features that best reflect the original signal data. In this study, the threshold is set at 80% of the cumulative variance to identify the dominant latent features. Figure 8a shows that the dominant singular value for the JLS1 specimens is two, explaining 95.8% of the variance. Similarly, for JLS2, 81.1% of the variance is explained by the dominant singular value (Figure 8b), and for JLS3, the dominant value explains 80% of the variance (Figure 8c). The dominance of these singular values is critical, as it demonstrates that a small number of latent features can explain a significant proportion of the total variance in the data. This indicates that these features effectively capture the essential characteristics of the original AE signals, allowing for efficient clustering and damage mode classification. The high variance explained by the selected singular values confirms the effectiveness of the SVD approach in reducing the dimensionality of the data, while preserving the most important information for subsequent damage analysis. The unsupervised k-means pattern recognition algorithm was used to examine the selected latent features. In this context, the Silhouette criterion is used to assess cluster quality by comparing the similarity of an object within its own cluster against its similarity to the objects in other clusters. A higher Silhouette score is indicative of a model characterized by well-delineated clusters. The Silhouette criterion returns k = 3 as the optimal number of clusters (see Figure 9a-c). This finding implies that the three-cluster model contains significant intracluster homogeneity and distinct intercluster separation and, therefore, is capable of elucidating the inherent structure of the dataset. \begin{table}
\begin{tabular}{l c} \hline \hline \multicolumn{2}{c}{**Training Parameters**} \\ \hline Max number of training epochs & 150 \\ Mini batch & 128 \\ Validation Frequency & 10 \\ Initial Learn Rate & 0.001 \\ Learn Rate Schedule & piecewise \\ Drop factor & 20 \\ Drop learning & 0.7 \\ Gradient Threshold & 1 \\ L2 Regularization & 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Training parameters of the deep autoencoder model. Figure 7: Effect of cross-validation folds (K) on RMSE values for different specimen types. Figure 10a-c illustrate each latent feature clustered from specimens JLS1, JLS2, and JLS3, respectively. The three distinct clusters of latent features reflect different damage modes observed during mechanical testing. Figure 8: Selection of dominant features from the bottleneck layer by SVD: (**a**) JLS1; (**b**) JLS 2; and (**c**) JLS3. Figure 9: Silhouette values of clusters for latent features of (**a**) JSL1; (**b**) JLS 2; and (**c**) JLS3. Recent studies have applied various forms of autoencoders, including deep convolutional, variational, and stacked autoencoders, for damage detection in different materials [64,65]. The methods have demonstrated improvements in the automated detection and classification of damage mechanisms. Despite these advances, the relationship between latent features and specific damage modes remains unexplored. This represents a significant gap that limits our understanding of damage mechanisms. To address this limitation, the model proposes analyzing the AE waveforms corresponding to the clustered data points. These analyses are carried out on the corresponding signals reconstructed by the decoder. Therefore, a frequency-domain analysis of the waveforms is performed using a fast Fourier transform. The objective is to accurately identify the frequency characteristics responsible for damage modes in bonded composite specimens. All waveforms analyzed were randomly selected to ensure a balanced representation of the data for analysis. The examination of the JLS 1 specimen is illustrated in Figure 11. The spectrum for Cluster 1 shows a prominent peak near 100 kHz, with other lower peaks up to about 300 kHz.