# Deep Autoencoder Framework for Classifying Damage Mechanisms in Repaired CFRP
## 3 Results and Discussions
### Damage Characterization Using AE Feature  
The second part of the damage characterization uses AE descriptors, the amplitude and entropy. The amplitude and entropy of the AE signals from the JLS specimens are clustered using the k-means algorithm. These features are often used to effectively characterize materials, including CFRP composites subjected to mechanical loading [72]. In the context of our study, the choice of amplitude and entropy descriptors for AE signal analysis is dictated by their ability to provide distinct and complementary insights into the dynamics of failure events [67]. The entropy characterizes the uncertainty or disorder of the signal data, thereby enabling a qualitative analysis of failure structures. Recently, several key studies have demonstrated the effectiveness of entropy in AE analysis. For example, [PERSON] et al. have demonstrated that wavelet entropy can effectively estimate spectral disorder in the AE signals, providing valuable information on fracture processes in concrete [73]. The use of entropy and amplitude thus enriches our understanding of failure mechanisms. The integration of these two measures significantly enhances the ability to distinguish between different types of damage, facilitating the characterization and classification of failure modes in CFRP composites. However, it is important to note that this method may not be universally applicable in all situations, and there are certain limitations when applying it to the current analysis. As explained in the previous subsection, the Silhouette criterion is applied to determine the optimal number of clusters. Figure 14a-c illustrate the Silhouette coefficient analysis, a widely used metric for evaluating cluster quality and determining the optimal number of clusters in partitional clustering algorithms like k-means [74]. The Silhouette coefficient assesses both cohesion within clusters and separation between clusters, with values ranging from \(-1\) to \(1\). Higher scores indicate better-defined clusters [75]. These figures show that three clusters provide the highest Silhouette scores, suggesting that this configuration yields the most coherent and well-separated clusters. In Figure 15 and Table 4, cluster assignments for specimens JLS1, JLS2, and JLS3 are presented. For specimen JLS1, the first cluster exhibits a low amplitude range of 40-48 dB and an entropy distribution from 0.01 to 1.54, indicating initial damage, such as microcracks. Cluster 2, with an amplitude range of 49-65 dB and entropy from 0.02 to 1.01, suggests damage progression, with signs of interlaminar cracks. The third cluster, spanning 67-99 dB in amplitude and 0.03-0.8 in entropy, reveals severe damage, possibly indicating critical failure. The specimen JLS2 exhibits damage beginning with a first cluster ranging from 40 to 58 dB in amplitude and 0.03-2.10 in entropy, suggesting a more varied initiation of damage, potentially due to debonding or microcracking. The second cluster, displaying an amplitude of 59-78 dB and an entropy of 0.02-1.35, indicates a progression towards moderate damage. The third cluster, from 79 to 100 dB in amplitude and 0.07-1.03 in entropy, denotes critical damage, with a strong indication of fiber breakages, signaling an advanced stage of structural degradation. For JLS3, the first cluster reveals an amplitude of 40-53 dB and an entropy distribution of 0.01-2.59, highlighting a wide range of initial damages, from minor debonding to various microcracks. The second cluster, with an amplitude of 54-75 dB and an entropy of 0.02-1.88, shows signs of more serious damage, likely more complex and extensive matrix cracking. Finally, the third cluster, with amplitudes of 76-100 dB and entropy of 0.04-1.52, signals very severe damage, such as fiber ruptures, indicating the most critical phase of degradation. The initial observation is that there are three modes of damage for each specimen, each with a slightly different distribution.