# Deep Autoencoder Framework for Classifying Damage Mechanisms in Repaired CFRP
## 3 Results and Discussions
### Results of Deep Autoencoder Training  
The AE signals acquired from the mechanical testing of the bonded composites are used to train the modeled DAE. During the training phase, the DAE is engaged in accurately reconstructing the AE's input signals. AE signals collected from JLS1, JLS2, and JLS3, each containing waveforms of length 5120 samples, were used to train and evaluate the model. The dataset contains 715 waveforms from JLS1, 393 waveforms from JLS2, and 827 waveforms from JLS3. The variation in the number of extracted waveforms across samples can be attributed to the manual bonding process of the adhesive, which introduces variability in adhesive thickness, void distribution, and bond uniformity. During the training process, the DAE reduced the dimension of the waveform into a low-dimensional space of four latent features at the bottleneck layer through the encoder. Then, it is decoded using the trained weights in the decoder layers to restore it to its original state. The k-fold cross-validation is used to improve training and validation by dividing the dataset into k = 10 subsets (or \"folds\"). At each training iteration, k - 1 datasets are used for training, while one remaining dataset is reserved for validation. This approach aims to reduce bias by using the majority of data for training in all k iterations. This process is performed on a PC with a speed of 2.92 GHz and a RAM of 16.0 GB. The hyperparameters for this DAE training were designed to optimize the model's performance. To achieve a balance between model convergence and the prevention of overfitting, training is continued for 250 epochs. The mini-batch size of 128 improves the efficiency of the computation and the stability of the gradient. Data shuffling is included at the start of each epoch, which maintains diversity within the mini-batches. Validation is repeated for every 15 mini-batches. A learning rate of 0.001 is used to ensure smooth convergence. To enhance the learning process, a piecewise learning rate schedule is implemented, which reduces the learning rate by a factor of 0.7 every 20 epochs (refer to Table 3). Figure 6a, Figure 6b, and Figure 6c each illustrate an example of an original signal and its re constructed signal from specimens JSL1, JSL2, and JSL3, respectively. These plots provide a visual comparison between the input signals and their corresponding reconstructed signals, demonstrating the effectiveness of the reconstruction process. The signals are presented in both the time and amplitude domains, allowing for a clear assessment of the reconstruction quality. The reconstruction error for each parametric study case was measured by root-mean-square error (RMSE) to assess the respective performance (see Figure 7). For JLS1, the average RMSE is approximately 0.170045. For JLS2, the average RMSE error is approximately 1.107225. Finally, for JLS3, the mean RMSE error is approximately 0.671855. The RMSE values reflect the reconstruction quality of the signals for each sample. A lower RMSE indicates better reconstruction quality, while a higher RMSE suggests larger discrepancies between the original and reconstructed signals. These values provide insight into how accurately the signal reconstruction process performs for each specimen. The main objective was to extract latent features that represent high-dimensional input data containing information about the damage mechanism of specimens under load and reduce them to low-dimensional features retaining the same information. To ensure efficiency, it is essential that the RMSE error is low, indicating that the model can reconstruct the data accurately, closely reflecting the original input. It should be noted that, in some cases, DAE is also used to reduce noise in the data [63]. Figure 6: Original and reconstructed signal based on deep autoencoder for **(a)** JLS 1; **(b)** JLS 2; and **(c)** JLS3. Damage Characterization Using Latent Features  
The latent features from the bottleneck layer are used for damage clustering.