# Deep Autoencoder Framework for Classifying Damage Mechanisms in Repaired CFRP
## 2 Materials and Methods
### Methods
#### 2.2.2 Deep Autoencoder (DAE)  
The architecture is composed of an encoder and a decoder block. The autoencoder is a specialized form of artificial neural network used to learn efficient features of unlabeled data, enabling it to estimate input variables (reconstruction) [37]. This is achieved by capturing the inherent relationships and statistical patterns between the input variables in the data [38; 39]. A schematic representation of the DAE is presented in Figure 3. The graphs in the lower part of Figure 4 highly illustrate the transformation process of complex input data by a deep autoencoder. Initially, the encoder reduces the dimensionality of this data, effectively transforming it from a high-dimensional space to a more compact, lower-dimensional representation in the latent space [40]. This is achieved by extracting the most significant attributes inherent to the data. Subsequently, the data are reconstructed into a simplified output by the decoder through the learned low-dimensional information in the feature space [41]. For the autoencoder, different types of neural network architectures can be used, depending on the specific data type. For instance, the convolutional neural networks (CNNs) are suitable for extracting features from spatial data, such as images. The long short-term memory networks (LSTMs) are used for sequential data such as time-series forecasting or speech recognition because of their ability to store long-term dependencies. The dense networks, known for their simplicity, are versatile in general pattern recognition, as they are able to encode data in a compact form and reconstruct it. The architecture chosen for this study is based on fully connected (dense) neural networks, which demonstrate an exceptional ability to encode data in a reduced-dimensional space and reconstruct it with high fidelity. The overview of the training parameters of the deep autoencoder model used in this study is presented in Table 2. The model architecture consists of eight layers organized into four stages: input, encoding, bottleneck, and decoding, leading to the regression output. The input dimensions of 5120 \(\times\) 715 correspond to the data, where 5120 is the signal length and 715 represents the number of samples collected from AE signals measured during a tensile test. The network undergoes a compression process, reducing the number of neurons from 425 to 256, and then to 128, with ReLU activations applied at each layer to enhance feature extraction. At the core, the bottleneck layer, composed of only four neurons and a ReLU activation, captures the essential features of the data. Figure 4: Schematic of deep autoencoder model architecture. The choice of four bottleneck neurons was based on the need to strike a balance between dimensionality reduction and feature retention, ensuring the model effectively captures the most important latent features while avoiding overfitting. This configuration was optimized through experimental trials and cross-validation. Architectures with fewer than four neurons failed to capture enough variance, resulting in poor clustering, while those with more neurons introduced redundant information, with minimal additional variance (below 5%) and reduced interpretability. A key design aspect involved evaluating the reconstruction error between the input and the output reconstructed by the decoder. Since the decoder reconstructs the signal based on the compressed representation generated by the encoder, the reconstruction quality directly measures the adequacy of the bottleneck. The goal was to reduce dimensionality while preserving data quality, which was verified by minimizing the difference between the input and output signals. The selected architecture with four bottleneck neurons achieved an optimal balance, minimizing reconstruction error while maintaining interpretability and efficient data compression [42]. This approach aligns with prior research.