## 3 Methodology
### Model Training and Validation  
Following the cleansing and splitting of the dataset, the training data are employed to train the target model during the training phase. In addition, the validation data are employed to assess the trained model and adjust the hyperparameters as necessary. As the efficacy of the ML/DL model is contingent upon the quality of the extracted features, two models are developed in this study: one for nonlinear feature extraction and another for clustering. AE was selected among the various architectures of DL methods due to its superiority in the selection and extraction of nonlinear features and reduction of data dimensionality [37]. Recently, various variants have been proposed to address disparate issues in a multitude of applications and domains [38]. To achieve this objective, a variety of Auto-Encoder (AE) variants are utilized, including Convolutional Neural Network (CNN)-based AE, Long Short-Term Memory (LSTM)-based AE, and standard AE. To illustrate the superiority of the proposed model, a comparison was conducted between the developed model and the other AE structure-based models.  
In general, AE can be divided into two main components, i.e., the encoder and the decoder [39]. The primary objective of the encoder is to transform the high-dimensional input data into a low-dimensional representation, commonly referred to as the latent code. Conversely, the decoder is tasked with converting the extracted features into the original input, effectively mapping the latent code as output back into the original data space, as seen in Figure 3. Equations (1) and (2) illustrate the encoder and decoder components of the CNN-based AE model, respectively.  
\[L=S_{enc}(WI+b) \tag{1}\]  
\[U=S_{dec}(W^{\prime}L+b^{\prime}) \tag{2}\]  
where \(S_{enc}\) and \(S_{dec}\) represent the activation function of the encoder and decoder, respectively. \(I\) is the input data, \(L\) is the latent feature, \(U\) is the output data. \(W\) and \(W^{\prime}\) are the encoder and decoder's weight, respectively. Finally, \(b\) and \(b^{\prime}\) represent the offset vector of the encoder and decoder, respectively.  
Table 1 illustrates the architecture parameters of the developed 1 dCNN-based AE model. Once the model architecture has been designed, the training process is initiated. Concurrently, each training set is validated against the corresponding validation data, allowing for the tuning and optimization of the hyperparameters associated with the model architecture. The objective of this phase is to identify the optimal hyperparameters that will result in the highest performance, as indicated by low loss and high accuracy.  
Once the feature extraction model is trained and optimized, a cluster model is developed based on the k-mean clustering algorithm. The core idea of the algorithm is to group the extracted features of the text data into different clusters according to their similarities [40]. The k-mean algorithm has been widely used in the last decade and has achieved great success in unsupervised learning [41]. Therefore, in this study, unlabeled features are used to train the cluster model, and the number of clusters was determined based on the number of failure classes, i.e., k = 4.