## 4 Model Evaluation  
The CWRU bearing dataset and NASA battery dataset are used in this study due to their extensive and well-documented features, making them ideal for TD feature extraction and predictive modeling. Case 1: The CWRU bearing dataset is used to extract fifteen TD features, which help in identifying potential bearing faults by analyzing vibration signals. The CWRU bearing dataset focuses on mechanical fault detection classification using SVM and LSTM models. The problem is formulated as a fault diagnosis problem, with normal and three main faulty conditions for each faulty diameter. The ranking for FSMs for the CWRU bearing dataset can be seen in Table 4. Features like AbsMax, P2P, and Complexity were consistently selected by multiple methods, highlighting their strong relevance. This feature selection process helps to reduce dataset dimensionality and boosts the capability of Machine Learning (ML) models to accurately classify faults. The graphics of the most frequently selected features are given in Figure 2.  
In the SVM algorithm, the RBF kernel is applied to manage non-linearly separable data by projecting the input features into a higher dimensional space for improved separability. The penalty parameter \(c\) is set to 9.65, balancing margin maximization and classification errors, while \(\gamma\) is set to 0.013, controlling the influence of individual data points for the bearing dataset. A 70-30% training-to-testing split is used to train and evaluate the models of datasets. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Feature**} & \multicolumn{5}{c}{**Feature Selection Methods**} \\ \cline{2-6}  & **MI** & **FS** & **SFS** & **RFE** & **RFI** \\ \hline Min & \(\bullet\) & & & \(\bullet\) & \(\bullet\) & \\ Max & \(\bullet\) & \(\bullet\) & & \(\bullet\) & \(\bullet\) & \(\bullet\) \\
**AbsMax** & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\ Mean & & \(\bullet\) & \(\bullet\) & & \(\bullet\) \\ Std & \(\bullet\) & \(\bullet\) & & & \(\bullet\) \\ RMS & \(\bullet\) & \(\bullet\) & & & \(\bullet\) \\ Skewness & & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\ Kurtosis & & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\ Var & \(\bullet\) & & & & \(\bullet\) \\
**P2P** & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\ IF & & & & \(\bullet\) & \\ CF & & & & \(\bullet\) & \\ SF & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\ Mobility & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\
**Complexity** & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \\ \hline \hline \end{tabular}  
* MI: Mutual Information, FS: Fisher Score, SFS: Sequential Feature Selection, RFE: Recursive Feature Elimination, and RFI: Random Forest Importance. “\(\bullet\)” are the selected features by FSMs.  
\end{table} 
Table 4: Feature selection for the CWRU bearing dataset. Figure 2: Graphic representations of the Absolute Maximum, Peak-to-Peak, and Complexity features. The LSTM model for the bearing dataset consists of 1 input LSTM layer with 64 units and a dense layer with 32 units, respectively, and an output layer. For multi-class classification problems, Categorical Cross-Entropy serves as the primary loss function to guide model optimization and SoftMax as an activation function. Two dropout ratios of 0.3 and, after the first dropout layer, one batch normalization layer, is applied for preventing overfitting. Then, 10-fold cross-validation is performed on both algorithms to ensure robust and generalizable performance. The features expressed in bold are the features selected by all FS methods in Table 4.  
Table 5 presents the performance evaluation of SVM and LSTM models using different FSMs on the CWRU bearing dataset. The models were evaluated using accuracy, precision, recall, and F1-score, with MI, FS, SFS, RFE, and RFI.