## 5 Research Methodology  
The research methodology is systematically structured to ensure an effective operative assessment of the proposed AHC-based feature selection method in fault diagnosis of IMs, as shown in Figure 3. Initially, data acquisition is conducted using the NI cRIO-9056 embedded controller, which captures three-phase voltage and current signals at the motor terminals with a 5 kHz sampling rate, ensuring high-resolution signal representation. Measurements are collected under diverse operating conditions to provide broad coverage of real-world fault scenarios. It is worth mentioning that each test scenario was conducted for a duration of 10 min to ensure consistency in data acquisition, class distribution balance, and fault pattern development. Nevertheless, the single-phase loss test was limited to 3 min due to the increased thermal stress imposed on the stator insulation, which could compromise machine integrity if exposed for an extended period. Once the signals are captured, they undergo a preprocessing stage, where a low-pass second-order Butterworth filter is employed to effectively attenuate high-frequency noise while maintaining the integrity of relevant fault-related features. This ensures clean, high-fidelity data, optimizing feature extraction for subsequent analysis. These filtered waveforms form the basis for the feature engineering stage, during which a comprehensive set of candidate features is extracted. Following feature extraction, data cleaning and standardization are initiated. This process comprises outlier detection and removal, and imputation of missing values. Subsequently, all numerical features are normalized using z-score standardization. The resulting dataset is then partitioned into 67 percent for training and 33 percent for testing to facilitate model validation. Considering the AHC-based feature selection phase, Spearman rank-order correlation coefficients are computed to construct a correlation matrix, from which a dendrogram is generated using [PERSON]'s linkage method. Inconsistency coefficients guide the removal of clusters, ensuring that highly collinear or redundant features are elimi  
Figure 2: Illustration of the performance of the SVC. nated. The outcome is a reduced feature subset that maximizes discriminative power while mitigating multicollinearity. Subsequently, hyperparameter optimization is conducted using the Successive Halving Algorithm (SVA) for each classifier. Considering a 5-fold cross-validation framework on the training data, the search space for the RFC included the number of estimators \(\in~{}\left\{10,50,100\right\}\), minimum samples per leaf \(\in~{}\left\{1,5,10\right\}\), and minimum samples required to split \(\in~{}\left\{2,4,7\right\}\). For the SVC with the RBF kernel, the penalty parameter \(C\in\left\{1,10,100,1000\right\}\) and kernel coefficient \(\gamma~{}\in~{}\left\{1e^{-3},1e^{-4},1e^{-5}\right\}\) were considered. For the multilayer perceptron (ANN), the hidden layer sizes \(\in~{}\left\{(50,),(100,),(150,)\right\}\), L2 regularization penalty \(\in~{}\left\{1e^{-4},1e^{-3},1e^{-2}\right\}\), while the maximum number of iterations was set to 1000. All experiments were conducted using a fixed random seed of 42 and identical hardware/software (Python 3.11.7; Numpy 1.26.4; Pandas 2.2.1; Scikit-learn 1.4.2; Intel Core i7-9700 CPU; 16 GB RAM) to ensure reproducibility. Finally, in the fault detection and classification stage, each classifier, trained on the AHC-selected feature subset with optimized hyperparameters, is evaluated using accuracy, precision, recall, and the F1-score. A comparative analysis against random forest-based  
Figure 3: The research methodology employed in this study, outlining the key steps and processes involved in fault diagnosis of IMs. feature selection and models trained on the full feature set demonstrates that the AHC approach yields superior generalization, higher class-balanced performance, and improved interpretability.