## 3 Results
The ROC curve measures separability, indicating the models' ability to differentiate among fault  
Figure 6: Two-dimensional representations of the ultrasonic data for the different dimensionality reduction methods evaluated: (**a**) PCA, (**b**) ICA (**c**) LDA, and (**d**) UMAP. classes. It summarizes the trade-off between TPR and FPR for a predictive model across various probability thresholds. To thoroughly examine and qualitatively evaluate our simulated outcomes across various models, we utilized the k-fold CV technique. This method enabled us to illustrate the differences in classification effectiveness, as shown in Figure 9. It displays the proportion of correct predictions made by each model out of the total number of predictions during 5-fold data splitting. The visual representation helps highlight the comparative strengths and weaknesses of each model, ensuring a comprehensive analysis. Figure 9 also demonstrated that the GB model had a higher proportion of correct predictions compared to the other ensemble methods, indicating its superior efficiency. Figure 7: Confusion matrix for different ensemble classifiers including the voting, Logit, GB, Adaboost, stacking, and bagging algorithms. Figure 8: ROC curves for the voting, Logit, GB, Adaboost, stacking, and bagging algorithms. Figure 9: Accuracy analysis of the models using k-fold CV. Figure 10 displays a boxplot showing result variations during cross-validation across different folds. This allows for an easy comparison of the accuracy. The boxplot provides a five-number summary: minimum, first quartile, median, third quartile, and maximum. The whiskers extend to depict the rest of the distribution, excluding outliers. As evident, the GB model exhibited the highest accuracy and precision with the lowest distribution range. The stacking classifier indeed showed promising results, ranking second in performance after the GB classifier among the various algorithms tested. Evaluation metrics of the classifiers are shown as a bar plot in Figure 11 and the overall evaluation results are shown in Figure 12. When focusing solely on the precision metric, the bagging classifier exhibited a marginally superior average than GB. Additionally, the voting classifier demonstrated commendable performance relative to the rest. Upon examining the average evaluation metrics such as accuracy, recall, precision, and F1-measure, it is evident that the GB model surpassed the other classifiers in overall performance. Among the classifiers, the GB algorithm's average accuracy (94.2%) was about 2% higher, average recall (86.5%) was about 6% higher, and average F1-measure (87.2%) was about 4% higher than the stacking classifier. GB iteratively builds an ensemble of trees, effectively capturing complex data patterns, handling noise, and dynamically weighing features. In comparison, Adaboost struggles with noisy data and outliers, while bagging, although reducing variance, fails to capture intricate patterns as effectively. Voting aggregates multiple models but falls short when individual models differ significantly in performance, and stacking's reliance on a strong meta-classifier cannot surpass GB's individual strength. Logistic regression, being a linear model, cannot handle the non-linear complexities of ultrasonic data, making GB's non-linear approach superior [29]. To further explore the effectiveness of dimensionality reduction techniques, we incorporated them as input features for the GB model. As mentioned before, the methods we examined included PCA, LDA, ICA, and UMAP. For a comprehensive understanding, Tables 2-5 provide an in-depth presentation of the respective results, including accuracy, recall, precision, and F1-measure metrics. The experimental data indicate that ICA was superior to the alternative dimensionality methods in terms of performance when used with the GB model. Figure 10: Boxplot of the accuracies for the six classifiers.