## 3 Results  
As discussed in the introduction, bearing and pipe faults in industrial mechanisms are often caused by a variety of factors. The dataset used in this study was obtained from UE Systems Co. [41] with 10 categories: 4 bearing conditions and 6 pipeline conditions. The dataset of 20,000 samples was split into 80% for training and 20% for testing, enhanced by applying a sliding window with data augmentation including rotating, flipping, and adding noise to the original data. Ultrasonic signals, like many types of real-world data, often exist in high-dimensional spaces and can benefit greatly from dimensionality reduction. This process simplifies the data without losing significant information, making it more manageable and useful for analysis and processing. Dimensionality reduction and feature visualization are crucial for interpreting high-dimensional data. Techniques such as PCA, LDA, ICA, and UMAP offer valuable insights into the data structure by projecting it into two dimensions. PCA captures the most variance by identifying principal components in unlabeled data, making it useful for general data analysis. LDA is tailored for supervised classification, maximizing class separability. ICA excels in identifying statistically independent components, uncovering hidden patterns. UMAP preserves both the local and global data structures, making it effective for visualizing clusters or groups. Figure 6 shows the 2D visualizations of the ultrasonic data using PCA, LDA, ICA, and UMAP, highlighting the distinctions revealed by each method. The outcomes were evaluated using several algorithms including voting, Logit, GB, AdaBoost, stacking, and bagging. To optimize the hyperparameters of the different classifiers, we employed a systematic method (i.e., grid search). This method involved an exhaustive search over specified parameter values to identify the best combination that enhances the model's performance. Among the hyperparameters, the \"number of estimators\" proved to be the most sensitive. Increasing this number generally improve accuracy but also increases the training time. Based on our experiments, we found that using an estimator count of 100 provided a good balance between achieving high accuracy and maintaining a reasonable computation time. In addition, for Logit, regularization strength and the optimization function were selected as 0.9 and 'lbfgs', respectively. For voting, the 'hard' function was used. For GB, the learning rate and depth of regression estimators were selected as 0.1, and 3, respectively. For bagging, the maximum number of samples was selected as 1000. For Adaboost, the learning rate was selected as 1. As shown in Figure 7, a confusion matrix was used to assess the classification effectiveness, revealing the notably high accuracy of the GB model. The confusion matrix illustrated the algorithms' ability to classify various ultrasonic fault states such as low lubrication, over-lubrication, slow speed, steam cavitation, motor boating, reciprocating, thermostatic, healthy pipe, and healthy motor. The main diagonal of the confusion matrix consists of the TP and TN. Higher values on this diagonal indicate better model performance. This tool allowed for quick evaluation of the model's predictions and highlighted potential areas of error in the ultrasonic dataset. In addition, in classification tasks, the ROC curve is an important tool for evaluating classifiers. It visually depicts the trade-off between the true positive rate (TPR) and the false positive rate (FPR), helping to determine a classifier's effectiveness in distinguishing between positive and negative instances. Essentially, a larger area under the ROC curve indicates a higher likelihood of correctly identifying true cases over false ones. As shown in Figure 8, the area under the ROC curve for each category of the dependent variable in GB consistently exceeded 0.99, demonstrating a high level of predictive precision.