# MOIRA-UNIMORE Bearing Data Set for Independent Cart Systems
## 8 Data Visualization and Analysis
### Single Cart Experiments  
Scatter plots derived from Experiment Types 1 and 2 are presented to analyze the distribution of features in single-cart configurations. All plots correspond to a nominal cart speed of 1000 mm/s. For Experiment Type 1, only the PCA scatter plots are included, as the no-fault profile (or normal profile) can easily be distinguished from the abnormal profile in most fault categories using PCA alone. Figures 11 and 12 illustrate that the PCA features corresponding to the healthy bearing state form a distinct cluster, clearly separated from the IR fault categories of all sizes. This distinction highlights the ability of PCA to reduce dimensionality while preserving the separability of the fault data. However, OR fault categories appear closer to the no-fault boundary, indicating overlapping feature distributions. Although this overlap suggests challenges in differentiating OR faults from the healthy state using PCA alone, further processing or advanced clustering techniques could help achieve a more compact and distinct representation for these fault classes. For Experiment Type 2 (Figures 13 and 14), both PCA and t-SNE scatter plots are utilized to provide a more comprehensive visualization of the feature set. These plots represent experimental data for which the IR fault orientation information is unknown, as it was not recorded during the experiment. PCA applied to data sets ranked by one-way analysis of variance (ANOVA) and Kruskal-Wallis methods results in highly scattered features, with limited separability observed across all fault classes of the top bearing, including IR and OR faults. This outcome indicates the limitations of PCA when applied to these specific feature rankings. In contrast, PCA applied to data sets ranked by unsupervised methods--Laplacian Score, Variance, and Monotonicity--yields a bimodal distribution, suggesting a better representation of the underlying structure for these rankings. Similarly, the t-SNE reduced feature sets exhibit consistent bimodal distributions in nearly all distance metrics, including Mahalanobis, Cosine, Chebyshev, and Euclidean. These visualizations demonstrate that t-SNE effectively captures the underlying patterns in the feature set, revealing separability across fault categories, even under varying distance metrics. This underscores the significance of dimensionality reduction techniques, particularly for nonlinear methods such as t-SNE, in visualizing and analyzing high-dimensional data sets. However, the bimodal nature of the distributions in both PCA and t-SNE suggests that further processing is necessary to transform the feature distributions into Gaussian-like clusters. Such transformations could lead to more compact clustering and improved classification performance, which remains an area for future work.  
Figure 11: PCA representation of the ranked feature set from Experiment Type 1, illustrating the IR and OR faults of the top bearing, with the IR fault oriented at 3 O’Clock.  
Figure 12: PCA representation of the ranked feature set from Experiment Type 1, illustrating the IR and OR faults of the bottom bearing, with the IR fault oriented at 3 O’Clock.