## 5 Conclusions  
The Rotor05 un configuration, with a centrally mounted disk, exhibits larger orbital diameters across all positions. Its boxplots and quantile analysis show wider ranges and more symmetrical distributions between left/right and upper/lower positions. The interquartile ranges are larger, indicating more variability in shaft positions. Quantile plots reveal curved trends, suggesting non-linear behavior in orbital positions across different percentiles. This configuration demonstrates consistent patterns in both horizontal and vertical planes. The Rotor025 un configuration, featuring an off-center disk, displays smaller orbital diameters in all positions. Boxplots and quantile analysis reveal narrower ranges and slight asymmetries between positions. Interquartile ranges are smaller, indicating more concentrated orbital paths. Quantile plots show more linear trends, particularly in horizontal and lower vertical positions. The upper vertical position exhibits a unique curved trend, suggesting complex dynamics due to the off-center disk placement and gravitational effects. The comparison between Rotor05 un and Rotor025 un reveals significant differences in orbital behavior, potentially linked to their critical speeds. Rotor025 un consistently shows smaller orbital radii and more concentrated distributions, suggesting a higher critical speed due to increased system stiffness from the off-center disk placement. This configuration's more linear quantile trends indicate more predictable behavior near the critical speed. Conversely, Rotor05 un's larger orbits and curved quantile trends suggest lower stiffness and potentially lower critical speed. The asymmetries observed in Rotor025 un, particularly in the vertical plane, may result from complex interactions between the off-center mass, gyroscopic effects, and the system's natural frequencies, influencing its response as it approaches and passes through the critical speed. The novelty of our orbital pattern analysis lies in its comprehensive approach to understanding rotor behavior. We introduce a probabilistic method to visualize and quantify shaft orbital positions, revealing subtle variations often missed by traditional approaches. Our cross-sectional analysis of horizontal and vertical planes uncovers asymmetries and directional dependencies in rotor behavior. We proposed a quantile-based comparison method, providing insights into how disk positioning affects rotor dynamics across different probability levels. We also introduce innovative visualization techniques, including 3D probability distributions and contour plots, for the intuitive interpretation of complex data. This detailed orbital analysis offers a more accurate representation of real-world rotor behavior, enhances our understanding of rotor dynamics, and provides practical tools for optimizing rotor design and predicting performance under various conditions. The random input variables, i.e., randomly selected for the simulation, were the damping and clearance in the bearings, and the added unbalanced mass to the disc. Other input parameters, such as geometry and material data for the shaft, were deterministic in  
Figure 25: Quantile comparison of both Rotor05 un and Rotor025 un configurations: (**a**) horizontal cross-section (A–A); (**b**) vertical cross-section (B–B). the presented work. Admittedly, the simulation can be performed with a larger number of random input variables. Our findings have direct practical applications to rotor system monitoring and design. We determined the orbital, i.e., the area where orbit points can occur. The orbital was described probabilistically, allowing us to draw conclusions about the probability of rotor deflection (in this case, at critical speeds). If we use this deflection information for Condition Monitoring, we can estimate the probability of a detected state occurring, which allows us to quantify the risk of an incorrect diagnostic conclusion.