## 1 Introduction  
Rotordynamics, a specialized branch of applied mechanics, plays a crucial role in the design and operation of rotating machinery across various industries, including energy, aerospace, and manufacturing. The study of rotor behavior, particularly at critical speeds, is fundamental to ensuring the safety, efficiency, and longevity of these systems. Recent advancements in computational methods and experimental techniques have enabled more sophisticated analyses of rotor dynamics, allowing engineers to better predict and mitigate potential issues [1]. One of the most significant challenges in rotordynamics is the accurate prediction and control of rotor behavior in the presence of unbalance and asymmetry [2]. While traditional models often assume ideal conditions, real-world rotors frequently exhibit imperfections that can significantly affect their dynamic response [3]. The impact of these imperfections becomes particularly critical as rotors operate at or near their critical speeds, where even small imbalances can lead to large amplitude vibrations [4]. This study focuses on two specific rotor configurations: one with a centrally mounted unbalanced disk (Rotor05 un) and another with an off-center unbalanced disk (Rotor025 un). By comparing these configurations, we aim to investigate how the position of an unbalanced mass affects the rotor's critical speed and orbital behavior. This comparison is important for understanding the complex interplay between rotor geometry, mass distribution, and dynamic response ([PERSON] _et al._, 2018). The research employs a combination of numerical simulations and statistical analysis to provide a comprehensive view of rotor behavior under different conditions. By utilizing Monte Carlo simulations, we account for the inherent variabilities in rotor systems, offering a more realistic prediction of their performance ([PERSON] _et al._, 2018). This probabilistic approach represents a significant advancement over deterministic methods, allowing for a more nuanced understanding of rotor dynamics. Recent studies have also shown the potential of methods based on machine learning in rotordynamics analysis. [PERSON] et al. (2018) presented a novel condition-monitoring methodology for induction motors, leveraging a high-dimensional set of hybrid features extracted from vibration and stator current analyses. The proposed approach utilizes artificial intelligence and machine learning techniques to optimize and reduce the feature space, enhancing the identification of multiple and combined faults occurring simultaneously. The effectiveness of the methodology is validated through a comprehensive experimental dataset encompassing healthy, single-fault, and combined-fault conditions. [PERSON] et al. (2018) developed a deep learning approach for rotor orbit reconstruction and fault diagnosis. Their method uses convolutional neural networks to analyze rotor orbit images, achieving high accuracy in fault classification. Other authors, like [PERSON] et al. (2019), used operational modal analysis for the online identification of critical speeds in rotating machinery. This method does not require system shutdown and can provide real-time data on rotor behavior. The scientific article presented by [PERSON] and colleagues (2019) introduces a method for diagnosing rotor system faults using orbit data. This method converts vibration data into a high-dimensional space and then reduces it using the ISOMAP algorithm. The resulting data are used to identify different rotor operating conditions. The method effectively differentiates between normal, misaligned, and rub-impact states without requiring prior knowledge of specific fault characteristics. [PERSON] et al. (2019) examined the vibration characteristics of pre-twisted rotating Ti-SiC composite airfoil blades. They employed a combination of the Mori-Tanaka method and Finite Element analysis to calculate material properties, ensuring reliability of their calculations.