## 1 Introduction
However, the authors do not model physically realistic boundary conditions. In particular, the supports' stiffness and the rotor's thermal expansion are not considered. Another work that considers the investigation of nonlinear processes [8] develops a hybrid finite element modeling (FEM) analytical cluster model that accurately captures nonlinear field distributions in induction motors. However, it demands detailed geometric and material data, making it challenging to apply in cases where such information is unavailable. The high computational complexity also limits its use in real-time diagnostics. The work by [9] introduces topological fractal multi-resolution analysis (TFMRA) for smart machinery fault diagnosis, which uses a combination of optimization and classification methods under wavelet structures and shows high robustness to signal nonlinearities. However, TFMRA is computationally intensive, making real-time deployment challenging. The study also omits a sensitivity analysis of parameter selection. In the last decade, many novel analytical methods have been developed that could be applied to machine diagnostics. The work by [10] proposes filtered and extended Park's vector approaches that detect broken rotor bars independently of slot count. However, these methods only target bar faults and fail to detect other defect categories. Their performance under load transients has also not been investigated. The work by [11] combines Hilbert, Gabor, and Fourier transforms for rotor health monitoring, offering intuitive phase/amplitude insights. However, it is sensitive to high-frequency noise and requires preprocessing. The effect of sensor bandwidth limitations is not discussed. The main research gaps in these studies include the lack of comprehensive physical modeling, inadequate consideration of real-world boundary conditions, oversimplified AI diagnostics, and insufficient scalability for industrial applications in the power industry and related enterprises, such as incomplete consideration of actual boundary conditions, such as support stiffness and thermal expansion [4; 7]; ignoring anisotropy of bearing stiffness, friction-induced nonlinearity, and temperature effects [1]; lack of comprehensive physical modeling, e.g., variable lubricant viscosity, thermal effects, and asymmetric loads [6]; assuming perfectly elastic contact and neglecting micro-roughness, wear, lubrication effects, and potential plastic deformations [12]; oversimplification of machine learning models [13; 14] and ignoring signal noise [15]; using simplified beam models that neglect nonlinearities, asymmetric mass distributions, and variations in material properties [2; 3]. Modern methods, such as methods based on artificial intelligence (AI) or machine learning (ML), are free of most limitations of classical techniques. They do not need a strict analytical process description to model it. Nevertheless, AI/ML-based methods typically require large, well-labeled datasets, are prone to overfitting and domain-shift errors, and often behave as \"black boxes\", which complicates certification or root cause analysis. Such a critical problem as the contact of the rotor with the bearing in the presence of gaps is considered in his work by [12]. The author proposes a new FEM model that includes geometric aspects of the contact. However, the contact is modeled as perfectly elastic without considering the micro-roughness of the surfaces or wear. Lubricating properties and possible plastic deformations of the contact zones are also not included. Accordingly, the simulation results will differ significantly from the real environment. AI and ML methods are increasingly used in today's technological trends. However, despite their impressive computational efficiency, they are often disconnected from physical reality, as the models are trained on artificial data created in a controlled environment. A review article by [13] provides a detailed analysis of the current AI methods used for rotor diagnostics.