## 2 Research Methodology
### Measurement Noises and Computational Complexity
The increased dimensionality of models, especially those in the finite element analysis (FEM) process or approximations of nonlinear dynamic phenomena, contributes to a considerable rise in computation time, thereby rendering such methods impossible to apply under real-time conditions. The study by [88] discusses model-order-reduction methods for high-frequency vibration problems and their efficiency and accuracy. The most important contribution is the development of the iterative system equivalent reduction expansion process (SEREP), which enables one to represent high-frequency dynamics accurately without having to calculate the complete modal matrix of the system. The author compares this method with classical methods, such as Guyan reduction, dynamic condensation, and the conventional SEREP, and demonstrates that the classical techniques have significant errors in the high-frequency range. The system equivalent reduction expansion process (SEREP) method was also used in [53] to reduce the degrees of freedom of the model, while the inverse eigensensitivity (IES) method was adopted to correct the adaptive stiffness value from experimental data. The reduced model contained 100% similarity between the computed and experimental modal characteristics, while using IES significantly enhanced vibration stability limit prediction. This proves the efficacy of a hybrid strategy in maintaining accuracy with a decrease in computational complexity. Aimed to develop dimensionality reduction in a system that considers the nonlinear nature of its elements' relation, the research by [85] accomplished the problem through the ISOMAP algorithm, which preserved the intrinsic geometry of data and enhanced automatic rotor state recognition. Orbital trajectory analysis was applied in the study, where the axial displacement data of the rotor were plotted in high-dimensional space. The research demonstrates that the ISOMAP method effectively reduces computational complexity compared to the classical signal processing techniques. In his study [28], the Guyan reduction method was used, which reduces the degrees of freedom while not losing the most significant dynamic characteristics of the system. This reduction was utilized to cut off the finite element model of the rotor, significantly reducing computational costs in the simulations. Correlation analysis was also applied to reduce the parameter space by selectively removing uninformative signal components. After model reduction, the study also used differential evolution (DE) to optimize the damping and bearing parameters. The technique reduced the computations needed without compromising accuracy in detecting multiple defects. Thus, it naturally follows classical methods, such as Guyan reduction, SEREP, and dynamic condensation, which are utilized in low-order elementary reduction of the system, allowing model simplification with a minimal loss of the physical characteristics. Modal analysis, i.e., balanced realization and modal truncation, allows for determining the most dominant dynamic modes so that one can focus only on the most dominant vibrational modes. Projection methods, such as proper orthogonal decomposition (POD), are utilized for dimension reduction of finite element models by eliminating redundant data without losing the system's dynamic features. Optimization and adaptive algorithms are used to enhance the accuracy of the reduced model through the iterative adjustment of parameters and the selection of the most significant degrees of freedom. Finally, artificial intelligence and neural network-based methods allow for automatic approximations of complex models, saving computational time and facilitating model reduction, even in nonlinear systems. Table 11 summarizes the most common attendant issues in the diagnostics of rotor systems. Complex models (e.g., FEA or nonlinear dynamics) often result in prohibitive computational loads that are impractical for real-time applications.