## 2 Research Methodology
### Comparative Information of Reviewed Methods
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Conception** & **Achievements** & **Problems** & **Methods, Techniques, and Algorithms** & **Domain*** \\ \hline \hline \multicolumn{4}{p{113.8 pt}}{[PERSON]—Theoretical and experimental identification of the simultaneous occurrence of unbalance and shaft bow in a Laval rotor [28].} \\ \hline Approach to model residual rotor bow; model reduction. & The method allows the identification of rotor bow and imbalance with highly accuracy; nevertheless, it has noise effects. & It is a straightforward rotor model that does not consider many factors like shaft weight and stiffness or system damping. & Finite element method (FEM); Guyan reduction; Laval rotor; differential reduction \\ \hline \hline \multicolumn{4}{p{113.8 pt}}{[PERSON]—An iterative system equivalent reduction expansion process for extraction of high frequency response from} \\ \hline An accurate and effective method of reducing the number of system’s DOFs. & The accuracy after system reduction with the proposed method is much better than for other considered reduction methods. & Accuracy and computation efficiency depend on the proper selection of the initial frequency range. & System equivalent reduction expansion process (SEREP); dynamic improved reduced system (DIRS); Guyan reduction. \\ \hline \hline \multicolumn{4}{p{113.8 pt}}{[PERSON]—Estimating unbalance and misalignment of a flexible rotating machine from a single run-down [27].} \\ \hline Regularization and filtering methods increase the stability of calculations. & This method allows for identifying misalignment and imbalance with high accuracy. & The accuracy of the method critically depends on the correct definition of model parameters. & Singular value decomposition (SVD); least squares method. & Classical \\ \hline \hline \multicolumn{4}{p{113.8 pt}}{[PERSON]—Theoretical–experimental study on a rotor with a residual shaft bow [55].} \\ \hline Effective isolation of residual rotor bow features from other signals. & The method shows adequately accurate results in residual bending identification. & The accuracy of the method critically depends on the accuracy of the sensor installation. & Daubechies wavelet; ISOMAP; principal component analysis (PCA). & Classical/ Reduction/ ML \\ \hline \hline \multicolumn{4}{p{113.8 pt}}{[PERSON]—Identification of unbalance in a rotor bearing system [36].} \\ \hline Improvements to the method of equivalent load minimization. & Ability to determine imbalance with a minimum number of measurements and to extend the method to other types of defects. & Approximation is required for unmeasured positions, which can lead to an accumulation of errors and inaccuracy in determining the defect parameters. & Modal expansion method; Newton–Raphson test squares method; fast Fourier transform (FFT). \\ \hline \hline \multicolumn{4}{p{113.8 pt}}{[PERSON]—Nonlinear dynamic behavior of a rotor-bearing system considering time-varying misalignment [50].} \\ \hline Considering rotor time-dependent deformation caused by misalignment; the model of oil-film behavior. & Identified the distribution of lubricant pressure in bearings caused by misalignment and its impact on stability. & Only laminar lubricant flow is considered; lubricant viscosity is considered independent of temperature. & FEM; FDM; over-relaxation method (QRM); Newmark-\(\beta\) method. & \multirow{2}{*}{Classical} \\ \hline \hline \multicolumn{4}{p{113.8 pt}}{[PERSON]—A fuzzy approach for the analysis of unbalanced nonlinear rotor systems [37].} \\ \hline Performing fuzzy logic on uncertain processes that are hard or impossible to model analytically. & Designed membership functions based on equations of motion to determine imbalance value in natural language terms. & The approach does not allow for determining & Fuzzy set; Runge–Kutta method. & Classical/ Uncertain \\ \hline \hline \end{tabular}
\end{table} 
Table 12: _Cont._