## 2 Research Methodology  
### Analysis of the Most Common Problems in the Diagnostics of the Rotor System  
This section offers an analysis of the most common problems in the diagnostics of rotor systems and possible ways to solve these problems, including experiences from the papers that have been observed. The information is summarized in tables for convenient usage purposes. This information can help researchers define the required methodological background for further research. The most common issues in rotor systems and methods to solve them are summarized in Table 1. \begin{table}
\begin{tabular}{l l l} \hline
**Issue** & **Identification Methods** & **References** \\ \hline \multicolumn{3}{c}{Finite element method (FEM)} & [22; 23; 24; 25; 26; 27; 28; 29] \\ \multicolumn{3}{c}{Operating deflection shape (ODS) method} & [23; 30] \\ \hline Fast Fourier transform (FFT) & [14; 24; 28; 31; 32; 33; 34] \\ \multicolumn{3}{c}{Short-term Fourier transform (STFT)} & [27; 32] \\ \multicolumn{3}{c}{Fractional-order analysis (Pavlenko’s approach)} & [35] \\ \multicolumn{3}{c}{Equivalent load minimization method (ELMM)} & [14] \\ \multicolumn{3}{c}{Joint input-state estimation algorithm (JISEA)} & [31] \\ \multicolumn{3}{c}{Modal balancing (MB)} & [22] \\ \multicolumn{3}{c}{Differential evolution (DE)} & [28] \\ \multicolumn{3}{c}{Singular value decomposition (SVD)} & [22; 27] \\ \multicolumn{3}{c}{Newton–Raphson method} & [25; 28; 36] \\ \multicolumn{3}{c}{Runge–[PERSON] methods} & [28; 29; 37] \\ \multicolumn{3}{c}{Least squares method} & [25; 27; 31; 36] \\ \multicolumn{3}{c}{Continuous wavelet transform (CWT)} & [32; 38] \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of the most common issues in rotor systems and methods to solve them. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Issue** & **Identification Methods** & **References** \\ \hline \multirow{8}{*}{Unbalance} & Random forest (RF) & [23] \\ \cline{2-3}  & k-nearest neighbors (KNN) & [24] \\ \cline{2-3}  & Principal component analysis (PCA) & [33] \\ \cline{2-3}  & Artificial neural network (ANN) & [25; 30] \\ \cline{2-3}  & Monte Carlo simulation (MCS) & [39] \\ \hline \multirow{8}{*}{Cracks} & Finite element method (FEM) & [40; 41; 42] \\ \cline{2-3}  & Hilbert–Huang transform (HHT) & [40; 43; 44] \\ \cline{2-3}  & Fast Fourier transform (FFT) & [40; 42; 43; 44; 45] \\ \cline{2-3}  & Strain energy release rate (SERR) & [40] \\ \cline{2-3}  & Discrete wavelet transform (DWT) & [32; 46] \\ \cline{2-3}  & Support vector machine (SVM) & [46; 47] \\ \cline{2-3}  & Artificial neural network (ANN) & [44; 47] \\ \cline{2-3}  & Decision tree (DT) & [46] \\ \cline{2-3}  & Random forest (RF) & [46] \\ \cline{2-3}  & k-nearest neighbors (KNN) & [46] \\ \cline{2-3}  & Newmark-\(\beta\) method & [40; 41] \\ \hline \multirow{8}{*}{Misalignment} & Finite element method (FEM) & [27; 48; 49; 50] \\ \cline{2-3}  & Finite difference method (FDM) & [50] \\ \cline{2-3}  & Orbit analysis & [48; 50; 49; 51] \\ \cline{2-3}  & Phase measurement & [27; 48] \\ \cline{2-3}  & Time-frequency analysis (TFA) & [51] \\ \cline{2-3}  & Singular value decomposition (SVD) & [27] \\ \cline{2-3}  & Support vector machine (SVM) & [52] \\ \cline{2-3}  & Discrete wavelet transform (DWT) & [52] \\ \cline{2-3}  & Short-term Fourier transform (STFT) & [52] \\ \cline{2-3}  & Decision tree (DT) & [52] \\ \cline{2-3}  & Newton–Raphson Method & [49] \\ \cline{2-3}  & Runge–Kutta Methods & [48; 49] \\ \cline{2-3}  & Least squares method & [27; 48; 51] \\ \cline{2-3}  & Newmark-\(\beta\) method & [49; 50] \\ \hline \multirow{8}{*}{Rotor bending} & Finite element method (FEM) & [28; 29; 53] \\ \cline{2-3}  & Finite element model updating (FEMU) & [53] \\ \cline{2-3}  & Fast Fourier transform (FFT) & [29] \\ \cline{2-3}  & Artificial neural network (ANN) & [54] \\ \cline{2-3}  & Feedforward neural network (FNN) & [54] \\ \cline{2-3}  & Short-term Fourier transform (STFT) & [54] \\ \cline{2-3}  & Wavelet transform (WT) & [28; 55] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._