## 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 [PERSON]—Time-varying harmonic analysis method based on adaptive frequency-shift filtering [87]. & The algorithm can effectively determine the system parameters, automatically segmented its steady-state interval. & High sensitivity to system parameters, detecting time delays. & Kalman filter; Prony-based algorithms; wavelet transform (WT); fast Fourier transform (FFT); infinite impulse response (IIR) filter; improved Teager energy operator (ITEO). & Classical \\ \hline [PERSON]—Unbalance localization through machine nonlinearities using an artificial neural network approach [26]. & The approach can localize imbalance with high accuracy while requiring a minimal number of sensors. & Does not identify imbalance causes; ANN must be retrained after minor system changes. & Butterworth low-pass filters; short-term Fourier transform (STFT). & Classical / AI \\ \hline [PERSON]—Steady-State Response Analysis of an Uncertain Rotor Based on Chebyshev Orthogonal Polynomials [93]. & The approach can localize imbalance with high accuracy while requiring a minimal number of sensors. & Does not identify imbalance causes; ANN must be retrained after minor system changes. & Butterworth low-pass filters; short-term Fourier transform (STFT). & Classical / AI \\ \hline [PERSON]—Steady-State Response Analysis of an Uncertain Rotor Based on Chebyshev Orthogonal Polynomials [93]. & Using only a few finite element evaluations & Bounds remain conservative; parameter correlations are ignored. & Chebyshev interval method (CIM); Monte Carlo simulation (MCS); Smolyak sparse-grid integration. & Uncertain \\ \hline [PERSON]—A novel nonlinear spectrum estimation method and its application in online condition assessment of bearing-rotor system [51]. & The method demonstrates stable diagnostic results, even in the presence of noise and structural changes. & Needs more research to recognize different types of faults and combined faults. & Support vector machine (SVM); nonlinear output frequency-response functions (NOFRFs); principal component analysis (PCA); Heuristic/ ML (NCA); nonlinear autoregressive with exogenous input (NARX); discrete Fourier transform (DFT). & Support vector machine (SVM); nonlinear output frequency-response functions (NOFRFs); principal component analysis (PCA); Heuristic/ ML (NCA); nonlinear autoregressive with exogenous input (NARX); discrete Fourier transform (DFT). & Uncertain \\ \hline [PERSON]—The sub-interval similarity: A general uncertainty quantification metric for both stochastic and interval model updating [94]. & SIC cuts parameter errors below 1\% and runs \(\sim\)500 (SIS) metric that unifies stochastic (Bayesian) and probabilistic methods. & Network (NARX); discrete Fourier transform (DFT). & Heuristic / \\ \hline [PERSON]—Adaptive parameterless empirical wavelet transform-based time-frequency analysis method and its application to rotor rubbing fault diagnosis [57]. & The proposed methodology shows better results on the problem with rotor friction than the empirical mode decomposition (EMD), and ensemble empirical mode decomposition (EEMD) methods. & Empirical mode decomposition (EMD); ensemble empirical mode decomposition mode decomposition (EEMD); Hilbert transform (HT). & Classical \\ \hline \hline \end{tabular}
\end{table} 
Table 12: _Cont._This table highlights a transition in rotor dynamics research from purely theoretical and linear models toward hybrid, data-driven, and uncertainty-aware frameworks. Classical models remain foundational, but AI and uncertainty quantification are becoming essential for addressing real-world complexities. There is significant room for synergy among these domains, particularly through hybrid modeling, real-time UQ, and experimentally validated AI systems. Additionally, in terms of domain classification overview, the following can be highlighted.