## 2 Research Methodology
### Bearing Faults
Nevertheless, the interval bounds are conservative, correlations among the inputs are neglected, and the study is limited to a linear oil-film representation without cracks or rub impacts. Scalability beyond seven interval variables and validation on high-fidelity rotors remain open challenges. Figure 26: Dynamic response of fan (**a**) and low-pressure turbine (**b**) considering interval uncertainties. The results of a comparative analysis of the methods for detecting bearing faults are summarized in Table 7. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Method** & **Advantages** & **Disadvantages** & **Domain * \\ \hline Finite element method (FEM) [59] & Allows accurate modeling of critical frequencies and rotor vibration shapes. & There is a need to determine the stiffness of bearings to obtain accurate results. & N/A \\ \hline Time-frequency analysis (TFA) & It allows the detection of short-term anomalies in the signal [51]. & Sensitive to the choice of transformation parameters, which can affect the diagnostic accuracy [60]. & TFD \\ \hline Wavelet transform (WT) [60] & High time-frequency resolution allows the detection of short-term anomalies in the signal. & The wave base’s choice affects the accuracy, which may require additional adjustment. & TFD \\ \hline Fast Fourier transform (FFT) & Fast and efficient signal conversion to the frequency domain [60]. & Sensitive to the choice of window length and averaging methods [51; 63]. & FD \\ \hline Principal component analysis (PCA) [51] & Efficiently highlighting the main patterns in large sets of vibration data. & Assumes linearity of data, which can be a limitation for complex nonlinear dependencies. & N/A \\ \hline \multirow{4}{*}{Teager energy operator (TEO) [60]} & Effective for detecting short-term pulses in vibration signals. & Sensitive to noise. & \\ \cline{2-3}  & It can effectively model nonlinear dependencies and adapt to complex problems. & Requires additional signal preprocessing to improve the quality of results. & TD/FD \\ \hline Artificial neural network (ANN) [59] & High accuracy with enough training data. & Requires a large amount of training data to work effectively. & N/A \\ \hline Convolutional neural networks (CNN) [61; 63; 16] & Automatically detects significant signal features without the need for manual processing. & Uninterpretable: It is difficult to explain what features the network uses for classification. & N/A \\ \hline Continuous wavelet transform (CWT) [61] & Effective for detecting local features and short-term anomalies in vibration signals. & The choice of the wave base affects the accuracy of the analysis and requires customization. & TFD \\ \hline Long short-term memory (LSTM) [61] & It can effectively detect long-term dependencies in data. & Requires a large amount of data for training to avoid overfitting. & N/A \\ \hline Generative adversarial networks (GAN) [61] & Improves classification accuracy by combining actual and generated data. & Poor tuning can cause training instability. & \\ \cline{2-3}  & Capable of detecting hidden patterns in complex multidimensional data. & Generated data may contain artifacts that affect the quality of analysis. & N/A \\ \hline Least squares method [59] & It reduces errors in the correlation of modal characteristics when updating the model. & It can produce physically incorrect model parameters if no constraints or regularization are applied. & N/A \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparative analysis of methods for detecting bearing faults.