## 2 Research Methodology
### Bearing Faults
The sensitivity of this method makes it vulnerable to random noise and artifacts that could lead to the incorrect identification of bearing defects. High noise levels can lead to incorrect diagnostic results (Figure 23). The detection method shows promising results for the outer race-bearing defects but demonstrates decreased reliability for complex faults like combined or irregular defects on the inner race or rolling elements. The complexity of vibration transmission from these elements and the masking effect of other vibration components creates detection challenges. Moreover, TEO demands preliminary impulse component extraction from signals by filtering for proper application. Choosing the wrong filter parameters might result in losing valuable data or adding unnecessary frequencies that make a diagnosis more complex. Figure 23: Teager energy spectra for different bearings: (**a**) normal bearing; (**b**) bearing with damaged outer race; (**c**) bearing with damaged inner race. Adopted from [60]. The paper by [51] applies a novel approach to nonlinear spectrum estimation to online rotor-bearing system condition monitoring. The central concept is the application of nonlinear output frequency response functions (NOFRFs) to fault classification and severity (Figure 24). The approach can be conditionally divided into several steps. Firstly, the authors obtained and reconstructed the low-frequency vibration signal harmonics. Then, according to the data acquired, they modeled the dynamic process via the nonlinear autoregressive with exogenous input (NARX) method to accurately represent the rotor system dynamics in a nonlinear spectrum. From the spectrum, rotor condition classification was conducted by the support vector machine (SVM) algorithm for automatic diagnosis. The novel method was compared with conventional methods (time-domain and frequency-domain features) through neighborhood component analysis (NCA) to select the relevant features. The experimental results show that the novel method has greater accuracy in rotor fault diagnosis than conventional signal analysis techniques (Figure 24). Nevertheless, the method possesses some drawbacks that should be improved. The fact that the analysis results rely on NARX model parameter tuning accuracy is crucial since it can be challenging in industrial environments. Another issue is that the technique lacks a general solution to different types of defects or composite defects. Since processes in bearings have a complex nonlinear nature, machine learning methods can be utilized for investigation. The study by [61] considers a technique for identifying various damages in sliding bearings and rotor defects using deep convolutional generative adversarial neural networks and machine learning methods. The authors introduced TF-DLGAN, integrating multiple major data processing procedures. Firstly, vibration signals were translated into time-frequency images using continuous wavelet transform (CWT) so that the faults' temporal dynamics and frequency features could be retrained. Then, the images were utilized to train a generative adversarial neural network (DCGAN) to generate realistic synthetic fault samples, which enlarges the training set and enhances the model performance. Then, the enlarged data were input into a 2D CNN and LSTM, where a deep convolutional neural network (CNN) automatically extracts discriminative fault features, and a long short-term memory (LSTM) learns the temporal dependencies between vibration signals, which is especially vital for rotary systems. The technique ensures high accuracy (99.7%), enhances stability regarding variations in the operating conditions, and offers  
Figure 24: Scatter diagrams of the NOFRFs: (**a**) conventional evaluation method; (**b**) novel evaluation method. Adopted from [51]. diagnostics, even under conditions of limited data, which is appropriate for introducing nuclear power engineering practice (Figure 25). Despite that, the authors note that the method has some limitations.