## 2 Related Work
### The EMD Method Based on IMF  
The Empirical Mode Decomposition (EMD) method has been widely adopted in rail transit applications due to its adaptive capability in decomposing non-stationary and non-linear bearing vibration signals into multiple IMF components. Each IMF component represents distinct signal characteristics at different time scales, effectively capturing local variations and complex vibration patterns. Subsequent fault diagnosis is typically performed through envelope spectrum analysis [12; 21; 22] or energy spectrum examination [12], where the extracted IMF components are systematically analyzed to identify fault-related features. While Hilbert transform and EEMD are well-established techniques, their combination for energy distribution decoupling represents a novel diagnostic paradigm. To address the challenges of rolling bearing fault identification, diverse advanced methodologies have been developed in recent studies [23; 24]. Furthermore, an information entropy-based methodology was established in reference [23], where a novel feature extraction and denoising framework was constructed. This approach incorporates an optimized wavelet threshold function to denoise Intrinsic Mode Function (IMF) components, thereby significantly improving diagnostic accuracy in fault detection. In reference [24], a distinctive feature extraction strategy combining Singular Value Decomposition (SVD) with Optimal Frequency Band Energy (OFBE) analysis was developed. This method enables precise fault characterization through comparative analysis with theoretical fault characteristic frequencies, facilitating the reliable determination of bearing fault types. In reference [25], the Advanced Complete Ensemble Empirical Mode Decomposition (ICEEMD) model was used to extract the fault features. However, calculating statistics merely describes certain characteristics of the vibration signal as a whole, ignoring the hidden information of complex signals. Reference [26] proposed a bearing fault diagnosis method that fully integrates Empirical Model Decomposition (CEEMDAN) and the Gray Wolf algorithm-optimized kernel Extreme Learning Machine (GWO-KELM) to improve the diagnosis success rate of bearing conditions. We carry out in a summary in Table 1.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Reference** & **Methodology** & **Advantage** & **Limitation** \\ \hline [PERSON] et al. (2023) [26] & CEEMDAN + GWO-KELM & Higher diagnosis success rate via optimized extreme learning & Limited interpretability of GWO-KELM \\ [PERSON] et al. (2023) [18] & STFT-CNN for direct time-frequency analysis & Avoids feature extraction-induced information loss & Sensitive to noise and data quality \\ [PERSON] et al. (2023) [17] & Wavelet packet decomposition + chaotic sparrow search-optimized DBN & Improved fault diagnosis accuracy through parameter optimization & Complex implementation; risk of overfitting \\ [PERSON] et al. (2024) [25] & ICEEMDAN for fault feature extraction & Superior noise robustness compared to traditional EMD & Computationally expensive \\ [PERSON] et al. (2024) [23] & IMF denoising via optimized wavelet threshold + information entropy EMD-based envelope/energy spectrum analysis & Improved diagnostic accuracy in noisy environments & Dependent on IMF quality \\ [PERSON] et al. (2024) [12] & Hybrid CNN-LSTM-GRU model & Enhanced spatiotemporal feature extraction & Mode mixing issues in EMD \\ [PERSON] et al. (2024) [19] & CWT and WPT for non-stationary signal reconstruction & Improved fault frequency prominence and detection accuracy & High computational complexity; requires large datasets \\ [PERSON] et al. (2024) [14] &
\begin{tabular}{p{113.8 pt} p{113.8 pt}} (\(\mathrm{\SIUnitSymbolMicro}\)24) \\ (\(\mathrm{