## 4 Fault Experiment Signal Analysis
### Paderborn University (PU) Dataset  
#### 4.2.1 Description of Experimental Equipment and Bearing Data  
The experimental data were provided by the Design and Drive Technology Center at Paderborn University. The test rig comprised basic components, such as a test motor, measuring shaft, bearing module, flywheel, and load motor, as illustrated in Figure 19. The failures included both human damage and accelerated experimental damage. Artificial damage was inflicted using traditional processing techniques such as drilling, EDM, and an electric engraver. The experiment included healthy conditions, as well as inner, outer, and compound faults. The stator current and vibration signals were collected using a current sensor and a piezoelectric accelerometer, respectively, with a 64 K sampling frequency and 4 s per sample, and the experiment included a total of 2560 samples. The test conditions included varying speeds of 900 r/min and 1500 r/min, loads of 0.1 Nm and 0.7 Nm, and radial forces of 1000 N and 400 N, and vibration signals recorded at radial forces of 1500 r/min, 0.7 Nm load, and 1000 N were utilized as the experimental dataset. Six distinct fault types were analyzed: healthy, IR1 (inner ring damage degree 1), IR2 (inner ring damage degree 2), OR1 (outer ring damage degree 1), OR2 (outer ring damage degree 2), and compound faults involving both the inner and outer rings.  
For each fault type, 200 samples were allocated to training, validation, and test sets in 60%, 20%, and 20% ratios, respectively. Table 8 displays the bearing dataset details. Firstly, the AOA optimized the VME parameters \([\alpha,\omega]\) to extract the desired mode components from the original vibration signals. Take outer fault 2 as an example; the best parameter combination identified is [2616, 4084]. Figure 20 illustrates the results of the parameter-optimized VME. In regard to the time-domain signal processed by the optimally parameterized VME, more impact components are observable. The interference spectrum lines around the fault characteristic frequency are significantly reduced in regard to the envelope spectrum. The signal is decomposed by optimizing \([\alpha,\omega]\) in VME, according to the optimal parameter combination listed in Table 9.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fault Type** & **Fault Level** & **Number of Samples** & **Level** \\ \hline Normal (N) & / & 200 & 0 \\ Inner Fault 1 & 1 & 200 & 1 \\ Inner Fault 2 & 2 & 200 & 2 \\ Outer Fault 1 & 1 & 200 & 3 \\ Outer Fault 2 & 2 & 200 & 4 \\ Compound & / & 200 & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Details of PU dataset.  
Figure 19: PU test rig.  
The divided training set and validation set are fed into the MRCNN for training. Figure 21 displays the training results, showing that the accuracy and loss curves stabilize after 15 iterations. The loss value approaches 0, while the accuracy approaches 100%. The test samples are input into the trained MRCNN for testing, with the outcomes depicted in the confusion matrix shown in Figure 22. Apart from one compound fault sample misclassified as inner fault 2, all other test samples are correctly identified, demonstrating the proposed method's accuracy.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fault Type** & [\(\alpha\),\(\omega\)] & **Fault Type** & [\(\alpha\),\(\omega\)] \\ \hline Normal & [863; 1363] & ORF1 & [1201; 2752] \\ IRF1 & [1827; 2059] & ORF2 & [2616; 4084] \\ IRF2 & [807; 3917] & COM & [1186; 4051] \\ \hline \hline \end{tabular}
\end{table}
Table 9: Optimal parameter combination for VME.  
Figure 20: Outer fault 2 after parameter-optimized VME: (**a**) time-domain signal; (**b**) signal spectrum; (**c**) envelope spectrum.  
Figure 21: Training curves: (**a**) accuracy curve; (**b**) loss curve.