# Bearing Fault Diagnosis Method Based on Improved VMD and Parallel Hybrid Neural Network
## 4 Results  
### Fault Signal Processing  
After the bearing fault data set is obtained, the envelope spectrum analysis method is used to analyze the fault data. Because the impact information generated by the rolling bearing in the fault state is very prominent, the envelope spectrum analysis method can accurately locate the side frequency and quickly obtain the modulation signal. The square envelope spectrum algorithm is based on the envelope spectrum algorithm. When solving the analytical signal of the vibration signal, the conjugate signal of the analytical signal is solved at the same time, and then, the square envelope signal of the vibration signal can be obtained by integrating the conjugate analytical signal and the analytical signal. Compared with the envelope spectrum algorithm, the square envelope spectrum signal can suppress noise and other unrelated signals, making the spectrum clearer. Due to the large number of fault data, it is impossible to analyze all the data. Therefore, Bearing1_4 and one of the CSV files with a fault tag of 1 are selected as a typical example. The rotating speed of Bearing1_4 under working conditions is 35 Hz, and the calculation formula of bearing fault characteristic frequency (13) is introduced to obtain the cage fault characteristic frequency FT =13.49 Hz of bearing Bearing1_4. At the same time, since the third octave of the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Bearing Data Set** & **Training Set** & **Test Set** & **Label** \\ \hline Bearing 1\_1 & (480, 1024) & (120, 1024) & 0 \\ Bearing 1\_4 & (480, 1024) & (120, 1024) & 1 \\ Bearing 2\_1 & (480, 1024) & (120, 1024) & 2 \\ Bearing 2\_2 & (480, 1024) & (120, 1024) & 3 \\ Bearing 3\_3 & (480, 1024) & (120, 1024) & 4 \\ Bearing 3\_5 & (480, 1024) & (120, 1024) & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: New bearing failure data set.  
characteristic frequency of cage fault is within 100 Hz, only the square envelope spectrum within 100 Hz is shown here, as shown in Figure 6:  
\[\text{FTF}=\frac{1}{2}N\bigg{[}1-\frac{dcosa}{D}\bigg{]} \tag{13}\]  
where \(N\) represents the bearing rotation frequency (unit: Hz), \(d\) represents the diameter of the rolling element, \(D\) represents the bearing pitch diameter, and \(a\) represents the contact angle of the rolling element.  
It can be seen from the figure that although the frequency doubling and frequency doubling of the fault frequency component are obvious, there are still some interferences. Considering the improved VMD method proposed to process the fault signal, its purpose is to denoise and filter the original signal to remove the presence of noise and mask the components unrelated to the fault, making the fault feature easier to detect. The reweighted kurtosis values corresponding to different reconstructed signals are shown in Figure 7.  
Figure 6: Square envelope spectral image of original signal.  
Figure 7: Reweighted kurtosis corresponding to different reconstructed signals.  
It can be seen from the figure that when the number of decomposition K is set to 6, the reweighted kurtosis value of the reconstructed signal is the largest. The reconstructed signal processed by the improved VMD algorithm removes some interference and retains the main impact signal, thus enhancing the fault characteristics of the original signal. The image comparison between the reconstructed signal and the original signal after VMD algorithm processing is shown in Figure 8:  
Using the reconstructed signal to draw the square envelope spectrum image, as shown in Figure 9. It can be found that after the improved VMD algorithm processing, the amplitude of the square envelope spectrum image at the fault feature frequency increases significantly, which improves the identifiability of the signal and reflects the superiority of the improved VMD algorithm in retaining the impact characteristics of the fault signal, laying the foundation for the use of deep learning network for feature extraction in a following paper.