## 4 Experimental Verification
### Case 2  
As a critical component of rotating machinery, rolling bearings can significantly impact its performance. This case conducts signal processing research on the open bearing fault data set [39] of Case Western Reserve University (CWRU) bearing data center and the rolling bearing data measured in the laboratory. The test bench used by the mechanism is shown in Figure 13, including drive motor, load motor, coupling, torque sensor, and other components, providing measured fault data of different fault positions and sizes. Among them, the drive end bearing is an SKF 6205, and the fan end bearing is an SKF 6203. The acceleration sensor is used for data acquisition and installed above the bearing pedestal at the drive end and fan end. The sampling frequency of the data acquisition system is 12 kHz. Based on the PNN model, this section carries out diagnostic experiments on four states of the rolling bearing in the CWRU open data set. The technical information is shown in Table 5. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Gears** & **Feature Extraction** & **Classification** & **Number of** & **Number of** & **Right** & **Misjudgment** & **Accuracy** \\
**Status** & **Algorithm** & **Algorithm** & **Training Sets** & **Test Sets** & **Right** & **Misjudgment** & **Rates** \\ \hline \multirow{6}{*}{Label 1} & IPSO-VMD & PNN & 70 & 30 & 29 & 1 & 96.67\% \\  & PSO-VMD & PNN & 70 & 30 & 28 & 2 & 93.33\% \\  & PSO-VMD & ELM & 70 & 30 & 26 & 4 & 86.67\% \\  & PSO-VMD & SVM & 70 & 30 & 27 & 3 & 90.00\% \\  & EMD & PNN & 70 & 30 & 24 & 6 & 80.00\% \\ \hline \multirow{6}{*}{Label 2} & IPSO-VMD & PNN & 70 & 30 & 29 & 1 & 96.67\% \\  & PSO-VMD & PNN & 70 & 30 & 27 & 3 & 90.00\% \\  & PSO-VMD & ELM & 70 & 30 & 24 & 6 & 80.00\% \\  & PSO-VMD & SVM & 70 & 30 & 26 & 4 & 86.67\% \\  & EMD & PNN & 70 & 30 & 24 & 6 & 80.00\% \\ \hline \multirow{6}{*}{Label 3} & IPSO-VMD & PNN & 70 & 30 & 30 & 0 & 100\% \\  & PSO-VMD & PNN & 70 & 30 & 28 & 2 & 93.33\% \\ \cline{1-1}  & PSO-VMD & ELM & 70 & 30 & 26 & 4 & 86.67\% \\ \cline{1-1}  & PSO-VMD & SVM & 70 & 30 & 28 & 2 & 93.33\% \\ \cline{1-1}  & EMD & PNN & 70 & 30 & 25 & 5 & 83.33\% \\ \hline \end{tabular}
\end{table} 
Table 4: Diagnostic results of gear failure samples. Figure 13: CWRU bearing data center test bench. The data of four states are searched by IPSO adaptive search, and the best parameter combination \(\left[\hat{K},\hat{\mu}\right]\) is shown in Table 6.  
Each IMF component of four status data processed by IPSO-VMD is obtained, and the correlation coefficient between each IMF component and the original signal is calculated as shown in Figure 14. The figure shows that all other IMF components are valid components. Further, the energy ratio feature of effective components is shown in Figure 15. It can be observed that the distribution trend of the five IMF components of the rolling element fault and inner ring fault is similar. The proportion of IMF2 and IMF3 is small while IMF5 is the largest, but the proportional energy ratio of the inner ring fault is larger than that of the rolling element fault. For outer ring faults, IMF1 and IMF5 are 0 in the first five order components, and the ratios of IMF1 and IMF2 are close, while there is little difference in energy; IMF3 accounts for the largest proportion, about 4.5 times of IMF3. For normal conditions, IMF1 accounts for the largest proportion, exceeding 0.5, while IMF5 accounts for the smallest. In summary, the energy ratios of IMF components of each order for different faults can effectively distinguish different types of faults. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Normal** & **Ball Failure** & **Inner Failure** & **Outer Failure** \\ \hline \([10,2950]\) & \([8,3000]\) & \([9,1850]\) & \([6,3400]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Optimum parameter combination for different status data. Figure 14: IMF component correlation coefficient of rolling bearing data.