# A Novel Rolling Bearing Fault Diagnosis Method Based on MFO-Optimized VMD and DE-OSELM
## 5 The Diagnosis Method Based on MFO-Optimized VMD and DE-OSELM
### Diagnostic Case Analysis  
The viability and effectiveness of the proposed approach were evaluated using the drivetrain dynamics simulator (DDS), as illustrated in Figure 12, manufactured by SpectraQuest [45]. The ER-16K rolling bearing type was utilized to obtain the corresponding vibration signals. The bearing had a pitch circle with a 15.16 mm diameter, nine rolling bodies with a diameter of 3.125 mm, and a contact angle of 0\({}^{\circ}\). The experiment was conducted with a motor frequency of 20 Hz, zero load, a sampling frequency of 12,800 Hz, and a sampling length of 200 KiB. Vibrations were captured under four operating conditions: normal operation, inner ring failure, outer ring failure, and rolling body failure. A total of 400 signals were recorded, consisting of 100 sets of vibration signals for each of the four operating conditions, with a signal length of 1024 samples per group. Ten groups of normal signals were randomly selected for this study, and their decomposition layers and quadratic penalty factor were optimized through the improved MFO algorithm to obtain an optimal combination of <10, 1535>. The VMD algorithm was then applied to decompose each signal using this optimized parameter combination, after which the EWCS value of each IMF was calculated. The findings are presented in Table 6. After VMD decomposition, the components of the reconstructed signal were simpler, and the fault frequency was more obvious. Figure 13 shows the spectrum diagram of the original signal and reconstructed signal with the rolling element fault. The feature matrix is input into both OSELM and DE-OSELM classification models, and their respective classification results are presented in Figure 14. Accordingly, it is evident from the figure that DE-OSELM achieves higher classification accuracy than OSELM, further reinforcing the effectiveness and universality of DE-OSELM. This comparison result provides robust evidence to support the superiority of DE-OSELM in classification performance. To validate the efficacy of our proposed technique, we input the results of both the fixed parameter <7, 2000> VMD and the MFO-optimized VMD into four distinct classification algorithms--ELM, OSELM, KNN, and DE-OSELM--for classification and recognition purposes. Table 7 displays the classification outcomes of the four techniques. Table 7 supports the efficacy of the proposed MFO-optimized VMD and DE-OSELM diagnostic methods, which demonstrate greater accuracy and reliability compared to the other three methods. Figure 12: Drivetrain dynamics simulator. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Classify** & **<8, 2000> VMD** & **MFO-Optimized VMD** \\ \hline ELM & 92.67\% & 96.17\% \\ OSELM & 92.70\% & 96.40\% \\ KNN & 88.00\% & 99.00\% \\ DE-OSELM & 99.73\% & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The comparison of classification accuracy of the four methods. At the same time, it is compared with two existing fault diagnosis methods, namely, the fault diagnosis method, based on EMD and OSELM [46], the fault diagnosis method, based on VMD and KNN [47], and results are shown in Table 8. From the results, we can see that their classification accuracy scores. The differences are 92.7% and 97.13%, and,