# 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
### Experimental Verification  
To assess the effectiveness and superiority of MFO-optimized VMD and DE-OSELM for detecting faults in rolling bearings, we conducted an experiment using actual operation data of the 6205 deep groove ball bearing type obtained from Western Reserve University's laboratory [44]. As illustrated in Figure 8, the simulation test bench for rolling bearing faults features a pitch circle diameter of 39.04 mm, as well as nine rolling bodies with a diameter of 7.94 mm each and 0\({}^{\circ}\)contact angle. The vibration signals were collected under four operating states: normal, inner ring failure, outer ring failure, and rolling body failure. Figure 7: The fault diagnosis process based on the MFO-optimized VMD and DE-OSELM. We shifted 100 groups of vibration signals for each state, with each group consisting of 1024 signal lengths, resulting in a total of 400 groups. Ten groups of normal signals were randomly selected for the experiment. The improved MFO algorithm was initiated with an initial population size of 30. The maximum number of iterations was set as 10, with m = 10 and \(p=5\). \(K\) and \(\alpha\) values were ranged between [4; 12] and [800, 3000]. Figure 9 shows the search results, and the optimized values for \(K\) and \(\alpha\) were determined to be 10 and 924, respectively. The EWCS index was utilized to screen the decomposed IMFs, and the EWCS values of each modal component for the ten groups of signals were presented in Table 4. Based on the screening outcomes of the ten groups of signals, the effective components of IMF1, IMF2, and IMF3 were identified. VMD decomposition was performed using K values of 10 and 924 on 400 sets of vibration signals in four different states. The energy characteristics of IMF1, IMF2, and \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Number** & **IMF1** & **IMF2** & **IMF3** & **IMF4** & **IMF5** & **IMF6** & **IMF7** & **IMF8** & **IMF9** & **IMF10** \\ \hline
1 & 0.2567 & 0.1588 & 0.6992 & \(-\)0.0227 & \(-\)0.1525 & \(-\)0.1820 & \(-\)0.1846 & \(-\)0.1875 & \(-\)0.1905 & \(-\)0.1951 \\
2 & 0.2619 & 0.1511 & 0.6659 & \(-\)0.0330 & \(-\)0.0545 & \(-\)0.1871 & \(-\)0.1900 & \(-\)0.1962 & \(-\)0.1995 & \(-\)0.2186 \\
3 & 0.2429 & 0.6247 & 0.6202 & \(-\)0.0846 & \(-\)0.1055 & \(-\)0.2465 & \(-\)0.2558 & \(-\)0.2649 & \(-\)0.2573 & \(-\)0.2732 \\
4 & 0.2742 & 0.6095 & 0.6110 & \(-\)0.0691 & \(-\)0.1873 & \(-\)0.2306 & \(-\)0.2464 & \(-\)0.2468 & \(-\)0.2514 & \(-\)0.2632 \\
5 & 0.3334 & 0.1268 & 0.6938 & \(-\)0.0299 & \(-\)0.1616 & \(-\)0.1851 & \(-\)0.1863 & \(-\)0.1892 & \(-\)0.1988 & \(-\)0.2030 \\
6 & 0.2352 & 0.6979 & 0.6859 & \(-\)0.0878 & \(-\)0.2282 & \(-\)0.2492 & \(-\)0.2538 & \(-\)0.2660 & \(-\)0.2597 & \(-\)0.2743 \\
7 & 0.1517 & 0.5070 & 0.6256 & \(-\)0.0689 & 0.0619 & \(-\)0.2390 & \(-\)0.2522 & \(-\)0.2584 & \(-\)0.2535 & \(-\)0.2742 \\
8 & 0.3234 & 0.1465 & 0.6228 & \(-\)0.0174 & \(-\)0.0514 & \(-\)0.1945 & \(-\)0.2002 & \(-\)0.2091 & \(-\)0.2042 & \(-\)0.2158 \\
9 & 0.2809 & 0.5466 & 0.5914 & \(-\)0.0520 & \(-\)0.2003 & \(-\)0.2183 & \(-\)0.2371 & \(-\)0.2374 & \(-\)0.2332 & \(-\)0.2408 \\
10 & 0.2337 & 0.1156 & 0.7296 & \(-\)0.0069 & \(-\)0.1555 & \(-\)0.1727 & \(-\)0.1865 & \(-\)0.1843 & \(-\)0.1828 & \(-\)0.1902 \\ Effective & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & & & & & & \\ IMFs & \(\surd\) & \(\surd\) & \(\surd\) & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The value of EWCS of each IMF for 10 groups of normal signals. Figure 8: The rolling bearing fault simulation test bench. Figure 9: The improved MFO convergence curve of the bearing signal. IMF3 were extracted, resulting in an eigenvector matrix that was normalized. Adding labels produced a 400 \(\times\) 4 eigenmatrix. The energy characteristic matrix was randomly partitioned into training and test sets at a ratio of 3:1, resulting in 300 training samples and 100 test samples. After VMD decomposition, the components of the reconstructed signal were simpler, and the fault frequency was more obvious.