## 4 DE-KELM-Based Gearbox Fault Classification
### Gearbox Fault Diagnosis Experimental Data
#### 5.2.1 Vibration Signals Decomposition through GWO-VMD and VMD, Respectively  
GWO-VMD was applied first to decompose the obtained gearbox vibration signals. The parameters of GWO are shown in Table 10; the optimal values of [\(K\), \(\alpha\)] obtained by GWO in the eight working conditions are shown in Table 11.  
For comparison, VMD was then applied to decompose the same experimental data. The value of \(\alpha\) was set to 2000, and the value of \(K\) was determined by the \"central frequency observation method\" [43]. The calculated values of \(K\) in the eight working conditions are listed in Table 12 with the value of \(\alpha\). With the parameter configurations shown in Tables 11 and 12, the vibration signals in the eight conditions were decomposed by GWO-VMD and VMD, respectively. Then the IMFs having correlation coefficients greater than 0.25 were taken to reconstruct the vibration signals. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Parameter Values or Ranges** \\ \hline Population number & 9 \\ Maximum iterations number & 100 \\ Mode Number & [2; 15] \\ Penalty factor range & [100, 6000] \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Parameter configuration of GWO. Figure 19: Process of contrast experiment I. \begin{table}
\begin{tabular}{c c} \hline \hline
**Gerbox Elements** & **Working Conditions** & **[\(K\), \(\alpha\)]** \\ \hline \multirow{3}{*}{Bearing} & healthy bearing & [11; 4018] \\  & inner ring fault & [15; 139] \\  & outer ring fault & [5; 2755] \\  & roller fault & [5; 2678] \\ \hline \multirow{3}{*}{Gear} & healthy gear & [5; 2330] \\  & pitting fault & [15; 100] \\ \cline{1-1}  & broken teeth & [5; 3652] \\ \cline{1-1}  & tooth root cracks & [5; 3019] \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Optimal values of [\(K\), \(\alpha\)] obtained by GWO in the eight working conditions. 2.2 Fault Classification Results on the Two Sets of Feature Vectors Obtained through GWO-VMD and VMD, Respectively  
After the reconstructed signals were obtained through the decomposition by GWO-VMD and VMD, respectively, 18 feature parameters were calculated on the 150 samples; thus, two 18 \(\times\) 150 feature matrices were obtained. Among the 150 samples in each condition, 130 were taken randomly to form a training set, and the remaining 20 were used to make up a testing set. The DE-KELM proposed in this paper was then applied to classify the two feature matrices, respectively. The parameter settings of the DE are shown in Table 6. Fault classification results by DE-KELM on the feature matrices calculated through GWO-VMD and VMD are shown in Figures 20 and 21, respectively. The classification accuracy of the two experiments is shown in Table 13.  
As can be seen from Figure 20 and Table 13, when the vibration signal was processed by GWO-VMD, DE-KELM classified all the 1040 training samples correctly and the classification accuracy was 100%; for the 160 testing samples, only 3 of them were misclassified, and the classification accuracy was 98.125%. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Signal Decomposition** & **Classification Accuracy** & **Classification Accuracy** \\
**Method** & **of the Training Set** & **of the Testing Set** \\  & **(by DE-KELM)** & **(by DE-KELM)** \\ \hline GWO-VMD & 100\% & 98.125\% \\ VMD & 100\% & 91.875\% \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Fault classification accuracy of the training and testing sets by DE-KELM. Figure 20: Fault classification results by DE-KELM on the feature matrix calculated through GWO-VMD-based decomposition method. From Figure 21 and Table 13, when the vibration signal was processed by the contrasting VMD method, for the 1040 training samples, DE-KELM also correctly classified with 100% accuracy; while for the 160 testing samples, 13 were misclassified, and the classification accuracy was 91.875%.