## 5 Experimental Verification and Analysis
### Case Study II: Fault Diagnosis of Gearbox
#### 5.2.2 The Performance of Proposed RMSDE-SOF  
The collected vibration signals are randomly divided into 200 samples for each type of fault, and the length of each sample is 4096. The ratio of the training set to the test set is 7:3. Figure 16 and Table 7 show the identification accuracy of four different fault diagnosis methods within 20 run times. The configuration of the computer used here is the same as that in Section 4.3. As is shown in Figure 16, the average accuracy of RMSDE-SOF is 95.58%, and the maximum classification accuracy is 98.33%. This shows that the method is also effective for the diagnosis of gear fault data sets. The classification accuracy of MSE-SOF is between 83.33% and 91.67%. Compared with the method proposed in this paper, the diagnostic accuracy is lower. The accuracy of MPE-SOF is slightly lower than that of MFE-SOF. MSE-SOF The classification accuracy of the MPE-SOF method was the lowest, with an average of 63.77%. Furthermore, in terms of the run time, RMSDE-SOF is the lowest. When the number of data samples is large, the advantage of RMSDE-SOF is more obvious. In order to display the details of the diagnosis results, the confusion matrix of the diagnosis results of four methods is constructed by selecting one of the test conditions. The specific results are shown in Figure 17. It can be seen from the confusion matrix that for method RMSDE-SOF, only 12 out of 420 test samples were misclassified. However, the number of misclassifications for the other three methods was 51, 78 and 153, respectively. The comparison results also demonstrate that the proposed RMSDE-SOF method performs best in extracting fault characteristics from the rotating machinery.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Name** & **Fault Type** & **Extent of Damage** & **Fault Size** \\ \hline C1 & Broken tooth & 1 & None \\ C2 & Pitting & 1 & None \\ C3 & Pitting & 2 & None \\ C4 & Root crack & 1 & 0.25 times tooth thickness \\ C5 & Root crack & 2 & 0.5 times tooth thickness \\ C6 & Surface wear & 1 & 0.4 times tooth thickness \\ C7 & Surface wear & 2 & 0.8 times tooth thickness \\ \hline \end{tabular}
\end{table}
Table 6: The specific information of bearing code.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Number of teeth & 14 \\ Modulus & 5 \\ Profile angle & 20\({}^{\circ}\) \\ Tooth height coefficient & 0.85 \\ Mean spiral angle & 35\({}^{\circ}\) \\ \hline \end{tabular}
\end{table}
Table 5: The specific structural parameters of the gear.  
To further demonstrate the advantages of the proposed method, the features of the extracted gear are visualized through t-SNE dimensionality reduction [27], and the resulting scatter diagram is shown in Figure 18. It can be seen from Figure 18 that each healthy cluster has a relatively independent center, and the overall concentration is excellent. The boundaries between clusters are also clear, without overlap, and are well separated. In terms of the influence of parameters, the laws of the gear dataset and the bearing dataset are consistent. The above analysis results further demonstrate the effectiveness of the proposed method in gearbox fault diagnosis, so this method has certain engineering application value in the health management of rotating machinery.