## 5 Experimental Verification and Analysis
### Case Study I: Fault Diagnosis of Rolling Bearing
#### 5.1.3 The Performance of Proposed RMSDE-SOF  
In order to explore the recognition effect of the extracted fault features input into the machine learning classifier, the SOF classifier mentioned above is introduced to classify the  
Figure 12: Calculation results of various entropy methods for bearing fault signals: (**a**) RMSDE, (**b**) MSE, (**c**) MFE, and (**d**) MPE.  
extracted entropy features. RMSDE-SOF, MSE-SOF, MFE-SOF, and MPE-SOF methods were used to analyze this bearing data set. Fifty samples of each health state are divided into a training set and test set, and the ratio of the training set to the test set is 3:2. Figure 13 and Table 4 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 13, the average accuracy of RMSDE-SOF is 97%, and the maximum classification accuracy is 100%. This shows that the method is effective for the diagnosis of the bear fault data set. The classification accuracy of MSE-SOF is between 80% and 95%. Compared with the method proposed in this paper, the diagnostic accuracy is lower. The classification accuracy of the MPE-SOF method was the lowest, with an average of 63.25%. Furthermore, in terms of the run time, RMSDE-SOF and MPE-SOF are relatively close, and the time consumption is ten times lower than that of MSE-SOF and MPE-SOF. Results further validate that the proposed method has certain advantages in both diagnostic ability and calculation efficiency, which provides an attractive avenue for entropy-based weak feature extraction.  
To further investigate the changes in algorithm performance with the selection of relevant parameters, the following experiments were conducted. First of all, the proportion of training samples in the RMSDE part was selected for research. The changes in training accuracy, testing accuracy, and time spent with the percentage of training samples are shown in Figure 14a. The results show that with the increase in the training sample percentage, the testing accuracy increased continuously, and the time spent increased almost linearly. When the percentage of RMSDE training samples increased to 60%, the training accuracy reached 99.33 \(\pm\) 0.66%, and the testing accuracy reached 98 \(\pm\) 1%, after which both the two accuracy rates remained almost unchanged. The second part is about the impact of scale factor \(\tau\). Select 60% as the training sample percentage; the particular results are shown in Figure 14b. It can be seen that when \(\tau\) was increased, the training accuracy and testing accuracy did not increase with it or even display a downward trend, but the time spent still increased continuously. This is due to the occurrence of redundant and invalid features. When \(\tau\) = 20, the overall effect is optimal.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **RMSDE-SOF** & **MSE-SOF** & **MFE-SOF** & **MPE-SOF** \\ \hline Max accuracy (\%) & 100 & 95 & 90 & 75 \\ Min accuracy (\%) & 90 & 80 & 70 & 55 \\ Average accuracy (\%) & 97.25 & 89.25 & 79.75 & 63.25 \\ Run time (s) & 13.99 & 125.41 & 138.22 & 13.87 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Diagnostic accuracy of different diagnostic methods in Case Study I.  
Figure 13: The classification accuracies of four methods in case study I.