## 4 Analysis of Experimental Results and Discussion
### The Results of Fault Diagnosis  
According to the RS-DET, \((f_{32},f_{6},f_{95},f_{19},f_{2})\) is selected to constitute the RS-DFV. The comparison between the effect of RS-DFV and the DFV in REB fault diagnosis are presented in Table 10. To verify the effectiveness of RS-DFV in REB fault diagnosis, three other comparison experiments of REB fault diagnosis are designed and carried out under the same conditions with the same data and classification methods. These comparison experiments are based on three other feature vectors such as SFI, FSR and AF. Comparisons among the five feature vectors are listed in Table 11. We also made a comparative experiment with other three feature selection method, such as filter, wrapper, filter the combination of filter and wrapper. These experiments used feature vectors with the same dimension, the same feature evaluation methods and classifiers. And the experimental results are shown in Table 12. In addition, the experimental results based on RS-DFV and four different classifiers are shown in Table 13.  
In Table 10, it is very obvious that REB fault diagnosis based on RS-DFV achieved a very ideal diagnostic accuracy close to 100%, and its time consumption for feature extraction, classifier training and diagnosis test are acceptable. Compared with DFV, RS-DFV significantly increased the diagnosis accuracy without taking a much longer time. This indicates that RS-DFV is more suitable for REB fault diagnosis than the DFV and that the rough set improved the performance of DFV in fault characterization. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **RF\({}_{1}\)** & **RF\({}_{2}\)** & **RF\({}_{3}\)** & **RF\({}_{4}\)** & **RF\({}_{5}\)** & **RF\({}_{6}\)** \\ \hline RF\({}_{1}\) & 0.0726 & 10.3140 & 8.4930 & 10.3088 & 5.9324 & 0.9872 \\ RF\({}_{2}\) & 10.3140 & 0.0667 & 4.5708 & 0.9597 & 8.0773 & 9.7451 \\ RF\({}_{3}\) & 8.4930 & 4.5708 & 0.2394 & 4.5622 & 5.5733 & 7.8007 \\ RF\({}_{4}\) & 10.3088 & 0.9597 & 4.5622 & 0.0657 & 8.0713 & 9.7399 \\ RF\({}_{5}\) & 5.9324 & 8.0773 & 5.5733 & 8.0713 & 0.2014 & 4.9514 \\ RF\({}_{6}\) & 0.9872 & 9.7451 & 7.8007 & 9.7399 & 4.9514 & 0.2538 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The average Euler distance based on the RS-DFV consisting of \((f_{32},f_{6},f_{95},f_{19},f_{2})\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**\(DA\)** & **RF\({}_{1}\)** & **RF\({}_{2}\)** & **RF\({}_{3}\)** & **RF\({}_{4}\)** & **RF\({}_{5}\)** & **RF\({}_{6}\)** \\ \hline DET & 0 & 0 & 2 & 3 & 2 & 4 \\ RS-DET & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The abnormal interruptions in the DET and the RS-DET. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**\(DA\)** & **RF\({}_{1}\)** & **RF\({}_{2}\)** & **RF\({}_{3}\)** & **RF\({}_{4}\)** & **RF\({}_{5}\)** & **RF\({}_{6}\)** \\ \hline \(DAi_{min}\) & 13.5978 & 14.3885 & 19.0569 & 14.6073 & 24.5849 & 3.8897 \\ \(DAi_{ave}\) & 99.0100 & 101.0101 & 25.8981 & 102.4107 & 32.3790 & 26.1015 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The \(DAi(min)\) and \(DAi(ave)\) based on the RS-DFV. In Table 11, the average diagnostic accuracy rate of the RS-DFV fault diagnosis method is much higher than that due to other feature vectors. Therefore, the distribution optimization technique of RS-DFV significantly improved the accuracy of REB fault diagnosis. It is clear that the RS-DFV method yielded the best testing accuracy rate and took the shortest time. Obviously, the fault diagnosis contrast test proved that RS-DFV realized the easiest and most effective fault sample representation and that the RS-DFV fault diagnosis method is very efficient for REB fault diagnosis. In Table 12, the average diagnostic accuracy rate of the RS-DFV fault diagnosis method is much higher than that which were based on other feature selection methods, and the corresponding feature