## 4 Analysis of Experimental Results and Discussion
### The Results of Fault Diagnosis
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Fault Classes**} & \multicolumn{5}{c}{**Average Diagnostic Rate**} \\ \cline{2-7}  & **RS-DFV-PNN** & **RS-DFV-RBF** & **RS-DFV-BP** & **RS-DFV-SVM** \\ \hline F1 & 100\% & 100\% & 100\% & 100\% & 100\% \\ F2 & 100\% & 100\% & 100\% & 100\% & 100\% \\ F3 & 99.51\% & 99.45\% & 99.51\% & 99.49\% \\ F4 & 100\% & 100\% & 100\% & 100\% \\ F5 & 99.47\% & 99.47\% & 99.48\% & 99.45\% \\ F6 & 100\% & 100\% & 100\% & 100\% \\ \hline \hline \end{tabular}  
* RS-DFV-PNN: Fault diagnosis based on RS-DFV and PNN; RS-DFV-RBF: Fault diagnosis based on RS-DFV and radical basis function neural networks; RS-DFV-BP: Fault diagnosis based on RS-DFV and back propagation neural networks; RS-DFV-SVM: Fault diagnosis based on RS-DFV and SVM.  
\end{table} 
Table 10: The experimental results of RS-DFV and DFV. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Feature Vector**} & \multicolumn{5}{c}{**The Average Diagnostic Rate**} & \multicolumn{1}{c}{**Training**} & \multicolumn{1}{c}{**Testing**} \\ \cline{2-9}  & **RF1** & **RF2** & **RF3** & **RF4** & **RF5** & **RF6** & **Mean** & **Time (ms)** \\ \hline RS-DFV & 100\% & 100\% & 99.51\% & 100\% & 99.47\% & 100\% & 99.83\% & 381 & 259 \\ DFV & 100\% & 100\% & 97.55\% & 93.63\% & 98.04\% & 94.61\% & 97.31\% & 377 & 261 \\ SFI & 93.97\% & 100\% & 99.33\% & 100\% & 88.09\% & 93.81\% & 95.87\% & 379 & 252 \\ FSR & 78.25\% & 66.78\% & 75.82\% & 56.04\% & 73.45\% & 44.26\% & 65.77\% & 389 & 243 \\ AF & 100\% & 100\% & 96.18\% & 99.93\% & 81.54\% & 96.49\% & 95.69\% & 1362 & 1194 \\ \hline \hline \end{tabular}  
* SFI: The feature vector constituted by the same feature items of RS-DFV; FSR: The feature vector constituted by the same number of features selected randomly; AF: The feature vector constituted by all the features.  
\end{table} 
Table 11: Comparison with other feature vectors. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Fault Classes**} & \multicolumn{5}{c}{**The Average Diagnostic Rate**} & \multicolumn{1}{c}{**Feature Selection**} \\ \cline{2-9}  & **RF1** & **RF2** & **RF3** & **RF4** & **RF5** & **RF6** & **Mean** & **Time (ms)** \\ \hline RS-DFV & 100\% & 100\% & 99.51\% & 100\% & 99.47\% & 100\% & 99.83\% & 117 \\ Filter & 94.93\% & 100\% & 100\% & 100\% & 84.34\% & 95.59\% & 95.81\% & 103.66 \\ Wrapper & 99.51\% & 100\% & 99.02\% & 100\% & 94.61\% & 83.33\% & 96.08\% & 7719.72 \\ Filter + Wrapper & 91.69\% & 100\% & 100\% & 100\% & 68.82\% & 80.66\% & 90.11\% & 2604.32 \\ \hline \hline \end{tabular}  
* RS-DFV-PNN: Fault diagnosis based on RS-DFV and PNN; RS-DFV-RBF: Fault diagnosis based on RS-DFV and radical basis function neural networks; RS-DFV-BP: Fault diagnosis based on RS-DFV and back propagation neural networks; RS-DFV-SVM: Fault diagnosis based on RS-DFV and SVM.  
\end{table} 
Table 12: Comparison with other feature selection methods. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Fault Classes**} & \multicolumn{2}{c}{**Diagnostic Rate**} & \multicolumn{2}{c}{**Time of Feature**} & \multirow{2}{*}{**Training Time (ms)**} & \multirow{2}{*}{**Testing Time (ms)**} \\ \cline{2-2} \cline{5-8}  & **RS-DFV** & **DFV** & **RS-DFV** & **RS-DFV** & **DFV** & **RS-DFV** & **DFV** \\ \hline RF1 & 100\% & 100\% & 113 & 103 & 369 & 371 & 257 & 265 \\ RF2 & 100\% & 100\% & 111 & 99 & 373 & 369 & 261 & 259 \\ RF3 & 99.51\% & 97.55\% & 127 & 101 & 38 selection time is much less. Obviously, RS-DFV found the best feature subset in the shortest time and achieved the best diagnostic accuracy with the same size feature subset and the same classifier. In Table 13, the four different classification methods all have achieved very satisfactory diagnostic accuracy. This further confirms the effectiveness of RS-DFV for rolling bearing fault diagnosis and shows that PNN reduces the classification complexity but does not affect the classification accuracy.