# A Novel Rolling Bearing Fault Diagnosis and Severity Analysis Method
## 6 Experiments and Results
### Fault Identification and Severity Analysis Experiment  
To illustrate the fault identification and severity analysis effect of the proposed fault diagnosis method for rolling bearings, various types and fault diameters introduced in Section 6.1 are taken into account in the experiments. For each vibration signal in the vibration sample set, the length of signal segments is set to 2400 and the first 120,000 points in each type of vibration signal are divided into 50 non-overlapping sub-signals. Twenty sub-signals of each vibration signal in each fault type are randomly selected as training samples and the remaining 30 samples are all taken as test samples. Therefore, a total of 880 training samples and 1320 testing samples are used for experiments. The feature vectors of the above samples are extracted by the WPEE, thus composing the feature vector sets under different fault conditions. The mRVM classifier is established for performing the fault identification of the rolling bearings. The Gaussian kernel function is selected; \(\sigma\) is the kernel parameter for mRVM\({}_{1}\) and mRVM\({}_{2}\). Each experiment is repeated 10 times and the fault identification accuracy irrespective of the load and fault diameter is shown in Table 5. It can be seen that both versions of the mRVM are able to classify the fault types of the rolling bearings with high recognition accuracy. mRVM\({}_{2}\) obtains satisfactory results in this experiment, with the classification accuracy reaching as high as 99.47%; however, the classification accuracy of mRVM\({}_{1}\) is slightly worse than that of mRVM\({}_{2}\). These results show that mRVM\({}_{2}\) offers better performance than mRVM\({}_{1}\) in an unknown sample classification. Table 6 shows the results of fault diameter identification with the same fault type irrespective of the load. The fault diameter identification of each fault type achieves excellent results and the fault severity identification accuracy exceeds 99%. Table 7 shows the results of the fault type and diameter identification irrespective of the load. The number of categories is 11 and the average classification accuracy is 98.75%. Table 8 shows the results of the fault type and diameter identification under the same load and the proposed fault diagnosis method still has a high identification accuracy. Tables 6-8 illustrates that the proposed fault severity analysis method based on the WPEE and mRVM exhibits good performance in the fault diagnosis of rolling bearings. Figure 9: Wavelet packet energy entropy clustering diagram under different fault conditions for a load of 2 hp. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Number of** \\ **Categories** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Number of** \\ **Training Samples** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Number of** \\ **Testing Samples** \\ \end{tabular} } & \multicolumn{2}{c}{**mRVM\({}_{1}\)**} & \multicolumn{2}{c}{**mRVM\({}_{2}\)**} \\ \cline{3-6}  & & & & **Average** & **Accuracy (\%)** & **Accuracy (\%)** \\ \hline
3 & 880 & 2200 & 0.23 & 98.96 & 0.4 & 99.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Fault identification accuracy irrespective of the load and the fault diameter. To further experimentally demonstrate the effectiveness and superiority of the proposed method, some comparisons are conducted between the present work and recently published works regarding bearing fault diagnosis using different methods. Table 9 reports the comparative result between the current study and the recently published literature. In Table 9, fault types and fault severities are combined to be diagnosed and a comparison is made on the basis of the feature extraction methods and fault classifier. The proposed fault diagnosis method has a better diagnostic effect than that of the recently published works.