## 4 Experiments and Results
### Experimental Results
Figure 8: _Cont._  
Tables 2 and 3 respectively show the experimental results of performance comparison of rolling bearing fault feature extraction algorithms and fault identification accuracy by combining different fault feature extraction methods with random forest. In Table 2, the average between-class distance of MAAPE is less than improved multiscale entropy (IMSE), improved multiscale fuzzy entropy (IMFE) and refined composite multiscale entropy (RCMSE), but the average within-class distance of MAAPE is the smallest. In addition, the average time-consuming of MAAPE is relatively the lowest compared with other feature extraction methods. In Table 3, the fault identification accuracy of MAAPE coupled with random forest is 96.0% and the identification accuracy is slightly lower than RCMPE and IMFE. However, the computational efficiency is the highest as shown in Table 2. Through the above experiments, it can be seen that the rolling bearing fault diagnosis method proposed in this paper has high fault identification accuracy and good execution efficiency, which is more suitable for applications with high real-time requirements. In order to illustrate the analytical ability of fault severity of the rolling bearing fault diagnosis method proposed in this paper, the identification accuracy experiments of different fault severity are carried out in this paper, and the experimental results are shown in Table 4. It can be seen from the experimental results that the fault accuracy of the proposed method is low when the ball elements \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feature Extraction Methods** & **Average Between-Class** & **Average Within-Class** & **Average** \\
**Methods** & **Distance** & **Distance** & **Time-Consuming (S)** \\ \hline MAAPE & 1.24 & 0.20 & 0.39 \\ IMFE & 0.95 & 0.23 & 0.57 \\ RCMPE & 0.96 & 0.30 & 1.11 \\ IMSE & 2.22 & 0.94 & 0.42 \\ IMFE & 3.72 & 0.33 & 17.30 \\ RCMSE & 4.02 & 0.38 & 0.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance comparison of rolling bearing fault feature extraction algorithms. Figure 8: MAAPE feature clustering diagram of each fault severity under different loads. (**a**) Load 0 hp. (**b**) Load 1 hp. (**c**) Load 2 hp. (**d**) Load 3 hp. \begin{table}
\begin{tabular}{c c} \hline \hline
**Feature Extraction Methods** & **Fault Identification Accuracy (\%)** \\ \hline MAAPE & 96.0\% \\ IMPE & 96.0\% \\ RCMPE & 97.50\% \\ IMSE & 84.25\% \\ IMFE & 96.25\% \\ RCMSE & 92.25\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fault identification accuracy by combining different fault feature extraction methods with random forest. fault severity is 14 mils and 21 mils, and the overall fault accuracy is 92.8%. As the vibration signal contains the natural vibration of rolling bearings, the influence of fault size and external interference, it will have a certain impact on the performance of AAPE fault feature extraction. In addition, the use of 20 different scales of AAPE feature vector to form the eigenvector will increase the uncertainty factor, thereby affecting the accuracy of fault identification. In spite of this, it can be seen from the experimental results that the fault diagnosis method proposed in this paper can analyze the severity of rolling bearing fault to a certain extent.