## 5 Conclusions  
A rolling bearing fault diagnosis method based on multiscale amplitude-aware permutation entropy (MAAPE) and random forest is proposed in this paper. The MAAPE-based fault feature extraction method is proposed for the first time. In order to effectively extract fault features in vibration signals of rolling bearings, this paper uses a coarse-grained process in MSE to obtain a set of coarse-grained time series under different scale factors, and extracts fault features contained in different coarse-grained time series through AAPE to obtain feature vectors representing fault information of rolling bearings. Then, the random forest classifier is adopted to identify the fault feature vector extracted from vibration signal of rolling bearings. The proposed fault diagnosis method can effectively identify the fault type of rolling bearings and the identification accuracy of four fault types is up to 96.0%. The proposed method can further analyze the fault severity of rolling bearings, and the identification accuracy under different fault severity is 92.8%.  
MAAPE can improve the stability of PE, become more sensitive to amplitude and frequency changes, and contribute to the description of fault characteristics. However, because it is too sensitive to the change of amplitude, it is easy for external interference to affect the extracted features, leading to a decline in identification accuracy. Therefore, how to avoid external interference and highlight bearing vibration signals before feature extraction will help improve the feature extraction effect of MAAPE. The following research direction is to further improve the fault feature description ability of MAAPE, and then improve the fault severity analysis ability of fault diagnosis method.  
[PERSON] clarified the research content and ideas, and completed the writing of this paper. [PERSON] and [PERSON] studied the method and carried out experiments. [PERSON] and [PERSON] analyzed the data and proofread the manuscript.  
This research was funded by the National Natural Science Foundation of China under grant numbers 61803128, 61801148 and Heilongjiang Province Natural Science Foundation under grant numbers F2016021 and LH2019F026.  
**Acknowledgments:** Thanks for the Bearing Data Center of Case Western Reserve University for supplying the rolling bearing data set.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Type Labels** & **NM** & **IR07** & **IR14** & **IR21** & **OR07** & **OR14** & **OR21** & **BE07** & **BE14** & **BE21** &
\begin{tabular}{c} **Identification** \\ **Accuracy (\%)** \\ \end{tabular} \\ \hline
**NM** & 40 & - & - & - & - & - & - & - & - & - & 100 \\
**IR07** & - & 40 & - & - & - & - & - & - & - & 100 \\
**IR14** & - & - & 39 & - & - & - & - & 1 & - & 97.5 \\
**IR21** & - & - & - & 40 & - & - & - & - & - & - & 100 \\
**OR07** & - & - & - & - & 40 & - & - & - & - & - & 100 \\
**OR14** & - & - & - & - & - & 39 & - & - & 1 & - & 97.5 \\
**OR21** & - & 1 & - & - & - & - & - & 39 & - & - & 97.5 \\
**BE07** & - & - & - & - & - & - & - & 40 & - & - & 100 \\
**BE14** & - & - & - & - & - & 2 & - & 2 & 34 & 2 & 85 \\
**BE21** & - & - & - & - & - & - & - & 4 & 1 & 35 & 87.5 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Identification rate of the proposed rolling bearing fault diagnosis method for different fault severity.