# Rotor Fault Diagnosis Method Based on VMD Symmetrical Polar Image and Fuzzy Neural Network
## 5 Conclusions  
This paper proposes a rotor fault diagnosis method based on VMD symmetrical polar image and fuzzy neural network. The method performs well in fault diagnosis of rotor vibration signal under different conditions. The conclusions are as follows:  
1. The two-dimensional snowflake image of the rotor vibration signal generated by the symmetric polar coordinate method is directly obtained from the time-domain signal and without the need for frequency analysis. Based on the parameter selection algorithm and CEF method, VMD can effectively eliminate noise disturbing components, strengthen fault feature components, and ensure the precision of image feature acquisition. Through five times recognition tests, the results show that the average recognition precision and standard deviation of the symmetrical polar coordinate image of the reconstructed rotor signal based on VMD are 98.4% and 0.5477. Compared  
Figure 18: K-cross-validation experiment results.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Classifier** & **Average Recognition Precision/\%** & **Training Time/s** & **Test Time/s** \\ \hline SVM & 96.4 & 25.83 & 10.63 \\ \hline BP neural network & 92.2 & 31.46 & 11.12 \\ \hline Random Forest & 93.6 & 24.72 & 10.77 \\ \hline Fuzzy neural network & 98.4 & 26.24 & 10.85 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Average recognition precision and calculation times of the four classifiers.  
with some similar signal decomposition methods (e.g., LMD are 92.8% and 0.8367, EMD are 92.6% and 0.8944 and EEMD are 93.8% and 1.3038), VMD could improve precision and stability of fault diagnosis.
2. For the rotor vibration signals under different working conditions, even in the case of small samples, the recognition rate of the fault diagnosis method based on VMD symmetric polar image and fuzzy neural network can reach 98%. Through the k-cross-validation experiment, the average recognition accuracy of this experiment is 99.2%, which demonstrates the robustness of the fuzzy neural network.
3. Compared with BP neural network, the fuzzy neural network has obvious superiority in identifying precision (e.g., the average recognition precision of the BP neural network is 92.2% and the fuzzy neural network is 98.4%) and saving calculation time (e.g., the training time and test time of BP neural network are 26.24 s and 10.85 s, fuzzy neural network are 26.24 s and 10.85 s). Compared with SVM and Random Forest, the fuzzy neural network also has a higher average recognition precision (SVM is 96.4% and Random Forest is 93.6%), and has the same computing efficiency.  
Limited by the laboratory conditions, this experimental device is mainly used to simulate the above four types of rotor faults. Through the study of relevant literature [1; 2; 3; 4; 5], these four types of rotor faults are common faults and have certain universality. If necessary requirements can be obtained in the future, the authors will continue to study fault diagnosis methods for other rotor faults (e.g., rotor part falling, oil film whirl, and rotor broken bar fault) on the basis of this study and the generalization ability of the model proposed in this paper.  
Conceptualization, X.Z. and X.W.; methodology, X.Z. and L.C.; writing--original draft preparation, X.Z., H.W. and Z.X.; writing--review and editing, X.Z., L.C. and Z.Y.; visualization, X.Z. and X.W.; funding acquisition, X.Z. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the Science and Technology Research Project of Jilin Provincial Department of Education (no. JJKH20220047 KJ and JJKH20230060 KJ), Jilin Science and Technology Development Plan Project (no. 20210203047 SF). These supports are gratefully acknowledged.  
Not applicable.  
The authors declare no conflict of interest.