# Rotor Fault Diagnosis Method Based on VMD Symmetrical Polar Image and Fuzzy Neural Network
## 4 Experimental Analysis
### Fault Diagnosis Results and Comparative Analysis  
The feature parameters extracted from the gray level co-occurrence matrix are used to form the state feature vector which is input to the fuzzy neural network for fault diagnosis. In this experiment, the dimension of input data is 6 and the dimension of output data is 1. It is determined that the number of input nodes in the network is 6 and the number of output nodes is 1. According to this situation, the number of selected membership functions is better to be 12 after the optimization. Therefore, the construction of the fuzzy neural network structure is 6-12-1. The center c and the width b of the membership function are randomly initialized, the maximum number of iterations is set to 1000, the initial network learning rate is 0.01, and the system error is 0.001. Figure 15 shows the fault recognition results of the proposed method. It could be seen that the fault recognition precision of the proposed method was 98%. The reliability of the proposed method in rotor fault feature extraction and fault recognition is verified. In order to further verify the advantages of this method, the following aspects are analyzed. (1) For examining VMD effects in the proposed method, LMD, EMD and EEMD are applied to decompose the same rotor vibration signal. The rotor signal is reconstructed by the above method according to the steps in this paper, then the fault feature sample set is constructed based on the characteristic parameters of the reconstructed signal symmetric polar image. For eliminating the influence of accidental error, each method is tested five times, and the average recognition precision and standard deviation of the five test results are taken as the evaluation indexes of the method. The comparison of the five test results is shown in Figure 16. The average recognition precision and standard deviation are shown in Table 7. It can be seen from Figure 16 and Table 7 that the proposed method has the highest recognition precision and the average recognition precision is 98.4%. The standard  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Working State**} & \multirow{2}{*}{**Group of Signals**} & \multicolumn{6}{c}{**Characteristic Parameter**} \\ \cline{3-8}  & & _mp_ & _ent_ & _con_ & _cor_ & _ene_ & _idm_ \\ \hline \multirow{4}{*}{Nor} & 1 & 0.8510 & 1.5074 & 0.5883 & 0.9395 &  
deviation of the proposed method is 0.5477, which is far lower than that of the other three methods. It shows that the proposed method can not only effectively reduce the influence of disturbing components on the precision of signal feature extraction, but also improve the precision and stability of fault diagnosis. (2) In order to study the influence of the partition ratio of the training sample set and test sample set on the recognition precision, the proportion of the training sample set and test sample set in each state is divided into five cases: 2/8, 4/6, 5/5, 6/4, 8/2 and five recognition times for each case. Figure 17 shows the average recognition results. Figure 16 shows that the proposed method still has the highest fault recognition precision under different proportions. The recognition precision of all methods increases with the increase of the proportion of training sample sets. If there are enough training samples, other methods can also obtain higher precision, but the computational efficiency will decrease. (3) In addition, a k-cross-validation experiment (\(k\) = 5) is used to demonstrate the robustness of the proposed model. During the experiment, 50 groups of rotor signal samples in each state are divided into five subsets. Each subset (10 samples) data is used as a verification set and the remaining four groups of subsets (40 samples) data are used \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Average Recognition Precision/\%** & **Standard Deviation** \\ \hline VMD & 98.4 & 0.5477 \\ LMD & 92.8 & 0.8367 \\ EMD & 92.6 & 0.8944 \\ EEMD & 93.8 & 1.3038 \\ \hline \hline \end{tabular}
\end{table}