# Gear Fault Diagnosis Based on Kurtosis Criterion VMD and SOM Neural Network
## 5 Fault Diagnosis and Result Analysis of SOM Neural Network
### Fault Diagnosis and Result Analysis
First, the gear fault signal was decomposed by EMD algorithm, then the kurtosis value was extracted, and then it was normalized as the input vector of SOM neural network. According to the above results, the gear fault identification rate of SOM neural network was the highest when the training times were 100 times.Therefore, the training times of SOM neural network are 100 times. The following Figure 24 shows the recognition diagram of gear fault signal by EMD algorithm is combined with the SOM neural network with 100 training times. As shown in Figure 24, the four fault types of gear fault, normal gear, gear with tooth wear, gear with tooth crack, and gear with tooth break were classified into six fault states and two unknown fault states emerged. When the number of training sessions of SOM neural network is 100, Table 14 shows the classification results of the training samples numbered 1, 2, 5, 6, 9, 10, 13, and 14 as training samples matrix input to SOM neural network when the number of training sessions is 100. Table 15 shows the classification results of samples numbered 3, 4, 7, 8, 11, 12, 15, and 16, which were input into the SOM neural network as the test sample matrices after 100 times of training. By comparing the classification results in Table 14, it can be seen that the classification results of test samples from fault training samples are not good, in which there is one identification error in the fault state of gear with tooth crack and gear with tooth break respectively, and two identification errors in the fault state of gear with tooth wear, resulting in a fault diagnosis identification rate of 50%. As can be seen from the comparison results in Tables 14 and 15, the EMD algorithm will not only generate mode mixing in the process of gear signal decomposition, but also reduce the accuracy of gear fault identification. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Gear Fault Type**} & \multirow{2}{*}{\begin{tabular}{c} **Training** \\ **Steps** \\ \end{tabular} } & \multirow{2}{*}{**Normal Gear**} & \multicolumn{2}{c}{\begin{tabular}{c} **Gear with** \\ **Tooth Wear** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Gear with** \\ **Tooth Crack** \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **Gear with** \\ **Tooth Break** \\ \end{tabular} } \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Sample number \\ **Classification** \\ results \\ \end{tabular} } & \multirow{2}{*}{100} & 1 & 2 & 5 & 6 & 9 & 10 & 13 & 14 \\ \cline{3-10}  & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Classification results for 1000 training sessions by EMD. Figure 24: SOM neural network classification results of gear fault when the number of training is 100 by EMD. According to the comparison results of Tables 3 and 4 with Tables 14 and 15, the advantages of VMD algorithm over EMD algorithm can be obtained, and the optimal training times of SOM can also be obtained. However, there are many classification algorithms. So how do we evaluate the advantages of SOM neural network over other classification algorithms? Here, the SVM algorithm is used for gear fault classification instead of SOM neural network, and the calculation results are shown in Table 16.  
According to the comparison of fault diagnosis accuracy in Table 16, compared with the EMD algorithm, the VMD algorithm can avoid mode mixing and other shortcomings in the EMD algorithm in terms of decomposition effect. In terms of the accuracy of gear fault diagnosis, the VMD algorithm has a higher accuracy than the EMD algorithm. As for the classification algorithm recognition rate of the SOM neural network, the overall fault diagnosis accuracy of the SOM neural network is much higher than that of the SVM algorithm whether it is matched with the EMD algorithm or the VMD algorithm.Therefore, the algorithm of VMD combined with SOM neural network has better advantages and better application prospects in gear fault diagnosis.