# 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  
Eight sets of data were extracted from 16 sets of sample data, including one set for each gear states. The remaining 8 sets of data were tested as test data sets. The kurtosis value normalization matrix was input into SOM neural network for classification and identification, and the following results were the training times of 100. The kurtosis value normalization matrix in Table 2 is used as training data to train the SOM neural network.As the number of training steps increases, theweight vector is constantly adjusted and the magnitude of theweight vector is also changed.Where, the weight connection between the input sample and the competition layer neuronsare shown in Figure 17, where the lightest color hexagon weight value is the smallest, and the black hexagon weight value is usually 0. As shown in Figure 18, the hexagon represents a neuron on the competition layer, the node of the neuron is represented by 32 equal-sized hexagons, and the short line between the hexagons represents the interconnection between the neurons.The difference in color between the diamond blocks located around the neurons indicates the difference in distance between the neurons. The SOM neural network forms clusters based on the distance between the neurons, and there is no clear boundary between the clustering results. From the color (light to dark) of the diamond block, the darker the color that the block is, the farther the distance between the neurons. Figure 16: SOM neural network neighbor neuron connections. Figure 17: Weight connection of SOM neural network neuronswhen the number of training is 100. Figure 19 is the recognition result of training times of 100:  
According to the clustering results of SOM neural network, adjacent neurons can be regarded as the same species, while neurons with more distant neighbors can be regarded as different species. In Table 3, the numerical values of the classification results indicate the location number of SOM neural network neurons, and the adjacent number indicates the adjacent neurons, which are regarded as the same species. As shown in Figure 12, the four fault types of gear fault, normal gear, gear with tooth wear, gear with tooth crack, and gear with tooth break are effectively distinguished. The accuracy of gear fault of SOM neural network is 100% when the number of trainings is 100. Among them, Table 3 shows the classification results of the training samples numbered 1, 2, 5, 6, 9, 10, 13, and 14, which were input into the SOM neural network as the training sample matrix and the training times were 100. Table 4 shows the classification results of the samples numbered 3, 4, 7, 8, 11, 12, 15, and 16, which were input into the SOM neural network as the test samples matrices after 100 times of training. By comparing the classification results in Table 3, it can be seen that all test samples have been correctly classified into the corresponding fault categories, and the fault diagnosis recognition rate is 100%. Figure 19: SOM neural network classification results of gear fault when the number of training is 100. \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 Sample number & \multirow{2}{*}{100} & 1 & 2 & 5 & 6 & 9 & 10 & 13 & 14 \\ \hline Classification results & \multirow{2}{*}{1} & 1 & 6 & 6 & 20 & 20 & 32 & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Classification results for 100 training sessions. Figure 18: Distance distribution of SOM neural network neurons when the number of training is 100.