## 4 Results and Discussions
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Gear Pitting Fault Diagnosis Method**} & **Training Accuracy** & **Validation Accuracy** & **Testing Accuracy** \\ \hline Proposed method: CNN with AE signals + GRU network with vibration signals & 1.00000 & 0.97333 & 0.98286 \\ \hline CNN with vibration signals + GRU network with AE signals & 1.00000 & 0.96952 & 0.98000 \\ \hline CNN with vibration signals + CNN with AE signals & 1.00000 & 0.96667 & 0.95714 \\ \hline CNN with vibration signals alone & 1.00000 & 0.92952 & 0.91429 \\ \hline GRU network with vibration signals alone & 1.00000 & 0.90190 & 0.89714 \\ \hline CNN with AE signals alone & 1.00000 & 0.68571 & 0.74571 \\ \hline GRU network with AE signals alone & 1.00000 & 0.56190 & 0.61714 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Gear pitting fault diagnosis accuracy of the presented method and the other methods. From Table 4, the method presented in this paper can achieve 100% diagnosis accuracy for five gear pitting fault conditions. For the other two gears, the pitting diagnosis accuracy reached 94%. In comparison with other methods in Table 4, the presented method gives much better results than the last 4 methods in Table 4 when only one type of signals is used. In comparison with the second and the third methods in Table 4, the performance of the presented method is slightly better. The method presented in this paper uses CNN to process AE data and GRU network to process vibration data. The reason is that the sampling frequency of the AE sensor is about 5 times of the vibration sensor. The number of features extracted from the AE signals is larger than that of the vibration signals. As discussed in Section 2 in this paper, the number of the parameters of a CNN is relatively small, and the number of the parameters of the GRU network is relatively large. Hence, it is computationally beneficial to use CNN to process a relatively larger volume of AE data and GRU network to process the relatively small volume of vibration data. If the GRU network is used to process the relatively larger volume of the AE data, the dimensionality of the data has to be reduced. The reduction of the dimensionality may result in loss of effective diagnostic information. Therefore, the method proposed in this paper that uses CNN to process the AE signals and the GRU network to process the vibration signals gives the best gear pitting fault diagnosis performance. To test the robustness of the proposed method for gear pitting fault diagnosis under different loading conditions, the diagnosis results were obtained by the proposed method at a constant speed of 1000 rpm with different loads and are provided in Table 5. To obtain the results in Table 5, the hyperparameters of the CNN and GRU network remain the same as those used for obtaining the results in Table 3. From Table 5, it can be seen that the training accuracy can reach 100% for all the loads. Since the accuracy results for the training are not significantly different from those for testing, there is not an over-fitting phenomenon for the results in Table 5. The accuracy of the testing is all above 94.86%, achieving a good gear pitting fault diagnosis result. The loss in each case is very low. As can be seen from Table 5, the training time in each case is not far away from the average of 838 s. As the load increases, there is an indication of a pattern of changes in fault diagnosis accuracy. This result shows that the performance presented method remains stable under different loads and shows the robustness and adaptability of the method for gear pitting fault diagnosis. It is well known that among all the parameters of deep learning, the learning rate is one of the most critical parameters. It has a great influence on the effect of the model. In order to test the effect of learning rate on the gear pitting fault diagnosis performance of the presented method, 20 different learning rates with an increment of 0.1 were tested.