## 4 Results and Discussions
The testing results are provided in Table 6.  
As shown in Table 6, in the range from 0.4 to 2.3, it can be seen that a training accuracy of 100% was obtained for all the tested learning rates. The validation accuracy is all above 95.3%, and the standard deviation was computed as 0.0093. The testing accuracy is above 93.3%, and the standard deviation was computed as 0.0056. It can be seen from Table 6 that the training loss is small for 20 tested learning rates. The average training time is about one thousand seconds. In summary, the presented method has a good performance for a large span of learning rate. This result once again verifies the effectiveness and robustness of the presented method for gear pitting fault diagnosis. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Working Condition** & **Training** & **Validation** & **Testing** & **Training** & **Training** \\
**Accuracy** & **Accuracy** & **Accuracy** & **Loss** & **Time (s)** \\ \hline
1000 RPM \_50N & 1.0000 & 0.99333 & 0.98857 & 0.00015 & 612.25 \\
1000 RPM \_100N & 1.0000 & 0.97333 & 0.98286 & 0.00014 & 1033.06 \\
1000 RPM \_200N & 1.0000 & 0.94762 & 0.95429 & 0.00014 & 1017.29 \\
1000 RPM \_300N & 1.0000 & 0.98095 & 0.98286 & 0.00009 & 903.42 \\
1000 RPM \_400N & 1.0000 & 0.93333 & 0.94857 & 0.00018 & 730.88 \\
1000 RPM \_500N & 1.0000 & 0.96571 & 0.96857 & 0.00016 & 732.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The gear pitting fault diagnosis results obtained by the proposed method at a constant speed of 1000 rpm with different loads. The confusion matrix of the obtained results is provided in Figure 9. As can be seen from Figure 9, the classification accuracy is 100% except for Condition 2 and Condition 6. 3 cases of Condition 2 were incorrectly diagnosed as Condition 6. Coincidentally, 3 cases of Condition 6 were incorrectly diagnosed: two as Condition 2 and one as Condition 7. The proposed method is accurate in classifying the gear pitting faults. To show the effectiveness of the concatenated features obtained by CNN to extract features from AE signals and GRU network to extract features from vibration signals, samples for t-SNE visualization were processed. The 3D result of the t-SNE visualization is shown in Figure 10. The 2D result of the t-SNE visualization is shown in Figure 11. It can be seen from the two figures that the concatenated features of the seven gear pitting conditions were accurately clustered. The clear clusters formed by the concatenated features obtained by the proposed method shown in 3D and 2D pictures indicate the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Learning** & **Training** & **Validation** & **Testing** & **Training** & **Training** \\
**Rate** & **Accuracy** & **Accuracy** & **Accuracy** & **Loss** & **Time (s)** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 6: The gear pitting fault diagnosis results under different learning rates. Figure 9: The confusion matrix by the presented method for the testing set. effectiveness of the proposed method for extracting features from the AE and vibration signals for gear pitting fault diagnosis. Future research will include extending the developed method into fault diagnosis of other rotating components such as bearings involving multiple heterogeneous sensor signals such as motor current, torque, strain gauge, vibration, and AE signals. The future research will also include investigation of the influence of noise and other external environmental conditions on the sensor signals and consequently to their method of effective measurement. Testing with a much larger set of samples should be investigated in the future research.