# Detection of Fitting in Gears Using a Deep Sparse Autoencoder
## 4 The Validation Results

Table 6: Detection results at mixed rotating speeds (trained with light loading samples and tested with heavy loading samples). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Gear Conditions** & **Training Accuracy (500 Nm)** & **Testing Accuracy (100 Nm)** \\ \hline Healthy & 99.45\% & 99.94\% \\ Pitting gear & 99.58\% & 99.84\% \\ Over all & 99.52\% & 99.89\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Detection results at mixed rotating speeds (trained with heavy loading samples and tested with light loading samples). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Gear Conditions**} & \multicolumn{2}{c}{**Training Accuracy (100 Nm)**} & \multicolumn{2}{c}{**Testing Accuracy (500 Nm)**} \\ \cline{2-5}  & **Without Supervised** & **With Supervised** & **Without Supervised** & **With Supervised** \\
**Fine-Tuning** & **Fine-Tuning** & **Fine-Tuning** & **Fine-Tuning** \\ \hline Healthy gear & 85.25\% & 90.50\% & 83.42\% & 89.85\% \\ Pitting gear & 85.85\% & 89.95\% & 81.15\% & 88.24\% \\ Overall accuracy & 85.55\% & 90.23\% & 82.29\% & 89.05\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Detection results of DNN at mixed rotating speeds (trained with light loading samples and tested with heavy loading samples). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Gear Conditions**} & \multicolumn{2}{c}{**Training Accuracy (100 Nm)**} & \multicolumn{2}{c}{**Testing Accuracy (500 Nm)**} \\ \cline{2-5}  & **Without Supervised** & **With Supervised** & **Without Supervised** & **With Supervised** \\
**Fine-Tuning** & **Fine-Tuning** & **Fine-Tuning** & **Fine-Tuning** & **Fine-Tuning** \\ \hline Healthy gear & 82.18\% & 90.25\% & 84.25\% & 91.50\% \\ Pitting gear & 84.15\% & 88.85\% & 85.17\% & 91.50\% \\ Overall accuracy & 83.17\% & 89.55\% & 84.71\% & 91.50\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Detection results of DNN at mixed rotating speeds (trained with heavy loading samples and tested with light loading samples). In comparing the results obtained by the DNN in Tables 8 and 9 with those obtained by the deep sparse autoencoder, one can see that the deep sparse autoencoder gives a better performance than the DNN based approach for gear pitting fault detection. In both cases, the detection accuracies obtained by the DNN are much lower than those of the deep sparse autoencoder. In comparison with the DNN, the presented method is more robust in automatically extracting the adaptive features for gear pitting detection. In addition, the presented method does not require the supervised fine-tuning process. Such advantage will increase the computational efficiency and enhance the robustness of the gear pitting fault detection in dealing with massive data. To verify the ability of the presented method for automatically adaptive features extraction, using a similar approach in [33], the principal component analysis (PCA) was employed to visualize the extracted features. The values of neurons in the last hidden layer were regarded as pitting fault features since they were used for pitting detection in the output layer. Therefore, 50 features were obtained by the deep sparse autoencoders. The first two principle components were used for the visualization since they carried out more than 90% information in the feature domain. Since pitting gear detection results at rotating speed of 1000 rpm is slightly more accurate than that at 100 rpm, only features obtained using signals at 100 rpm were plotted for observation. The scatter plot of principle components of the features automatically extracted from datasets A, B, E and F are presented in Figure 10.  
It can be observed from Figure 10 that the features of the same health condition are grouped in the corresponding clusters which are clearly separated from each other. In comparison with Figure 10a,c, Figure 10b,d show a better clustering performance and more clear separation boundary between the healthy and pitting gear conditions.