# Detection of Fitting in Gears Using a Deep Sparse Autoencoder
## 4 The Validation Results  
The proposed deep sparse autoencoder structure was implemented to accomplish the greedy deep dictionary learning. The vibration signals along the \(z\) vertical direction were used in this study since they contain the richest vibration information among the three monitored directions. At first, the gear pitting detection was carried on using signals with light loading as the training data and signals with heavy loadings as the testing data, respectively. Loadings of 100 Nm torque and 500 Nm torque were used as light loading condition and heavy loading condition, respectively. Signals at rotating speeds of 100, 200, 500 and 1000 rpm were used for validation tests. To study the influence of different rotating speeds on the pitting gear fault detection performance of the deep sparse autoencoder, 100 and 1000 rpm were selected as low and high speed for independent validations. The length of the samples was decided to ensure that at least one revolution of the output driven gear was included. Therefore, there were 23,000 data points in each sample for signals at 100 rpm and 15,000 data points for signals at a speed of at least 200 rpm. Thus, 26 samples of signals at 100 rpm were generated for healthy gear and pitting gear, respectively. Hence, there were 52 samples in the training dataset and 52 samples in the testing dataset. Similarly, 40 samples of signals at 1000 rpm were generated for each gear condition, with 80 samples in the training dataset and 80 samples in the testing dataset. The structure of the deep sparse autoencoder was designed separately for signals at 100 rpm and signals at the speed of over 100 rpm as: one input layer (23,000 neurons for signals at 100 rpm and 15,000 neurons for signals at the speed over 100 rpm), four hidden layers (1000-500-200-50 neurons), and one output layer (2 neurons). Particularly, following the suggestions in [31], the sparsity parameter in each sparse autoencoder was set as \(\beta=3\) and \(\rho=0.005\). The sparse representations of the original signals were imported into  
Figure 9: The waveforms of raw vibration data for normal and pitting gear at various rotating speeds under loading conditions of 100 Nm and 500 Nm. (**a**)waveforms of healthy signals with 100 Nm; (**b**) waveforms of healthy signals with 500 Nm; (**c**) waveforms of faulty signals with 100 Nm; (**d**) waveforms of faulty signals with 500 Nm. classifier for pitting gear fault detection. The last hidden layers of 50 neurons and the output layer of 2 neurons were constructed as a simple backpropagation neural network as a classifier for gear pitting detection. The two neurons in the output layer were setup for classifying the input signals as either gear pitting fault or normal gear. The training parameters of the back propagation neural network classifier were set as: training epoch was 100, learning rate was 0.05 and the momentum was 0.05. For each gear condition, the models were executed 5 times to get average detection accuracy. The detection results are shown in Table 3.  
The detection results in Table 3 show a good adaptive learning performance of the presented method. The testing accuracy is high as 98.88% overall, which is slightly lower than the training accuracy. It can be explained as that signals at light loading condition contain less fault significant information. Furthermore, the same designed deep sparse autoencoder structure was experimented with heavy loading training data and light loading testing data. The detection results are shown in Table 4.  
It can be observed from Table 4 that in comparison with results shown in Table 3, the testing accuracy is slightly higher than the training accuracy. The better adaptive feature extraction and fault detection results are benefited from that the signals with heavy loading condition contain more fault significant information. The results in Tables 3 and 4 show marginal influence of the rotating shaft speeds on the pitting fault detection performance.