# Bearing Fault Diagnosis Based on Improved Convolutional Deep Belief Network
## 3 Experimental Validation
### Diagnosis Results and Comparative Analysis
#### 3.2.2 Comparison with Standard CDBN  
The test results of the standard CDBN are illustrated in Figure 11a,c. The figure shows that the improved CDBN was able to achieve higher accuracy than the standard CDBN, especially in outer-race faults and ball faults. However, for IO fault types, namely, label 12, the classification accuracies of both models had no obvious optimization because of the difficulty in catching distinguishable features. In general, the proposed improved CDBN model had better performance compared with the standard CDBN model. Figure 12 reveals the comparison of the second-layer reconstruction error between the standard and the improved CDBN models. Take dataset1 for example. During training, the reconstruction errors of both models decreased smoothly with the increase of the training batch, whereas the improved model had a much smaller reconstruction error. The same phenomenon occurred in the reconstruction error of the first layer of the two models, and the training accuracy rate increased slightly with the increase of epoch. The difference between final training accuracy and test accuracy was about 2%, which is not much different. A commonly used method for high-dimensional data analysis is t-distribution stochastic neighbor embedding (tSNE). tSNE can reduce any dimension to less than three at will. As shown in Figure 13, \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**ModelLabel**} & \multirow{2}{*}{**1**} & \multirow{2}{*}{**2**} & \multirow{2}{*}{**3**} & \multirow{2}{*}{**4**} & \multirow{2}{*}{**5**} & \multirow{2}{*}{**6**} & \multirow{2}{*}{**7**} & \multirow{2}{*}{**8**} & \multirow{2}{*}{**9**} & \multirow{2}{*}{**10**} & \multirow{2}{*}{**11**} & \multirow{2}{*}{**12**} & \multirow{2}{*}{**13**} & \multicolumn{2}{c}{**Average**} \\  & & & & & & & & & & & & & & & & & & & \\ \hline SAE & 100 & 100 & 100 & 100 & 95 & 99 & 40 & 100 & 0 & 100 & 100 & 100 & 100 & 87.23 \\ ANN & 90 & 74 & 79 & 38 & 0 & 50 & 100 & 98 & 100 & 20 & 100 & 0 & 100 & 65.31 \\ DBN & 0 & 96 & 95 & 90 & 96 & 89 & 43 & 91 & 71 & 94 & 77 & 85 & 100 & 79.00 \\ Proposed model & 98 & 100 & 100 & 100 & 73 & 99 & 90 & 100 & 100 & 100 & 94 & 86 & 100 & 96.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of testing results of dataset2 under load 1 kN by different models. Figure 12: Comparison of second-layer reconstruction error when training (**a**) standard CDBN and (**b**) improved CDBN. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**ModelLabel**} & \multirow{2}{*}{**1**} & \multirow{2}{*}{**2**} & \multirow{2}{*}{**3**} & \multirow{2}{*}{**4**} & \multirow{2}{*}{**5**} & \multirow{2}{*}{**6**} & \multirow{2}{*}{**7**} & \multirow{2}{*}{**8**} & \multirow{2}{*}{**9**} & \multirow{2}{*}{**10**} & \multirow{2}{*}{**11**} & \multirow{2}{*}{**12**} & \multirow{2}{*}{**13**} & \multicolumn{2}{c}{**Average**} \\  & & & & & & & & & & & & & & & & & & & \\ \hline SAE & 100 & 83 & 33 & 0 & 20 & 82 & 100 & 8 & 100 & 100 & 100 & 100 & 100 & 100 & 71.23 \\ ANN & 100 & 96 & 76 & 59 & 0 & 61 & 100 & 100 & 100 & 100 & 0 & 100 & 0 & 100 & 76.31 \\ DBN & 100 & 100 & 97 & 98 & 90 & 87 & 96 & 79 & 91 & 100 & 100 & 65 & 95 & 92.15 \\ Proposed model & 100 & 100 & 100 & 100 & 98 & 96 & 96 & 100 & 100 & 100 & 86 & 100 & 98.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of testing results of dataset1 under load 0 kN by different models. an intuitive feature distribution was obtained by using tSNE to visualize the features of the standard and improved CDBN. The results indicate the obvious optimization effect of the proposed method on feature processing. CDBN integrates convolution operation into origin DBN, which makes it have a stronger feature extraction capability. On the basis of the standard CDBN, a filter was introduced to filter out noise, so that the improved CDBN model has a more stable learning ability.