## 5 Implementation and Results
### Comparison between DCNN and Ada-DCNN  
First, the DCNNs corresponding to the three types of samples in Figure 7 are built and denoted as FD-Net, TFD-Net, and ThD-Net, respectively. As an example, the final structure and parameters of the FD-Net is illustrated in Figure 8. Each network is iteratively tuned to specify the structure and hyperparameters such as layer and channel numbers, kernel sizes, and so on. Once the training of DCNNs is completed, the activations of the last FC layer are extracted for the training of the AdaBoost tree-based ensemble classifier. The accuracy of DCNNs is used as an indicator of the feature extraction performance. To compare the diagnosis performance of a DCNN and corresponding Ada-DCNN, four accuracy levels (S1-S4) are achieved for each DCNNs in the validation process.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Wa** & **C** & **I** & **L** & **S** & **K** \\ \hline RMS/Mean & P\_P/RMS & P\_P/Mean & P\_P/R & m3/\(m_{2}^{3/2}\) & m\({}_{4}\)/\(m_{2}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: The basic dimensional statistics.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Types** & **IR** & **OR** & **RE** & **NC** & **Total** \\ \hline numbers of sample & 944 & 708 & 944 & 236 & 2832 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Sample numbers of faulty and normal conditions.  
Figure 7: Three types of image samples corresponding to: (**a**) Frequency domain, size \(128\times 62\) (FD); (**b**) time-frequency domain (TFD), size \(256\times 256\); and (**c**) three-domains (ThD), size \(256\times 265\).  
The fault diagnosis performance of a DCNN and corresponding Ada-DCNN are compared under four accuracy levels as in Table 6, and the accuracy of DCNNs, as well as the improvements by Ada-DCNNs in four levels, are shown in Figure 9a.  
The results indicate that the diagnosis accuracy of Ada-DCNN is obviously higher than the related DCNN in all accuracy levels. Figure 9b shows the difference of accuracy between the DCNNs and related Ada-DCNNs. It can be seen that the improvement declines with the growing of DCNN accuracy from S1 to S4 for the three networks, which is not difficult to understand as the accuracy increases more slowly when it approaches the ceiling (100%). A further calculation shows that the average accuracy of DCNNs from S1 to S4 is improved by an absolute value of 15.37%, 12.29%, 10.40%, and 5.14%, respectively.  
The training details of the DCNNs and classification results of the Ada-DCNNs are not provided due to the limitation of space. As an example, we only give the training and validation processes of FD-Net and the fusion matrix of the corresponding Ada-DCNN in the accuracy level S1 as in Figure 10.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Accuracy** & \multicolumn{2}{c}{**TFD-Net**} & \multicolumn{2}{c}{**ThD-Net**} & \multicolumn{2}{c}{**FD-Net**} \\ \cline{2-7}
**Level** & **DCNN** & **Ada-DCNN** & **DCNN** & **Ada-DCNN** & **DCNN** & **Ada-DCNN** \\ \hline S1 (\%) & 55.85 & 65.78 & 54.43 & 65.96 & 53.01 & 77.66 \\ S2 (\%) & 65.43 & 76.24 & 62.94 & 72.52 & 67.02 & 83.51 \\ S3 (\%) & 75.89 & 84.22 & 79.79 & 91.67 & 79.26 & 90.25 \\ S4 (\%) & 82.09 & 89.18 & 86.52 & 92.20 & 85.64 & 88.30 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison between the performance of DCNNs and corresponding Ada-DCNNs under four accuracy levels.  
Figure 8: The final structure and related parameters of FD-Net.  
Figure 9: Comparison between DCNNs and Ada-DCNNs in 4 accuracy levels: (**a**) Accuracy of DCNNs as well as the increment by Ada-DCNN in 4 accuracy levels; (**b**) Difference of accuracy between DCNNs and related Ada-DCNNs in 4 accuracy levels.