## 5 Implementation and Results
### Robustness of the Hybrid Ada-DCNN  
Based on studies in Sections 5.1 and 5.2, the hybrid Ada-DCNN has been proved to have the best in fault diagnosis compared to Ada-DCNN and DCNN. In the construction of DCNNs, there are some situations where one or several DCNN(s) have difficulty achieving a satisfying accuracy (e.g., above 70%) for effective extraction of features. How much impact will it generate on the performance of hybrid Ada-DCNN in such situations?  
In this part, we investigate the robustness of the hybrid Ada-DCNN by dropping the accuracy of several DCNNs to a low level and estimate the corresponding performance of the hybrid Ada-DCNN. For this purpose, the best performance (97.70%) corresponding to [S4, S4, S4] in Table 7 is used as a reference, and three schemes are adopted, where one, two, and three DCNNs are chosen for dropping, respectively, to estimate the robustness of the hybrid Ada-DCNN.  
Table 8 presents the changes under each scheme and the corresponding accuracy, reduction part of the Hybrid Ada-DCNN, Ada-DCNNs, and DCNNs. Figure 12 shows more details of the reductions before and after dropping.  
According to the results, the accuracy reduction of hybrid Ada-DCNN increases with the average dropped amplitude of DCNNs increasing. However, the average reduction of hybrid Ada-DCNN is 1.83%, 4.31%, and 12.29% in absolute terms separately for schemes 1-3, which are much lower than those corresponding to 10.11%, 20.21%, and 26.75% of DCNNs, respectively. The accuracy of hybrid Ada-DCNN is declined within an absolute value of 5% when one and two DCNNs dropped. The largest reduction is 12.29%, which occurs when all the DCNNs dropped, which generally does not happen. Additionally, it is found in Figure 12d that the accuracy reduction of hybrid Ada-DCNN is  
Figure 11: The comparison of the hybrid Ada-DCNN, Ada-DCNN, and DCNN in 4 accuracy levels: (**a**) The accuracy of hybrid Ada-DCNN, Ada-DCNN, and DCNN; (**b**) The comparison of the hybrid Ada-DCNN, Ada-DCNN, and DCNN in 4 accuracy levels.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & **Scheme** & \multicolumn{3}{c}{**One DCNN Dropped**} & \multicolumn{3}{c}{**Two DCNNs Dropped**} & \multicolumn{3}{c}{**Three DCNNs Dropped**} \\ \hline \multirow{3}{*}{**Change**} & **TFD-Net** & / & / & S4\(\rightarrow\)S1 & / & S4\(\rightarrow\)S1 & S4\(\rightarrow\)S1 & S4\(\rightarrow\)S1 & S4\(\rightarrow\)S2 & S4\(\rightarrow\)S1 \\  & **ThD-Net** & / & S4\(\rightarrow\)S1 & / & S4\(\rightarrow\)S1 & / & S4\(\rightarrow\)S1 & S4\(\rightarrow\)S2 & S4\(\rightarrow\)S1 \\  & **FD-Net** & S4\(\rightarrow\)S1 & / & / & S4\(\rightarrow\)S1 & S4\(\rightarrow\)S1 & / & S4\(\rightarrow\)S2 & S4\(\rightarrow\)S1 & S4\(\rightarrow\)S1 \\ \hline
**Accuracy (\%)** & **Hybrid Ada-DCNN** & 97.34 & 93.62 & 96.63 & 91.31 & 95.21 & 93.62 & 88.48 & 84.22 & 83.51 \\ \hline \multirow{3}{*}{**Reduction**} & **Ada-CNN** & 10.87 & 10.70 & 8.75 & 21.57 & 19.62 & 19.44 & 25.65 & 27.48 & 27.13 \\  & **Average of DCNNs** & 0.00 & 0.89 & 0.00 & 4.43 & 0.00 & 0.89 & 19.50 & 23.58 & 21.10 \\ \cline{1-1}  & **Maximum of DCNNs** & 0.35 & 4.08 & 1.06 & 6.38 & 2.48 & 4.08 & 9.22 & 13.48 & 14.18 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Performance of the hybrid Ada-DCNN, Ada-DCNNs, and DCNNs under different schemes (“/” represents no change).  
closely correlated with the change of maximal accuracy of DCNNs, which validates the conclusion obtained in Section 5.2 again.  
The results above prove good robustness of the proposed hybrid fault diagnosis scheme.