# Improved Hierarchical Adaptive Deep Belief Network for Bearing Fault Diagnosis
## 4 Experimental Analysis
### Experimental Validation  
Tables 4-7 show the testing results of the hierarchical fault diagnosis model. Table 4 presents the fault-type identified results. According to Table 4, model 1 can accurately identify the bearing fault type. The average test accuracy of the 10 experiments was 99.95%. Figure 8 shows the specific fault-type identification results of experiments 2 and 6. In experiment 2, a roller fault sample was misclassified as an inner fault. Experiment 6 exhibited the same result. Tables 5-7 show the fault-degree identification results in outer race, roller, and inner race, respectively.  
Tables 8 and 9 list the comparisons among three methods. It can be seen that the proposed approach achieved better performance. The generalizability of the DBN model has been improved, to guarantee the convergence speed effectively and achieve an optimal point, thereby achieving increased precision. As illustrated in Table 9, the raised approach also obtained outstanding results.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Experiment** \\ **Number** \\ \end{tabular} } & \multicolumn{4}{c}{**Fault Degree Recognition (mm)**} \\ \cline{2-5}  & **0.2** & **0.3** & **0.4** & **0.5** & **Average** \\ \hline
1 & 100\% & 100\% & 100\% & 100\% & 100  
Taking the fault type identification as an example, Figure 10 depicts the errors' trends of training and testing models in the global fine-tuning iterations and shows satisfactory convergence trends. Figure 11 shows the training and testing accuracy trends of fault type recognition in the global fine-tuning iterations. It can be clearly seen that the proposed method can achieve faster convergence and higher accuracy, compared with standard DBN. Similarly, Figure 12 generally exhibits desirable accuracy improvements of the proposed method for roller fault degree recognition.  
Principal component analysis (PCA) is a typical method for dimensionality reduction and has been widely used in fields such as data noise cancellation and data compression to eliminate redundancy. As shown in Figures 13-16, PCA was used to visualize features obtained by the proposed method. The clustering performance of the original signal was not good, and the characteristics of each fault type were mixed and difficult to distinguish. The reason for these improvements may be that the proposed adaptive DBN based on the NM method has stronger classification ability than the traditional SVM shallow layer network, thereby effectively realizing bearing fault diagnosis. The independent adaptive learning rate can effectively optimize the generalizability of the DBN and ensure the representativeness of the deep features of the extracted data. Generally, the hierarchical fault diagnosis network gets desirable outcomes and performs better than traditional methods.  
Figure 11: Accuracies’ trends of (**a**) training and (**b**) testing models for identifying fault type.  
Figure 12: Accuracy trends of (**a**) training and (**b**) testing models for roller fault degree recognition.  
Figure 13: Feature visualization of signals under various fault types: (**a**) raw data features and (**b**) proposed method.