## 4 Case Studies
### Case Study 1: Variable Operating Conditions Transfer Experiment

Table 2: The CWRU dataset details for each operating condition. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Task** & **Source** & **Target** & **Labeled Proportion** \\ \hline T\({}_{01}\): 0\(\rightarrow\)1 & 1797 rpm & 1772 rpm & \(\frac{1}{2}\) \\ T\({}_{12}\): 1\(\rightarrow\)2 & 1772 rpm & 1750 rpm & \(\frac{1}{2}\) \\ T\({}_{23}\): 2\(\rightarrow\)3 & 1750 rpm & 1730 rpm & \(\frac{1}{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Partial details of fault diagnosis tasks in this case. Taking task T\({}_{31}\) as an example, the accuracy and loss curves of the model are shown in Figure 10. With the increase in training epochs, the accuracy of the fault label classifier was continuously improved, approaching 99% in 50 epochs and tended to be stable. Meanwhile, the testing loss gradually declined until it approached 0.0087 within about 40 epochs, then kept stable. From the result, it can be inferred that after sufficient training epochs, the proposed network can effectively extract domain-invariant features of vibration signals and accurately perform cross-domain detection, which indicates that the designed diagnosis network is reasonable. Next, the influence of the evaluation metrics was investigated. In addition to accuracy, precision, recall, and F1 score were selected to evaluate the validity of the fault detections. Three representative tasks, T\({}_{01}\), T\({}_{12}\), and T\({}_{23}\), were used as examples for analysis, and the results are shown in Figure 11. It can be observed that the overall evaluation metrics of the three tasks are above 99.2%, and T\({}_{01}\), T\({}_{23}\), and T\({}_{12}\) decrease sequentially. Specifically, precision, recall, and F1 score of each task were relatively stable and close to their corresponding precision. The satisfactory transfer performance between domains was achieved using the proposed networks, which demonstrates that the proposed networks are suitable for domain adaptation with high robustness. Furthermore, Figure 12 presents the fault diagnosis result of T\({}_{21}\) after ten repeated calculations by using the confusion matrix. The vertical axis of the confusion matrix denotes the true label, and the horizontal axis is the predicted label. From the figure, it can be seen that the average detection accuracy of the seven health states is 99.7%; the diagnosis performance is satisfactory. Specifically, IF-07, OF-07, BF-14, and NO all have 100% detection accuracy, which implies that they have not assigned the label to others, with BF-14 having received the wrong category from IF-14. BF-07 and OF-14 can accept the error misclassification of each other. BF-07 has the lowest accuracy rate of 98.8%, and more BF-07 elements are assigned to OF-14. The results indicated that even though half of training data lack health condition labels, the proposed approach can still achieve the precise diagnosis of seven health conditions in the target domain. Thus, the effectiveness of the proposed approach for domain adaptation detection is verified in the presence of insufficient labels. Furthermore, Figure 13 shows the ROC curve of the fault diagnosis result of task T\({}_{23}\). As can be seen from the figure, all the fault classification curves coincide, for except some deviation in the OF-14 curve, where the IF-07 and OF-07 curves overlap with the NO curve. This means that seven kinds of bearing fault classification can be perfectly diagnosed by using proposed networks, which also proves the validity of the proposed networks. Figure 10: Training accuracy and loss curves.