## 4 Case Studies
### Case Study 2: Insufficient Source Domain Label Transfer Experiment  
To highlight the effectiveness of the proposed networks in fault detection on small samples of labeled data, this experiment further expands the gap between the number of labeled and unlabeled data in the source domain. For the vibration signal data collected at the sampling frequency of 12 kHz, 1/2, 1/4, 1/8, and 1/16 of the source domain images are selected as labeled data, and the rest are unlabeled data. Moreover, the diagnostic tasks T\({}_{01}\), T\({}_{12}\), T\({}_{23}\), T\({}_{21}\), and T\({}_{31}\) are performed for experimental evaluations. In this case study, experiments were conducted to compare the proposed networks with three other commonly used transfer learning models, namely deep adaptation network (DAN), Deep CORAL, and DANN. The structure of the CNN feature extractor used for comparison is the same as that of the proposed networks, and each group of trials was performed 10 times and averaged. Figure 11: The precision, recall, and F1 score for T\({}_{01}\), T\({}_{12}\) and T\({}_{23}\). Figure 12: Confusion matrix of fault detection results. The diagnosis accuracies of the proposed method were compared with other popular transfer methods, the comparison results are shown in Table 5. From the comparison results, it can be seen that the network proposed in this experiment can still identify fault labels with an average accuracy of 98.32%, even though the number of labeled samples is only one in sixteen. Moreover, compared to the other transfer models, the accuracy fluctuation of the proposed model tends to be stable when the labeled proportion is changed. This illustrates the excellent robustness of the proposed method in extreme cases. On the other hand, the proposed networks produce higher detection accuracy than other diagnosis models, and are always higher than DANN. This is because the proposed model dynamically adjusts the proportion of marginal distribution and conditional distribution when extracting domain-invariant features, while DANN only considers the adaptation of marginal distribution. Figure 14 manifests that with the decrease in labeled data in source domain, the proposed model still maintains high accuracy, while other transfer learning methods exhibit the overfitting phenomenon. It also indicates that when the labeled data are insufficient, the proposed method can effectively alleviate the overfitting phenomenon, and provide high accuracy results. Additionally, transfer adversarial networks are proven to maximize the utilization of limited labeled data. To visually present the training results of different transfer models, taking the 1/16 experiment as an example, t-SNE dimensionality reduction processing was performed on the last hidden layer of DAN, Deep CORAL, DANN, and the proposed networks, respectively. The features were plotted into the 2D space, and the outcome of the visualization is shown as Figure 15.  
Figure 15 depicts that all four methods can separate the fault classifications from the original distribution, but the DAN network and the Deep CORAL network cannot completely overcome the difference in feature marginal distribution, and it is prone to the negative transfer phenomenon when there are few available labeled data. On the other  
Figure 13: The ROC curve of fault diagnosis result.