## 4 Experiment Study
### Results and Discussion for RUL Prediction
#### 4.3.2 Results and Discussion of Cross-Working Condition RUL Prediction  
After the initial degradation detection, we can obviously see that there are certain differences in the number of degradation samples among different bearings. This is because  
Figure 5: Reconstruction ability comparison based on DACAEN and DCAE for Bearing 1-1. (**a**) The first degenerated sample. (**b**) The eighth degenerated sample. Figure 6: Comparison with popular HIs for Bearing 1-1. (**a**) Different HIs. (**b**) Partial enlarged view of (**a**). they have undergone different degradation processes. In order to achieve high-precision life prediction results, the degenerate samples with a similar total number are grouped into one class. In combination with the working conditions (three working conditions), three migration conditions were constructed, with one working condition as the source domain and the remaining two as the target domain, namely: working condition 1\(\rightarrow\)2 and 3, working condition 2\(\rightarrow\)1 and 3, and working condition 3\(\rightarrow\)1 and 2. For the remaining bearings, Bearing 2-2 is selected as the source domain, and Bearing 1-1 is regarded as the test domain. Table 5 lists the specific test and RUL prediction tasks. The prediction tasks are set as follows. (1) Evaluation Indicators for Prediction Results  
This paper is concerned with the mapping between signal features and RUL labels. The method is considered as a regression problem. Therefore, this paper uses three metrics for performance evaluation, namely mean absolute error (MAE), root mean squared error (RMSE), and Score [29]. It has been shown that the higher the score function score in the indicator, the better the model's prediction. The smaller the MAE and RMSE, the better the model's prediction. (2) Results and Discussion  
According to the cross-working condition RUL prediction tasks, the trained JTMN network is used to infer the RUL of the test sample. The prediction results for all the RUL prediction tasks are shown in Figures 7-9. Figure 10: RUL prediction results under the 1\(\rightarrow\)2 and 3 transfer condition. Figure 9: RUL prediction results under the 3\(\rightarrow\)1 and 2 transfer condition. It can be seen from the figures that the quantitative results of cross-working RUL prediction using JTMN are stable and better than the baseline, which once again proves the superiority of the proposed method. Figure 13 shows the RUL prediction results of Bearing 1-1. Although this prediction method is not a cross-working condition RUL prediction, it is further proved from the RUL curve and the MAE, RMSE, and Score that the proposed method can significantly reduce the distribution difference to enhance the prediction performance compared to the baseline method. Figure 11: RUL prediction results under the 2\(\rightarrow\)1 and 3 transfer condition. Figure 12: RUL prediction results under the 3\(\rightarrow\)1 and 2 transfer condition. Figure 13: RUL prediction results using the proposed method and baseline under the 2\(\rightarrow\)1 transfer condition. (**a**) RUL prediction results for Bearing 1-1. (**b**) MAE, RMSE, and Score for Bearing 1-1. Comparison experiment and ablation study  
The JTMN framework proposed in this paper is mainly the addition of joint domain adaptation loss, called VDR-RSD, which combines the representation ability of the distribution discrepancy of VDR and the representation ability of the feature manifold distribution of RSD to effectively enhance the model's learning of cross-domain invariant features, further enhancing cross-working condition RUL prediction performance. In order to explore the mechanisms of these losses in domain adaptive learning, the following ablation experimental studies were conducted to investigate their respective roles by gradually adding mechanisms. First, the prediction method of traditional distance measurement MMD is added based on the deep learning prediction model as the baseline.