## 5 Conclusions  
This paper proposes an RUL prediction framework of rolling bearing based on multi-domain mixed features and improved TCN. To better extract the key features, a signal noise reduction method based on DBOVMD adaptively determines the optimal parameter combinations of VMD to reduce the signal noise, and ISOMAP is used to reduce the dimension of multi-domain mixed features. KFCM is used to determine the FPT of early degradation time points to mark the label of data. TCNMABG can predict the bearing RUL better, with an average reduction of 40.72% in the MSE value of the bearing RUL prediction error based on the XJTU-SY dataset and an average reduction of 65.96% in the MSE value of the bearing RUL prediction error based on the FEMTO-ST dataset.  
The method proposed in this paper offers novel suggestions and ideas for researchers in the field of remaining useful life prediction. However, further improvements are required to enhance the model complexity. In future studies: (1) A feature extraction method for multi-modal data fusion can be designed by integrating information from various sensors and data sources, such as vibration, temperature, sound, and other signals. This will enhance the overall perception of the deteriorating state of rolling bearing. (2) By incorporating embedded transfer learning and domain adaptive methods, valuable degradation features can be accurately extracted under different working conditions and environments. (3) Research on the uncertainty of remaining useful life prediction models to improve the reliability and interpretability of prediction results.  
Conceptualization, F.Z. and X.C.; methodology, F.Z.; software, F.Z.; validation, J.Z., Y.D. and X.G.; formal analysis, F.Z.; investigation, F.Z.; resources, Y.D.; data curation, F.Z.; writing--original draft preparation, F.Z.; writing--review and editing, F.Z. and J.Z.; visualization, F.Z. and J.Z.; supervision, J.Z.; project administration, X.C.; funding acquisition, X.C. All authors have read and agreed to the published version of the manuscript.  
Figure 16: Comparison of RUL prediction results for bearings1_4 on the PHM dataset test set.  
**Funding:** The research was supported by the National Natural Science Foundation of China, grant numbers \"51834006\", \"51875451\" and \"52274158\", the China Postdoctoral Science Foundation, grant numbers \"2022 MD713793\" and the Outstanding Youth Science Fund of Xi'an University of Science and Technology under grant number \"22002\".  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The experimental data are vibration acceleration data collected from the accelerated life bench test of rolling bearing, which comes from the PHM data challenge held by the Institute of Electrical and Electronics Engineers (IEEE) in 2012. In addition, the data used to support this study are available at [[https://bioowang.tech/xjtu-sy-bearing-datasets/](https://bioowang.tech/xjtu-sy-bearing-datasets/)]([https://bioowang.tech/xjtu-sy-bearing-datasets/](https://bioowang.tech/xjtu-sy-bearing-datasets/)) (accessed on 10 January 2024).  
**Acknowledgments:** The authors would like to acknowledge the National Natural Science Foundation of China (Grant No. 51834006, 51875451 and 52274158).  
**Conflicts of Interest:** The authors declare no conflicts of interest.