# Reliability Modeling and Analysis of Multi-Degradation of Momentum Wheel Based on Copula Function
## 6 Conclusions  
In this paper, the reliability of the momentum wheel is studied using the degenerate modeling based on the wiener stochastic process. The main factors affecting the reliability of the momentum wheel are analyzed and the momentum wheel degeneracy model with single degradation and multiple degradation is established. Compared with the existing methods, the main innovation of this paper is its proposition of a momentum wheel degradation model based on the multi-degenerate variables of the Wiener stochastic process. When the correlation between the two degradation quantities is unknown, the Copula function is used to fuse the two. The edge distribution gives a joint distribution of momentum wheel reliability. The results show that the edge distribution of lubricants and currents is obtained through the Wiener random process degradation modeling method, and then the Copula function is used to calculate the joint distribution. The resulting momentum wheel degradation model is consistent with practical engineering experience. It would be a good reference for the reliability calculation of equipment with multiple degeneracy and unknown correlation between variables.  
Due to the lack of momentum wheel degradation data under the same working conditions of the same model, an empirical study of the prediction method cannot be completed yet. In the process of single degradation modeling, the common degenerative process of the Wiener stochastic process is used to construct the degradation trajectory function of the two residuals of lubricant residual quantity and current. However, in practical applications, there are other factors that have a significant impact on the life of the momentum wheel. For example, we would further study how to use the modeling and analysis of the performance degradation process when considering the impact of environmental, use, and manufacturing factors on the life and reliability of moving parts (for example, analysis of the cyclical rise mechanism of bearing temperature). In addition, further theoretical and experimental research is needed.  
In summary, this research provides a new idea for the reliability modeling and analysis of the momentum wheel, and the proposed method can be further applied in complex electromechanical coupling systems with a high reliability, long life and monitorable degradation data.  
Conceptualization, Y.-F.L.; methodology, H.-Z.H.; investigation, M.H.; resources, Y.C.; writing--original draft preparation, S.B. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Project of Science and Technology on Reliability Physics and Application Technology of Electronic Component Laboratory under grant number 61428060305.  
Figure 4: Comparison between Couple-based reliability function and independent reliability function.  
**Acknowledgments:** Special thanks to [PERSON] (University of Electronic Science and Technology of China) for his instructive advice and useful suggestions on the thesis and methodology.  
**Conflicts of Interest:** The authors declare no conflict of interest.