# Reliability Modeling and Analysis of Multi-Degradation of Momentum Wheel Based on Copula Function
###### Abstract  
The momentum wheel is a key component of the satellite attitude control system and has a direct impact on the reliability and overall life of the satellite. The momentum wheel has the characteristics of a high reliability, long life, and complex failure mechanics, which leads to expensive maintenance and a low reliability of the test sample. Therefore, it is challenge to implement an accelerated life test. The traditional life data statistical method has great difficulty in solving the reliability analysis of the momentum wheel. A reliability calculation method based on copula function for multi-degradation is proposed. Firstly, the key factors affecting the reliability of the momentum wheel are analyzed, and the lubricant residual quantity and current are selected as the degradation quantity. Secondly, the wiener process is used to model the degradation of a single degradation quantity, and the edge distribution function of the momentum wheel reliability is obtained. Considering that the correlation between multiple degradation quantities has a non-negligible influence on the reliability analysis result, the copula function is introduced to describe the correlation, and the edge distributions are fused to obtain the joint distribution function of the momentum wheel reliability. reliability; degradation; copula function; wiener process; momentum wheel +
Footnote †: journal: Medical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China; [EMAIL_ADDRESS] (Y.-F.L. ); [EMAIL_ADDRESS] (M.H. ); [EMAIL_ADDRESS] (S.B.) Footnote †: journal: Medical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China; [EMAIL_ADDRESS] (Y.-F.L  
prediction method [7]. Existing research shows that in satellite attitude control systems, momentum wheel failure is related to many factors [8]. Seasonal changes in the external environment, bearing temperature, failure of the lubricant system, micro-vibration, current, speed, and other factors may affect the life of the momentum wheel [9]. The existing data-based residual life prediction methods mostly consider only the effect of a single degradation amount on the remaining life. In reality, the life of the momentum wheel is influenced by multiple factors. For example, [10] studied the physical properties of lubricant failure, established a lubricant wear model to predict the life of the JB-3 momentum wheel bearing assembly and [11] took the momentum wheel bearing temperature as the life characteristic of the momentum wheel and used it. Empirical mode decomposition extracts time trends, establishes the degradation model of momentum wheel, and performs on-orbit momentum wheel life prediction; [12] uses the RVM-PF-based prediction method and takas momentum wheel bearing temperature and other indicators as life cycle characteristics of momentum wheel, completing the establishment of the momentum wheel degradation model and its life prediction; [13] analyzed the data of a model of five momentum wheel bearing temperature data, its shaft temperature performance degradation trend modeling, used to predict the momentum wheel remaining life. Moreover, [14] pointed out that the key to the failure of the momentum wheel is the remaining oil quantity of the oil supply system. The failure mechanism of the momentum wheel lubrication is studied to obtain the life reliability curve of the satellite momentum wheel. In addition, [15] studies the momentum wheel shaft. As a result of the test data, it was found that the slow rising trend of the current data was caused by the increase in bearing friction. A time series model of momentum wheel currents was established. Based on its performance degradation characteristics, momentum wheel life prediction curves were deduced. Ref. [16] was based on two similar models of momentum wheel product data, assuming that their lifetimes obey Weibull distribution, and the Weibull distribution was estimated.