多退化变量下基于Copula函数的陀螺仪剩余寿命预测方法

针对惯性导航系统中陀螺仪多退化变量条件下的剩余寿命（RUL）预测问题，提出了一种基于Copula函数的多退化变量剩余寿命预测方法。首先，针对退化变量间不同的退化轨迹，采用不同的方法进行退化建模，并对于陀螺漂移系数样本标准差数据波动性随时间递增的特性，提出了一种方差时变的正态随机过程退化建模方法，得到了陀螺仪剩余寿命的边缘分布函数。然后，通过Copula函数来描述退化变量之间的相关性，将得到的剩余寿命的边缘分布进行融合，得到了陀螺仪剩余寿命的联合分布函数。最后，通过陀螺仪实例分析验证了方法的适用性和可行性。

Multiple Degradation Variables Modeling for Remaining Useful Life Estimation of Gyros Based on Copula Function

This paper proposes a model for the remaining useful life (RUL) estimation of gyros with multiple degradation variables based on the Copula function. Frist, because the different degradation variables may have different degradation paths, different models are adopted to obtain a marginal distribution of the RUL. And since the fluctuations of some degradation data increase over time, a normal stochastic process whose variance is the function of time is adopted for describing the degradation process. Then, a RUL joint distribution combining these marginal distributions is obtained based on the characteristics of the Copula function. Finally, the degradation data of gyro drift from a practical experiment are used to illustrate the feasibility and applicability of our model.