基于vine copula多状态相依系统可靠性分析

多状态系统相依建模是系统可靠性评估研究的重要课题，现有研究大多应用多元copula函数研究具有相同相依关系的系统，不适用于具有差异性的复杂相依多状态系统可靠性建模。鉴于此，本项目借助比多元copula模型更为灵活、高效的vine copula函数研究多状态相依系统可靠性评估问题。首先从vine copula系统相依建模出发，以数理统计方法和可靠性理论为支撑，结合数值模拟研究系统可靠性评估方法；其次，基于vine copula和贝叶斯网络的概率图模型性质建立pair-copula贝叶斯网络系统可靠性模型，研究系统状态转移的规律和相依性对可靠性评估的影响；最后，利用统计模型选择准则、条件独立性检验以及vine copula结构简化方法简化系统可靠性模型，降低模型复杂度，实现高效估计模型参数和可靠性特征的目的。本项目研究将为多状态相依系统可靠性分析提供有效的解决方法。

Dependence modeling for multi-state system is an important topic in system reliability evaluation. In the literature, most of them focus on the system with the same dependence structure using a multivariate copula function, which is not suitable for a complex dependent multi-state system in the presence of different dependence features. Therefore, comparing with the multivariate copula, this project starts modeling with a more flexible and efficient vine copula based system dependence model. Supported by mathematical statistical methods and reliability theory, we combine the numerical simulation study to investigate the approaches of system reliability evaluation. Then we introduce a pair-copula Bayesian network system reliability model considering the features of probabilistic graph models between vine copula and Bayesian network, and explore the transition law of system states and the dependence influence on reliability evaluation. Finally, a simplified system reliability model is proposed based on the statistical model selection criteria, the conditional independence tests and the vine copula structure reduction methods so that the complexity of the model can be reduced and the model parameters and reliability characteristics are efficiently estimated. The research of this project will provide an efficient method for the reliability analysis of multi-state dependent system.