混合不确定性下基于Copula建模及高效代理模型的结构可靠性方法研究

复杂结构系统特定的物理结构和恶劣的工作环境导致结构失效模式的多样性、损伤机理的不确定性及损伤传播过程的高度非线性，目前在结构可靠性分析及优化设计和结构时变可靠性分析等方面有诸多亟待解决的难点问题。针对结构系统中变量和失效模式复杂非线性相关问题，研究混合不确定性下典型Copula、非对称Copula及混合Copula函数选择构造和基于Copula函数的相关性建模方法。针对结构失效模式、损伤机理的复杂性及基于有限元分析计算量较大的问题，研究混合不确定性下兼顾效率和精度的高效代理模型构建方法及基于高精度代理模型的结构可靠性分析与优化设计方法。鉴于结构的失效、性能退化及载荷等往往是随时间变化的过程，研究混合不确定性下基于高效代理模型的结构时变可靠性分析方法。研究成果将为混合不确定性下的结构可靠性分析与优化设计提供新理论和新方法，对于保障复杂结构系统的可靠性和安全性有重要的理论意义及工程应用价值。

The features of multiple failure modes, uncertain damage mechanism and highly non-linearity of damage mechanism propagation are caused by the specific physical structure and poor working conditions of complex structural systems. Nowadays, there are still many difficult problems that need to be solved for complex structural systems in the fields of structural reliability analysis and design optimization as well as time-dependent reliability analysis. Typical Copula and asymmetrical copula as well as mixed Copula functions under mixed uncertainties are studied to model the dependences for complex structural systems with the complicated correlation problems. Due to the complex of failure modes and damage mechanism of structural systems as well as the low computational efficiency using finite element analysis, the efficient methods for constructing an efficient and accurate surrogate model is presented, then reliability analysis and reliability-based design optimization under mixed uncertainties based on the constructed surrogate models are presented. Since structural failures, performance degradation and load conditions etc. are time-dependent processes, time-dependent reliability analysis for structural systems under mixed uncertainties based on the efficient surrogate models are presented. The novel techniques of structural reliability analysis and reliability-based design optimization under mixed uncertainties for structural systems will be provided, and the research results have important theoretical significance and application values to guarantee the reliability and safety of the complex structural systems.