针对复杂机械结构参数个数的高维性、性能指标演化的时变性、随机变量间的统计相关性、函数关系的隐式性等特点，研究对系统输入输出关系进行相乘型展开与降维逼近的数学方法，提出复杂函数分数阶矩的高效计算方法，形成结构响应分布规律精确预测的理论方法。针对系统故障模式多且相关性耦合程度高的特点，研究统筹系统失效的顺序统计量建模方法，以及时变可靠性分析的寿命统计量建模方法，基于分数阶矩理论，获得顺序统计量与寿命统计量的概率分布，形成系统可靠性分析与动态失效率研究的理论方法。针对结构运行过程中性能指标逐渐发生演化的事实，研究系统响应方差的动态分解理论，建立参数全局性重要度判别的概率模型，探明结构性能退化的物理机理，在生命全周期的视角下，揭示随机因素对系统失效概率及其动态失效率的全局性影响规律，获取引发系统失效的重要参数、重要部件、关键故障模式与失效链，为复杂机械结构系统的安全可靠运行提供参考和建议。

High-dimensional modeling parameters, time-dependent performance functions, statistically dependent input variables, and implicit input-output relationship are primary characteristics of modern structural engineering systems encountered in reliability and global sensitivity analyses. Objective of the project will investigate: (a) mathematical method on multiplicative decomposition and approximation of high-dimensional models, (b) an effective approach for response probability distribution estimation, (c) computationally efficient reliability analysis of structural systems with a large number of failure modes as well as statistically dependent random variables, (d) modern numerical method to account for failure mechanisms of a system under deterioration. With the development of the proposed project, probability distribution of dimensionless order statistic that describes system failure will be determined. An effective methodology for time-variant system reliability analysis will be proposed. Time-dependent variance decomposition of degraded structural system will be developed to identify important failure mode, weak component and link from a life cycle perspective of the system. In summary, the project will provide effective approaches on uncertainty propagation and quantification of complex mechanical systems.