围绕复杂结构一体化优化与概率设计的工程背景，借鉴矩阵的基本思想，提出工程系统多目标优化与可靠性设计的矢量代理模型方法，解决设计参数和目标之间的耦合相关性和同步性带来的设计精度和效率问题，并从数学和工程角度分别研究向量函数逼近分析和工程系统优化与可靠性设计。主要研究内容包括：复杂向量函数逼近的矢量代理模型方法研究；基于矢量代理模型的工程系统多目标优化设计方法研究；基于矢量代理模型的工程系统多目标可靠性设计方法研究；基于多级矢量代理模型的工程系统多层次多目标可靠性设计方法研究。并以向量函数逼近分析、发动机热端部件与叶尖间隙优化与概率设计为例，加以验证。本项目为实现工程系统多目标优化和可靠性设计这一类工程问题，提供有效方法与手段。研究成果在丰富和发展概率理论和系统可靠性理论方面具有重要的学术意义,在航空、航天、航海、工业、土建等工程领域多目标/一体化设计中也具有现实的应用前景。

Around the realistic engineering background of integrated optimization and probabilistic design of complex structures, this project develops vector surrogate modeling methodologies of Engineering system multi-object optimization and reliability design by assimilating the basic thought of matric, the purposes of which are to address the precision and efficiency issues of coupling and correlation among design parameters and design objects as well as the synchronism of design process. Meanwhile, both the approximation analysis of vector function and the optimization and reliability design of engineering systems are deeply studied from mathematical and engineering perspectives. The main research contents comprise the vector surrogate model methodologies of complex vector functions as well as engineering system multi-object vector optimization design and reliability design methodologies and multi-layer multi-object reliability design based on vector surrogate models. The developed methodologies and models are validated by the approximation analyses of vector functions and the multi-object optimization and probabilistic designs of aeroengine hot-end components and turbine blade-tip clearance. This project will provide an all-purpose methodology and technique for carrying out the multi-object optimization and reliability design of engineering systems. This project has important academic significations in developing and enriching probability theory and system reliability theory, as well as realistic application perspectives for multi-object/ Integrated designs in many engineering fields such as aerospace, navigation, industry, civil, and so forth.