混合不确定性下基于自适应代理模型的结构可靠性分析与优化设计方法研究

由于结构系统的复杂性、失效模式的耦合性和多样性、服役环境的恶劣性等因素，导致极限状态方程、约束条件和目标函数常为隐函数形式，其大量耗时的数值仿真分析在工程中难以承受。鉴于此，本项目分别研究混合不确定性下具有局部/全局精度的自适应代理模型构建方法，为高效结构可靠性分析与优化设计奠定基础；针对工程中的高维问题，研究降维技术与自适应代理模型的高效协同机制，建立混合不确定性下基于活跃子空间降维与自适应代理模型的高维可靠性分析方法；针对现有基于故障机理的可靠性方法与基于数据驱动的可靠性方法彼此独立的局限性，构建两者相联系的有机桥梁与高效融合机制，建立集成两者的统一可靠性分析方法；针对现有的结构可靠性优化设计方法对复杂工程问题效率低和鲁棒性差等不足，研究混合不确定下基于自适应代理模型的高效可靠性优化设计方法。研究成果为保障复杂系统的可靠性和安全性提供了新理论与新方法，具有重要的理论意义及工程应用价值。

The limit-state functions (performance functions) and constraint conditions as well as objective functions are often implicit functions due to many complex factors (e.g., the complex structure of systems, the various failure modes and their coupling effects, poor working conditions), then many time-consuming numerical simulations are unbearable in engineering applications. For the problems of limit-state functions and constraint conditions as well as objective functions are implicit functions, adaptive surrogate models with both local and global accuracies are respectively developed under mixed uncertainties, which provide the foundations for efficient reliability analysis and design optimization. For high dimensions in engeering, the efficient integrated mechanisms of both dimensionality reduction and adaptive surrogate models are researched, and an effective reliability analysis method based on active subspace and adaptive surrogate models is proposed. Since the physics of failure-based reliability methods and data driven based reliability methods are mutually independent, the bridge of these two different kinds of methods is established, and a unified reliability analysis method for both is proposed. Since the existing reliability-based design optimization methods perform poorly in terms of efficiency and applicability for real applications, the effective reliability-based design optimization method based on adaptive surrogate models under mixed uncertainties is developed. The research findings have great theoretical significance and applicable value, and also provide new effective theories and methods to guarantee the reliability and safety of complex systems.