考虑时变效应的结构可靠性分析与优化设计的非概率集合方法研究

The reliability for long life-time structures is influenced by the plenty of uncertain factors included in "People, Machines, Material, Specification, Environment", which represent many special features, such as multi-source, poor information etc. Due to the reasons such as material aging, damage accumulation and variable loads, their reliability during the service process exhibits a distinct time-variant effect. Thus the traditional tim-invariant reliability theory based on probabilistic method will be not applicable when dealing with the problems of reliability analysis and optimization design of long life-time structures with time-varying and less information on uncertainty. In this project, based on the non-probabilistic set theory, researches on the time-variant reliability analysis and reliability-based optimization for large-scale structures will be developed. The main studies will focus on the non-probabilistic uncertainty quantification methods for time-variant parameters, configurations of interval models for structural load/resistance, time-variant interval response analysis methods, the establishing method for the component/system-level reliability model and measure index, the optimal maintenance and reinforcement decising methods for existing structures as well as optimization methods for designing structures, etc. The purpose of this project is to realize the application of the proposed non-probabilistic mathematical models and numerical algorithms in the long life-time structural analysis and evaluation, and to enrich and develop the existing theory of time-variant reliability and reliability-based optimization. This research to be performed will propose an optional supplementary method to further improve the safety and economy of design for engineering structures.

长寿命结构的可靠性问题涉及大量不确定性因素，它们广泛存在于"人、机、料、法、环"各环节当中，具有多源性、贫信息等特点。伴随着结构长期使用过程中材料老化、损伤累积和载荷可变等原因的出现，传统基于概率方法的时不变可靠性理论，在处理具有时变效应和贫不确定信息特性的长寿命结构可靠性分析与设计问题已不再适用。本项目将基于非概率集合理论，构建考虑时变效应的结构可靠性分析与优化设计技术,主要研究结构时变不确定参数的非概率集合定量化方法，时变结构载荷/抗力区间模型建立和时变结构区间响应分析方法，时变结构的构件级与系统级的非概率集合可靠性模型和度量指标的建立方法，服役结构的最优维护加固决策方法和拟建结构的最优设计技术。本项目拟将提出的非概率集合模型及数值算法应用到长寿命周期结构的设计中，丰富和发展现有时变结构可靠性分析及可靠性优化理论，为提高工程时变结构设计的安全性和经济性提供一种有效的方法补充。

针对现有的基于概率方法的时不变可靠性分析理论在处理具有时变效应和贫信息特性的长寿命结构可靠性分析与设计问题不再适用的情况，以非概率集合理论和可靠性优化思想为理论框架，综合考虑了结构的时变特性，建立了考虑时变效应的的结构可靠性分析与优化设计的非概率集合方法。首先分析了时变结构的多源不确定性，提出了多源时变不确定性的非概率定量化方法，同时开展了不确定性传播分析，对时变结构载荷和抗力模型及不确定性响应进行了分析研究；其次，对非概率区间模型和凸模型开展了研究，以此为基础，结合时间离散思想和首次穿越理论建立了时变结构的非概率可靠性分析模型、提出了可靠性度量指标，同时考虑了结构系统多失效模式及其相关性，建立了时变结构的系统级非概率可靠性分析模型和度量指标；通过对同一结构开展概率可靠性分析和非概率可靠性分析，验证了两者的相容性；此外，建立了结构时变非概率可靠性优化模型，针对在役结构和拟建结构，分别构建了以时变非概率可靠性为约束的优化框架，为对在役结构开展最经济的维修、对拟建结构进行保证安全的减重设计，提供了理论指导。本项目提出的数学模型及数值算法可应用到复杂结构（飞行器、桥梁、建筑等）的分析评估中，丰富和发展了现有长寿命周期结构可靠性分析及可靠性优化理论体系，为解决工程时变结构的安全性和经济性问题提供了可行的理论参考。