结构概率确信可靠性评估、重要性分析及优化设计理论研究

It is commonly difficult to achieve failure samples of high-reliability and long-life structures, and probability theory and convex set cannot deal with such a poor sample problem due to the fact that they require to collect sufficient samples to determine accurate probability distribution and variation range for uncertain parameter. Fuzzy set theory is classical approach for such a problem, which needs experiences of domain experts to estimate membership function, but it does not comply with the duality axiom. Uncertainty theory and probability theory are two mathematical systems to rationally deal with indeterminacy and they follow the duality axiom; the former is for modelling belief degrees relevant to human epistemic uncertainty, while the latter is for modelling frequencies associated with natural aleatory uncertainty. Based on uncertainty theory and probability theory, new methodologies on structural reliability assessment, importance measure analysis and reliability-based design optimization for structures will be investigated, and this proposal focuses on the following important research topics: (1)Study new structural belief reliability theory and structural probabilistic belief reliability theory; (2)Investigate new structural belief importance measure analysis theory and structural probabilistic belief importance measure analysis theory; (3)Study new belief reliability based design optimization and probabilistic belief reliability based design optimization for structures; (4)Develop software platform. The proposed research covers scientific research topics in the areas of structural reliability, importance measure analysis and reliability-based design optimization for structures subjected to uncertain variable defined by uncertain theory and random variable defined by probability theory. The research results to be developed will provide a suite of novel theoretical methods and useful practical tools for reliability assessment, importance measure analysis and reliability-based design optimization of engineering structures with epistemic uncertainty and aleatory uncertainty.

高可靠长寿命结构难以获取失效样本，概率论与凸集需收集足够样本以确定变量精确概率分布与变动范围，难以处理样本匮乏问题；模糊集是这类问题的经典方法，需要领域专家经验以确定隶属函数，但不满足对偶公理。不确定理论与概率论是处理不确定性的两大理性数学系统，满足对偶公理，前者针对涉及人类认知不确定的确信度问题，后者针对涉及自然客观不确定的频率问题。本项目将基于不确定理论与概率论开展结构可靠性评估、重要性分析及优化设计理论研究：(1)研究结构确信可靠性与结构概率确信可靠性理论；(2)研究结构确信重要性分析与结构概率确信重要性分析理论；(3)研究结构确信可靠性优化设计与结构概率确信可靠性优化设计理论；(4)开发软件平台。本项目研究复杂结构可靠性评估、重要性分析及优化设计的重要科学问题，将为该领域研究提供新思路、新模型及新方法，研究成果可以直接应用于工程结构评估、分析及设计，具有重要的科学意义和工程应用价值

可靠性评估、灵敏度分析、优化设计是国内外学术界和工程界的研究热点难题。本课题在可靠性评估、灵敏度分析、优化设计等相关领域开展了深入研究：以经典应力-强度干涉理论为基础，结合概率论与不确定理论，建立了一种概率-不确定应力-强度干涉理论，并建立了概率确信可靠性理论雏形，以描述认知不确定性与客观不确定性共存时的实际工程问题；应力具有客观不确定性，服从概率分布；强度具有认知不确定性，服从不确定分布；定义了基于应力-强度理论的改进可靠性模型，并提出采用概率失效确信度来描述不可靠程度；定义了概率失效确信度关于随机应力分布参数的灵敏度分析以及概率失效确信度关于不确定强度分布参数的灵敏度分析；提出了概率失效确信度及灵敏度分析求解的数值模拟法和解析法。基于概率失效确信度，考虑分布参数存在的认知不确定性，定义了概率失效确信度关于认知不确定分布参数的全局灵敏度，以量化不确定分布参数对整个系统的可靠性影响，并提出有限差分法求解全局灵敏度。基于Cornell不确定可靠性指标，考虑分布参数存在的认知不确定性，定义了Cornell不确定可靠性指标关于认知不确定分布参数的全局灵敏度，以量化不确定分布参数对整个系统的可靠性影响，并提出有限差分法求解全局灵敏度。在此基础上，提出一种基于不确定失效可能度的结构可靠性优化设计模型；提出一种基于不确定可靠性指标的结构可靠性优化设计模型；并给出相应的求解方法。此外，针对辐照环境下电源系统开展了退化分析及可靠性评估研究；针对复杂系统的加速寿命试验方案优化设计方法开展了研究；针对考虑随机初始值的加速退化试验优化设计与退化建模开展了研究。已发表论文14篇，其中SCI或EI论文10篇；申请国家发明专利28项，其中授权8项；研制软件6个；直接或间接培养硕士研究生17人(毕业)。