基于非精确随机模拟的多态不确定性与结构可靠性理论研究

In structural reliability engineering practice, the scarcity, incompleteness, and imprecision of data commonly result in the existence of both aleatory and epistemic uncertainties of basic variables (including both excitations and structural parameters), which make up the polymorphic uncertainty. Current researches show that failing to make or wrongly making a separation between the different types of uncertainties may result in large estimation error of reliability. Based on correctly separating the polymorphic uncertainty, this project will develop a new methodology framework, called imprecise stochastic simulation, so as to study the uncertainty and reliability theories subjected to imperfect data. Firstly, the polymorphic uncertainty characterization models and methods will be devised for imperfect data; secondly, the imprecise stochastic simulation will be developed for polymorphic uncertainty propagation so as to realizing the polymorphic uncertainty quantification of structure responses, as well as the assessment and updating of structure reliability; thirdly, based on imprecise stochastic simulation, a polymorphic sensitivity analysis method will be developed for analyzing the importance of basic variables, identifying the key failure factors, and analyzing the importance of epistemic uncertainty; finally, an engineering software will be developed, and the uncertainty quantification challenging problems and typical aircraft mechanism will be taken as examples for engineering application and demonstration research. This research will establish a new theory and methodology framework of structural reliability under imperfect knowledge, which will provide an important complementarity for the generic reliability technique, and further promote the applications of the reliability theory in mechanical engineering, civil engineering, etc.

在结构可靠性工程实践中，数据缺乏、不完整及非精确导致基本变量（包括激励和结构参数等）存在随机和认知不确定性，合称多态不确定性。现有研究表明：若不区分或错误区分不确定性类型，可能导致可靠性分析结果存在较大误差。本项目以多态不确定性分离思想为指导，通过建立一套非精确随机模拟方法体系，对不完善数据下的不确定性与可靠性理论进行研究。首先，建立不完善数据的多态不确定性表征模型与方法；其次，基于非精确随机模拟进行多态不确定性传递研究，实现结构响应多态不确定性量化与可靠性评估及更新；再次，基于非精确随机模拟建立多态敏感性分析方法，实现基本变量重要性分析、关键失效因素识别及认知重要性分析。最后还将编制工程应用软件，并以不确定性量化挑战问题和飞机典型机构为例进行应用与验证研究。本研究将形成一套新的不完善数据下的结构可靠性理论与方法体系，对完善可靠性共性技术并推进其在机械、土木等领域的应用具有重要意义。

结构可靠性理论的工程实践中遇到的最具挑战的问题是所获取的数据具有匮乏、不完整、不精确等特点，导致随机与认知不确定性并存，在不完备数据下实现结构参数、材料属性参数及载荷激励等的高可信不确定性建模，并在此基础上实现结构可靠性的高可信评估是所需解决的关键问题。针对上述问题，本项目开展了三个方面的研究：1）建立了不完备数据下多态不确定性建模与模型推断方法；2）建立了多态不确定性输入下结构响应性能不确定性量化与可靠性评估数值分析方法研究；3）建立多态敏感度分析方法，实现变量重要性分析。针对上述内容，开展了系统性理论研究，主要成果包括：1）针对不完备数据，建立了“概率-概率盒-区间”的统一建模框架、模型推断方法和各模型的边界条件；2）建立了多态不确定性输入下结构性能不确定性量化与可靠性分析的非侵入式非精确随机模拟方法、非侵入式非精确概率积分法和贝叶斯自适应协同优化方法，极大提高了各类问题的求解效率，且具有较好的全局收敛性；3）建立了贝叶斯全局敏感度分析方法用于分析不确定性参数重要性。在上述研究基础上开发了两个不确定性量化与设计的软件，集成上述理论成果，并进行了若干实际工程问题应用与验证研究。上述成果对完善可靠性共性技术，对推进可靠性理论在机械工程领域应用具有重要意义。