用于具有多失效模式和带相关不确定性结构可靠性分析的基于有限数据的非概率凸多面体模型

A non-probabilistic convex polyhedron model for reliability analysis of structures with multiple failure modes and correlated uncertainties based on limited data

本文提出了一种新的非概率可靠性模型,关注不确定性条件下结构可靠性评估,称为凸多面体可靠性模型.与现有的概率和非概率区间模型不同,凸多面体模型考虑用多维凸多面体描述不确定变量空间.与区间模型相比,凸多面体模型更紧凑,反映了基于有限信息的不确定变量之间的相关性.在所提出的准则中,面积/体积比被视作可靠性指标.然后,利用基于最可能失效点的线性化方法和分段线性化方法对非线性极限状态函数的情况进行了讨论和处理.在此基础上,研究了基于非概率凸多面体可靠性模型的多失效模式结构系统可靠性分析的有效方法.最后,通过三个实例验证了该方法的有效性和适用性.通过与现有可靠性模型的比较,结果表明,概率可靠性模型和非概率可靠性模型评估的可靠性是相容的.

This paper proposes a novel non-probabilistic reliability model called the convex polyhedron reliability model,focusing on structural reliability assessment under uncertain conditions.Unlike existing probabilistic and non-probabilistic interval models,the convex polyhedron model considers the situation where a multi-dimensional convex polyhedron describes the uncertain variable space.Compared with the interval model,the convex polyhedron model is more compact and reflects the correlation between uncertain variables based on limited information.The area/volume ratio is introduced to be referred to as the reliability index in the proposed framework.Then the case of the nonlinear limit state function is discussed and addressed by the most likely failure point-based linearization method and the piecewise linearization method.Furthermore,this paper investigates an effective approach to dealing with the structural system reliability analysis problem with multiple failure modes based on the proposed non-probabilistic convex polyhedron reliability model.Finally,three examples are provided to verify the effectiveness and applicability of the proposed method.Through comparison with the existing reliability models,the results show that the reliability evaluated by the probabilistic reliability model and non-probabilistic reliability model are compatible.