基于广义超椭球模型的结构非概率可靠性指标  

Non-Probabilistic Reliability Indexes Based on the Generalized Super Ellipsoid Model

作　　者：乔心州[1] 赵悦童 方秀荣[1] 刘鹏[1] QIAO Xinzhou;ZHAO Yuetong;FANG Xiurong;LIU Peng(College of Mechanical Engineering,Xi’an University of Science and Technology,Xi’an 710054,P.R.China)

机构地区：[1]西安科技大学机械工程学院,西安710054

出　　处：《应用数学和力学》2024年第4期458-469,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51775427)。

摘　　要：非概率凸集合模型仅需获知结构不确定性的范围或界限来度量结构可靠性,因而适用于小样本不确定性结构工程问题.针对广义超椭球模型,对其非概率可靠性度量问题进行了研究.首先,提出了基于广义超椭球模型的简单非概率可靠性指标,定义为结构功能函数的均值与离差之比,并讨论了该可靠性指标的不一致性问题.其次,为克服上述不一致性问题,提出了一种比例因子非概率可靠性指标,定义为不确定域向外扩大或向内收缩时,失效面与不确定域接触的最小比例因子.最后,通过3个工程算例分析验证了所提非概率可靠性指标的有效性和可行性.The non-probabilistic convex model only requires the bounds or domains of structural uncertain parameters to measure structural reliability,and therefore is more appropriate for engineering structures with limited experimental data.The problem of non-probabilistic reliability measurement of the generalized super ellipsoid model was studied.A simple non-probabilistic reliability index was first proposed to evaluate the safety degree of a structure,which was defined as the ratio of the mean value of the performance function to its deviation.The inconsistency problem in the simple non-probabilistic reliability index was further discussed.To overcome the above inconsistency problem,a ratio factor reliability index was then presented,which was defined as the minimum ratio factor at which the failure surface is in contact with the uncertainty domain contracting inward or expanding outward.Three numerical examples demonstrate the validity and feasibility of the proposed non-probabilistic reliability indexes.

关 键 词：广义超椭球模型 非概率可靠性 简单非概率可靠性指标 比例因子非概率可靠性指标 

分 类 号：O213.2[理学—概率论与数理统计]