一种结构不确定分析的改进多维平行六面体模型  

An Improved Multidimensional Parallelepiped Model for Structural Uncertainty Analysis

作　　者：乔心州[1] 张锦瑞 方秀荣[1] 刘鹏[1] QIAO Xinzhou;ZHANG Jinrui;FANG Xiurong;LIU Peng(School of Mechanical Engineering,Xi an University of Science and Technology,Xi'an 710054,Shaanxi,China)

机构地区：[1]西安科技大学机械工程学院,陕西西安710054

出　　处：《兵工学报》2024年第6期1877-1888,共12页Acta Armamentarii

基　　金：国家自然科学基金项目(51775427)。

摘　　要：多维平行六面体模型是一种能够同时考虑相关变量和独立变量的非概率凸集模型,更适用于工程结构中常见的多源不确定性问题。为更加有效合理地度量结构不确定性,提出一种改进多维平行六面体模型。通过定义区间变量的相关角和边缘区间,给出模型不确定域的显式表达式,进而给出依据实验样本点构建多维平行六面体模型的方法。3个算例分析结果表明,改进多维平行六面体模型能够较好地反映区间变量之间的相关性,是一种比传统多维平行六面体模型更为紧凑合理的模型。The multidimensional parallelepiped model is a non-probabilistic convex set model that can take into account dependent and independent variables simultaneously.Therefore,it is more suitable for the“multi-source uncertainty”problems in engineering structures.An improved multidimensional parallelepiped model is presented to more reasonably and efficiently quantify the structural uncertainties.An explicit expression for the uncertainty domain of the parallelepiped model is given by defining the correlation angle and marginal intervals of interval variables.A method is further formulated to construct a multidimensional parallelepiped model based on the experimental sample points.The analyzed results of three numerical examples show that the proposed model can better reflect the correlation of interval variables,and has a more compactness and rationality than the traditional multidimensional parallelepiped model.

关 键 词：多维平行六面体模型 非概率凸集模型 变量相关性 不确定域显式表达式 

分 类 号：TB114.3[理学—概率论与数理统计]