Abstract

In this paper, an improved first order approximate reliability analysis method based on evidence theory is developed to evaluate the uncertain structures reliability. Firstly, the uncertain variables are described by using frame of discernment (FD) and the basic probability assignment (BPA). Secondly, the improved HL-RF (iHL-RF) method and Newton method are used to solve the most possible point(MPP) and the bound points, respectively. Thirdly, the limit-state functions are approximated by first order Taylor series at all key points obtained by most possible point and bound points. Then, based on the above approximate limit-state functions, the extremum analysis of all focal element is performed to solve the reliability measure indexes: the belief measure (Bel) and plausibility measure (Pl). Finally, two numerical examples and two engineering applications are discussed to verify the effectivity of the presented method.

摘要

本文提出了一种改进的基于证据理论的一阶近似可靠性分析方法来评价不确定结构的可靠性。首先，利用识别框架（FD）和基本概率赋值（BPA）对不确定变量进行描述。其次，采用改进的HL-RF（iHL-RF）方法和牛顿法分别求解最可能点（MPP）和界点。第三，极限状态函数在所有关键点处由最可能点和界点得到的一阶泰勒级数逼近。然后，基于上述近似极限状态函数，对所有焦元进行极值分析，求解可靠性度量指标：置信度（Bel）和似真度（Pl）。最后，