非概率区间模型可靠性指标的梯度投影算法  

The gradient projection method for non-probabilistic reliability index based on interval model

作　　者：李世军[1] 樊建平[1] 漆炜[2] 陈旭勇[3] 

机构地区：[1]华中科技大学土木工程与力学学院,武汉430074 [2]湖北省交通运输厅通信信息中心,武汉430030 [3]武汉工程大学环境与城市建设学院,武汉430074

出　　处：《计算力学学报》2013年第2期192-197,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(10972084);国家科技支撑计划(2008BAC36B03)资助项目

摘　　要：考虑不确定参数为区间变量,研究求解非概率可靠性指标的有效搜索算法。基于函数梯度法的基本思想,构造搜索方向,建立迭代算法格式,将传统的用于概率可靠性分析的梯度投影法用于非概率可靠性指标的求解。当收敛点为非最可能失效点时,提出了空间降维算法,并给出了整个搜索算法的计算步骤。通过数值算例,验证了本文提出的搜索迭代算法的有效性和正确性。A new search algorithm for effectively solving non-probabilistic reliability index is presented and discussed using the interval model of uncertain in this study. Based on the basic concept of function gradient,the gradient projection method,which conventionally used to analyze probabilistic reliability, is adopted to solve non-probabilistic reliability index by creating search directions and establishing iterative computation formulation. When the convergence point is not the most possible failure one,the spatial di- mensional reduction is proposed. The calculation steps of the gradient projection method are also presented. The numerical examples have illustrated the search efficiency and validity of the proposed algorithm.

关 键 词：可靠性指标 非概率可靠性 梯度投影 区间模型 无穷范数 

分 类 号：O213.2[理学—概率论与数理统计] TB114[理学—数学]