结构非概率可靠性指标的求解方法

在结构的非概率可靠性方法中，结构的可靠性是用非概率可靠性指标来度量的。本文研究了区间变量的一般运算规则，给出了非概率可靠性指标的三种求解方法：定义法、转换法和优化法。给出了定义法的具体描述和实现方法，并给出了转换法的一般求解步骤和一种可通用的区间优化算法的实现过程。三种方法的给出，基本上解决了结构可靠性分析中非概率可靠性指标的求解问题。实例计算表明所提方法是有效和可行的。

Procedures for computing the non-probabilistic reliability index of uncertain structures

When available data are limited, or insufficient information is available for verifying a probabilistic model, a non-probabilistic set model may be a valid alternative. In the non-probabilistic reliability theory that we proposed in several previous papers, structural reliability is measured by the non-probabilistic reliability index. In the paper, general arithmetic of interval variables was studied. Three procedures called, respectively, definitional procedure, transformational procedure and procedure by optimization, for computing the non-probabilistic reliability index were presented. Some detailed process of realization of the procedures was given. The procedure by definition or by transformation, where accuracy results may be given, can be used for computing structural reliability of general problems. For the problems in which the limit state functions are complex, the procedure by optimization may be used for reliability computation. Three numerical examples were provided to illustrate the validity and feasibility of the presented procedures.