超椭球模型下结构非概率可靠性指标的迭代算法

An iteration approach for structural non-probabilistic reliability analysis based on hyper-ellipsoidal models

迭代算法对于非概率可靠性指标的求解及其优化问题具有重要意义。本文基于不确定参数的超椭球描述,研究求解非概率可靠性指标的迭代算法。针对极限状态方程非线性情况较高时可能存在不收敛的问题,提出一个检测严重迂回振荡的判据,并在HL-RF迭代公式的基础上引入修正解,在一定程度上克服迭代不收敛的问题。数值算例验证了迭代算法的正确性和有效性。

This paper investigates the iteration algorithms for the non-probabilistic reliability analysis of structures using hyper-ellipsoidal models of uncertainties. For the purpose of alleviating the convergence difficulties of the reliability index calculation in presence of highly nonlinear limit-state functions, the paper proposed a criterion for detecting Zig-zag iterations and a modified iteration scheme based on the HL-RF algorithm. The numerical example demonstrates the validity and efficiency of the present method. The proposed techniques are also shown to be capable of improving the iteration convergence in eval- uating the non-probabilistic reliability index.