基于自适应步长参数的快速一次可靠度计算方法

为能够快速搜索到极限状态函数的设计点以实现快速一次可靠度计算方法,在已有的基于迭代算法(HLRF)的设计点搜索方法的基础上,借助不精确一维搜索Shi-Shen准则,提出了基于自适应步长参数的一次可靠度计算方法(aHLRF).相比传统的方法,aHLRF不仅具有收敛保证,而且还能利用已有迭代信息自适应地选取算法参数.从计算效率、鲁棒性等方面对aHLRF进行了探讨和算例对比.结果显示:新方法可极大地提高一次可靠度的计算效率,尤其在设计点附近非线性强的情况下优势更为明显.

Fast First Order Reliability Method Based on Adaptive Step Size Parameters

Abstract： The key problem for fast first order reliability method (FORM) is to quickly find out the design point of limit state function. After analyzing some HLRF based design point searching algorithms, a novel FORM was proposed based on the Shi-Shen line search rule. As this FORM is based on adaptive step size parameters, it is referred to as aHLRF. Compared with the traditional HLRF-based method, the aHLRF not only is globally convergent, but also can adaptively estimate some important algorithm parameters using previous iteration information. The robustness and efficiency of the aHLRF were also discussed. Examples illustrate that the aHLRF is very efficiency for estimating the first order reliability probability, especially for problems whose the nonlinearity of limit state function near the design point is very large.