可靠性分析的改进加权响应面法

为了克服响应面法(Response surface method简称RSM)在计算大规模工程时效率低下和计算可靠性指标敏感度时偶尔误差大的问题,提出一个高效率的改进加权响应面方法.此方法首先构造一次响应面函数,然后在可能存在失效点的被缩小范围内采用轴向采样来得到样本点,构造二次响应面函数；通过从之前的样本组里增加新的样本点,给予靠近失效点的样本点更高的权重来更新响应面函数.通过几个算例表明:比较双加权响应面方法,此方法具有更高的准确性和计算效率.

An improved response surface method based on weighted regression for reliability analysis

In order to overcome these problems that the response surface method(RSM) is time consuming for large-scale applications and sometimes shows large errors in the calculation of the sensitivity of the reliability index with respect to random variables,this study proposes an efficient and improved RSM based on weighted regression.In the proposed method,a linear RSF is constructed at first and a quadratic RSF is formed using the axial experimental points selected from the reduced region where the MPFP is likely to exist.The RSF is updated successively by adding one new experimental point to the previous set of experimental points and giving higher weight to the experimental points closer to the most probable failure point(MPFP).Numerical examples are presented to demonstrate the improved accuracy and computational efficiency of the proposed method compared to the RSM based on a double weighted regression.