结构可靠性分析中考虑高次项修正的组合响应面法

Response Surface Combination Improved by High Order Term for Structural Reliability Analysis

响应面法被广泛地应用于大型复杂结构隐式极限状态方程的可靠性分析,然而至今响应面法的精度仍是未完全得以解决的问题。分析并指出了影响响应面法精度的主要因素,针对这些影响响应面法精度的主要因素,提出了考虑高次项修正的组合响应面法,该方法在真实极限状态方程对结构失效概率贡献较大的区域以一组主次响应面来近似,并对每一个响应面采用高次项予以修正,从而使得响应法的精度得以大幅提高,算例结果证明了所提方法的可行性与精度。

In the reliability estimation of large complex structures, response surface method （REM） has been widely suggested as a way to estimate failure probability of the actual but implicit limit state equation. Nevertheless, the precision of the RSM turns out to be subjected to further studies. The major factors which have significant effects on the precision of the RSM are analyzed, and they are the following four points： 1） Location of the sampling points used to determine the response surface; 2） Degree of the nonlinearity in the vicinity of the design point of the actual implicit limit state equation; 3） Approximate degree of the response surface matching the actual implicit limit state equation; 4） Coefficients of variation in the basic random variables. By taking these major factors into consideration, the paper devotes to research a combination response surfaces method. The main and multiple secondary response surfaces are combined to approximate the region which has great contribution to the failure probability of the large complex structure. Each response surface is corrected by the high order term of actual limit surface for more accurate result. The advantage in the precision of the presented method is verified by the illustrations.