一种在响应面法中选取样本点的新方法

An new method for selecting sampling points in response surface method

响应面法中的样本点选取对拟合极限状态曲面的收敛速度及精度至关重要,文中提出了一种区别于通常以插值点为中心展开生成样本点组的新方法:在求解过程中,用插值点逐步替代初始样本点组中距离验算点较远的点,其目的是使所选取的样本点较集中于验算点附近,重新构成下一轮迭代所需的一组样本点,直至满足收敛条件。算例表明,采用新方法可使结构的分析次数显著减少,同时也改善了对于非线性程度很高的极限功能函数求解的收敛性。该方法用于大型复杂结构的可靠度分析中可进一步提高计算效率。

As a approximation method, response surface method （RSM） is widely used to alleviate the computational burden of structural reliability analysis. However, the conventional RSM, whose sampling points are positioned according to interpolate point, seems to be ineffective for the large and complex structural reliability analysis problems. It is important that Positioning sampling points close to the actual limit state surface for both the speed and precision of fitting the actual surface. Therefore, a new strategy for positioning sampling points is proposed in this paper, which in the group of initial sampling points only one point is replaced by interpolate point generated in every iteration step, the point is of the largest distance between the two. Then, a new group of points is formed to perform the next iteration process until the convergence condition is meet. So, only one structural analysis is performed in every iteration step, while 2n＋ 1 structural analysis is needed to performed in conventional RSM. Examples are given to demonstrate the advantages of the new method proposed in the paper for both convergence and computational costs. And it is of applicable significance.