一种改进的结构可靠度分析中响应面法

在实际工程结构的可靠度分析中,极限功能函数通常很难用明确的表达式表达,响应面法因其自身的优点得到了广泛的应用.为进一步提高求解效率,提出了一种改进措施,在迭代求解过程中,不同于通常的每次都在插值点处展开2n 1个样本点,而是用插值点逐步替代距离极限状态曲面最远的点,直至收敛到给定的精度要求.通过算例进行的对比分析证明,改进的响应面法在没有降低计算精度的前提下,使有限元分析次数显著减少.该方法尤其适用于大型复杂结构的可靠度分析.

An improved response surface method for structural reliability analysis

For reliability analysis of large and complex structural systems problems,response surface method(RSM) is widely used to simulate the limit performance function which is unknown.To increase the calculation efficiency,a new improved method is proposed,in which the group of sample points(2n 1 points) are replaced one by one by interpolation points in the iterative process until the convergence condition is met.In every iteration step,only one point,that is of the largest distance between it and interpolation point,is replaced.Consequently,the response surfaces make full use of every sample point that is calculated by finite element method program.Examples are given to demonstrate that the proposed method enhances the calculation efficiency greatly,especially for reliability analysis of large and complex structure.