非线性隐式极限状态方程失效概率计算的组合响应面法

A COMPOSITE RESPONSE SURFACE METHOD FOR FAILURE PROBABILITY CALCULATION OF NONLINEAR IMPLICIT LIMIT STATE EQUATION

提出组合响应面的新方法,用以计算设计点附近非线性程度较大的隐式极限状态方程的失效概率。该方法用主响应面和多个次响应面近似对失效概率贡献较大的区域,其响应面函数形式为不含交叉的二次多项式。主响应面依据传统响应面法通过选择适当的插值点和迭代运算获得,其设计点为主设计点。延坐标轴正负方向偏移主设计点得到拟均值点。以拟均值点为基础得到一组次响应面和次设计点。通过主次响应面在各自设计点处的切平面建立组合响应面近似原隐式极限状态方程,并计算其失效概率。算例结果说明所提方法具有较高精度。

To solve failure probability of the implicit limit state equation with high curvature in the vicinity of the design point, a new composite response surface method （RSM） is presented. The major response surface and some sub-response surfaces are adopted in the method. The function form of response surface is taken as a quadratic polynomial without cross terms. According to the conventional RSM, the major response surface is obtained by the proper selection of sampling points and iterative calculation. The design point of the major response surface is named as the major design point. A pair of quasi-mean value points are taken by perturbing the major design point along the positive and negative direction of each coordinate axis. Based on the quasi-mean value point, a pair of sub-response surfaces are obtained in the similar manner as the major response surface. And the tangent hypersurfaces of all response surfaces are used to fit the actual implicit limit state equation and solve failure probability. Illustrations show that the accuracy of the present method is very high.