Composite response surface method for failure probability calculation of nonlinear implicit limit state equation

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.