Adaptive response surface method based on a double weighted regression technique

In structural reliability analysis where the structural response is computed from the finite element method, the response surface method is frequently used. Typically, the response surface is built from polynomials whereof unknown coefficients are estimated from an implicit limit state function numerically defined at fitting points. The locations of these points must be selected in a judicious way to reduce the computational time without deteriorating the quality of the polynomial approximation. To contribute to the development of this method, we propose some improvements. The response surface is successively formed in a cumulative manner. An adaptive construction of the numerical design is proposed. The response surface is fitted by the weighted regression technique, which allows the fitting points to be weighted according to (i) their distance from the true failure surface and (ii) their distance from the estimated design point. This method aims to minimize computational time while producing satisfactory results. The efficiency and the accuracy of the proposed method can be evaluated from examples taken from the literature.