Abstract：Response surface approximation and collocation point selection are two important problems of response surface method for structural reliability analysis. In this paper, a vector cooperative response surface for structural reliability analysis was constructed by the cooperative basis vectors, while the optimal probabilistic collocation points were slelected from large numbers of candidate points according to the full row rank criterion of collocation point matrix. The preconditioned stochastic Krylov subspace was defined using the global stiffness matrix and force vector, and the stochastic nodal displacement vector was expanded subsequently in the subspace to develop vector cooperative response surface hierarchically. The stochastic row vector was constructed by the combination of basic random variables in accord with cooperative basis vectors. The collocation point matrix was constructed by the stochastic row vector with particular collocation points and the optimal probabilistic collocation points were slelected according to the full row rank criterion of collocation point matrix. Finally the unknown coefficients of cooperative response surface were determined by the regression analysis. The results show that the proposed method can reduce the number of probabilistic collocation points significantly on the condition of ensuring high accuracy, global applicability and fast convergence, comparing with the traditional response surface method and stochastic response surface method.
2014, Vol. 35 
