中文摘要：

针对现有的随机响应面法（SRSM）和层递响应面法（CRSM）存在的局限性，本文结合预处理随机Krylov子空间法，建立了基于Natal变换的向量型层递响应面法，并应用于含非高斯型互相关随机变量的结构可靠度分析。首先，利用预处理随机KryIov子空间的层递基向量近似展开结构的总体节点位移向量，建立向量型层递响应面；然后，根据Nataf变换建立非高斯型互相关随机变量与独立标准正态随机变量之间的关系式，将独立标准正态空间内由Hermite多项式的根组合形成的概率配点变换成非高斯空间内的概率配点，并通过回归分析确定层递响应面的待定系数。计算结果表明，本文建立的CRSM属于向量型响应面法，能较好地处理含非高斯型互相关随机变量的结构可靠度分析问题，计算精度和效率均较高，且具有良好的全域性。

英文摘要：

A novel vectorial cooperative response surface method （CRSM） for structural reliability analysis involving correlated non-Gaussian random variables was proposed based on the preconditioned stochastic Krylov subspace and the Nataf transformation in this paper, to extend the applicability of the existing SRSM and CRSM in non-Gaussian random variables. The preconditioned stochastic Krylov sub- space was defined using the global stiffness matrix and force vector the stochastic nodal displacement vector was expanded subsequently in the subspace to develop vectorial cooperative response surface hier- archically. The correlation coefficients of the independent standard normal random variables were deter- mined by applying the Nataf transformation to the correlated non-Gaussian random variables. The collo- cation points selected from combinations of the roots of polynomial chaos of one-order higher than the order of the response surface were mapped into the non-Gaussian random variable space from the inde- pendent standard normal random variable space. Finally, the unknown coefficients of cooperative response surface were determined by solving the system of linear random algebraic equations. Two numerical examples show that the proposed method is of high accuracy,global applicability and fast convergence for structural reliability analysis involving correlated non-Gaussian random variables.