基于等概率近似变换的 向量型层递响应面法分析结构可靠度

基于正交变换和等概率近似变换,研究建立了随机变量为非高斯互相关的工程结构可靠度分析的向量型层递响应面法。首先利用正交变换将非高斯互相关随机变量变换为互不相关的非高斯标准随机变量,建立结构总体刚度矩阵和荷载列阵,据此定义预处理器并形成预处理随机Krylov子空间,进而利用该空间的层递基向量将结构总体节点位移向量近似展开,建立关于互不相关非高斯标准随机变量的层递响应面；然后根据等概率近似变换,将独立标准正态空间的样本点转换为层递响应面在非高斯空间中的概率配点；最后通过回归分析确定层递响应面待定系数,并利用层递响应面建立极限状态方程求解结构可靠度。分析表明：该文提出的等概率近似变换方法不仅成功地将层递响应面法拓展到非高斯互相关随机变量下的结构可靠度分析,而且方法简便、适用范围广、计算精度和效率较高,具有良好的全域性。

VECTOR COOPERATIVE RESPONSE SURFACE METHOD FOR STRUCTURAL RELIABILITY ANALYSIS BASED ON APPROXIMATELY EQUIVALENT PROBABILITY TRANSFORMATIONS

An improved vector cooperative response surface method (CRSM) for structural reliability analysis involving non-Gaussian correlated random variables was proposed based on the orthogonal and approximately equivalent probability transformations. First, according to the orthogonal transformation, the non-Gaussian correlated random variables were mapped into the uncorrelated non-Gaussian standardized random variables to establish global stiffness matrices and load vectors. The preconditioner was defined by the global structure stiffness matrix to form a preconditioner Krylov subspace, and the stochastic global nodal displacement vector of structure was expanded subsequently in the subspace to develop vector cooperative response surface hierarchically. The collocation 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 independent standard normal random variable space according to approximately equivalent probability transformation. Finally, the unknown coefficients of cooperative response surface (CRS) were determined by the regression analysis and structural reliability analysis was implemented based on the limit state function constructed by the CRS. Results show that the proposed method is of high accuracy, global applicability and fast convergence for structural reliability analysis involving non-Gaussian correlated random variables.