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杨绿峰,杨显峰,余波.基于Nataf变换的层递响应面法分析结构可靠度[J].计算力学学报,2014,31(2):155~160

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基于Nataf变换的层递响应面法分析结构可靠度

Cooperative response surface method for structural reliability analysis based on Nataf transformation

投稿时间：2012-10-15 修订日期：2013-02-24

DOI：10.7511/jslx201402003

中文关键词: 可靠度层递响应面法非高斯随机变量预处理随机Krylov子空间 Nataf变换

英文关键词:reliability cooperative response surface method non-Gaussian random variable preconditioned stochastic Krylov subspace Nataf transformation

基金项目:国家自然科学基金（51168003）；人社部留学人员择优（[2012]258号）；广西自然科学基金重大（2012GXNSFEA053002）及主席基金（2010GXNSFD169008）资助项目.

作者	单位	E-mail
杨绿峰	广西大学土木建筑工程学院工程防灾与结构安全教育部重点实验室, 南宁 530004 广西壮族自治区住房和城乡建设厅, 南宁 530028
杨显峰	广西大学土木建筑工程学院工程防灾与结构安全教育部重点实验室, 南宁 530004 广州瀚华建筑设计有限公司, 广州 510655
余波	广西大学土木建筑工程学院工程防灾与结构安全教育部重点实验室, 南宁 530004	gxuyubo@gxu.edu.cn

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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Nataf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Krylov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 subspace 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 hierarchically.The correlation coefficients of the independent standard normal random variables were determined by applying the Nataf transformation to the correlated non-Gaussian random variables.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.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.

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