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基于最优概率配点的向量型层递响应面法分析结构可靠度

ISSN号：0254-7805
期刊名称：固体力学学报
时间：2014.4.15
页码：189-198
分类：O211[理学—概率论与数理统计;理学—数学]
作者机构：[1]广西大学土木建筑工程学院,广西防灾减灾与工程安全重点实验室,南宁530004, [2]广西壮族自治区住房和城乡建设厅,南宁530028, [3]广州瀚华建筑设计有限公司,广州510655
相关基金：国家自然学基金项目（51168003,51368006）,人社部留学人员择优资助项目（2012258）,广西自然科学基金重大项目（2012GxNsFEA053002）和青年基金项目（2013GXNSFBA019237）,广西高校科学技术研究项目（2013YB009）,广西科学研究与技术开发计划项目（桂科攻1377001-11）和广西熏点实验室系统性研究项目（2013ZDX06）资助.
相关项目：大跨预应力混凝土箱型梁桥完整性与可靠性研究

关键词：结构可靠度, 层递响应面法, 配点矩阵, 最优概率配点, structural reliability, cooperative response surface method, collocation point matrix, opti-mal probabilistic collocation point

中文摘要：

概率配点的选取策略是响应面法研究的关键问题之一．论文提出了配点矩阵行满秩原则，据此筛选层递响应面的最优概率配点．首先利用结构总体刚度矩阵和荷载列阵定义预处理随机Krylov子空间，并利用该空间的层递基向量近似展开结构的总体节点位移向量，建立层递响应面表达式；然后利用层递基向量所对应的基本随机变量组合构造随机行向量，并形成配点矩阵，根据配点矩阵行满秩原则筛选确定层递响应面的最优概率配点，进而通过回归分析确定层递响应面的待定系数．分析表明，层递响应面法具有良好的全域性且待定系数极少；基于配点矩阵行满秩原则筛选最优概率配点能够排除大部分作用不大的配点，大幅减少概率配点数目，与传统响应面法及随机响应面法相比，层递响应面法能够取得更好的计算效率和精度．

英文摘要：

Response surface approximation and collocation point selection are two important problems of the response surface method for structural reliability analysis. In this paper, a vector cooperative re- sponse surface for structural reliability analysis was constructed by the cooperative basis vectors, while the optimal probabilistic collocation points were selected 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 coopera- tive basis vectors. The collocation point matrix was constructed by the stochastic row vector with particular collocation points and the optimal probabilistic collocation points were selected according to the full row rank criterion of collocation point matrix. Finally the unknown coefficients of the cooperative response surface were determined by the regression analysis. The results show that the proposed method, comparing with the traditional response surface method and the stochastic response surface method, can reduce the number of probabilistic collocation points significantly but still ensure the high accuracy, global applicabili- ty and fast convergence.

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