基于概率空间剖分的结构非线性随机反应分析  

Stochastic Nonlinear Response Analysis of Structures Based on Partition of Probability-assigned Space

作　　者：陈建兵[1] 李杰[2] 

机构地区：[1]同济大学土木工程学院,上海200092 [2]同济大学土木工程防灾国家重点实验室,上海200092

出　　处：《华中科技大学学报（城市科学版）》2008年第4期1-5,共5页Journal of Huazhong University of Science and Technology

基　　金：国家自然科学基金创新研究群体科学基金(50621062);教育部新世纪优秀人才支持计划

摘　　要：在概率密度演化理论的框架下,发展了基于概率空间剖分的多维空间选点方法。引入点集Voronoi域内的概率作为点集的赋得概率,对点集的F-偏差进行了以赋得概率替代均匀概率的修正。在此基础上,进行误差估计,提出了以点集的修正F-偏差、一阶偏差和二阶偏差均尽可能小为准则的点集选取方法——两步选点法。分析实例表明,基于概率空间剖分的选点方法具有较高的精度和效率。文中最后指出需要进一步研究的问题。In the framework of probability density evolution theory, a point selection strategy via partition of probability-assigned space is developed. The assigned probability attached to a point set is defined as the probability over the Voronoi cell of the points. The F-discrepancy which is used to measure the goodness of point set is modified where the equi-probability is replaced by the assigned probability. On the above basis, the error estimate is studied and the criterion of minimizing the modified F-discrepancy and the first and second discrepancy is proposed, consequently, a two-step procedure is developed. Numerical examples indicate that the proposed approach is of acceptable accuracy and of high efficiency. The problems need to be further studied are pointed out.

关 键 词：概率密度演化 概率空间 剖分 非线性结构 随机反应 

分 类 号：TU311.3[建筑科学—结构工程] O324[理学—一般力学与力学基础]