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

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.