摘要
提出了随机结构响应密度演化分析的映射降维算法.在一般线性与非线性随机结构分析中,采用近年发展起来的密度演化方法,能够获得动力响应的瞬时概率密度函数及其演化过程,具有较好的精度.当具有多个随机变量时,采用常规的格栅型选点将导致过大的计算工作量.基于Cantor集合映射的基本思想,将多维空间中的离散网格点逐次两两降维,按照概率测度值进行排序、取点,从而将具有多个随机变量的随机结构分析问题的计算工作量降到与仅含单一随机变量的随机结构分析相当的水平.与随机模拟结果的比较表明:建议的方法具有较高的精度和效率.
A mapping-based dimension-reduction algorithm for probability density evolution analysis of stochastic structural responses is proposed. In recent years, an original probability density evolution method, which is capable of evaluating the instantaneous probability density functions of stochastic responses of general multi-degree-of-freedom nonlinear structures, has been developed. In the case of only one or two random parameters involved, a grid-type representative point set is feasible and of fair efficiency. When multiple ranom parameters are involved, however, the grid-type point sets will make the number of the chosen discretized representative points increase almost exponentially against the number of the random parameters, leading to prohibitively large computational efforts. In the present paper, starting with the idea of Cantor set mapping, a dimension-reduction algorithm is developed. In the proposed approach, the strategy of picking out points from the grid-type point set for the case of two random parameters is firstly discussed in detail. In this case, the grid-type points are sorted according to the associated such that the sum of the probability in each subset is probability and divided into a certain number of subsets almost at the same level but usually not identical. One single point is then picked out, say, deterministically or randomly, in each subset with the associated probability equaling to the sum of the probability in this subset. All the above chosen points form the finally used discretized representative point set. In the case of multiple random parameters, the above procedure is iteratively employed and finally the number of the picked out points is almost at the same level as that needed in the case of only one single random parameter. Consequently, the computational efforts in the problem involving multiple random parameters could be reduced to the level of the problem involving one single random parameter. The comparison with the Monte Carlo simulation demonstrates that the proposed
出处
《力学学报》
EI
CSCD
北大核心
2005年第4期460-466,共7页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家创新研究群体科学基金(50321803)国家自然科学基金(10402030)资助项目.~~
关键词
随机结构
动力响应
密度演化方法
Cantor集合论
映射降维算法
stochastic structures, dynamic response, probability density evolution method, Cantor＇s set theory, mapping-based dimension-reduction algorithm
