%0 Journal Article
%T The mapping-based dimension-reduction algorithm for probability density evolution analysis of stochastic structural responses<br>随机结构响应密度演化分析的映射降维法
%A & strXing &
%A <br>李杰
%A 陈建兵
%J 力学学报
%D 2005
%I 
%X 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 method is of accuracy and efficiency.
%K stochastic structures
%K dynamic response
%K probability density evolution method
%K Cantor's set theory
%K mapping-based dimension-reduction algorithm<br>随机结构
%K 动力响应
%K 密度演化方法
%K Cantor集合论
%K 映射降维算法
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=5D344E2AD54D14F8&jid=4100DA4A1A3BA1B0CE5AD99AE1DFB420&aid=D80EB0F7DA384096&yid=2DD7160C83D0ACED&vid=42425781F0B1C26E&iid=E158A972A605785F&sid=E0172F1A638CE984&eid=4D4C81DBA842B7BD&journal_id=0459-1879&journal_name=力学学报&referenced_num=3&reference_num=12