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《Acta Mechanica Sinica》 2005-04
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THE MAPPING-BASED DIMENSION-REDUCTION ALGORITHM FOR PROBABILITY DENSITY EVOLUTION ANALYSIS OF STOCHASTIC STRUCTURAL RESPONSES

Li Jie Chen Jianbing (School of Civil Engineering, Tongji University, Shanghai 200092, China)  
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 random 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 probability and divided into a certain number of subsets such that the sum of the probability in each subset is 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.
【Fund】: 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.~~
【CateGory Index】: TU311.3
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