PARTITION OF PROBABILITY-ASSIGNED SPACE IN PROBABILITY DENSITY EVOLUTION ANALYSIS OF NONLINEAR STRUCTURES
Stochastic response analysis of MDOF nonlinear structures subject to such loadings as earthquake and strong wind has long been a challenging problem. In the past few years, starting with the principle of preservation of probability and revisiting it from the state space description and random event description, a family of probabilitydensity evolution method (PDEM) has been developed, which is applicable to dynamic response analysis of linear and nonlinear stochastic structures, dynamic reliability evaluation and system reliability analysis of structures. The present paper addresses the problem of selecting representative points in the PDEM. Using the Voronoi cells of a point set, the probability-assigned space is partitioned and the assigned probabilities are determined for the representative point set. By examining the error in approximating the original cumulative distribution function by the empirical distribution function and the error in approximating the probability density function of the responses by the numerical solution, two types of discrepancies,including the modified F-discrepancy and the first and second order discrepancies, are defined, The representative point sets should make these discrepancies as small as possible. A two-step procedure is proposed that a uniform point set will first be generated and then it will be transformed according to the parametric density. Numerical examples demonstrate that the proposed point-generating algorithm is of satisfactory accuracy and efficiency. The problems open are discussed.
Nonlinear structure Stochastic response Probability density evolution method (PDEM) Assigned probability Partition of probability-assigned space
Jian-Bing Chen Jie Li
State Key Laboratory of Disaster Reduction in Civil Engineering & School of Civil Engineering,Tongji University, Shanghai 200092, P.R. China
国际会议
第十届国际结构工程青年学者研讨会(The Tenth International Symposium on Structural Engineering for Young Experts)
长沙
英文
280-285
2008-10-19（万方平台首次上网日期，不代表论文的发表时间）