不同分布随机参数结构非线性地震反应的概率密度演化
Probability Density Evolution Analysis of Nonlinear Seismic Response of Structures with Random Parameters Following Different Distributions

摘要： 为了准确把握实际工程结构在地震作用下的整体性能,需要合理考虑结构参数的随机性.本文采用概率密度演化理论,结合以广义F-偏差最小化为准则的点集优选策略,实现了含有数十个随机参数的多自由度结构非线性随机反应分析.在此基础上,重点考察了基本随机参数的不同分布类型和不同变异系数对结构非线性反应特性的影响.研究表明,由于结构随机参数不同分布类型的影响,结构反应的二阶矩差异可达±30%;当基本变量变异系数很小和很大时,不同分布类型对二阶矩的影响程度均较大但影响趋势相反,因而存在结构反应二阶矩对不同分布类型不敏感的变异系数值域.随机参数的分布类型对结构反应的概率密度函数影响显著,甚至可能导致定性性质的改变.
Abstract: The randomness of structural parameters should be reasonably taken into account to assess the global performance of complex structures subjected to seismic actions. In the present paper, incorporating the generalized F-discrepancy (GF-discrepancy) based optimal point selection strategy and the probability density evolution method (PDEM), the effects of different distribution types and different coefficients of variation of the random parameters on the response of a multi-degree-of-freedom nonlinear structure with tens of random parameters are studied. The results show that the difference between the second-order moments of the structural responses with different types of distributions could be in the order of ±30%. When the coefficients of variation of the basic parameters are either very small or fairly large, the effects of different types of distributions on the second-order moments of responses are relatively large, but in an opposite tendency. Therefore, there exists a range of the coefficients of variation in which the different types of distributions have little effects on the second-order moments of responses. However, the probability density functions (PDFs) of the responses are always affected considerably, even may change qualitatively by the types of distributions of the random parameters