随机脉动风场的谱表示降维模拟  

Dimension reduction based spectral representation of stochastic fluctuation wind field simulation

作　　者：刘章军[1,2] 刘增辉[1,2] LIU Zhang-jun;LIU Zeng-hui(Hubei Key Laboratory of Disaster Prevention and Reduction(China Three Gorges University) , Yichang 443002, China;College of Civil Engineering & Architecture, China Three Gorges University, Yichang 443002, China)

机构地区：[1]防灾减灾湖北省重点实验室(三峡大学),湖北宜昌443002 [2]三峡大学土木与建筑学院,湖北宜昌443002

出　　处：《振动工程学报》2018年第1期49-56,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51778343;51278282);三峡大学研究生科研创新基金资助项目(SDYC2016014)

摘　　要：基于正交随机变量的谱表示,引入随机函数的约束条件,提出了随机脉动风场模拟的谱表示降维方法。从谱表示模拟公式中所需随机变量的数量及约束条件两方面,厘清了经典谱表示与基于正交随机变量谱表示的区别。将正交随机变量集表达为两个基本随机变量的正交函数形式,使基于正交随机变量谱表示的随机度从数万降低为2,极大地减少了随机脉动风场模拟的计算量。通过构造两类不同的正交随机函数形式,分别对高层建筑沿高度变化的水平向脉动风场进行模拟,均能获得较高的模拟精度,检验了此方法的有效性。研究表明:此方法仅需2个基本随机变量即可在密度层次上反映脉动风场的概率特性,且生成的233条代表性时程构成一个完备的概率集,进而可结合概率密度演化理论进行工程结构抗风可靠度精细化分析。With consideration of the formulation of random functions,which serve as random constraints,a renewed scheme of the spectral representation method(SRM)with orthogonal random variables for the simulation of the stochastic fluctuation wind field is proposed in this paper.In terms of the number of random variables and the constraint conditions in the formula-tion of the SRM,the differences between the conventional SRM with random phase angles and the SRM with orthogonal ran-dom variables are clarified.By representing the set of the orthogonal random variables as the orthogonal random functions with respect to two elementary random variables,the random degrees of the SRM with orthogonal random variables are greatly re-duced from tens of thousands to2.As a result,the computational effort of the stochastic fluctuation wind field simulation is ef-fectively reduced.The effectiveness and availability of the proposed approach are verified by constructing two kinds of orthogo-nal random functions to accurately simulate the horizontal fluctuation wind field acting along the height of a high-rise building.It is indicated that the proposed approach can reflect the probability characteristics of the fluctuation wind field at the density function level with only two elementary random variables.And it only needs to generate233representative samples which con-stitute a complete probability set.Thus,the proposed approach can combine with the probability density evolution theory to accurately analyze the reliability of complicated engineering structures subjected to wind excitations.

关 键 词：脉动风场 随机振动 谱表示 随机函数 降维模拟 

分 类 号：TU3121[建筑科学—结构工程] O324[理学—一般力学与力学基础]