平稳随机脉动风场模拟的高维概率空间选点法

Points Selection in High-Dimensional Random-Variate Space for Simulating Stationary Stochastic Wind Field

为进行结构抗风可靠度分析,需对作用在结构上平稳随机脉动风场进行模拟。采用谱表达法描述脉动风场往往涉及成千上万个随机变量,会造成“维数灾难”问题。基于此,本文提出一类高维概率空间选点法保障模拟的精度和效率,主要由3个步骤组成:高维概率空间的分解、正交子空间选点和随机配对得到高维概率空间离散代表点及赋得概率。采用本文的方法模拟了某30层框架剪力墙结构上沿高度变化的水平风场,研究表明:本文的方法在二阶统计意义上具有很高的模拟精度和效率,可用少量的代表性样本构建完备的概率集合,进一步结合概率密度演化法可对结构风振响应进行精细化概率评价。

To perform wind-resistant reliability analysis of structures,it is necessary to simulate the stationary stochastic fluctuating wind field.Simulating the stochastic fluctuating wind fields through spectral representation me-thod(SRM)often involves thousands of random variables,leading to the“curse of dimensionality”.On this basis,this paper proposes a new method for points selection in high-dimensional random-variate space to ensure the accuracy and efficiency of SRM.The new method mainly consists of three steps:the decomposition of high-dimensional random-variate space,the points selection in the orthogonal subspaces,and the random pairing to obtain the representative points and assigned probabilities in high-dimensional random-variate space.The proposed method is used to investigate the horizontal wind field acting along the height of a 30-story frame-shear wall structure.The results show that the proposed method is of high accuracy and efficiency for the simulation in the second-order statistical sense and a complete probability set can be constructed by only using a small number of representative sample processes.Besides,the proposed method can be further combined with the probability density evolution method to elaborately evaluate the probabilistic response of wind-induced vibration of structures.