脉动风速连续随机场的降维模拟

基于标准正交随机变量的波数谱表示，通过定义标准正交随机变量集的随机函数形式，建立了连续时空随机场模拟的波数谱-随机函数方法。同时，引入快速傅里叶变换（FFT）的算法，极大地提高了波数谱-随机函数方法的模拟效率。在波数谱-随机函数模拟方法中，仅需两个基本随机变量即可在概率密度层次上描述时空随机场的概率特性，并利用数论方法选取基本随机变量的代表性点集，实现对连续时空随机场模拟的降维表达。数值算例表明，当模拟相同数量的样本时，综合考虑模拟的效率和精度两方面，该文方法与传统的波数谱表示方法不分伯仲，但该文方法所需的基本随机变量最少，生成的代表性样本数量少且构成一个完备的概率集，从而可结合概率密度演化理论实现结构随机动力反应及动力可靠度的精细化分析。最后，结合Kaimal风速谱及Davenport空间相干函数模型，模拟了水平向脉动风速连续随机场，验证了该文方法的有效性和优越性。

SIMULATION OF FLUCTUATING WIND VELOCITY CONTINUOUS STOCHASTIC FIELD BY DIMENSION REDUCTION APPROACH

Based on the frequency-wavenumber spectrum representation correlating with the standard orthogonal random variables, a hybrid approach of frequency-wavenumber spectrum and a random function for simulating the continuous spatio-temporal stochastic field is proposed by introducing the random function of standard orthogonal random variable sets. Meanwhile, the simulation efficiency of the proposed approach is greatly enhanced by employing Fast Fourier Transform (FFT) algorithm technique. Benefiting from the proposed approach, the probability characteristics of the spatio-temporal stochastic field can be described on the probability density level with only two elementary random variables. Therefore, the complete representative point sets with assigned probabilities of the elementary random variables can be obtained through the number-theoretical method. As a result, the dimension reduction representation of the continuous spatio-temporal stochastic field can be realized. Numerical examples indicate that when using the same number of samples and taking the efficiency and accuracy into consideration at the same time, the proposed approach have a similar simulation result to the conventional frequency-wavenumber spectrum representation. However, the smallest number of the elementary random variables is needed in the proposed approach, which leads to a smaller number of representative samples with a complete probability set. Consequently, it could naturally be combined with the probability density evolutionary method (PDEM) to carry out the accurate analysis of stochastic dynamic response and dynamic reliability assessment of engineering structures. Finally, combining the Kaimal fluctuating wind velocity spectrum with Davenport spatial coherence function, a numerical example of simulation for horizontal-fluctuating-wind velocity continuous stochastic field is presented to verify the accuracy and superiority of the proposed approach.