随机风场模拟的连续本征正交分解-随机函数方法

摘要

Based on a continuous proper orthogonal decomposition (POD) of time-spatial stochastic fields,a hybrid continuous POD-random function approach for simulation of time-space stochastic fields was proposed by introducing random function expression forms of orthogonal random variable sets.Utilizing the continuous POD technique based on the cross power spectral density function (CPSDF),a stochastic field was expressed as a superposition of finite lower order proper modes to realize the order reduction treatment of the original stochastic field.With the random function expression for orthogonal random variable sets,an original stochastic field was accurately described in the second order statistical meaning using only two basic random variables.It was shown that the number of basic random variables in the proposed approach is the minimum compared with that in the classical POD approach;all representative time histories of fluctuating wind velocity obtained construct a complete probability set.Lastly,taking Kaimal fluctuating wind velocity spectrum as an example,a stochastic wind field in horizontal direction was simulated and analyzed to verify the higher accuracy of the proposed approach.%在时-空随机场的连续本征正交分解(POD)基础上,通过引入正交随机变量集的随机函数表达形式,提出了时-空随机场模拟的连续本征正交分解-随机函数法.基于互功率谱密度函数的连续POD法将时-空随机场表达为有限个本征模态的叠加,实现了对原时-空随机场的高效降阶处理;正交随机变量集的随机函数表达,则实现了仅用两个基本随机变量即可在二阶统计意义上对原时-空随机场的精确描述.与传统的POD方法相比,本方法所需的基本随机变量最少,且生成的脉动风速代表性时程可构成一个完备的概率集;最后,以Kaimal脉动风速谱为例,进行了水平向随机风场的模拟分析,验证了该方法的高效精确性.