基于协方差本征变换与谐波合成法的随机风场模拟  

Simulation of stochastic wind field based on covariance proper transformation and weighted amplitude wave superposition

作　　者：张佳文[1] 郭文华[1,2] 项超群[1] 

机构地区：[1]中南大学土木工程学院,长沙410075 [2]中南大学高速铁路建造技术国家工程实验室,长沙410075

出　　处：《振动与冲击》2013年第21期197-203,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(51078356);铁道部科技研究开发计划重大项目(2008G031-Q)

摘　　要：为解决谐波合成法模拟多变量随机脉动风场计算效率低下,内存易超限的问题,提出了协方差本征变换与谐波合成法相结合的风场模拟新方法。在谐波合成法和协方差本征变换的基础上,采用基于方差比的模态截断准则缩阶互谱密度矩阵,以减少矩阵的Cholesky分解次数,同时运用FFT技术来提高谐波项的合成速度,并给出了该方法的误差控制指标。通过算例表明上述方法可有效减少整个模拟过程的计算时间,采用方差比模态截断准则可保证所有节点位置的样本方差具有较高精度,模拟样本的功率谱密度、相关函数与目标值较为符合,并且具有较好的随机性。证实了所提出方法可以高效、准确地的模拟出随机脉动风场。In order to reduce computing amount and memory consumption of the weighted amplitude wave superposition method, an improved method combining the weighted amplitude wave superposition method and the covariance proper transformation method was proposed here. On the basis of these two methods, with the mode truncation criteria based on the variance ratio, the reduced order matrix of principal components of the cross-spectral density matrix was employed to conduct the Cholesky decomposition. Furthermore, an error control index was defined to estimate the simulation precision. A computing algorithm was put forward and its efficiency was enhanced with FFT. Finally, The simulation procedure was applied to an example and the results showed that the proposed method remarkably saves the simulation time, the mode truncation criteria based on the variance ratio improves the computing accuracy; the cross- power spectral density functions, and the cross-correlation functions are in good agreement with the expected target values; the method presented here is an accurate and effective one to simulate a stochastic wind field.

关 键 词：协方差本征变换 谐波合成法 方差比 模态截断准则 随机风场 FFT技术 

分 类 号：TU393.3[建筑科学—结构工程]