基于相干函数矩阵的风场本征正交分解  

Proper orthogonal decomposition of wind velocity fields based on coherency matrix

作　　者：胡亮[1,2] 顾明[1] 李黎[3] 

机构地区：[1]同济大学土木工程防灾国家重点实验室,上海200092 [2]华南理工大学亚热带建筑科学国家重点实验室,广东广州510640 [3]华中科技大学土木工程与力学学院,湖北武汉430074

出　　处：《振动工程学报》2010年第1期64-68,共5页Journal of Vibration Engineering

基　　金：国家自然科学基金重大研究计划重点项目(90715040);国家自然科学基金创新群体项目(50621062);国家科技支撑计划(2006BAJ06B05);华南理工大学亚热带建筑科学国家重点实验室开放基金(200822)

摘　　要：提出了基于相干函数矩阵的风场本征正交分解(CPOD,Coherency matrix-based POD)。首先推导了基于功率谱函数矩阵的本征正交分解。通过引入功率谱矩阵的预分解,将推导过程中的功率谱矩阵特征值分解改进为相干函数矩阵的特征值分解,得到了CPOD的表达式。对CPOD作频域离散化,得到了基于CPOD的谱表示法随机风场模拟公式。以模拟某18点脉动风速场为算例,对比分析了CPOD与SPT振型的特征并验证了所提模拟算法的有效性。结果表明,CPOD的显式分离特性使得它具有比POD更加明确的物理意义,并适用于风场特征分析。This paper presents coherency matrix-based proper orthogonal decomposition （CPOD）, which boasts an improved form of power spectral matrix-based POD. Original formulas of POD are derived for a multi-correlated stationary stochastic vector process, involving the eigen-decomposition of its cross power spectral density matrixes. These matrixes are substituted by the product of the coherency matrixes and the diagonal auto spectral matrixes, resulting the CPOD on the basis of the eigen-decomposition of only coherency matrixes. The continuous formulas are immediately discretized into the CPOD-based spectral representation method t^at serves as a simulation tool for stochastic loading. Application of this method to a stochastic wind velocity field is included as a numerical example. The CPOD eigenvalues and eigenvectors （modes） of this wind field are computed and described in detail in comparison to the corresponding items of POD, which indicates a more straightforward link between CPOD modes and distribution patterns of the wind field.

关 键 词：本征正交分解(POD) 相干函数矩阵 风场模拟 

分 类 号：TU973.32[建筑科学—结构工程]