基于双加权POD的建筑物风压场重构

A bi-weighted-POD and its application on wind pressure field

本征正交分解法(Proper Orthogonal Decomposition,POD)是一种基于2阶统计量的降阶方法,通过寻找一组正交单位基使得随机场在新坐标下能有更简洁的描述。本文提出了面积和均方根双加权POD,将其应用于建筑物风压场重构。从均方值角度对POD进行推导,证明POD是均方值意义上的最佳展开方式;在新的推导框架下对POD进行双加权优化,使之能较好地捕捉风压场中能量较低的相干结构;对5∶1矩形风压场进行重构,初步验证了双加权POD的可行性。结果表明:双加权POD可以较好地重构5∶1矩形风压场,重构风压场各空间点的重构精度一致,且能够基本还原所有空间点的时程和功率谱密度。与面积加权POD相比,双加权POD能够显著提高风压场低能量区域的降阶模型重构精度。

Proper Orthogonal Decomposition(POD)is a reduced order modeling(ROM)method based on 2nd-order statics,which simplifies the investigated wind-pressure field in a new coordinate system formed by a set of orthonormal basis.This paper suggests a method of bi-weighted POD(which weights POD by area and at the same time by root-mean-square),and applies this method to the modal reduction of pressure field around buildings.Firstly,we introduce the POD expansion in a mean-square method,which demonstrates that POD is the optimal choice of ROM in the mean-square sense.Furthermore,we modify the original POD by the bi-weighting-method to improve its capacity of identifying coherent structures with lower energy in pressure field.For the last part,the validity of bi-weighted POD is roughly examined by a case study which applies the method to the pressure field of a 5∶1 rectangular cylinder.It turns out that the modified POD method improves the ROM accuracy at the area associated with lower energy in a significant way.In the meantime,a wind-pressure field ROM constructed by bi-weighted POD captures vital information provided by the original wind-pressure field and is spatially accuracy-consistent.