基于双加权POD的建筑物风压场重构

张昊; 杨雄伟; 李明水

doi:10.11729/syltlx20210146

基于双加权POD的建筑物风压场重构

doi: 10.11729/syltlx20210146

张昊^{1, 2,},
杨雄伟^{1, 2},
李明水^{1, 2, ,}

1.
西南交通大学风工程试验研究中心，成都　610031
2.
风工程四川省重点实验室，成都　610031

基金项目: 国家自然科学基金（51878580）

详细信息

作者简介:
张昊：（1994—），男，四川成都人，硕士研究生。研究方向：结构风工程。通信地址：四川省成都市金牛区二环路北一段111号西南交通大学九里校区土木工程学院（610031）。E-mail：Jetzhang_chengdu@163.com

通讯作者:
E-mail：lms_rcwe@126.com

中图分类号: TU312⁺.1
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出版历程
- 收稿日期: 2021-10-20
- 修回日期: 2022-03-28
- 录用日期: 2022-03-30
- 网络出版日期: 2022-05-24

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

ZHANG Hao^{1, 2
,},
YANG Xiongwei^{1, 2},
LI Mingshui^{1, 2
, ,}

1.
Research Centre for Wind Engineering, Southwest Jiaotong University, Chengdu　610031, China
2.
Key Laboratory for Wind Engineering of Sichuan Province, Chengdu　610031, China

摘要

摘要: 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，它通过寻找一组正交单位基使得随机场在新坐标下能有更加简洁的描述。本文提出了面积和均方根双加权POD，并将其应用于建筑物风压场重构。首先，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；然后，在新的推导框架下对POD进行双加权优化，使之能够较好地捕捉风压场中能量较低的相干结构；最后，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，重构风压场在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与功率谱密度。与面积加权的POD相比，双加权POD能够显著提升风压场低能量区域的降阶模型重构精度。
- 本征正交分解法 /
- 双加权POD /
- 风压场重构 /
- 5∶1矩形
Abstract: 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.
- Proper Orthogonal Decomposition /
- Bi-weighted POD /
- ROM of pressure field /
- 5∶1 rectangular cylinder

HTML全文

图 1 风洞中的测压模型

Figure 1. Building model layout

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图 2 测压孔布置

Figure 2. Geometry of building model and pressure tap locations

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图 3 各测点平均风压系数与脉动风压系数

Figure 3. Distribution of mean and fluctuating pressure coefficients on building model

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图 4 修正前后的前6阶空间POD模态

Figure 4. 1st – 6th spatial modes with and without spatial adjustments

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图 5 加权前后模态能量累积比

Figure 5. Cumulative proportion of mode energy with and without weighting

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图 6 前11阶模态驻点、分离点、再附点的POD重构

Figure 6. 11-order ROM of Stationary point, separation point and reattachment point

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图 7 双加权与面积加权POD前11阶模态重构的整体效果

Figure 7. 11-order ROM accuracy, with and without weighting

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图 8 双加权及面积加权POD时间模态的模态系数

Figure 8. Mode coefficients of temporal modes with and without weighting

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