本征正交分解在数据处理中的应用及展望  

APPLICATION AND OUTLOOK OF PROPER ORTHOGONAL DECOMPOSITION IN DATA PROCESSING

作　　者：路宽 张亦弛 靳玉林 车子璠 张昊鹏 郭栋[1] Lu Kuan;Zhang Yichi;Jin Yulin;Che Zifan;Zhang Haopeng;Guo Dong(School of Mechanics,Civil Engineering and Architecture,Institute of Vibration Engineering,Northwestern Polytechnical University,Xi′an,710129,China;High tech research and development center of the Ministry of science and technology,Beijing,100124,China;School of Mechanical Engineering,Southwest Jiaotong University,Chengdu,610031,China)

机构地区：[1]西北工业大学振动工程研究所,力学与土木建筑学院,西安710129 [2]科学技术部高技术研究发展中心,北京100044 [3]西南交通大学机械工程学院,成都610031

出　　处：《动力学与控制学报》2022年第5期20-33,共14页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(12072263,11802235);中国博士后科学基金资助项目(2021T140033,2021M690274)。

摘　　要：本征正交分解(Proper Orthogonal Decomposition,POD)是对高维复杂非线性系统进行降维处理的有效方法之一.本文对POD方法在一系列实际工程领域降维中的研究进行了综述.首先简要介绍POD方法的发展历史,简述POD方法分类,随后详细列举POD方法在粒子图像测速(Particle Image Velocimetry,PIV)技术、计算流体力学(Computational Fluid Dynamics,CFD)数据处理中的应用.对比了POD方法和动态模态分解(Dynamic Mode Decomposition,DMD)方法在实际工程应用中各自的优缺点,结果表明在流场稳定脉动时可采用DMD方法,而其他随时间变化的流场采用POD方法更合适.最后对POD方法的发展尤其是在人工智能领域的应用做出展望.Proper orthogonal decomposition(POD)is one of the effective methods to reduce dimension of high-dimensional complex nonlinear systems.This paper summarizes research of POD method in dimension reduction in various practical engineering fields.Firstly,development history of POD method is briefly introduced,and classification of POD method is described.Then,applications of POD method in particle image velocimetry(PIV)technology and computational fluid dynamics(CFD)data processing are listed in detail.The advantages and disadvantages of POD method and dynamic mode decomposition(DMD)method in practical engineering application are compared.The results show that DMD method can be used when the flow field is steady and pulsating,while POD method is more suitable for other time-varying flow fields.Finally,development of POD method,especially its application in the field of artificial intelligence,is prospected.

关 键 词：本征正交分解 降维 高维系统 粒子图像测速 计算流体力学 

分 类 号：V219[航空宇航科学与技术—航空宇航推进理论与工程]