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

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.