基于Gappy POD的流场数据填补方法

Gappy Proper Orthogonal Decomposition for Flow Data Reconstruction

本征正交分解方法(proper orthogonal decomposition,POD)是一种数据驱动的流场特征信息提取技术,可以按能量大小给出流场的结构模态,并且可以通过较少阶模态叠加获得高阶数据的近似描述.将该方法结合一组线性方程,即构成Gappy POD方法,可实现对缺失流场的重构.论文从样本数据已知和样本数据不完全已知两种情况展开,对Gappy POD方法在缺失流场数据填补方面的应用进行了研究.首先,对于样本数据已知的情况,研究了样本参数范围内任意参数值下的重构能力;其次,对于样本数据不完全已知的情况,研究了模态阶数、缺失率以及样本数对缺失流场重构精度的影响规律.结果表明,Gappy POD方法可以高效再现参数范围内的任意完整流场数据.但是,对于缺失率较高的样本集,需要适当增加样本数以提高重构精度.

The proper orthogonal decomposition(POD)is a data-driven feature information extraction technology of flow,which can give the mode of the flow field by the amount of energy,and can obtain an approximate description of the high order data by lower order mode superposition.This method combined with a set of linear equations will form the Gappy POD method,which can achieve reconstruction of the missing flow.This paper studied the application of the Gappy POD method in filling the missing flow field data,developing from two cases where the snapshots are known and the snapshots are not completely known.Firstly,for the case where the snapshots are known,the reconstruction ability under any parameter value within the range of snapshots parameters was studied.Secondly,for the case that the snapshots are not completely known,the influence of modal order,Gappy rate and snapshot number on the accuracy of missing flow field reconstruction were studied.The results show that the Gappy POD method can efficiently reproduce any complete flow field data within the parameter range.However,for snapshots with high Gappy rates,it is necessary to increase the number of snapshots appropriately to improve the reconstruction accuracy.