Dynamic mode decomposition for non-uniformly sampled data

Dynamic mode decomposition for non-uniformly sampled data We propose an original approach to estimate dynamic mode decomposition (DMD) modes from non-uniformly sampled data. The proposed strategy processes a time-resolved sequence of flow snapshots in three steps. First, a reduced-order modeling of the non-missing data is made by proper orthogonal decomposition to obtain a low-order description of the state space. Second, the missing data are determined with maximum likelihood by coupling a linear dynamical state-space model with the Expectation-Maximization algorithm. Third, the DMD modes are finally estimated on the reconstructed data with a multiple linear regression method called orthonormalized partial least squares regression. This methodology is assessed for the flow past a NACA0012 airfoil at 20° of angle of attack and a Reynolds number of 103. The flow measurements are obtained with time-resolved particle image velocimetry and artificially subsampled at different ratios of missing data. The results show that the proposed method can reproduce the dominant DMD modes and the main structures of the flow fields for 50 and 75 % of missing data. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Experiments in Fluids Springer Journals

Dynamic mode decomposition for non-uniformly sampled data

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Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Engineering; Engineering Fluid Dynamics; Fluid- and Aerodynamics; Engineering Thermodynamics, Heat and Mass Transfer
ISSN
0723-4864
eISSN
1432-1114
D.O.I.
10.1007/s00348-016-2165-1
Publisher site
See Article on Publisher Site

Abstract

We propose an original approach to estimate dynamic mode decomposition (DMD) modes from non-uniformly sampled data. The proposed strategy processes a time-resolved sequence of flow snapshots in three steps. First, a reduced-order modeling of the non-missing data is made by proper orthogonal decomposition to obtain a low-order description of the state space. Second, the missing data are determined with maximum likelihood by coupling a linear dynamical state-space model with the Expectation-Maximization algorithm. Third, the DMD modes are finally estimated on the reconstructed data with a multiple linear regression method called orthonormalized partial least squares regression. This methodology is assessed for the flow past a NACA0012 airfoil at 20° of angle of attack and a Reynolds number of 103. The flow measurements are obtained with time-resolved particle image velocimetry and artificially subsampled at different ratios of missing data. The results show that the proposed method can reproduce the dominant DMD modes and the main structures of the flow fields for 50 and 75 % of missing data.

Journal

Experiments in FluidsSpringer Journals

Published: May 14, 2016

References

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