Dynamic mode decomposition for non-uniformly sampled data

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.