Flow prediction using dynamic mode decomposition with time-delay embedding based on local measurement

Abstract

We develop a method for the prediction of flow fields based on local particle image velocimetry (PIV) measurement. High spatial resolution can be achieved by focusing PIV on local flow regions; however, it is difficult for standard dynamic mode decomposition (DMD) to predict the temporally resolved flow field based on limited information in sub-domain. In this regard, the local flow field is embedded using time-delay to augment the spatial dynamics. As such, both high temporally and spatially resolved flow fields can be faithfully obtained from local PIV measurement using the DMD method. Using fabricated patterns, we demonstrate that DMD with time-delay embedding can faithfully predict dynamic patterns over a long time interval, whereas the standard DMD can only match the ground truth briefly following initiation. Using PIV measurement of a wake flow and a highly dynamic sweeping jet flow, the DMD with time-delay embedding can increase the temporal resolution up to 100 times with a prediction error rate of approximately 8%. Compared with wake flow, where unsteady flow patterns are relatively weak, a sweeping jet flow demonstrates that the prediction performance is improved even more significantly using time-delay embedding compared with standard DMD when the flow is highly dynamic. For sweeping jet flow, the prediction error rate can drop from 56% using standard DMD to 8.3% by embedding a time-delay smaller than five steps, for a small cost of calculation time. In addition, the DMD with time-delay embedding shows robustness to small noise. For data with high noise whose signal-to-noise ratio is 15, the method has an error rate of less than 5%.