Filling gappy PIV experimental data of unsteady turbulent flows using dynamic mode decomposition with Kalman filter

Particle image velocimetry (PIV) can capture large datasets of spatio-temporal flow fields but often suffer from incomplete measurements due to optical distortion, low seeding density, or equipment limitations. These data gaps can prevent detailed analysis of turbulence which typically requires the computation of the velocity gradient tensor. To address this challenge, we propose a data recovery and denoising framework that combines Kalman filter with dynamic mode decomposition (DMD). The Kalman filter is used to reduce measurement noise, thereby enhancing data quality and enabling more accurate recovery of temporal dynamics. Simultaneously, DMD is utilized to extract coherent structures and reconstruct missing flow fields in high-dimensional, spatio-temporal data. To validate the proposed method, we have used a direct numerical simulation (DNS) dataset of rapidly accelerated and decelerated pipe flows as a ground truth for comparison.

DMD is first applied to noisy PIV data to compute the transition matrix that governs the temporal evolution of the flow field. Next, based on the transition matrix obtained, a Kalman filter is employed to estimate and suppress both observation and perturbation noise. This filtering process yields a denoised version of the PIV data that reflects more accurately the true flow behavior. Finally, the denoised data are used in a second DMD reconstruction step to reconstruct the missing measurements in the original data. Our method demonstrates good performance in approximating the true flow dynamics even when the artificial noise and gaps are added to the DNS data. We then apply the Kalman filter–DMD approach to experimental 2D PIV data, showcasing its robustness to noise and its ability to fill data gaps while preserving essential flow features. This integrated method provides a promising tool for enhancing the reliability of PIV data in experimental fluid mechanics.