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Modal analysis techniques are used to identify patterns and developreduced-order models in a variety of fluid applications. However,experimentally acquired flow fields may be corrupted with incorrect and missingentries, which may degrade modal decomposition. Here we use robust principalcomponent analysis (RPCA) to improve the quality of flow field data byleveraging global coherent structures to identify and replace spurious datapoints. RPCA is a robust variant of principal component analysis (PCA), alsoknown as proper orthogonal decomposition (POD) in fluids, that decomposes adata matrix into the sum of a low-rank matrix containing coherent structuresand a sparse matrix of outliers and corrupt entries. We apply RPCA filtering toa range of fluid simulations and experiments of varying complexities and assessthe accuracy of low-rank structure recovery. First, we analyze direct numericalsimulations of flow past a circular cylinder at Reynolds number 100 withartificial outliers, alongside similar PIV measurements at Reynolds number 413.Next, we apply RPCA filtering to a turbulent channel flow simulation from theJohns Hopkins Turbulence database, demonstrating that dominant coherentstructures are preserved in the low-rank matrix. Finally, we investigate PIVmeasurements behind a two-bladed cross-flow turbine that exhibits bothbroadband and coherent phenomena. In all cases, we find that RPCA filteringextracts dominant coherent structures and identifies and fills in incorrect ormissing measurements. The performance is particularly striking when flow fieldsare analyzed using dynamic mode decomposition, which is sensitive to noise andoutliers.

Robust Principal Component Analysis for Modal Decomposition of Corrupt Fluid Flows