Fusing computational and experimental flow data with Gappy POD

Gappy Proper Orthogonal Decomposition (POD) is a simple but powerful method for data fusion and offers efficient means to harmonize data, i.e. improve the consistency between various sets of data. The basic idea behind Gappy POD for data fusion is that the POD analysis of computational flow solutions at different flow conditions yields a set of empirical modes, which describes the dominant behavior or dynamics of a given flow problem in an optimal sense, i.e. for any given basis size, the error between the original and reconstructed data is minimized. Given a suitable set of POD modes derived from computational data, the Gappy POD solves a small and thus inexpensive least squares problem to determine a set of coefficients such that the reconstruction (linear combination of modes) optimally matches the experimental data. Besides its capability to harmonize data, the Gappy POD approach offers additional benefits, such as the prediction of quantities that were not measured experimentally. It can also be seen as a way to correct complete numerical flow solutions if limited experimental data is available. The lecture will present the Gappy POD in the context of aircraft aerodynamics and Particle Image Velocimetry (PIV).