Bayesian Gappy Proper Orthogonal Decomposition for Aerodynamic Data Fusion

During the development of an aircraft, a multitude of aerodynamic data are required for different flight conditions throughout the flight envelope. Nowadays, a large portion of these data are routinely acquired by computational fluid dynamics simulations. However, due to modeling and convergence issues especially for extreme flight conditions, numerical data cannot be reliably generated for the entire flight envelope yet. Hence, numerical data are complemented by data from wind tunnel experiments and flight testing. However, the data from these different sources will always show some discrepancies to deal with. Data fusion methods aim at combining the individual strengths and weaknesses of data from different sources in order to provide a consistent data set for the entire parameter domain. In this work we propose an extension to the well-established Gappy proper orthogonal decomposition technique by reformulating the least-squares problem as a regression task. A Bayesian perspective is imposed to account for uncertainties during the data fusion process. This involves a kernelized regression formulation that also addresses the problem of linearity imposed by the dimensionality reduction method and therefore adds more flexibility to the approach. The performance and robustness of the approach is demonstrated investigating an industrially relevant, large-scale aircraft test case fusing high-quality experimental and numerical data. Compared to the established Gappy POD approach, the new method shows a significantly improved agreement with the observed wind tunnel data for the investigated test case. In addition, the new approach enables to provide credible bounds for the fused result, which serve as an indicator for the associated uncertainty.