Aerodynamic database error filtering via SVD-like methods

A method is presented to filter out errors in multidimensional databases. The method does not require any a priori information about the nature of the errors, which need not be small, neither random, nor exhibit zero mean. Instead, they are only required to be relatively uncorrelated to the clean information contained in the database. The method presented is based on an improved multidimensional extension by the authors (2016) [21] of a seminal gappy reconstruction method, due to Everson and Sirovich (1995) [18], who developed a two-dimensional method, based on SVD, able to reconstruct lost information at known database positions. The improved gappy reconstruction method is evolved in this paper as an error filtering method in two steps, since it is adapted to first (a) identify the error locations in the database and then (b) reconstruct the information in these locations by treating the associated data as gappy data. The resulting method filters out O(1) errors in an efficient fashion, for both random and systematic errors. Also, the method performs well both when errors are concentrated and when they are spread along the database. The method is illustrated and tested in several toy model and aerodynamic databases, obtained by discretizing a transcendental function and CFD-calculating the pressure on the surface of a wing for varying values of the angle of attack.