Aerodynamic database error filtering via high order singular value decomposition

Abstract

Escuela Técnica Superior de Ingenieros Aeronéuticos Departamento de Vehículos Aeroespaciales Doctor of Philosophy Aerodynamic database error filtering via high order singular value decompositionby Artur Andrzej JARZABEK A method is presented to filter errors out in multidimensional databases. The method does not require any a priori information about the nature the errors. In particular, the errors need not to 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 is based on an improved extension of a seminal iterative gappy reconstruction method (able to reconstruct lost information at known positions in the database) due to Everson and Sirovich (1995).The improved gappy reconstruction method is evolved 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, both when these are random and when they are systematic, and also both when they concentrated and when they are spread along the database. The performance of the method is first illustrated using a two-dimensional toy model database resulting from discretizing a transcendental function and then tested on two CFD-calculated, three-dimensional aerodynamic databases containing the pressure coefficient on the surface of a wing for varying values of the angle of attack.A more general performance analysis of the method is presented with the intention of quantifying the randomness factor the method admits maintaining a correct performance and secondly, quantifying the size of error the method can detect. Lastly, some improvements of the method are proposed with their respective verification.iii UNIVERSIDAD POLITÉCNICA DE MADRID ResumenEscuela Técnica Superior de Ingenieros Aeronéuticos Departamento de Vehículos Aeroespaciales Doctorado Filtrado de errores en bases de datos aerodinámicas a través de la descomposición en valores sigulares para tensores de alto ordenpor Artur Andrzej JARZABEK Esta Tesis presenta un nuevo método para filtrar errores en bases de datos multidimensionales. Este método no precisa ninguna información a priori sobre la naturaleza de los errores. En concreto, los errrores no deben ser necesariamente pequeños, ni de distribución aleatoria ni tener media cero. El único requerimiento es que no estén correlados con la información limpia propia de la base de datos.Este nuevo método se basa en una extensión mejorada del método básico de reconstrucción de huecos (capaz de reconstruir la información que falta de una base de datos multidimensional en posiciones conocidas) inventado por Everson y Sirovich (1995).El método de reconstrucción de huecos mejorado ha evolucionado como un método de filtrado de errores de dos pasos: en primer lugar, (a) identifica las posiciones en la base de da...