@unpublished{upm40982,
          number = {10.20868/UPM.thesis.40982},
           title = {Aerodynamic database error filtering via high order singular value decomposition},
          school = {Aeronauticos},
          author = {Artur Andrzej Jarzabek},
            year = {2016},
             url = {http://oa.upm.es/40982/},
        abstract = {Esta Tesis presenta un nuevo m{\'e}todo para filtrar errores en bases de datos multidimensionales. Este m{\'e}todo no precisa ninguna informaci{\'o}n a priori sobre la naturaleza de los errores. En concreto, los errrores no deben ser necesariamente peque{\~n}os, ni de distribuci{\'o}n aleatoria ni tener media cero. El {\'u}nico requerimiento es que no est{\'e}n correlados con la informaci{\'o}n limpia propia de la base de datos. Este nuevo m{\'e}todo se basa en una extensi{\'o}n mejorada del m{\'e}todo b{\'a}sico de reconstrucci{\'o}n de huecos (capaz de reconstruir la informaci{\'o}n que falta de una base de datos multidimensional en posiciones conocidas) inventado por Everson y Sirovich (1995). El m{\'e}todo de reconstrucci{\'o}n de huecos mejorado ha evolucionado como un m{\'e}todo de filtrado de errores de dos pasos: en primer lugar, (a) identifica las posiciones en la base de datos afectadas por los errores y despu{\'e}s, (b) reconstruye la informaci{\'o}n en dichas posiciones tratando la informaci{\'o}n de {\'e}stas como informaci{\'o}n desconocida. El m{\'e}todo resultante filtra errores O(1) de forma eficiente, tanto si son errores aleatorios como sistem{\'a}ticos e incluso si su distribuci{\'o}n en la base de datos est{\'a} concentrada o esparcida por ella. Primero, se ilustra el funcionamiento delm{\'e}todo con una base de datosmodelo bidimensional, que resulta de la dicretizaci{\'o}n de una funci{\'o}n transcendental. Posteriormente, se presentan algunos casos pr{\'a}cticos de aplicaci{\'o}n del m{\'e}todo a dos bases de datos tridimensionales aerodin{\'a}micas que contienen la distribuci{\'o}n de presiones sobre un ala a varios {\'a}ngulos de ataque. Estas bases de datos resultan de modelos num{\'e}ricos calculados en CFD. ABSTRACT 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 resultingmethod 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 toymodel database resulting fromdiscretizing 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.}
}