Aerodynamic database reconstruction via gappy high order singular value decomposition

Abstract

Aerodynamic database reconstruction via gappy high order singular value decompositionby Ana Isabel MORENO LÓPEZ A method based on an iterative application of high order singular value decomposition is derived for the reconstruction of missing data in multidimensional databases. The method is inspired by a seminal gappy reconstruction method for two-dimensional databases invented by Everson and Sirovich (1995) and improved by Beckers and Rixen (2003) and Venturi and Karniadakis (2004). In addition, the method is adapted to treat both noisy and structured-but-nonrectangular databases.The method is calibrated and illustrated using a three-dimensional toy model database that is obtained by discretizing a transcendental function. The performance of the method is tested on three aerodynamic databases for the flow past a wing, one obtained by a semi-analytical method, and two resulting from computational fluid dynamics. The method is finally applied to an experimental database consisting in a non-exhaustive parameter space measurement of forces for a box-wing configuration.iii ResumenReconstrucción de bases de datos aerodinámicas a través de la descomposición en valores sigulares para tensores de alto orden por Ana Isabel MORENO LÓPEZ Esta Tesis se centra en el desarrollo de un método para la reconstrucción de bases de datos experimentales incompletas de más de dos dimensiones. Como idea general, consiste en la aplicación iterativa de la descomposición en valores singulares de alto orden sobre la base de datos incompleta. Este nuevo método se inspira en el que ha servido de base para la reconstrucción de huecos en bases de datos bidimensionales inventado por Everson y Sirovich (1995) que a su vez, ha sido mejorado por Beckers y Rixen (2003) y simultáneamente por Venturi y Karniadakis (2004). Además, se ha previsto la adaptación de este nuevo método para tratar el posible ruido característico de bases de datos experimentales y a su vez, bases de datos estructuradas cuya información no forma un hiperrectángulo perfecto.Se usará una base de datos tridimensional de muestra como modelo, obtenida a través de una función transcendental, para calibrar e ilustrar el método. A continuación se detalla un exhaustivo estudio del funcionamiento del método y sus variantes para distintas bases de datos aerodinámicas. En concreto, se usarán tres bases de datos tridimensionales que contienen la distribución de presiones sobre un ala. Una se ha generado a través de un método semi-analítico con la intención de estudiar distintos tipos de discretizaciones espaciales. El resto resultan de dos modelos numéricos calculados en CFD. Porúltimo, el método se aplica a una base de datos experimental de más de tres dimensiones que contiene la medida de fuerzas de una configuración ala de Prandtl obtenida de una campaña de ensayos en túnel de viento, donde se estudiaba un amplio espacio de parámetros geométricos de la configuración que como resultado ha generado una base de datos donde la información está dispersa.v

Physics-Constrained Bayesian Neural Network for Fluid Flow Reconstruction with Sparse and Noisy Data

“…Proper orthogonal decomposition (POD) [4] or dynamic mode decomposition (DMD) [5,6] are commonly used for flow feature extraction. For instance, Gappy POD has been applied for steady and unsteady flow-field reconstruction in various applications [7][8][9][10][11][12]. To overcome the linearity limitations of POD and DMD, deep learning based approaches (e.g., autoencoder neural networks) have been recently developed to extract nonlinear latent representations of the flow field from massive offline data [13].…”

Aerodynamic database error filtering via high order singular value decomposition

“…From Equation (6.1), CF and s min are related to the gappy reconstruction method and their influence on the reconstruction errors have been proven insignificant [35,36]. Therefore, for now on CF = 0.1 and s min = 4, are set analogically to previous analyses.…”

“…Therefore, a sampling method can be designed that would allow, for instance, to minimise the number of experimental runs needed to reconstruct the complete domain by applying the methodology presented in [35,36]. This method would iteratively analyse the database showing the highest errors between two consecutive reconstructions and thus identifying them as the crucial points.…”

“…A substantial increase in computational time efficiency has been shown for reciprocating engines, requiring real-time control [33], and conceptual design of aircraft components [34]. However, from the point of view of this Thesis, the most important application of HOSVD is employing it in reconstructing missing data in multidimensional databases contaminated with noise [35,36]. The method called gappy-noisy-HOSVD method is based on the iterative method to reconstruct lost data in two-dimensional databases invented by Everson and Sirovich, later improved independently by Beckers et al and Venturi et al The main contribution is its expansion to multidimensional databases and the optimisation of the number of retained modes which minimises the noise influence on data reconstruction.…”

“…The triple-iterative error filtering method is the core of this Thesis and will enable the method to recognize very well both random and systematic errors without any a priori knowledge of the clean database and the nature of the errors. Additionally, once the error positions are known, they are treated as gappy points and are reconstructed using missing data reconstruction methods based on SVD, which yield very small reconstruction errors [35]. Finally, replacing SVD with HOSVD will allow to treat multidimensional databases in an analogous manner, which is one of the important aspects of this Thesis.…”