Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

Non-linear data-driven modelling on multidimensional fields : an application to hydro-morphodynamic coastal flows

This thesis contributions belong to the general framework of data-based and physically-based data-driven modelling. An efficient approach for Machine Learning (ML), as well as a speed-up technique for Data Assimilation (DA), have been developed. For this purpose, Dimensionality Reduction (DR) and stochastic spectral modelling were used. In particular, a coupling between Proper Orthogonal Decomposition (POD) and Polynomial Chaos Expansion is at the center of this thesis contributions. POD and PCE have widely proved their worth in their respective frameworks, and the idea was to combine them for optimal field measurement based forecasting, and ensemble-based acceleration technique for variational DA. For this purpose, (i) a physically interpretable POD-PCE ML for non-linear multidimensional fields was developed in the Neural Networks (NN) paradigm and (ii) a hybrid ensemble-variational DA approach for parametric calibration was proposed with adapted calculations of POD-PCE metamodelling error covariance matrix. The proposed techniques were assessed in the context of an industrial application, for the study of sedimentation in a coastal power plant's water intake. Water intakes ensure plant cooling via a pumping system. They can be subject to sediment accumulation, which represents a clogging risk and requires costly dredging operations. For monitoring and safety reasons, the power plant stakeholders asked for a predictive tool that could be run in operational conditions. Data collected during many years of monitoring in the study area were provided. The objective was then to achieve comprehensive analysis of the flow and sediment dynamics, as well as to develop an optimal model in terms of forecasting accuracy, physical meaning, and required computational time. Uncertainty reduction and computational efficiency were therefore starting points for all proposed contributions. In addition to the previously proposed methods, Uncertainty Quantification (UQ) studies were undertaken. Specifically, (i) uncertainties related to tidal hydrodynamic modelling, resulting from common modelling choices (domain size, empirical closures) were investigated. POD patterns resulting from measurements and numerical scenarios were compared; (ii) UQ study of the sediment transport modelling in the intake, in a highdimensional framework, was achieved. Investigations were based on appropriate DR. In fact, POD patterns of Boundary Conditions (BC) and Initial Conditions (IC), resulting from hydrodynamic simulations outputs and from bathymetry measurements respectively, were used. A perspective of this work would be to implement a hybrid POD-PCE model, using both measured and numerically emulated data, to better understand and predict complex physical processes. This approach would offer a complete, fast and efficient tool for operational predictions

Contributions to improve the technologies supporting unmanned aircraft operations

Mención Internacional en el título de doctorUnmanned Aerial Vehicles (UAVs), in their smaller versions known as drones, are becoming increasingly important in today's societies. The systems that make them up present a multitude of challenges, of which error can be considered the common denominator. The perception of the environment is measured by sensors that have errors, the models that interpret the information and/or define behaviors are approximations of the world and therefore also have errors. Explaining error allows extending the limits of deterministic models to address real-world problems. The performance of the technologies embedded in drones depends on our ability to understand, model, and control the error of the systems that integrate them, as well as new technologies that may emerge. Flight controllers integrate various subsystems that are generally dependent on other systems. One example is the guidance systems. These systems provide the engine's propulsion controller with the necessary information to accomplish a desired mission. For this purpose, the flight controller is made up of a control law for the guidance system that reacts to the information perceived by the perception and navigation systems. The error of any of the subsystems propagates through the ecosystem of the controller, so the study of each of them is essential. On the other hand, among the strategies for error control are state-space estimators, where the Kalman filter has been a great ally of engineers since its appearance in the 1960s. Kalman filters are at the heart of information fusion systems, minimizing the error covariance of the system and allowing the measured states to be filtered and estimated in the absence of observations. State Space Models (SSM) are developed based on a set of hypotheses for modeling the world. Among the assumptions are that the models of the world must be linear, Markovian, and that the error of their models must be Gaussian. In general, systems are not linear, so linearization are performed on models that are already approximations of the world. In other cases, the noise to be controlled is not Gaussian, but it is approximated to that distribution in order to be able to deal with it. On the other hand, many systems are not Markovian, i.e., their states do not depend only on the previous state, but there are other dependencies that state space models cannot handle. This thesis deals a collection of studies in which error is formulated and reduced. First, the error in a computer vision-based precision landing system is studied, then estimation and filtering problems from the deep learning approach are addressed. Finally, classification concepts with deep learning over trajectories are studied. The first case of the collection xviiistudies the consequences of error propagation in a machine vision-based precision landing system. This paper proposes a set of strategies to reduce the impact on the guidance system, and ultimately reduce the error. The next two studies approach the estimation and filtering problem from the deep learning approach, where error is a function to be minimized by learning. The last case of the collection deals with a trajectory classification problem with real data. This work completes the two main fields in deep learning, regression and classification, where the error is considered as a probability function of class membership.Los vehículos aéreos no tripulados (UAV) en sus versiones de pequeño tamaño conocidos como drones, van tomando protagonismo en las sociedades actuales. Los sistemas que los componen presentan multitud de retos entre los cuales el error se puede considerar como el denominador común. La percepción del entorno se mide mediante sensores que tienen error, los modelos que interpretan la información y/o definen comportamientos son aproximaciones del mundo y por consiguiente también presentan error. Explicar el error permite extender los límites de los modelos deterministas para abordar problemas del mundo real. El rendimiento de las tecnologías embarcadas en los drones, dependen de nuestra capacidad de comprender, modelar y controlar el error de los sistemas que los integran, así como de las nuevas tecnologías que puedan surgir. Los controladores de vuelo integran diferentes subsistemas los cuales generalmente son dependientes de otros sistemas. Un caso de esta situación son los sistemas de guiado. Estos sistemas son los encargados de proporcionar al controlador de los motores información necesaria para cumplir con una misión deseada. Para ello se componen de una ley de control de guiado que reacciona a la información percibida por los sistemas de percepción y navegación. El error de cualquiera de estos sistemas se propaga por el ecosistema del controlador siendo vital su estudio. Por otro lado, entre las estrategias para abordar el control del error se encuentran los estimadores en espacios de estados, donde el filtro de Kalman desde su aparición en los años 60, ha sido y continúa siendo un gran aliado para los ingenieros. Los filtros de Kalman son el corazón de los sistemas de fusión de información, los cuales minimizan la covarianza del error del sistema, permitiendo filtrar los estados medidos y estimarlos cuando no se tienen observaciones. Los modelos de espacios de estados se desarrollan en base a un conjunto de hipótesis para modelar el mundo. Entre las hipótesis se encuentra que los modelos del mundo han de ser lineales, markovianos y que el error de sus modelos ha de ser gaussiano. Generalmente los sistemas no son lineales por lo que se realizan linealizaciones sobre modelos que a su vez ya son aproximaciones del mundo. En otros casos el ruido que se desea controlar no es gaussiano, pero se aproxima a esta distribución para poder abordarlo. Por otro lado, multitud de sistemas no son markovianos, es decir, sus estados no solo dependen del estado anterior, sino que existen otras dependencias que los modelos de espacio de estados no son capaces de abordar. Esta tesis aborda un compendio de estudios sobre los que se formula y reduce el error. En primer lugar, se estudia el error en un sistema de aterrizaje de precisión basado en visión por computador. Después se plantean problemas de estimación y filtrado desde la aproximación del aprendizaje profundo. Por último, se estudian los conceptos de clasificación con aprendizaje profundo sobre trayectorias. El primer caso del compendio estudia las consecuencias de la propagación del error de un sistema de aterrizaje de precisión basado en visión artificial. En este trabajo se propone un conjunto de estrategias para reducir el impacto sobre el sistema de guiado, y en última instancia reducir el error. Los siguientes dos estudios abordan el problema de estimación y filtrado desde la perspectiva del aprendizaje profundo, donde el error es una función que minimizar mediante aprendizaje. El último caso del compendio aborda un problema de clasificación de trayectorias con datos reales. Con este trabajo se completan los dos campos principales en aprendizaje profundo, regresión y clasificación, donde se plantea el error como una función de probabilidad de pertenencia a una clase.I would like to thank the Ministry of Science and Innovation for granting me the funding with reference PRE2018-086793, associated to the project TEC2017-88048-C2-2-R, which provide me the opportunity to carry out all my PhD. activities, including completing an international research internship.Programa de Doctorado en Ciencia y Tecnología Informática por la Universidad Carlos III de MadridPresidente: Antonio Berlanga de Jesús.- Secretario: Daniel Arias Medina.- Vocal: Alejandro Martínez Cav

Modeling and Simulation in Engineering

The general aim of this book is to present selected chapters of the following types: chapters with more focus on modeling with some necessary simulation details and chapters with less focus on modeling but with more simulation details. This book contains eleven chapters divided into two sections: Modeling in Continuum Mechanics and Modeling in Electronics and Engineering. We hope our book entitled "Modeling and Simulation in Engineering - Selected Problems" will serve as a useful reference to students, scientists, and engineers