Linear Approach to the Orbiting Spacecraft Thermal Problem

A linear method is developed for solving the nonlinear differential equations of a lumped-parameter thermal model of a spacecraft moving in a closed orbit. This method, based on perturbation theory, is compared with heuristic linearizations of the same equations. The essential feature of the linear approach is that it provides a decomposition in thermal modes, like the decomposition of mechanical vibrations in normal modes. The stationary periodic solution of the linear equations can be alternately expressed as an explicit integral or as a Fourier series. This method is applied to a minimal thermal model of a satellite with ten isothermal parts (nodes), and the method is compared with direct numerical integration of the nonlinear equations. The computational complexity of this method is briefly studied for general thermal models of orbiting spacecraft, and it is concluded that it is certainly useful for reduced models and conceptual design but it can also be more efficient than the direct integration of the equations for large models. The results of the Fourier series computations for the ten-node satellite model show that the periodic solution at the second perturbative order is sufficiently accurate.

Characterizing chaos in a type of fractional duffing's equation

We characterize the chaos in a fractional Duffing’s equation computing the Lyapunov exponents and the dimension of the strange attractor in the effective phase space of the system. We develop a specific analytical method to estimate all Lyapunov exponents and check the results with the fiduciary orbit technique and a time series estimation method.

The Zero-Removing Property and Lagrange-Type Interpolation Series

The classical Kramer sampling theorem, which provides a method for obtaining orthogonal sampling formulas, can be formulated in a more general nonorthogonal setting. In this setting, a challenging problem is to characterize the situations when the obtained nonorthogonal sampling formulas can be expressed as Lagrange-type interpolation series. In this article a necessary and sufficient condition is given in terms of the zero removing property. Roughly speaking, this property concerns the stability of the sampled functions on removing a finite number of their zeros.

Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces of entire functions which includes as a particular case the classical Shannon sampling theory. This abstract setting allows us to obtain a sort of converse result and to characterize when the sampling formula associated with an analytic Kramer kernel can be expressed as a Lagrange-type interpolation series. On the other hand, the de Branges spaces of entire functions satisfy orthogonal sampling formulas which can be written as Lagrange-type interpolation series. In this work some links between all these ideas are established.

Optimizing Functional Network Representation of Multivariate Time Series

By combining complex network theory and data mining techniques, we provide objective criteria for optimization of the functional network representation of generic multivariate time series. In particular, we propose a method for the principled selection of the threshold value for functional network reconstruction from raw data, and for proper identification of the network's indicators that unveil the most discriminative information on the system for classification purposes. We illustrate our method by analysing networks of functional brain activity of healthy subjects, and patients suffering from Mild Cognitive Impairment, an intermediate stage between the expected cognitive decline of normal aging and the more pronounced decline of dementia. We discuss extensions of the scope of the proposed methodology to network engineering purposes, and to other data mining tasks.

Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two different tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally efficient and does not require any ad hoc symbolization process. We find that the method correctly distinguishes between reversible and irreversible stationary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic processes (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identify the irreversible nature of the series

Unsupervised method to classify PM10 pollutant concentrations

In this paper a method based mainly on Data Fusion and Artificial Neural Networks to classify one of the most important pollutants such as Particulate Matter less than 10 micrometer in diameter (PM10) concentrations is proposed. The main objective is to classify in two pollution levels (Non-Contingency and Contingency) the pollutant concentration. Pollutant concentrations and meteorological variables have been considered in order to build a Representative Vector (RV) of pollution. RV is used to train an Artificial Neural Network in order to classify pollutant events determined by meteorological variables. In the experiments, real time series gathered from the Automatic Environmental Monitoring Network (AEMN) in Salamanca Guanajuato Mexico have been used. The method can help to establish a better air quality monitoring methodology that is essential for assessing the effectiveness of imposed pollution controls, strategies, and facilitate the pollutants reduction.

Optical systems design using the SMS method and optimizations

Resumen El diseño de sistemas ópticos, entendido como un arte por algunos, como una ciencia por otros, se ha realizado durante siglos. Desde los egipcios hasta nuestros días los sistemas de formación de imagen han ido evolucionando así como las técnicas de diseño asociadas. Sin embargo ha sido en los últimos 50 años cuando las técnicas de diseño han experimentado su mayor desarrollo y evolución, debido, en parte, a la aparición de nuevas técnicas de fabricación y al desarrollo de ordenadores cada vez más potentes que han permitido el cálculo y análisis del trazado de rayos a través de los sistemas ópticos de forma rápida y eficiente. Esto ha propiciado que el diseño de sistemas ópticos evolucione desde los diseños desarrollados únicamente a partir de la óptica paraxial hasta lo modernos diseños realizados mediante la utilización de diferentes técnicas de optimización multiparamétrica. El principal problema con el que se encuentra el diseñador es que las diferentes técnicas de optimización necesitan partir de un diseño inicial el cual puede fijar las posibles soluciones. Dicho de otra forma, si el punto de inicio está lejos del mínimo global, o diseño óptimo para las condiciones establecidas, el diseño final puede ser un mínimo local cerca del punto de inicio y lejos del mínimo global. Este tipo de problemática ha llevado al desarrollo de sistemas globales de optimización que cada vez sean menos sensibles al punto de inicio de la optimización. Aunque si bien es cierto que es posible obtener buenos diseños a partir de este tipo de técnicas, se requiere de muchos intentos hasta llegar a la solución deseada, habiendo un entorno de incertidumbre durante todo el proceso, puesto que no está asegurado el que se llegue a la solución óptima. El método de las Superficies Múltiples Simultaneas (SMS), que nació como una herramienta de cálculo de concentradores anidólicos, se ha demostrado como una herramienta también capaz utilizarse para el diseño de sistemas ópticos formadores de imagen, aunque hasta la fecha se ha utilizado para el diseño puntual de sistemas de formación de imagen. Esta tesis tiene por objeto presentar el SMS como un método que puede ser utilizado de forma general para el diseño de cualquier sistema óptico de focal fija o v afocal con un aumento definido así como una herramienta que puede industrializarse para ayudar al diseñador a afrontar de forma sencilla el diseño de sistemas ópticos complejos. Esta tesis está estructurada en cinco capítulos: El capítulo 1, es un capítulo de fundamentos donde se presentan los conceptos fundamentales necesarios para que el lector, aunque no posea una gran base en óptica formadora de imagen, pueda entender los planteamientos y resultados que se presentan en el resto de capítulos El capitulo 2 aborda el problema de la optimización de sistemas ópticos, donde se presenta el método SMS como una herramienta idónea para obtener un punto de partida para el proceso de optimización. Mediante un ejemplo aplicado se demuestra la importancia del punto de partida utilizado en la solución final encontrada. Además en este capítulo se presentan diferentes técnicas que permiten la interpolación y optimización de las superficies obtenidas a partir de la aplicación del SMS. Aunque en esta tesis se trabajará únicamente utilizando el SMS2D, se presenta además un método para la interpolación y optimización de las nubes de puntos obtenidas a partir del SMS3D basado en funciones de base radial (RBF). En el capítulo 3 se presenta el diseño, fabricación y medidas de un objetivo catadióptrico panorámico diseñado para trabajar en la banda del infrarrojo lejano (8-12 μm) para aplicaciones de vigilancia perimetral. El objetivo presentado se diseña utilizando el método SMS para tres frentes de onda de entrada utilizando cuatro superficies. La potencia del método de diseño utilizado se hace evidente en la sencillez con la que este complejo sistema se diseña. Las imágenes presentadas demuestran cómo el prototipo desarrollado cumple a la perfección su propósito. El capítulo 4 aborda el problema del diseño de sistemas ópticos ultra compactos, se introduce el concepto de sistemas multicanal, como aquellos sistemas ópticos compuestos por una serie de canales que trabajan en paralelo. Este tipo de sistemas resultan particularmente idóneos para él diseño de sistemas afocales. Se presentan estrategias de diseño para sistemas multicanal tanto monocromáticos como policromáticos. Utilizando la novedosa técnica de diseño que en este capítulo se presenta el diseño de un telescopio de seis aumentos y medio. En el capítulo 5 se presenta una generalización del método SMS para rayos meridianos. En este capítulo se presenta el algoritmo que debe utilizarse para el diseño de cualquier sistema óptico de focal fija. La denominada optimización fase 1 se vi introduce en el algoritmo presentado de forma que mediante el cambio de las condiciones iníciales del diseño SMS que, aunque el diseño se realice para rayos meridianos, los rayos skew tengan un comportamiento similar. Para probar la potencia del algoritmo desarrollado se presenta un conjunto de diseños con diferente número de superficies. La estabilidad y potencia del algoritmo se hace evidente al conseguirse por primera vez el diseño de un sistema de seis superficies diseñado por SMS. vii Abstract The design of optical systems, considered an art by some and a science by others, has been developed for centuries. Imaging optical systems have been evolving since Ancient Egyptian times, as have design techniques. Nevertheless, the most important developments in design techniques have taken place over the past 50 years, in part due to the advances in manufacturing techniques and the development of increasingly powerful computers, which have enabled the fast and efficient calculation and analysis of ray tracing through optical systems. This has led to the design of optical systems evolving from designs developed solely from paraxial optics to modern designs created by using different multiparametric optimization techniques. The main problem the designer faces is that the different optimization techniques require an initial design which can set possible solutions as a starting point. In other words, if the starting point is far from the global minimum or optimal design for the set conditions, the final design may be a local minimum close to the starting point and far from the global minimum. This type of problem has led to the development of global optimization systems which are increasingly less sensitive to the starting point of the optimization process. Even though it is possible to obtain good designs from these types of techniques, many attempts are necessary to reach the desired solution. This is because of the uncertain environment due to the fact that there is no guarantee that the optimal solution will be obtained. The Simultaneous Multiple Surfaces (SMS) method, designed as a tool to calculate anidolic concentrators, has also proved useful for the design of image-forming optical systems, although until now it has occasionally been used for the design of imaging systems. This thesis aims to present the SMS method as a technique that can be used in general for the design of any optical system, whether with a fixed focal or an afocal with a defined magnification, and also as a tool that can be commercialized to help designers in the design of complex optical systems. The thesis is divided into five chapters. Chapter 1 establishes the basics by presenting the fundamental concepts which the reader needs to acquire, even if he/she doesn‟t have extensive knowledge in the field viii of image-forming optics, in order to understand the steps taken and the results obtained in the following chapters. Chapter 2 addresses the problem of optimizing optical systems. Here the SMS method is presented as an ideal tool to obtain a starting point for the optimization process. The importance of the starting point for the final solution is demonstrated through an example. Additionally, this chapter introduces various techniques for the interpolation and optimization of the surfaces obtained through the application of the SMS method. Even though in this thesis only the SMS2D method is used, we present a method for the interpolation and optimization of clouds of points obtained though the SMS3D method, based on radial basis functions (RBF). Chapter 3 presents the design, manufacturing and measurement processes of a catadioptric panoramic lens designed to work in the Long Wavelength Infrared (LWIR) (8-12 microns) for perimeter surveillance applications. The lens presented is designed by using the SMS method for three input wavefronts using four surfaces. The powerfulness of the design method used is revealed through the ease with which this complex system is designed. The images presented show how the prototype perfectly fulfills its purpose. Chapter 4 addresses the problem of designing ultra-compact optical systems. The concept of multi-channel systems, such as optical systems composed of a series of channels that work in parallel, is introduced. Such systems are especially suitable for the design of afocal systems. We present design strategies for multichannel systems, both monochromatic and polychromatic. A telescope designed with a magnification of six-and-a-half through the innovative technique exposed in this chapter is presented. Chapter 5 presents a generalization of the SMS method for meridian rays. The algorithm to be used for the design of any fixed focal optics is revealed. The optimization known as phase 1 optimization is inserted into the algorithm so that, by changing the initial conditions of the SMS design, the skew rays have a similar behavior, despite the design being carried out for meridian rays. To test the power of the developed algorithm, a set of designs with a different number of surfaces is presented. The stability and strength of the algorithm become apparent when the first design of a system with six surfaces if obtained through the SMS method.

Impedance of foundations using the Boundary Integral Equation Method

Dynamic soil-structure interaction has been for a long time one of the most fascinating areas for the engineering profession. The building of large alternating machines and their effects on surrounding structures as well as on their own functional behavior, provided the initial impetus; a large amount of experimental research was done,and the results of the Russian and German groups were especially worthwhile. Analytical results by Reissner and Sehkter were reexamined by Quinlan, Sung, et. al., and finally Veletsos presented the first set of reliable results. Since then, the modeling of the homogeneous, elastic halfspace as a equivalent set of springs and dashpots has become an everyday tool in soil engineering practice, especially after the appearance of the fast Fourier transportation algorithm, which makes possible the treatment of the frequency-dependent characteristics of the equivalent elements in a unified fashion with the general method of analysis of the structure. Extensions to the viscoelastic case, as well as to embedded foundations and complicated geometries, have been presented by various authors. In general, they used the finite element method with the well known problems of geometric truncations and the subsequent use of absorbing boundaries. The properties of boundary integral equation methods are, in our opinion, specially well suited to this problem, and several of the previous results have confirmed our opinion. In what follows we present the general features related to steady-state elastodynamics and a series of results showing the splendid results that the BIEM provided. Especially interesting are the outputs obtained through the use of the so-called singular elements, whose description is incorporated at the end of the paper. The reduction in time spent by the computer and the small number of elements needed to simulate realistically the global properties of the halfspace make this procedure one of the most interesting applications of the BIEM.

A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation

Stochastic model updating must be considered for quantifying uncertainties inherently existing in real-world engineering structures. By this means the statistical properties,instead of deterministic values, of structural parameters can be sought indicating the parameter variability. However, the implementation of stochastic model updating is much more complicated than that of deterministic methods particularly in the aspects of theoretical complexity and low computational efficiency. This study attempts to propose a simple and cost-efficient method by decomposing a stochastic updating process into a series of deterministic ones with the aid of response surface models and Monte Carlo simulation. The response surface models are used as surrogates for original FE models in the interest of programming simplification, fast response computation and easy inverse optimization. Monte Carlo simulation is adopted for generating samples from the assumed or measured probability distributions of responses. Each sample corresponds to an individual deterministic inverse process predicting the deterministic values of parameters. Then the parameter means and variances can be statistically estimated based on all the parameter predictions by running all the samples. Meanwhile, the analysis of variance approach is employed for the evaluation of parameter variability significance. The proposed method has been demonstrated firstly on a numerical beam and then a set of nominally identical steel plates tested in the laboratory. It is found that compared with the existing stochastic model updating methods, the proposed method presents similar accuracy while its primary merits consist in its simple implementation and cost efficiency in response computation and inverse optimization.

Development of a method of assessment of the problem-solving competence at the technical University of Madrid.

The competence evaluation promoted by the European High Education Area entails a very important methodological change that requires guiding support to help lecturers carry out this new and complex task. In this regard, the Technical University of Madrid (UPM, by its Spanish acronym) has financed a series of coordinated projects with the objective of developing a model for teaching and evaluating core competences and providing support to lecturers. This paper deals with the problem-solving competence. The first step has been to elaborate a guide for teachers to provide a homogeneous way to asses this competence. This guide considers several levels of acquisition of the competence and provides the rubrics to be applied for each one. The guide has been subsequently validated with several pilot experiences. In this paper we will explain the problem-solving assessment guide for teachers and will show the pilot experiences that has been carried out. We will finally justify the validity of the method to assess the problem-solving competence.

Transformación de series numéricas temporales en secuencias simbólicas

El Trabajo de Fin de Grado aborda el tema del Descubrimiento de Conocimiento en series numéricas temporales, abordando el análisis de las mismas desde el punto de vista de la semántica de las series. La gran mayoría de trabajos realizados hasta la fecha en el campo del análisis de series temporales proponen el análisis numérico de los valores de la serie, lo que permite obtener buenos resultados pero no ofrece la posibilidad de formular las conclusiones de forma que se puedan justificar e interpretar los resultados obtenidos. Por ello, en este trabajo se pretende crear una aplicación que permita realizar el análisis de las series temporales desde un punto de vista cualitativo, en contraposición al tradicional método cuantitativo. De esta forma, quedarán recogidos todos los elementos relevantes de la serie temporal que puedan servir de estudio en un futuro. Para abordar el objetivo propuesto se plantea un mecanismo para extraer de la serie temporal la información que resulta de interés para su análisis. Para poder hacerlo, primero se formaliza el conjunto de comportamientos relevantes del dominio, que serán los símbolos a mostrar en la salida de la aplicación. Así, el método que se ha diseñado e implementado transformará una serie temporal numérica en una secuencia simbólica que recoge toda la semántica de la serie temporal de partida y resulta más intuitiva y fácil de interpretar. Una vez que se dispone de un mecanismo para transformar las series numéricas en secuencias simbólicas, se pueden plantear todas las tareas de análisis sobre dichas secuencias de símbolos. En este trabajo, aunque no se entra en este post-análisis de estas series, sí se plantean distintos campos en los que se puede avanzar en el futuro. Por ejemplo, se podría hacer una medida de la similitud entre dos secuencias simbólicas como punto de partida para la tarea de comparación o la creación de modelos de referencia para análisis posteriores de las series temporales. ---ABSTRACT---This Final-year Project deals with the topic of Knowledge Discovery in numerical time series, addressing time series analysis from the viewpoint of the semantics of the series. Most of the research conducted to date in the field of time series analysis recommends analysing the values of the series numerically. This provides good results but prevents the conclusions from being formulated to allow justification and interpretation of the results. Thus, the purpose of this project is to create an application that allows the analysis of time series, from a qualitative point of view rather than a quantitative one. This way, all the relevant elements of the time series will be gathered for future studies. The design of a mechanism to extract the information that is of interest from the time series is the first step towards achieving the proposed objective. To do this, all the key behaviours in the domain are set, which will be the symbols shown in the output. The designed and implemented method transforms a numerical time series into a symbolic sequence that takes in all the semantics of the original time series and is more intuitive and easier to interpret. Once a mechanism for transforming the numerical series into symbolic sequences is created, the symbolic sequences are ready for analysis. Although this project does not cover a post-analysis of these series, it proposes different fields in which research can be done in the future. For instance, comparing two different sequences to measure the similarities between them, or the creation of reference models for further analysis of time series.

Síntesis de series temporales de centelleo troposférico

Los sistemas de telecomunicación que trabajan en frecuencias milimétricas pueden verse severamente afectados por varios fenómenos atmosféricos, tales como la atenuación por gases, nubes y el centelleo troposférico. Una adecuada caracterización es imprescindible en el diseño e implementación de estos sistemas. El presente Proyecto Fin de Grado tiene como objetivo el estudio estadístico a largo plazo de series temporales de centelleo troposférico en enlaces de comunicaciones en trayecto inclinado sobre la banda Ka a 19,7 GHz. Para la realización de este estudio, se dispone como punto de partida de datos experimentales procedentes de la baliza en banda Ka a 19,7 GHz del satélite Eutelsat Hot Bird 13A que han sido recopilados durante siete años entre julio de 2006 y junio de 2013. Además, se cuenta como referencia teórica con la aplicación práctica del método UIT-R P.618-10 para el modelado del centelleo troposférico en sistemas de telecomunicación Tierra-espacio. Esta información permite examinar la validez de la aplicación práctica del método UIT-R P.1853-1 para la síntesis de series temporales de centelleo troposférico. Sobre este sintetizador se variará la serie temporal de contenido integrado de vapor de agua en una columna vertical por datos reales obtenidos de bases de datos meteorológicas ERA-Interim y GNSS con el objetivo de comprobar el impacto de este cambio. La primera parte del Proyecto comienza con la exposición de los fundamentos teóricos de los distintos fenómenos que afectan a la propagación en un enlace por satélite, incluyendo los modelos de predicción más importantes. Posteriormente, se presentan los fundamentos teóricos que describen las series temporales, así como su aplicación al modelado de enlaces de comunicaciones. Por último, se describen los recursos específicos empleados en la realización del experimento. La segunda parte del Proyecto se inicia con la muestra del proceso de análisis de los datos disponibles que, más tarde, permiten obtener resultados que caracterizan el centelleo troposférico en ausencia de precipitación, o centelleo seco, para los tres casos de estudio sobre los datos experimentales, sobre el modelo P.618-10 y sobre el sintetizador P.1853-1 con sus modificaciones. Al haber mantenido en todo momento las mismas condiciones de frecuencia, localización, clima y periodo de análisis, el estudio comparativo de los resultados obtenidos permite extraer las conclusiones oportunas y proponer líneas futuras de investigación. ABSTRACT. Telecommunication systems working in the millimetre band are severely affected by various atmospheric impairments, such as attenuation due to clouds, gases and tropospheric scintillation. An adequate characterization is essential in the design and implementation of these systems. This Final Degree Project aims to a long-term statistical study of time series of tropospheric scintillation on slant path communications links in Ka band at 19.7 GHz. To carry out this study, experimental data from the beacon in Ka band at 19.7 GHz for the Eutelsat Hot Bird 13A satellite are available as a starting point. These data have been collected during seven years between July 2006 and June 2013. In addition, the practical application of the ITU-R P.618-10 method for tropospheric scintillation modeling of Earth-space telecommunication systems has been the theoretical reference used. This information allows us to examine the validity of the practical application of the ITU-R P.1853-1 method for tropospheric scintillation time series synthesis. In this synthesizer, the time series of water vapor content in a vertical column will be substituted by actual data from meteorological databases ERA-Interim and GNSS in order to test the impact of this change. The first part of the Project begins with the exposition of the theoretical foundations of the various impairments that affect propagation in a satellite link, including the most important prediction models. Subsequently, it presents the theoretical foundations that describe the time series, and its application to communication links modeling. Finally, the specific resources used in the experiment are described. The second part of the Project starts with the exhibition of the data analysis process to obtain results that characterize the tropospheric scintillation in the absence of precipitation, or dry scintillation, for the three study cases on the experimental data, on the P.618-10 model and on the P.1853-1 synthesizer with its modifications. The fact that the same conditions of frequency, location, climate and period of analysis are always maintained, allows us to draw conclusions and propose future research lines by comparing the results.

On a comparison method to reaction-diffusion systems and its applications to chemotaxis

In this paper we consider a general system of reaction-diffusion equations and introduce a comparison method to obtain qualitative properties of its solutions. The comparison method is applied to study the stability of homogeneous steady states and the asymptotic behavior of the solutions of different systems with a chemotactic term. The theoretical results obtained are slightly modified to be applied to the problems where the systems are coupled in the differentiated terms and / or contain nonlocal terms. We obtain results concerning the global stability of the steady states by comparison with solutions of Ordinary Differential Equations.

Development of a method of assessment of the problem-solving competency at the Technical University of Madrid

The competence evaluation promoted by the European High Education Area entails a very important methodological change that requires guiding support to help lecturers carry out this new and complex task. In this regard, the Technical University of Madrid (UPM, by its Spanish acronym) has financed a series of coordinated projects with the objective of developing a model for teaching and evaluating core competences and providing support to lecturers. This paper deals with the problem solving competence. The first step has been to elaborate a guide for teachers to provide an homogeneous way to asses this competence. This guide considers several levels of acquisition of the competence and provided the rubrics to be applied for each one. The guide has been subsequently validated with several pilot experiences. In this paper we will explain the problem-solving assessment guide for teachers and will show the pilot experiences that has been carried out. We will finally justify the validity of the method to assess the problem solving competence.