Knowledge-based spatiotemporal linear abstraction

We present a theoretical framework and a case study for reusing the same conceptual and computational methodology for both temporal abstraction and linear (unidimensional) space abstraction, in a domain (evaluation of traffic-control actions) significantly different from the one (clinical medicine) in which the method was originally used. The method, known as knowledge-based temporal abstraction, abstracts high-level concepts and patterns from time-stamped raw data using a formal theory of domain-specific temporal-abstraction knowledge. We applied this method, originally used to interpret time-oriented clinical data, to the domain of traffic control, in which the monitoring task requires linear pattern matching along both space and time. First, we reused the method for creation of unidimensional spatial abstractions over highways, given sensor measurements along each highway measured at the same time point. Second, we reused the method to create temporal abstractions of the traffic behavior, for the same space segments, but during consecutive time points. We defined the corresponding temporal-abstraction and spatial-abstraction domain-specific knowledge. Our results suggest that (1) the knowledge-based temporal-abstraction method is reusable over time and unidimensional space as well as over significantly different domains; (2) the method can be generalized into a knowledge-based linear-abstraction method, which solves tasks requiring abstraction of data along any linear distance measure; and (3) a spatiotemporal-abstraction method can be assembled from two copies of the generalized method and a spatial-decomposition mechanism, and is applicable to tasks requiring abstraction of time-oriented data into meaningful spatiotemporal patterns over a linear, decomposable space, such as traffic over a set of highways.

Estudio de las dinámicas de pérdida de peso corporal en los programas de ejercicio físico y nutrición = Study of the dynamics of body weight loss in exercise and nutritional programs

Introducción. La obesidad puede definirse como una enfermedad metabólica crónica de origen multifactorial, lo que provoca trastornos o problemas físicos y psicológicos a la persona, con patologías asociadas que limitan la esperanza de vida y deterioran la calidad de la misma, siendo determinante para sus áreas sociales y laborales. Este trastorno metabólico crónico se caracteriza por una acumulación excesiva de energía en el cuerpo en forma de grasa, lo que lleva a un aumento de peso con respecto al valor esperado por sexo, edad y altura. La gestión y el tratamiento de la obesidad tienen objetivos más amplios que la pérdida de peso e incluyen la reducción del riesgo y la mejora de la salud. Estos pueden ser alcanzados por la pérdida modesta de peso (es decir, 10.5% del peso corporal inicial), la mejora del contenido nutricional de la dieta y un modesto incremento en la actividad física y condición física. La dieta es uno de los métodos más populares para perder peso corporal. El ejercicio es otra alternativa para perder peso corporal. El aumento de ejercicio provoca un desequilibrio cuando se mantiene la ingesta calórica. También tiene ventajas, como la mejora del tono muscular, la capacidad cardiovascular, fuerza y flexibilidad, aumenta el metabolismo basal y mejora el sistema inmunológico. Objetivos. El objetivo de esta tesis es contribuir en un estudio de intervención para aclarar la evolución del peso corporal durante una intervención de dieta y ejercicio. Para ello, se evaluaron los efectos de la edad, sexo, índice de masa corporal inicial y el tipo de tratamiento en las tendencias de pérdida de peso. Otro objetivo de la tesis era crear un modelo de regresión lineal múltiple capaz de predecir la pérdida de peso corporal después del periodo de intervención. Y, por último, determinar el efecto sobre la composición corporal (peso corporal, índice de masa corporal, la masa grasa, y la masa libre de grasa) de las diferentes intervenciones basadas en ejercicios (fuerza, resistencia, resistencia combinada con fuerza, y las recomendaciones de actividad física (grupo control)) en combinación con dieta de adultos con sobrepeso y obesidad, después de la intervención, así como los cambios de la composición corporal 3 años más tarde. Diseño de la investigación. Los datos empleados en el análisis de esta tesis son parte del proyecto “Programas de Nutrición y Actividad Física para el tratamiento de la obesidad” (PRONAF). El proyecto PRONAF es un estudio clínico sobre programas de nutrición y actividad física para el sobrepeso y la obesidad, desarrollado en España durante varios años de intervención. Fue diseñado, en parte, para comparar diferentes tipos de intervención, con el objetivo de evaluar su impacto en las dinámicas de pérdida de peso, en personas con sobrepeso y obesidad. Como diseño experimental, el estudio se basó en una restricción calórica, a la que, en algunos casos, se le añadió un protocolo de entrenamiento (fuerza, resistencia, o combinado, en igualdad de volumen e intensidad). Las principales variables para la investigación que comprende esta tesis fueron: el peso corporal y la composición corporal (masa grasa y masa libre de grasa). Conclusiones. En esta tesis, para los programas de pérdida de peso en personas con sobrepeso y obesidad con un 25-30% de la restricción calórica, el peso corporal se redujo significativamente en ambos sexos, sin tener en cuenta la edad y el tipo de tratamiento seguido. Según los resultados del estudio, la pérdida de peso realizada por un individuo (hombre o mujer) durante los seis meses puede ser representada por cualquiera de las cinco funciones (lineal, potencial, exponencial, logarítmica y cuadrática) en ambos sexos, siendo la cuadrática la que tiende a representarlo mejor. Además, se puede concluir que la pérdida de peso corporal se ve afectada por el índice de masa corporal inicial y el sexo, siendo mayor para las personas obesas que para las de sobrepeso, que muestran diferencias entre sexos sólo en la condición de sobrepeso. Además, es posible calcular el peso corporal final de cualquier participante involucrado en una intervención utilizando la metodología del proyecto PRONAF sólo conociendo sus variables iniciales de composición corporal. Además, los cuatro tipos de tratamientos tuvieron resultados similares en cambios en la composición corporal al final del período de intervención, con la única excepción de la masa libre de grasa, siendo los grupos de entrenamiento los que la mantuvieron durante la restricción calórica. Por otro lado, sólo el grupo combinado logra mantener la reducción de la masa grasa (%) 3 años después del final de la intervención. ABSTRACT Introduction. Obesity can be defined as a chronic metabolic disease from a multifactorial origin, which leads to physical and psychological impacts to the person, with associated pathologies that limit the life expectancy and deteriorate the quality of it, being determinant for the social and labor areas of the person. This chronic metabolic disorder is characterized by an excessive accumulation of energy in the body as fat, leading to increased weight relative to the value expected by sex, age and height. The management and treatment of obesity have wider objectives than weight loss alone and include risk reduction and health improvement. These may be achieved by modest weight loss (i.e. 5–10% of initial body weight), improved nutritional content of the diet and modest increases in physical activity and fitness. Weight loss through diet is one of the most popular approaches to lose body weight. Exercise is another alternative to lose body weight. The increase of exercise causes an imbalance when the caloric intake is maintained. It also has advantages such as improved muscle tone, cardiovascular fitness, strength and flexibility, increases the basal metabolism and improves immune system. Objectives. The aim of this thesis is to contribute with an interventional study to clarify the evolution of the body weight during a diet and exercise intervention. For this, the effects of age, sex, initial body mass index and type of treatment on weight loss tendencies were evaluated. Another objective of the thesis was to create a multiple linear regression model able to predict the body weight loss after the intervention period. And, finally, to determine the effect upon body composition (body weight, body mass index, fat mass, and fat-free mass of different exercise-based interventions (strength, endurance, combined endurance and strength, and physical activity recommendations group (control group)) combined with diet in overweight and obese adults, after intervention as well as body composition changes 3 years later. Research Design. The data used in the analysis of this thesis are part of the project "Programs of Nutrition and Physical Activity for the treatment of obesity" (PRONAF). The PRONAF project is a clinical trial program about nutrition and physical activity for overweight and obesity, developed in Spain for several years of intervention. It was designed, in part, to compare different types of intervention, in order to assess their impact on the dynamics of weight loss in overweight and obese people. As experimental design, the study was based on caloric restriction, which, in some cases, added a training protocol (strength, endurance, or combined in equal volume and intensity). The main research variables comprising this thesis were: body weight and body composition outcomes (fat mass and fat-free mass). Conclusions. In this thesis, for weight loss programs in overweight and obese people with 25-30% of caloric restriction, the body weight was significantly decreased in both sexes, regardless the age and type of followed treatment. According to the results of the study, the weight loss performed by an individual (male or female) during six months can be represented by any of the five functions (linear, power law, exponential, logarithmic and quadratic) in both sexes, being the quadratic one which tends to represent it better. In addition, it can be concluded that the body weight loss is affected by the initial body mass index and sex condition, being greater for the obese people than for the overweight one, showing differences between sexes only in the overweight condition. Moreover, it is possible to calculate the final body weight of any participant engaged in an intervention using the PRONAF Project methodology only knowing their initial body composition variables. Furthermore, the four types of treatments had similar results on body composition changes at the end of the intervention period, with the only exception of fat-free mass, being the training groups the ones that maintained it during the caloric restriction. On the other hand, only the combined group achieved to maintain the fat mass (%) reduced 3 years after the end of the intervention.

On the role of global flow instability analysis in closed loop flow control

Control of linear flow instabilities has been demonstrated to be an effective theoretical flow control methodology, capable of modifying transitional flows on canonical geometries such as the plane channel and the flat-plate boundary layer. Extending the well-developed theoretical flow control techniques to flows over or through complex geometries requires addressing the issue of efficient capturing of the leading members of the global eigenspectrum pertinent to such flows. The present contribution describes state-of-the-art modal global instability analysis methodologies recently developed in our group, based on matrix formation and time-stepping, respectively. The relative performance of these algorithms is assessed on the recovery of BiGlobal and TriGlobal eigenspectra in the spanwise periodic and the cubic lid-driven cavity, respectively; the adjoint eigenspectrum in the latter flow is recovered for the first time. For three-dimensional flows without any homogeneous spatial direction, the time-stepping methodology was found to outperform the matrix-forming approach and permit recovering the leading TriGlobal eigenmodes in an three-dimensional open cavity of aspect ratio L : D : W = 5 : 1 : 1; theoretical flow control of this configuration is underway.

Magnetic Attitude Control System for a Small Satellite. Impact on the Thermal Performance

El principal objetivo de la tesis es estudiar el acoplamiento entre los subsistemas de control de actitud y de control térmico de un pequeño satélite, con el fin de buscar la solución a los problemas relacionados con la determinación de los parámetros de diseño. Se considera la evolución de la actitud y de las temperaturas del satélite bajo la influencia de dos estrategias de orientación diferentes: 1) estabilización magnética pasiva de la orientación (PMAS, passive magnetic attitude stabilization), y 2) control de actitud magnético activo (AMAC, active magnetic attitude control). En primer lugar se presenta el modelo matemático del problema, que incluye la dinámica rotacional y el modelo térmico. En el problema térmico se considera un satélite cúbico modelizado por medio de siete nodos (seis externos y uno interno) aplicando la ecuación del balance térmico. Una vez establecido el modelo matemático del problema, se estudia la evolución que corresponde a las dos estrategias mencionadas. La estrategia PMAS se ha seleccionado por su simplicidad, fiabilidad, bajo coste, ahorrando consumo de potencia, masa coste y complejidad, comparado con otras estrategias. Se ha considerado otra estrategia de control que consigue que el satélite gire a una velocidad requerida alrededor de un eje deseado de giro, pudiendo controlar su dirección en un sistema inercial de referencia, ya que frecuentemente el subsistema térmico establece requisitos de giro alrededor de un eje del satélite orientado en una dirección perpendicular a la radiación solar incidente. En relación con el problema térmico, para estudiar la influencia de la velocidad de giro en la evolución de las temperaturas en diversos puntos del satélite, se ha empleado un modelo térmico linealizado, obtenido a partir de la formulación no lineal aplicando un método de perturbaciones. El resultado del estudio muestra que el tiempo de estabilización de la temperatura y la influencia de las cargas periódicas externas disminuye cuando aumenta la velocidad de giro. Los cambios de temperatura se reducen hasta ser muy pequeños para velocidades de rotación altas. En relación con la estrategia PMAC se ha observado que a pesar de su uso extendido entre los micro y nano satélites todavía presenta problemas que resolver. Estos problemas están relacionados con el dimensionamiento de los parámetros del sistema y la predicción del funcionamiento en órbita. Los problemas aparecen debido a la dificultad en la determinación de las características magnéticas de los cuerpos ferromagnéticos (varillas de histéresis) que se utilizan como amortiguadores de oscilaciones en los satélites. Para estudiar este problema se presenta un modelo analítico que permite estimar la eficiencia del amortiguamiento, y que se ha aplicado al estudio del comportamiento en vuelo de varios satélites, y que se ha empleado para comparar los resultados del modelo con los obtenidos en vuelo, observándose que el modelo permite explicar satisfactoriamente el comportamiento registrado. ABSTRACT The main objective of this thesis is to study the coupling between the attitude control and thermal control subsystems of a small satellite, and address the solution to some existing issues concerning the determination of their parameters. Through the thesis the attitude and temperature evolution of the satellite is studied under the influence of two independent attitude stabilization and control strategies: (1) passive magnetic attitude stabilization (PMAS), and (2) active magnetic attitude control (AMAC). In this regard the mathematical model of the problem is explained and presented. The mathematical model includes both the rotational dynamics and the thermal model. The thermal model is derived for a cubic satellite by solving the heat balance equation for 6 external and 1 internal nodes. Once established the mathematical model of the problem, the above mentioned attitude strategies were applied to the system and the temperature evolution of the 7 nodes of the satellite was studied. The PMAS technique has been selected to be studied due to its prevalent use, simplicity, reliability, and cost, as this strategy significantly saves the overall power, weight, cost, and reduces the complexity of the system compared to other attitude control strategies. In addition to that, another control law that provides the satellite with a desired spin rate along a desired axis of the satellite, whose direction can be controlled with respect to the inertial reference frame is considered, as the thermal subsystem of a satellite usually demands a spin requirement around an axis of the satellite which is positioned perpendicular to the direction of the coming solar radiation. Concerning the thermal problem, to study the influence of spin rate on temperature evolution of the satellite a linear approach of the thermal model is used, which is based on perturbation theory applied to the nonlinear differential equations of the thermal model of a spacecraft moving in a closed orbit. The results of this study showed that the temperature stabilization time and the periodic influence of the external thermal loads decreases by increasing the spin rate. However, the changes become insignificant for higher values of spin rate. Concerning the PMAS strategy, it was observed that in spite of its extended application to micro and nano satellites, still there are some issues to be solved regarding this strategy. These issues are related to the sizing of its system parameters and predicting the in-orbit performance. The problems were found to be rooted in the difficulties that exist in determining the magnetic characteristics of the ferromagnetic bodies (hysteresis rods) that are applied as damping devices on-board satellites. To address these issues an analytic model for estimating their damping efficiency is proposed and applied to several existing satellites in order to compare the results with their respective in-flight data. This model can explain the behavior showed by these satellites.

On the role of global flow instability analysis in closed loop flow control

Control of linear flow instabilities has been demonstrated to be an effective theoretical flow control methodology, capable of modifying transitional flow on canonical geometries such as the plane channel and the flat-plate boundary layer.

A sensorless virtual slave control scheme for kinematically dissimilar master-slave teleoperation

The use of telerobotic systems is essential for remote handling (RH) operations in radioactive areas of scientific facilities that generate high doses of radiation. Recent developments in remote handling technology has seen a great deal of effort being directed towards the design of modular remote handling control rooms equipped with a standard master arm which will be used to separately control a range of different slave devices. This application thus requires a kinematically dissimilar master-slave control scheme. In order to avoid drag and other effects such as friction or other non-linear and unmodelled slave arm effects of the common position-position architecture in nonbackdrivable slaves, this research has implemented a force-position control scheme. End-effector force is derived from motor torque values which, to avoid the use of radiation intolerant and costly sensing devices, are inferred from motor current measurement. This has been demonstrated on a 1-DOF test-rig with a permanent magnet synchronous motor teleoperated by a Sensable Phantom Omni® haptic master. This has been shown to allow accurate control while realistically conveying dynamic force information back to the operator.

Global instability analysis and control of three-dimensional long open cavity flow

The three-dimensional wall-bounded open cavity may be considered as a simplified geometry found in industrial applications such as leading gear or slotted flats on the airplane. Understanding the three-dimensional complex flow structure that surrounds this particular geometry is therefore of major industrial interest. At the light of the remarkable former investigations in this kind of flows, enough evidences suggest that the lateral walls have a great influence on the flow features and hence on their instability modes. Nevertheless, even though there is a large body of literature on cavity flows, most of them are based on the assumption that the flow is two-dimensional and spanwise-periodic. The flow over realistic open cavity should be considered. This thesis presents an investigation of three-dimensional wall-bounded open cavity with geometric ratio 6:2:1. To this aim, three-dimensional Direct Numerical Simulation (DNS) and global linear instability have been performed. Linear instability analysis reveals that the onset of the first instability in this open cavity is around Recr 1080. The three-dimensional shear layer mode with a complex structure is shown to be the most unstable mode. I t is noteworthy that the flow pattern of this high-frequency shear layer mode is similar to the observed unstable oscillations in supercritical unstable case. DNS of the cavity flow carried out at different Reynolds number from steady state until a nonlinear saturated state is obtained. The comparison of time histories of kinetic energy presents a clearly dominant energetic mode which shifts between low-frequency and highfrequency oscillation. A complete flow patterns from subcritical cases to supercritical case has been put in evidence. The flow structure at the supercritical case Re=1100 resembles typical wake-shedding instability oscillations with a lateral motion existed in the subcritical cases. Also, This flow pattern is similar to the observations in experiments. In order to validate the linear instability analysis results, the topology of the composite flow fields reconstructed by linear superposition of a three-dimensional base flow and its leading three-dimensional global eigenmodes has been studied. The instantaneous wall streamlines of those composited flows display distinguish influence region of each eigenmode. Attention has been focused on the leading high-frequency shear layer mode; the composite flow fields have been fully recognized with respect to the downstream wave shedding. The three-dimensional shear layer mode is shown to give rise to a typical wake-shedding instability with a lateral motions occurring downstream which is in good agreement with the experiment results. Moreover, the spanwise-periodic, open cavity with the same length to depth ratio has been also studied. The most unstable linear mode is different from the real three-dimensional cavity flow, because of the existence of the side walls. Structure sensitivity of the unstable global mode is analyzed in the flow control context. The adjoint-based sensitivity analysis has been employed to localized the receptivity region, where the flow is more sensible to momentum forcing and mass injection. Because of the non-normality of the linearized Navier-Stokes equations, the direct and adjoint field has a large spatial separation. The strongest sensitivity region is locate in the upstream lip of the three-dimensional cavity. This numerical finding is in agreement with experimental observations. Finally, a prototype of passive flow control strategy is applied.

Discrete linear stability and sensitivity analysis of fluid flows

Este trabajo presenta un método discreto para el cálculo de estabilidad hidrodinámica y análisis de sensibilidad a perturbaciones externas para ecuaciones diferenciales y en particular para las ecuaciones de Navier-Stokes compressible. Se utiliza una aproximación con variable compleja para obtener una precisión analítica en la evaluación de la matriz Jacobiana. Además, mapas de sensibilidad para la sensibilidad a las modificaciones del flujo de base y a una fuerza constante permiten identificar las regiones del campo fluido donde una modificacin (ej. fuerza puntual) tiene un efecto estabilizador del flujo. Se presentan cuatro casos de prueba: (1) un caso analítico para comprobar la derivación discreta, (2) una cavidad cerrada a bajo Reynolds para mostrar la mayor precisión en el cálculo de los valores propios con la aproximación de paso complejo, (3) flujo 2D en un cilindro circular para validar la metodología, y (4) flujo en un cavidad abierta, presentado para validar el método en casos de inestabilidades convectivamente inestables. Los tres últimos casos mencionados (2-4) se resolvieron con las ecuaciones de Navier-Stokes compresibles, utilizando un método Discontinuous Galerkin Spectral Element Method. Se obtuvo una buena concordancia para el caso de validación (3), cuando se comparó el nuevo método con resultados de la literatura. Además, este trabajo muestra que para el cálculo de los modos propios directos y adjuntos, así como para los mapas de sensibilidad, el uso de variables complejas es de suprema importancia para obtener una predicción precisa. El método descrito es aplicado al análisis para la estabilización de la estela generada por un disco actuador, que representa un modelo sencillo para hélices, rotores de helicópteros o turbinas eólicas. Se explora la primera bifurcación del flujo para un disco actuador, y se sugiere que está asociada a una inestabilidad de tipo Kelvin-Helmholtz, cuya estabilidad se controla con en el número de Reynolds y en la resistencia del disco actuador (o fuerza resistente). En primer lugar, se verifica que la disminución de la resistencia del disco tiene un efecto estabilizador parecido a una disminución del Reynolds. En segundo lugar, el análisis hidrodinmico discreto identifica dos regiones para la colocación de una fuerza puntual que controle las inestabilidades, una cerca del disco y otra en una zona aguas abajo. En tercer lugar, se muestra que la inclusión de un forzamiento localizado cerca del actuador produce una estabilización más eficiente que al forzar aguas abajo. El análisis de los campos de flujo controlados confirma que modificando el gradiente de velocidad cerca del actuador es más eficiente para estabilizar la estela. Estos resultados podrían proporcionar nuevas directrices para la estabilización de la estela de turbinas de viento o de marea cuando estén instaladas en un parque eólico y minimizar las interacciones no estacionarias entre turbinas. ABSTRACT A discrete framework for computing the global stability and sensitivity analysis to external perturbations for any set of partial differential equations is presented. In particular, a complex-step approximation is used to achieve near analytical accuracy for the evaluation of the Jacobian matrix. Sensitivity maps for the sensitivity to base flow modifications and to a steady force are computed to identify regions of the flow field where an input could have a stabilising effect. Four test cases are presented: (1) an analytical test case to prove the theory of the discrete framework, (2) a lid-driven cavity at low Reynolds case to show the improved accuracy in the calculation of the eigenvalues when using the complex-step approximation, (3) the 2D flow past a circular cylinder at just below the critical Reynolds number is used to validate the methodology, and finally, (4) the flow past an open cavity is presented to give an example of the discrete method applied to a convectively unstable case. The latter three (2–4) of the aforementioned cases were solved with the 2D compressible Navier–Stokes equations using a Discontinuous Galerkin Spectral Element Method. Good agreement was obtained for the validation test case, (3), with appropriate results in the literature. Furthermore, it is shown that for the calculation of the direct and adjoint eigenmodes and their sensitivity maps to external perturbations, the use of complex variables is paramount for obtaining an accurate prediction. An analysis for stabilising the wake past an actuator disc, which represents a simple model for propellers, helicopter rotors or wind turbines is also presented. We explore the first flow bifurcation for an actuator disc and it suggests that it is associated to a Kelvin- Helmholtz type instability whose stability relies on the Reynolds number and the flow resistance applied through the disc (or actuator forcing). First, we report that decreasing the disc resistance has a similar stabilising effect to an decrease in the Reynolds number. Second, a discrete sensitivity analysis identifies two regions for suitable placement of flow control forcing, one close to the disc and one far downstream where the instability originates. Third, we show that adding a localised forcing close to the actuator provides more stabilisation that forcing far downstream. The analysis of the controlled flow fields, confirms that modifying the velocity gradient close to the actuator is more efficient to stabilise the wake than controlling the sheared flow far downstream. An interesting application of these results is to provide guidelines for stabilising the wake of wind or tidal turbines when placed in an energy farm to minimise unsteady interactions.

Automated wordlength optimization framework for multi-source statistical interval-based analysis of nonlinear systems with control-flow structures

El uso de aritmética de punto fijo es una opción de diseño muy extendida en sistemas con fuertes restricciones de área, consumo o rendimiento. Para producir implementaciones donde los costes se minimicen sin impactar negativamente en la precisión de los resultados debemos llevar a cabo una asignación cuidadosa de anchuras de palabra. Encontrar la combinación óptima de anchuras de palabra en coma fija para un sistema dado es un problema combinatorio NP-hard al que los diseñadores dedican entre el 25 y el 50 % del ciclo de diseño. Las plataformas hardware reconfigurables, como son las FPGAs, también se benefician de las ventajas que ofrece la aritmética de coma fija, ya que éstas compensan las frecuencias de reloj más bajas y el uso más ineficiente del hardware que hacen estas plataformas respecto a los ASICs. A medida que las FPGAs se popularizan para su uso en computación científica los diseños aumentan de tamaño y complejidad hasta llegar al punto en que no pueden ser manejados eficientemente por las técnicas actuales de modelado de señal y ruido de cuantificación y de optimización de anchura de palabra. En esta Tesis Doctoral exploramos distintos aspectos del problema de la cuantificación y presentamos nuevas metodologías para cada uno de ellos: Las técnicas basadas en extensiones de intervalos han permitido obtener modelos de propagación de señal y ruido de cuantificación muy precisos en sistemas con operaciones no lineales. Nosotros llevamos esta aproximación un paso más allá introduciendo elementos de Multi-Element Generalized Polynomial Chaos (ME-gPC) y combinándolos con una técnica moderna basada en Modified Affine Arithmetic (MAA) estadístico para así modelar sistemas que contienen estructuras de control de flujo. Nuestra metodología genera los distintos caminos de ejecución automáticamente, determina las regiones del dominio de entrada que ejercitarán cada uno de ellos y extrae los momentos estadísticos del sistema a partir de dichas soluciones parciales. Utilizamos esta técnica para estimar tanto el rango dinámico como el ruido de redondeo en sistemas con las ya mencionadas estructuras de control de flujo y mostramos la precisión de nuestra aproximación, que en determinados casos de uso con operadores no lineales llega a tener tan solo una desviación del 0.04% con respecto a los valores de referencia obtenidos mediante simulación. Un inconveniente conocido de las técnicas basadas en extensiones de intervalos es la explosión combinacional de términos a medida que el tamaño de los sistemas a estudiar crece, lo cual conlleva problemas de escalabilidad. Para afrontar este problema presen tamos una técnica de inyección de ruidos agrupados que hace grupos con las señales del sistema, introduce las fuentes de ruido para cada uno de los grupos por separado y finalmente combina los resultados de cada uno de ellos. De esta forma, el número de fuentes de ruido queda controlado en cada momento y, debido a ello, la explosión combinatoria se minimiza. También presentamos un algoritmo de particionado multi-vía destinado a minimizar la desviación de los resultados a causa de la pérdida de correlación entre términos de ruido con el objetivo de mantener los resultados tan precisos como sea posible. La presente Tesis Doctoral también aborda el desarrollo de metodologías de optimización de anchura de palabra basadas en simulaciones de Monte-Cario que se ejecuten en tiempos razonables. Para ello presentamos dos nuevas técnicas que exploran la reducción del tiempo de ejecución desde distintos ángulos: En primer lugar, el método interpolativo aplica un interpolador sencillo pero preciso para estimar la sensibilidad de cada señal, y que es usado después durante la etapa de optimización. En segundo lugar, el método incremental gira en torno al hecho de que, aunque es estrictamente necesario mantener un intervalo de confianza dado para los resultados finales de nuestra búsqueda, podemos emplear niveles de confianza más relajados, lo cual deriva en un menor número de pruebas por simulación, en las etapas iniciales de la búsqueda, cuando todavía estamos lejos de las soluciones optimizadas. Mediante estas dos aproximaciones demostramos que podemos acelerar el tiempo de ejecución de los algoritmos clásicos de búsqueda voraz en factores de hasta x240 para problemas de tamaño pequeño/mediano. Finalmente, este libro presenta HOPLITE, una infraestructura de cuantificación automatizada, flexible y modular que incluye la implementación de las técnicas anteriores y se proporciona de forma pública. Su objetivo es ofrecer a desabolladores e investigadores un entorno común para prototipar y verificar nuevas metodologías de cuantificación de forma sencilla. Describimos el flujo de trabajo, justificamos las decisiones de diseño tomadas, explicamos su API pública y hacemos una demostración paso a paso de su funcionamiento. Además mostramos, a través de un ejemplo sencillo, la forma en que conectar nuevas extensiones a la herramienta con las interfaces ya existentes para poder así expandir y mejorar las capacidades de HOPLITE. ABSTRACT Using fixed-point arithmetic is one of the most common design choices for systems where area, power or throughput are heavily constrained. In order to produce implementations where the cost is minimized without negatively impacting the accuracy of the results, a careful assignment of word-lengths is required. The problem of finding the optimal combination of fixed-point word-lengths for a given system is a combinatorial NP-hard problem to which developers devote between 25 and 50% of the design-cycle time. Reconfigurable hardware platforms such as FPGAs also benefit of the advantages of fixed-point arithmetic, as it compensates for the slower clock frequencies and less efficient area utilization of the hardware platform with respect to ASICs. As FPGAs become commonly used for scientific computation, designs constantly grow larger and more complex, up to the point where they cannot be handled efficiently by current signal and quantization noise modelling and word-length optimization methodologies. In this Ph.D. Thesis we explore different aspects of the quantization problem and we present new methodologies for each of them: The techniques based on extensions of intervals have allowed to obtain accurate models of the signal and quantization noise propagation in systems with non-linear operations. We take this approach a step further by introducing elements of MultiElement Generalized Polynomial Chaos (ME-gPC) and combining them with an stateof- the-art Statistical Modified Affine Arithmetic (MAA) based methodology in order to model systems that contain control-flow structures. Our methodology produces the different execution paths automatically, determines the regions of the input domain that will exercise them, and extracts the system statistical moments from the partial results. We use this technique to estimate both the dynamic range and the round-off noise in systems with the aforementioned control-flow structures. We show the good accuracy of our approach, which in some case studies with non-linear operators shows a 0.04 % deviation respect to the simulation-based reference values. A known drawback of the techniques based on extensions of intervals is the combinatorial explosion of terms as the size of the targeted systems grows, which leads to scalability problems. To address this issue we present a clustered noise injection technique that groups the signals in the system, introduces the noise terms in each group independently and then combines the results at the end. In this way, the number of noise sources in the system at a given time is controlled and, because of this, the combinato rial explosion is minimized. We also present a multi-way partitioning algorithm aimed at minimizing the deviation of the results due to the loss of correlation between noise terms, in order to keep the results as accurate as possible. This Ph.D. Thesis also covers the development of methodologies for word-length optimization based on Monte-Carlo simulations in reasonable times. We do so by presenting two novel techniques that explore the reduction of the execution times approaching the problem in two different ways: First, the interpolative method applies a simple but precise interpolator to estimate the sensitivity of each signal, which is later used to guide the optimization effort. Second, the incremental method revolves on the fact that, although we strictly need to guarantee a certain confidence level in the simulations for the final results of the optimization process, we can do it with more relaxed levels, which in turn implies using a considerably smaller amount of samples, in the initial stages of the process, when we are still far from the optimized solution. Through these two approaches we demonstrate that the execution time of classical greedy techniques can be accelerated by factors of up to ×240 for small/medium sized problems. Finally, this book introduces HOPLITE, an automated, flexible and modular framework for quantization that includes the implementation of the previous techniques and is provided for public access. The aim is to offer a common ground for developers and researches for prototyping and verifying new techniques for system modelling and word-length optimization easily. We describe its work flow, justifying the taken design decisions, explain its public API and we do a step-by-step demonstration of its execution. We also show, through an example, the way new extensions to the flow should be connected to the existing interfaces in order to expand and improve the capabilities of HOPLITE.

A non-linear analysis of lying a floating pipeline on the seabed

In this article, a model for the determination of displacements, deformations and tensions of a submarine pipeline during the construction is presented. The process is carried out from an initial floating situation to the final laying position on the seabed. The existence of currents and small waves are also considered. Firstly, this technique, usually applied to polyethylene pipelines, is described in this paper as well as some real world examples, as well as the variables that can be modified to control the behavior of the structure. A detailed description of the actions in this process is considered, specially the ones related to marine environment, as Archimedes force, current and sea waves. The behavior of the pipeline is modeled with a non linear elasto dynamic model where geometric non linearities are taken into account. A 3-D beam model, without cross section deformation effects, is developed. Special care is taken in the numerical analysis, developed within an updated lagrangian formulation framework, with the sea bed contact, the follower forces due to the external water pressures and the dynamic actions. Finally, some subroutines are implemented into ANSYS to simulate the two dimensional case, where the whole construction process is achieved. With this software, a sensibility analysis of the bending moments, axial forces and stresses obtained with different values of the control variables in order to optimize the construction steps. These control variables are, the axial load in the pipe, the inundated inner length and the distance of the control barge from the coast.

Optimal impulsive collision avoidance in low earth orbit

This paper presents a high-accuracy fully analytical formulation to compute the miss distance and collision probability of two approaching objects following an impulsive collision avoidance maneuver. The formulation hinges on a linear relation between the applied impulse and the objects? relative motion in the b-plane, which allows one to formulate the maneuver optimization problem as an eigenvalue problem coupled to a simple nonlinear algebraic equation. The optimization criterion consists of minimizing the maneuver cost in terms of delta-V magnitude to either maximize collision miss distance or to minimize Gaussian collision probability. The algorithm, whose accuracy is verified in representative mission scenarios, can be employed for collision avoidance maneuver planning with reduced computational cost when compared with fully numerical algorithms.