Reduced order adaptive models for systems of PDEs using POD

In this work we propose a method to accelerate time dependent numerical solvers of systems of PDEs that require a high cost in computational time and memory. The method is based on the combined use of such numerical solver with a proper orthogonal decomposition, from which we identify modes, a Galerkin projection (that provides a reduced system of equations) and the integration of the reduced system, studying the evolution of the modal amplitudes. We integrate the reduced model until our a priori error estimator indicates that our approximation in not accurate. At this point we use again our original numerical code in a short time interval to adapt the POD manifold and continue then with the integration of the reduced model. Application will be made to two model problems: the Ginzburg-Landau equation in transient chaos conditions and the two-dimensional pulsating cavity problem, which describes the motion of liquid in a box whose upper wall is moving back and forth in a quasi-periodic fashion. Finally, we will discuss a way of improving the performance of the method using experimental data or information from numerical simulations

Interactions between roughness and topography in hydraulic models

Analysis of river flow using hydraulic modelling and its implications in derived environ-mental applications are inextricably connected with the way in which the river boundary shape is represented. This relationship is scale-dependent upon the modelling resolution which in turn determines the importance of a subscale performance of the model and the way subscale (surface and flow) processes are parameterised. Commonly, the subscale behaviour of the model relies upon a roughness parameterisation whose meaning depends on the dimensionality of the hydraulic model and the resolution of the topographic represen¬tation scale. This latter is, in turn, dependent on the resolution of the computational mesh as well as on the detail of measured topographic data. Flow results are affected by this interactions between scale and subscale parameterisation according to the dimensionality approach. The aim of this dissertation is the evaluation of these interactions upon hy¬draulic modelling results. Current high resolution topographic source availability induce this research which is tackled using a suitable roughness approach according to each di¬mensionality with the purpose of the interaction assessment. A 1D HEC-RAS model, a 2D raster-based diffusion-wave model with a scale-dependent distributed roughness parame-terisation and a 3D finite volume scheme with a porosity algorithm approach to incorporate complex topography have been used. Different topographic sources are assessed using a 1D scheme. LiDAR data are used to isolate the mesh resolution from the topographic content of the DEM effects upon 2D and 3D flow results. A distributed roughness parameterisation, using a roughness height approach dependent upon both mesh resolution and topographic content is developed and evaluated for the 2D scheme. Grain-size data and fractal methods are used for the reconstruction of topography with microscale information, required for some applications but not easily available. Sensitivity of hydraulic parameters to this topographic parameterisation is evaluated in a 3D scheme at different mesh resolu¬tions. Finally, the structural variability of simulated flow is analysed and related to scale interactions. Model simulations demonstrate (i) the importance of the topographic source in a 1D models; (ii) the mesh resolution approach is dominant in 2D and 3D simulations whereas in a 1D model the topographic source and even the roughness parameterisation impacts are more critical; (iii) the increment of the sensitivity to roughness parameterisa-tion in 1D and 2D schemes with detailed topographic sources and finer mesh resolutions; and (iv) the topographic content and microtopography impact throughout the vertical profile of computed 3D velocity in a depth-dependent way, whereas 2D results are not affected by topographic content variations. Finally, the spatial analysis shows that the mesh resolution controls high resolution model scale results, roughness parameterisation control 2D simulation results for a constant mesh resolution; and topographic content and micro-topography variations impacts upon the organisation of flow results depth-dependently in a 3D scheme. Resumen La topografía juega un papel fundamental en la distribución del agua y la energía en los paisajes naturales (Beven and Kirkby 1979; Wood et al. 1997). La simulación hidráulica combinada con métodos de medición del terreno por teledetección constituyen una poderosa herramienta de investigación en la comprensión del comportamiento de los flujos de agua debido a la variabilidad de la superficie sobre la que fluye. La representación e incorporación de la topografía en el esquema hidráulico tiene una importancia crucial en los resultados y determinan el desarrollo de sus aplicaciones al campo medioambiental. Cualquier simulación es una simplificación de un proceso del mundo real, y por tanto el grado de simplificación determinará el significado de los resultados simulados. Este razonamiento es particularmente difícil de trasladar a la simulación hidráulica donde aspectos de la escala tan diferentes como la escala de los procesos de flujo y de representación del contorno son considerados conjuntamente incluso en fases de parametrización (e.g. parametrización de la rugosidad). Por una parte, esto es debido a que las decisiones de escala vienen condicionadas entre ellas (e.g. la dimensionalidad del modelo condiciona la escala de representación del contorno) y por tanto interaccionan en sus resultados estrechamente. Y por otra parte, debido a los altos requerimientos numéricos y computacionales de una representación explícita de alta resolución de los procesos de flujo y discretización de la malla. Además, previo a la modelización hidráulica, la superficie del terreno sobre la que el agua fluye debe ser modelizada y por tanto presenta su propia escala de representación, que a su vez dependerá de la escala de los datos topográficos medidos con que se elabora el modelo. En última instancia, esta topografía es la que determina el comportamiento espacial del flujo. Por tanto, la escala de la topografía en sus fases de medición y modelización (resolución de los datos y representación topográfica) previas a su incorporación en el modelo hidráulico producirá a su vez un impacto que se acumulará al impacto global resultante debido a la escala computacional del modelo hidráulico y su dimensión. La comprensión de las interacciones entre las complejas geometrías del contorno y la estructura del flujo utilizando la modelización hidráulica depende de las escalas consideradas en la simplificación de los procesos hidráulicos y del terreno (dimensión del modelo, tamaño de escala computacional y escala de los datos topográficos). La naturaleza de la aplicación del modelo hidráulico (e.g. habitat físico, análisis de riesgo de inundaciones, transporte de sedimentos) determina en primer lugar la escala del estudio y por tanto el detalle de los procesos a simular en el modelo (i.e. la dimensionalidad) y, en consecuencia, la escala computacional a la que se realizarán los cálculos (i.e. resolución computacional). Esta última a su vez determina, el detalle geográfico con que deberá representarse el contorno acorde con la resolución de la malla computacional. La parametrización persigue incorporar en el modelo hidráulico la cuantificación de los procesos y condiciones físicas del sistema natural y por tanto debe incluir no solo aquellos procesos que tienen lugar a la escala de modelización, sino también aquellos que tienen lugar a un nivel subescalar y que deben ser definidos mediante relaciones de escalado con las variables modeladas explícitamente. Dicha parametrización se implementa en la práctica mediante la provisión de datos al modelo, por tanto la escala de los datos geográficos utilizados para parametrizar el modelo no sólo influirá en los resultados, sino también determinará la importancia del comportamiento subescalar del modelo y el modo en que estos procesos deban ser parametrizados (e.g. la variabilidad natural del terreno dentro de la celda de discretización o el flujo en las direcciones laterales y verticales en un modelo unidimensional). En esta tesis, se han utilizado el modelo unidimensional HEC-RAS, (HEC 1998b), un modelo ráster bidimensional de propagación de onda, (Yu 2005) y un esquema tridimensional de volúmenes finitos con un algoritmo de porosidad para incorporar la topografía, (Lane et al. 2004; Hardy et al. 2005). La geometría del contorno viene definida por la escala de representación topográfica (resolución de malla y contenido topográfico), la cual a su vez depende de la escala de la fuente cartográfica. Todos estos factores de escala interaccionan en la respuesta del modelo hidráulico a la topografía. En los últimos años, métodos como el análisis fractal y las técnicas geoestadísticas utilizadas para representar y analizar elementos geográficos (e.g. en la caracterización de superficies (Herzfeld and Overbeck 1999; Butler et al. 2001)), están promoviendo nuevos enfoques en la cuantificación de los efectos de escala (Lam et al. 2004; Atkinson and Tate 2000; Lam et al. 2006) por medio del análisis de la estructura espacial de la variable (e.g. Bishop et al. 2006; Ju et al. 2005; Myint et al. 2004; Weng 2002; Bian and Xie 2004; Southworth et al. 2006; Pozd-nyakova et al. 2005; Kyriakidis and Goodchild 2006). Estos métodos cuantifican tanto el rango de valores de la variable presentes a diferentes escalas como la homogeneidad o heterogeneidad de la variable espacialmente distribuida (Lam et al. 2004). En esta tesis, estas técnicas se han utilizado para analizar el impacto de la topografía sobre la estructura de los resultados hidráulicos simulados. Los datos de teledetección de alta resolución y técnicas GIS también están siendo utilizados para la mejor compresión de los efectos de escala en modelos medioambientales (Marceau 1999; Skidmore 2002; Goodchild 2003) y se utilizan en esta tesis. Esta tesis como corpus de investigación aborda las interacciones de esas escalas en la modelización hidráulica desde un punto de vista global e interrelacionado. Sin embargo, la estructura y el foco principal de los experimentos están relacionados con las nociones espaciales de la escala de representación en relación con una visión global de las interacciones entre escalas. En teoría, la representación topográfica debe caracterizar la superficie sobre la que corre el agua a una adecuada (conforme a la finalidad y dimensión del modelo) escala de discretización, de modo que refleje los procesos de interés. La parametrización de la rugosidad debe de reflejar los efectos de la variabilidad de la superficie a escalas de más detalle que aquellas representadas explícitamente en la malla topográfica (i.e. escala de discretización). Claramente, ambos conceptos están físicamente relacionados por un

Computational methods to create and analyze a digital gene expression atlas of embryo development from microscopy images

Abstract The creation of atlases, or digital models where information from different subjects can be combined, is a field of increasing interest in biomedical imaging. When a single image does not contain enough information to appropriately describe the organism under study, it is then necessary to acquire images of several individuals, each of them containing complementary data with respect to the rest of the components in the cohort. This approach allows creating digital prototypes, ranging from anatomical atlases of human patients and organs, obtained for instance from Magnetic Resonance Imaging, to gene expression cartographies of embryo development, typically achieved from Light Microscopy. Within such context, in this PhD Thesis we propose, develop and validate new dedicated image processing methodologies that, based on image registration techniques, bring information from multiple individuals into alignment within a single digital atlas model. We also elaborate a dedicated software visualization platform to explore the resulting wealth of multi-dimensional data and novel analysis algo-rithms to automatically mine the generated resource in search of bio¬logical insights. In particular, this work focuses on gene expression data from developing zebrafish embryos imaged at the cellular resolution level with Two-Photon Laser Scanning Microscopy. Disposing of quantitative measurements relating multiple gene expressions to cell position and their evolution in time is a fundamental prerequisite to understand embryogenesis multi-scale processes. However, the number of gene expressions that can be simultaneously stained in one acquisition is limited due to optical and labeling constraints. These limitations motivate the implementation of atlasing strategies that can recreate a virtual gene expression multiplex. The developed computational tools have been tested in two different scenarios. The first one is the early zebrafish embryogenesis where the resulting atlas constitutes a link between the phenotype and the genotype at the cellular level. The second one is the late zebrafish brain where the resulting atlas allows studies relating gene expression to brain regionalization and neurogenesis. The proposed computational frameworks have been adapted to the requirements of both scenarios, such as the integration of partial views of the embryo into a whole embryo model with cellular resolution or the registration of anatom¬ical traits with deformable transformation models non-dependent on any specific labeling. The software implementation of the atlas generation tool (Match-IT) and the visualization platform (Atlas-IT) together with the gene expression atlas resources developed in this Thesis are to be made freely available to the scientific community. Lastly, a novel proof-of-concept experiment integrates for the first time 3D gene expression atlas resources with cell lineages extracted from live embryos, opening up the door to correlate genetic and cellular spatio-temporal dynamics. La creación de atlas, o modelos digitales, donde la información de distintos sujetos puede ser combinada, es un campo de creciente interés en imagen biomédica. Cuando una sola imagen no contiene suficientes datos como para describir apropiadamente el organismo objeto de estudio, se hace necesario adquirir imágenes de varios individuos, cada una de las cuales contiene información complementaria respecto al resto de componentes del grupo. De este modo, es posible crear prototipos digitales, que pueden ir desde atlas anatómicos de órganos y pacientes humanos, adquiridos por ejemplo mediante Resonancia Magnética, hasta cartografías de la expresión genética del desarrollo de embrionario, típicamente adquiridas mediante Microscopía Optica. Dentro de este contexto, en esta Tesis Doctoral se introducen, desarrollan y validan nuevos métodos de procesado de imagen que, basándose en técnicas de registro de imagen, son capaces de alinear imágenes y datos provenientes de múltiples individuos en un solo atlas digital. Además, se ha elaborado una plataforma de visualization específicamente diseñada para explorar la gran cantidad de datos, caracterizados por su multi-dimensionalidad, que resulta de estos métodos. Asimismo, se han propuesto novedosos algoritmos de análisis y minería de datos que permiten inspeccionar automáticamente los atlas generados en busca de conclusiones biológicas significativas. En particular, este trabajo se centra en datos de expresión genética del desarrollo embrionario del pez cebra, adquiridos mediante Microscopía dos fotones con resolución celular. Disponer de medidas cuantitativas que relacionen estas expresiones genéticas con las posiciones celulares y su evolución en el tiempo es un prerrequisito fundamental para comprender los procesos multi-escala característicos de la morfogénesis. Sin embargo, el número de expresiones genéticos que pueden ser simultáneamente etiquetados en una sola adquisición es reducido debido a limitaciones tanto ópticas como del etiquetado. Estas limitaciones requieren la implementación de estrategias de creación de atlas que puedan recrear un multiplexado virtual de expresiones genéticas. Las herramientas computacionales desarrolladas han sido validadas en dos escenarios distintos. El primer escenario es el desarrollo embrionario temprano del pez cebra, donde el atlas resultante permite constituir un vínculo, a nivel celular, entre el fenotipo y el genotipo de este organismo modelo. El segundo escenario corresponde a estadios tardíos del desarrollo del cerebro del pez cebra, donde el atlas resultante permite relacionar expresiones genéticas con la regionalización del cerebro y la formación de neuronas. La plataforma computacional desarrollada ha sido adaptada a los requisitos y retos planteados en ambos escenarios, como la integración, a resolución celular, de vistas parciales dentro de un modelo consistente en un embrión completo, o el alineamiento entre estructuras de referencia anatómica equivalentes, logrado mediante el uso de modelos de transformación deformables que no requieren ningún marcador específico. Está previsto poner a disposición de la comunidad científica tanto la herramienta de generación de atlas (Match-IT), como su plataforma de visualización (Atlas-IT), así como las bases de datos de expresión genética creadas a partir de estas herramientas. Por último, dentro de la presente Tesis Doctoral, se ha incluido una prueba conceptual innovadora que permite integrar los mencionados atlas de expresión genética tridimensionales dentro del linaje celular extraído de una adquisición in vivo de un embrión. Esta prueba conceptual abre la puerta a la posibilidad de correlar, por primera vez, las dinámicas espacio-temporales de genes y células.

Computational Methods for Identification of Vibrating Structures

System identification deals with the problem of building mathematical models of dynamical systems based on observed data from the system" [1]. In the context of civil engineering, the system refers to a large scale structure such as a building, bridge, or an offshore structure, and identification mostly involves the determination of modal parameters (the natural frequencies, damping ratios, and mode shapes). This paper presents some modal identification results obtained using a state-of-the-art time domain system identification method (data-driven stochastic subspace algorithms [2]) applied to the output-only data measured in a steel arch bridge. First, a three dimensional finite element model was developed for the numerical analysis of the structure using ANSYS. Modal analysis was carried out and modal parameters were extracted in the frequency range of interest, 0-10 Hz. The results obtained from the finite element modal analysis were used to determine the location of the sensors. After that, ambient vibration tests were conducted during April 23-24, 2009. The response of the structure was measured using eight accelerometers. Two stations of three sensors were formed (triaxial stations). These sensors were held stationary for reference during the test. The two remaining sensors were placed at the different measurement points along the bridge deck, in which only vertical and transversal measurements were conducted (biaxial stations). Point estimate and interval estimate have been carried out in the state space model using these ambient vibration measurements. In the case of parametric models (like state space), the dynamic behaviour of a system is described using mathematical models. Then, mathematical relationships can be established between modal parameters and estimated point parameters (thus, it is common to use experimental modal analysis as a synonym for system identification). Stable modal parameters are found using a stabilization diagram. Furthermore, this paper proposes a method for assessing the precision of estimates of the parameters of state-space models (confidence interval). This approach employs the nonparametric bootstrap procedure [3] and is applied to subspace parameter estimation algorithm. Using bootstrap results, a plot similar to a stabilization diagram is developed. These graphics differentiate system modes from spurious noise modes for a given order system. Additionally, using the modal assurance criterion, the experimental modes obtained have been compared with those evaluated from a finite element analysis. A quite good agreement between numerical and experimental results is observed.

Comparing linear and non linear wind flow models

Assessing wind conditions on complex terrain has become a hard task as terrain complexity increases. That is why there is a need to extrapolate in a reliable manner some wind parameters that determine wind farms viability such as annual average wind speed at all hub heights as well as turbulence intensities. The development of these tasks began in the early 90´s with the widely used linear model WAsP and WAsP Engineering especially designed for simple terrain with remarkable results on them but not so good on complex orographies. Simultaneously non-linearized Navier Stokes solvers have been rapidly developed in the last decade through CFD (Computational Fluid Dynamics) codes allowing simulating atmospheric boundary layer flows over steep complex terrain more accurately reducing uncertainties. This paper describes the features of these models by validating them through meteorological masts installed in a highly complex terrain. The study compares the results of the mentioned models in terms of wind speed and turbulence intensity.

Core physics and safety analysis of Generation-IV Sodium Fast Reactors using existing and newly developed computational tools

El futuro de la energía nuclear de fisión dependerá, entre otros factores, de la capacidad que las nuevas tecnologías demuestren para solventar los principales retos a largo plazo que se plantean. Los principales retos se pueden resumir en los siguientes aspectos: la capacidad de proporcionar una solución final, segura y fiable a los residuos radiactivos; así como dar solución a la limitación de recursos naturales necesarios para alimentar los reactores nucleares; y por último, una mejora robusta en la seguridad de las centrales que en definitiva evite cualquier daño potencial tanto en la población como en el medio ambiente como consecuencia de cualquier escenario imaginable o más allá de lo imaginable. Siguiendo estas motivaciones, la Generación IV de reactores nucleares surge con el compromiso de proporcionar electricidad de forma sostenible, segura, económica y evitando la proliferación de material fisible. Entre los sistemas conceptuales que se consideran para la Gen IV, los reactores rápidos destacan por su capacidad potencial de transmutar actínidos a la vez que permiten una utilización óptima de los recursos naturales. Entre los refrigerantes que se plantean, el sodio parece una de las soluciones más prometedoras. Como consecuencia, esta tesis surgió dentro del marco del proyecto europeo CP-ESFR con el principal objetivo de evaluar la física de núcleo y seguridad de los reactores rápidos refrigerados por sodio, al tiempo que se desarrollaron herramientas apropiadas para dichos análisis. Efectivamente, en una primera parte de la tesis, se abarca el estudio de la física del núcleo de un reactor rápido representativo, incluyendo el análisis detallado de la capacidad de transmutar actínidos minoritarios. Como resultado de dichos análisis, se publicó un artículo en la revista Annals of Nuclear Energy [96]. Por otra parte, a través de un análisis de un hipotético escenario nuclear español, se evalúo la disponibilidad de recursos naturales necesarios en el caso particular de España para alimentar una flota específica de reactores rápidos, siguiendo varios escenarios de demanda, y teniendo en cuenta la capacidad de reproducción de plutonio que tienen estos sistemas. Como resultado de este trabajo también surgió una publicación en otra revista científica de prestigio internacional como es Energy Conversion and Management [97]. Con objeto de realizar esos y otros análisis, se desarrollaron diversos modelos del núcleo del ESFR siguiendo varias configuraciones, y para diferentes códigos. Por otro lado, con objeto de poder realizar análisis de seguridad de reactores rápidos, son necesarias herramientas multidimensionales de alta fidelidad específicas para reactores rápidos. Dichas herramientas deben integrar fenómenos relacionados con la neutrónica y con la termo-hidráulica, entre otros, mediante una aproximación multi-física. Siguiendo este objetivo, se evalúo el código de difusión neutrónica ANDES para su aplicación a reactores rápidos. ANDES es un código de resolución nodal que se encuentra implementado dentro del sistema COBAYA3 y está basado en el método ACMFD. Por lo tanto, el método ACMFD fue sometido a una revisión en profundidad para evaluar su aptitud para la aplicación a reactores rápidos. Durante ese proceso, se identificaron determinadas limitaciones que se discutirán a lo largo de este trabajo, junto con los desarrollos que se han elaborado e implementado para la resolución de dichas dificultades. Por otra parte, se desarrolló satisfactoriamente el acomplamiento del código neutrónico ANDES con un código termo-hidráulico de subcanales llamado SUBCHANFLOW, desarrollado recientemente en el KIT. Como conclusión de esta parte, todos los desarrollos implementados son evaluados y verificados. En paralelo con esos desarrollos, se calcularon para el núcleo del ESFR las secciones eficaces en multigrupos homogeneizadas a nivel nodal, así como otros parámetros neutrónicos, mediante los códigos ERANOS, primero, y SERPENT, después. Dichos parámetros se utilizaron más adelante para realizar cálculos estacionarios con ANDES. Además, como consecuencia de la contribución de la UPM al paquete de seguridad del proyecto CP-ESFR, se calcularon mediante el código SERPENT los parámetros de cinética puntual que se necesitan introducir en los típicos códigos termo-hidráulicos de planta, para estudios de seguridad. En concreto, dichos parámetros sirvieron para el análisis del impacto que tienen los actínidos minoritarios en el comportamiento de transitorios. Concluyendo, la tesis presenta una aproximación sistemática y multidisciplinar aplicada al análisis de seguridad y comportamiento neutrónico de los reactores rápidos de sodio de la Gen-IV, usando herramientas de cálculo existentes y recién desarrolladas ad' hoc para tal aplicación. Se ha empleado una cantidad importante de tiempo en identificar limitaciones de los métodos nodales analíticos en su aplicación en multigrupos a reactores rápidos, y se proponen interesantes soluciones para abordarlas. ABSTRACT The future of nuclear reactors will depend, among other aspects, on the capability to solve the long-term challenges linked to this technology. These are the capability to provide a definite, safe and reliable solution to the nuclear wastes; the limitation of natural resources, needed to fuel the reactors; and last but not least, the improved safety, which would avoid any potential damage on the public and or environment as a consequence of any imaginable and beyond imaginable circumstance. Following these motivations, the IV Generation of nuclear reactors arises, with the aim to provide sustainable, safe, economic and proliferationresistant electricity. Among the systems considered for the Gen IV, fast reactors have a representative role thanks to their potential capacity to transmute actinides together with the optimal usage of natural resources, being the sodium fast reactors the most promising concept. As a consequence, this thesis was born in the framework of the CP-ESFR project with the generic aim of evaluating the core physics and safety of sodium fast reactors, as well as the development of the approppriated tools to perform such analyses. Indeed, in a first part of this thesis work, the main core physics of the representative sodium fast reactor are assessed, including a detailed analysis of the capability to transmute minor actinides. A part of the results obtained have been published in Annals of Nuclear Energy [96]. Moreover, by means of the analysis of a hypothetical Spanish nuclear scenario, the availability of natural resources required to deploy an specific fleet of fast reactor is assessed, taking into account the breeding properties of such systems. This work also led to a publication in Energy Conversion and Management [97]. In order to perform those and other analyses, several models of the ESFR core were created for different codes. On the other hand, in order to perform safety studies of sodium fast reactors, high fidelity multidimensional analysis tools for sodium fast reactors are required. Such tools should integrate neutronic and thermal-hydraulic phenomena in a multi-physics approach. Following this motivation, the neutron diffusion code ANDES is assessed for sodium fast reactor applications. ANDES is the nodal solver implemented inside the multigroup pin-by-pin diffusion COBAYA3 code, and is based on the analytical method ACMFD. Thus, the ACMFD was verified for SFR applications and while doing so, some limitations were encountered, which are discussed through this work. In order to solve those, some new developments are proposed and implemented in ANDES. Moreover, the code was satisfactorily coupled with the thermal-hydraulic code SUBCHANFLOW, recently developed at KIT. Finally, the different implementations are verified. In addition to those developments, the node homogenized multigroup cross sections and other neutron parameters were obtained for the ESFR core using ERANOS and SERPENT codes, and employed afterwards by ANDES to perform steady state calculations. Moreover, as a result of the UPM contribution to the safety package of the CP-ESFR project, the point kinetic parameters required by the typical plant thermal-hydraulic codes were computed for the ESFR core using SERPENT, which final aim was the assessment of the impact of minor actinides in transient behaviour. All in all, the thesis provides a systematic and multi-purpose approach applied to the assessment of safety and performance parameters of Generation-IV SFR, using existing and newly developed analytical tools. An important amount of time was employed in identifying the limitations that the analytical nodal diffusion methods present when applied to fast reactors following a multigroup approach, and interesting solutions are proposed in order to overcome them.

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.

Computational model for local damage assesment of structures

In the last years many studies have been developed to analyze the seismic behavior throug the damage concept. In fact, the evaluation of the structural damage is important in order to quantify the safety of new and existing structures and, also, to establish a framework for seismic retrofitting decision making of structures. Most proposed models are based on a post-earthquake evaluation in such a way they uncouple the computation of the structural response from that of damage. However, there are other models which include explicity the existing coupling between the degradation and the structural mechanical beaviour. Those models are closer to the physical reality and its formulation is based on the principles of Continuum Damage Mechanics. In the present work, a coupled model is formulated using a simplified application of the Continuum Damage Mechanics to the analysis of frames and allows its representation in standard finite element programs. This work is part of the activities developed by the Structural Mechanics Department (UPM) within ICONS (European Research Project on Innovative Seismic Design Concepts for New and Existing Structures).

Simulation of impulse response for indoor visible light communications using 3D CAD models

n this article, a tool for simulating the channel impulse response for indoor visible light communications using 3D computer-aided design (CAD) models is presented. The simulation tool is based on a previous Monte Carlo ray-tracing algorithm for indoor infrared channel estimation, but including wavelength response evaluation. The 3D scene, or the simulation environment, can be defined using any CAD software in which the user specifies, in addition to the setting geometry, the reflection characteristics of the surface materials as well as the structures of the emitters and receivers involved in the simulation. Also, in an effort to improve the computational efficiency, two optimizations are proposed. The first one consists of dividing the setting into cubic regions of equal size, which offers a calculation improvement of approximately 50% compared to not dividing the 3D scene into sub-regions. The second one involves the parallelization of the simulation algorithm, which provides a computational speed-up proportional to the number of processors used.

Continuum models of the mechanical behavior of rolled and die-cast magnesium alloys

En los últimos años ha habido una fuerte tendencia a disminuir las emisiones de CO2 y su negativo impacto medioambiental. En la industria del transporte, reducir el peso de los vehículos aparece como la mejor opción para alcanzar este objetivo. Las aleaciones de Mg constituyen un material con gran potencial para el ahorro de peso. Durante la última década se han realizado muchos esfuerzos encaminados a entender los mecanismos de deformación que gobiernan la plasticidad de estos materiales y así, las aleaciones de Mg de colada inyectadas a alta presión y forjadas son todavía objeto de intensas campañas de investigación. Es ahora necesario desarrollar modelos que contemplen la complejidad inherente de los procesos de deformación de éstos. Esta tesis doctoral constituye un intento de entender mejor la relación entre la microestructura y el comportamiento mecánico de aleaciones de Mg, y dará como resultado modelos de policristales capaces de predecir propiedades macro- y microscópicas. La deformación plástica de las aleaciones de Mg está gobernada por una combinación de mecanismos de deformación característicos de la estructura cristalina hexagonal, que incluye el deslizamiento cristalográfico en planos basales, prismáticos y piramidales, así como el maclado. Las aleaciones de Mg de forja presentan texturas fuertes y por tanto los mecanismos de deformación activos dependen de la orientación de la carga aplicada. En este trabajo se ha desarrollado un modelo de plasticidad cristalina por elementos finitos con el objetivo de entender el comportamiento macro- y micromecánico de la aleación de Mg laminada AZ31 (Mg-3wt.%Al-1wt.%Zn). Este modelo, que incorpora el maclado y tiene en cuenta el endurecimiento por deformación debido a las interacciones dislocación-dislocación, dislocación-macla y macla-macla, predice exitosamente las actividades de los distintos mecanismos de deformación y la evolución de la textura con la deformación. Además, se ha llevado a cabo un estudio que combina difracción de electrones retrodispersados en tres dimensiones y modelización para investigar el efecto de los límites de grano en la propagación del maclado en el mismo material. Ambos, experimentos y simulaciones, confirman que el ángulo de desorientación tiene una influencia decisiva en la propagación del maclado. Se ha observado que los efectos no-Schmid, esto es, eventos de deformación plástica que no cumplen la ley de Schmid con respecto a la carga aplicada, no tienen lugar en la vecindad de los límites de baja desorientación y se hacen más frecuentes a medida que la desorientación aumenta. Esta investigación también prueba que la morfología de las maclas está altamente influenciada por su factor de Schmid. Es conocido que los procesos de colada suelen dar lugar a la formación de microestructuras con una microporosidad elevada, lo cuál afecta negativamente a sus propiedades mecánicas. La aplicación de presión hidrostática después de la colada puede reducir la porosidad y mejorar las propiedades aunque es poco conocido su efecto en el tamaño y morfología de los poros. En este trabajo se ha utilizado un enfoque mixto experimentalcomputacional, basado en tomografía de rayos X, análisis de imagen y análisis por elementos finitos, para la determinación de la distribución tridimensional (3D) de la porosidad y de la evolución de ésta con la presión hidrostática en la aleación de Mg AZ91 (Mg- 9wt.%Al-1wt.%Zn) colada por inyección a alta presión. La distribución real de los poros en 3D obtenida por tomografía se utilizó como input para las simulaciones por elementos finitos. Los resultados revelan que la aplicación de presión tiene una influencia significativa tanto en el cambio de volumen como en el cambio de forma de los poros que han sido cuantificados con precisión. Se ha observado que la reducción del tamaño de éstos está íntimamente ligada con su volumen inicial. En conclusión, el modelo de plasticidad cristalina propuesto en este trabajo describe con éxito los mecanismos intrínsecos de la deformación de las aleaciones de Mg a escalas meso- y microscópica. Más especificamente, es capaz de capturar las activadades del deslizamiento cristalográfico y maclado, sus interacciones, así como los efectos en la porosidad derivados de los procesos de colada. ---ABSTRACT--- The last few years have seen a growing effort to reduce CO2 emissions and their negative environmental impact. In the transport industry more specifically, vehicle weight reduction appears as the most straightforward option to achieve this objective. To this end, Mg alloys constitute a significant weight saving material alternative. Many efforts have been devoted over the last decade to understand the main mechanisms governing the plasticity of these materials and, despite being already widely used, high pressure die-casting and wrought Mg alloys are still the subject of intense research campaigns. Developing models that can contemplate the complexity inherent to the deformation of Mg alloys is now timely. This PhD thesis constitutes an attempt to better understand the relationship between the microstructure and the mechanical behavior of Mg alloys, as it will result in the design of polycrystalline models that successfully predict macro- and microscopic properties. Plastic deformation of Mg alloys is driven by a combination of deformation mechanisms specific to their hexagonal crystal structure, namely, basal, prismatic and pyramidal dislocation slip as well as twinning. Wrought Mg alloys present strong textures and thus specific deformation mechanisms are preferentially activated depending on the orientation of the applied load. In this work a crystal plasticity finite element model has been developed in order to understand the macro- and micromechanical behavior of a rolled Mg AZ31 alloy (Mg-3wt.%Al-1wt.%Zn). The model includes twinning and accounts for slip-slip, slip-twin and twin-twin hardening interactions. Upon calibration and validation against experiments, the model successfully predicts the activity of the various deformation mechanisms and the evolution of the texture at different deformation stages. Furthermore, a combined three-dimensional electron backscatter diffraction and modeling approach has been adopted to investigate the effect of grain boundaries on twin propagation in the same material. Both experiments and simulations confirm that the misorientation angle has a critical influence on twin propagation. Non-Schmid effects, i.e. plastic deformation events that do not comply with the Schmid law with respect to the applied stress, are absent in the vicinity of low misorientation boundaries and become more abundant as misorientation angle increases. This research also proves that twin morphology is highly influenced by the Schmid factor. Finally, casting processes usually lead to the formation of significant amounts of gas and shrinkage microporosity, which adversely affect the mechanical properties. The application of hydrostatic pressure after casting can reduce the porosity and improve the properties but little is known about the effects on the casting’s pores size and morphology. In this work, an experimental-computational approach based on X-ray computed tomography, image analysis and finite element analysis is utilized for the determination of the 3D porosity distribution and its evolution with hydrostatic pressure in a high pressure diecast Mg AZ91 alloy (Mg-9wt.%Al-1wt.%Zn). The real 3D pore distribution obtained by tomography is used as input for the finite element simulations using an isotropic hardening law. The model is calibrated and validated against experimental stress-strain curves. The results reveal that the pressure treatment has a significant influence both on the volume and shape changes of individuals pores, which have been precisely quantified, and which are found to be related to the initial pore volume. In conclusion, the crystal plasticity model proposed in this work successfully describes the intrinsic deformation mechanisms of Mg alloys both at the mesoscale and the microscale. More specifically, it can capture slip and twin activities, their interactions, as well as the potential porosity effects arising from casting processes.

Mixed models for short-run forecasting of electricity prices: Application for the Spanish market

Short-run forecasting of electricity prices has become necessary for power generation unit schedule, since it is the basis of every profit maximization strategy. In this article a new and very easy method to compute accurate forecasts for electricity prices using mixed models is proposed. The main idea is to develop an efficient tool for one-step-ahead forecasting in the future, combining several prediction methods for which forecasting performance has been checked and compared for a span of several years. Also as a novelty, the 24 hourly time series has been modelled separately, instead of the complete time series of the prices. This allows one to take advantage of the homogeneity of these 24 time series. The purpose of this paper is to select the model that leads to smaller prediction errors and to obtain the appropriate length of time to use for forecasting. These results have been obtained by means of a computational experiment. A mixed model which combines the advantages of the two new models discussed is proposed. Some numerical results for the Spanish market are shown, but this new methodology can be applied to other electricity markets as well

Linear latent force models using Gaussian Processes

Purely data-driven approaches for machine learning present difficulties when data are scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data-driven modeling with a physical model of the system. We show how different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology, and geostatistics.

Nonlinear models for lateral dynamics of railway vehicles on bridges subject to wind action

The study of lateral dynamics of running trains on bridges is of importance mainly for the safety of the traffic, and may be relevant for laterally compliant bridges. These studies require threedimensional coupled vehicle-bridge models, wheree consideration of wheel to rail contact is a key aspect. Furthermore, an adequate evaluation of safety of rail traffic requires nonlinear models. A nonlinear coupled model is proposed here for vehicle-structure vertical and lateral dynamics. Vehicles are considered as fully three-dimensional multibody systems including gyroscopic terms and large rotation effects. The bridge structure is modeled by means of finite elements which may be of beam, shell or continuum type and may include geometric or material nonlinearities. The track geometry includes distributed track alignment irregularities. Both subsystems (bridge and vehicles) are described with coordinates in absolute reference frames, as opposed to alternative approaches which describe the multibody system with coordinates relative to the base bridge motion. The wheelrail contact employed is a semi-Hertzian model based on realistic wheel-rail profiles. It allows a detailed geometrical description of the contact patch under each wheel including multiple-point contact, flange contact and uplift. Normal and tangential stresses in each contact are integrated at each time-step to obtain the resultant contact forces. The models have been implemented within an existing finite element analysis software with multibody capabilities, Abaqus (Simulia Ltd., 2010). Further details of the model are presented in Antolín et al. (2012). Representative applications are presented for railway vehicles under lateral wind action on laterally compliant viaducts, showing the relevance of the nonlinear wheel-rail contact model as well as the interaction between bridge and vehicle.

Region-based moving object detection using spatially conditioned nonparametric models in a GPU

A novel GPU-based nonparametric moving object detection strategy for computer vision tools requiring real-time processing is proposed. An alternative and efficient Bayesian classifier to combine nonparametric background and foreground models allows increasing correct detections while avoiding false detections. Additionally, an efficient region of interest analysis significantly reduces the computational cost of the detections.

A methodology to calibrate structural finite element models for reinforced concrete structures subject to blast loads

Civil buildings are not specifically designed to support blast loads, but it is important to take into account these potential scenarios because of their catastrophic effects, on persons and structures. A practical way to consider explosions on reinforced concrete structures is necessary. With this objective we propose a methodology to evaluate blast loads on large concrete buildings, using LS-DYNA code for calculation, with Lagrangian finite elements and explicit time integration. The methodology has three steps. First, individual structural elements of the building like columns and slabs are studied, using continuum 3D elements models subjected to blast loads. In these models reinforced concrete is represented with high precision, using advanced material models such as CSCM_CONCRETE model, and segregated rebars constrained within the continuum mesh. Regrettably this approach cannot be used for large structures because of its excessive computational cost. Second, models based on structural elements are developed, using shells and beam elements. In these models concrete is represented using CONCRETE_EC2 model and segregated rebars with offset formulation, being calibrated with continuum elements models from step one to obtain the same structural response: displacement, velocity, acceleration, damage and erosion. Third, models basedon structural elements are used to develop large models of complete buildings. They are used to study the global response of buildings subjected to blast loads and progressive collapse. This article carries out different techniques needed to calibrate properly the models based on structural elements, using shells and beam elements, in order to provide results of sufficient accuracy that can be used with moderate computational cost.