Numerical Error Prediction and its applications in CFD using tau-estimation

Nowadays, Computational Fluid Dynamics (CFD) solvers are widely used within the industry to model fluid flow phenomenons. Several fluid flow model equations have been employed in the last decades to simulate and predict forces acting, for example, on different aircraft configurations. Computational time and accuracy are strongly dependent on the fluid flow model equation and the spatial dimension of the problem considered. While simple models based on perfect flows, like panel methods or potential flow models can be very fast to solve, they usually suffer from a poor accuracy in order to simulate real flows (transonic, viscous). On the other hand, more complex models such as the full Navier- Stokes equations provide high fidelity predictions but at a much higher computational cost. Thus, a good compromise between accuracy and computational time has to be fixed for engineering applications. A discretisation technique widely used within the industry is the so-called Finite Volume approach on unstructured meshes. This technique spatially discretises the flow motion equations onto a set of elements which form a mesh, a discrete representation of the continuous domain. Using this approach, for a given flow model equation, the accuracy and computational time mainly depend on the distribution of nodes forming the mesh. Therefore, a good compromise between accuracy and computational time might be obtained by carefully defining the mesh. However, defining an optimal mesh for complex flows and geometries requires a very high level expertize in fluid mechanics and numerical analysis, and in most cases a simple guess of regions of the computational domain which might affect the most the accuracy is impossible. Thus, it is desirable to have an automatized remeshing tool, which is more flexible with unstructured meshes than its structured counterpart. However, adaptive methods currently in use still have an opened question: how to efficiently drive the adaptation ? Pioneering sensors based on flow features generally suffer from a lack of reliability, so in the last decade more effort has been made in developing numerical error-based sensors, like for instance the adjoint-based adaptation sensors. While very efficient at adapting meshes for a given functional output, the latter method is very expensive as it requires to solve a dual set of equations and computes the sensor on an embedded mesh. Therefore, it would be desirable to develop a more affordable numerical error estimation method. The current work aims at estimating the truncation error, which arises when discretising a partial differential equation. These are the higher order terms neglected in the construction of the numerical scheme. The truncation error provides very useful information as it is strongly related to the flow model equation and its discretisation. On one hand, it is a very reliable measure of the quality of the mesh, therefore very useful in order to drive a mesh adaptation procedure. On the other hand, it is strongly linked to the flow model equation, so that a careful estimation actually gives information on how well a given equation is solved, which may be useful in the context of _ -extrapolation or zonal modelling. The following work is organized as follows: Chap. 1 contains a short review of mesh adaptation techniques as well as numerical error prediction. In the first section, Sec. 1.1, the basic refinement strategies are reviewed and the main contribution to structured and unstructured mesh adaptation are presented. Sec. 1.2 introduces the definitions of errors encountered when solving Computational Fluid Dynamics problems and reviews the most common approaches to predict them. Chap. 2 is devoted to the mathematical formulation of truncation error estimation in the context of finite volume methodology, as well as a complete verification procedure. Several features are studied, such as the influence of grid non-uniformities, non-linearity, boundary conditions and non-converged numerical solutions. This verification part has been submitted and accepted for publication in the Journal of Computational Physics. Chap. 3 presents a mesh adaptation algorithm based on truncation error estimates and compares the results to a feature-based and an adjoint-based sensor (in collaboration with Jorge Ponsín, INTA). Two- and three-dimensional cases relevant for validation in the aeronautical industry are considered. This part has been submitted and accepted in the AIAA Journal. An extension to Reynolds Averaged Navier- Stokes equations is also included, where _ -estimation-based mesh adaptation and _ -extrapolation are applied to viscous wing profiles. The latter has been submitted in the Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering. Keywords: mesh adaptation, numerical error prediction, finite volume Hoy en día, la Dinámica de Fluidos Computacional (CFD) es ampliamente utilizada dentro de la industria para obtener información sobre fenómenos fluidos. La Dinámica de Fluidos Computacional considera distintas modelizaciones de las ecuaciones fluidas (Potencial, Euler, Navier-Stokes, etc) para simular y predecir las fuerzas que actúan, por ejemplo, sobre una configuración de aeronave. El tiempo de cálculo y la precisión en la solución depende en gran medida de los modelos utilizados, así como de la dimensión espacial del problema considerado. Mientras que modelos simples basados en flujos perfectos, como modelos de flujos potenciales, se pueden resolver rápidamente, por lo general aducen de una baja precisión a la hora de simular flujos reales (viscosos, transónicos, etc). Por otro lado, modelos más complejos tales como el conjunto de ecuaciones de Navier-Stokes proporcionan predicciones de alta fidelidad, a expensas de un coste computacional mucho más elevado. Por lo tanto, en términos de aplicaciones de ingeniería se debe fijar un buen compromiso entre precisión y tiempo de cálculo. Una técnica de discretización ampliamente utilizada en la industria es el método de los Volúmenes Finitos en mallas no estructuradas. Esta técnica discretiza espacialmente las ecuaciones del movimiento del flujo sobre un conjunto de elementos que forman una malla, una representación discreta del dominio continuo. Utilizando este enfoque, para una ecuación de flujo dado, la precisión y el tiempo computacional dependen principalmente de la distribución de los nodos que forman la malla. Por consiguiente, un buen compromiso entre precisión y tiempo de cálculo se podría obtener definiendo cuidadosamente la malla, concentrando sus elementos en aquellas zonas donde sea estrictamente necesario. Sin embargo, la definición de una malla óptima para corrientes y geometrías complejas requiere un nivel muy alto de experiencia en la mecánica de fluidos y el análisis numérico, así como un conocimiento previo de la solución. Aspecto que en la mayoría de los casos no está disponible. Por tanto, es deseable tener una herramienta que permita adaptar los elementos de malla de forma automática, acorde a la solución fluida (remallado). Esta herramienta es generalmente más flexible en mallas no estructuradas que con su homóloga estructurada. No obstante, los métodos de adaptación actualmente en uso todavía dejan una pregunta abierta: cómo conducir de manera eficiente la adaptación. Sensores pioneros basados en las características del flujo en general, adolecen de una falta de fiabilidad, por lo que en la última década se han realizado grandes esfuerzos en el desarrollo numérico de sensores basados en el error, como por ejemplo los sensores basados en el adjunto. A pesar de ser muy eficientes en la adaptación de mallas para un determinado funcional, este último método resulta muy costoso, pues requiere resolver un doble conjunto de ecuaciones: la solución y su adjunta. Por tanto, es deseable desarrollar un método numérico de estimación de error más asequible. El presente trabajo tiene como objetivo estimar el error local de truncación, que aparece cuando se discretiza una ecuación en derivadas parciales. Estos son los términos de orden superior olvidados en la construcción del esquema numérico. El error de truncación proporciona una información muy útil sobre la solución: es una medida muy fiable de la calidad de la malla, obteniendo información que permite llevar a cabo un procedimiento de adaptación de malla. Está fuertemente relacionado al modelo matemático fluido, de modo que una estimación precisa garantiza la idoneidad de dicho modelo en un campo fluido, lo que puede ser útil en el contexto de modelado zonal. Por último, permite mejorar la precisión de la solución resolviendo un nuevo sistema donde el error local actúa como término fuente (_ -extrapolación). El presenta trabajo se organiza de la siguiente manera: Cap. 1 contiene una breve reseña de las técnicas de adaptación de malla, así como de los métodos de predicción de los errores numéricos. En la primera sección, Sec. 1.1, se examinan las estrategias básicas de refinamiento y se presenta la principal contribución a la adaptación de malla estructurada y no estructurada. Sec 1.2 introduce las definiciones de los errores encontrados en la resolución de problemas de Dinámica Computacional de Fluidos y se examinan los enfoques más comunes para predecirlos. Cap. 2 está dedicado a la formulación matemática de la estimación del error de truncación en el contexto de la metodología de Volúmenes Finitos, así como a un procedimiento de verificación completo. Se estudian varias características que influyen en su estimación: la influencia de la falta de uniformidad de la malla, el efecto de las no linealidades del modelo matemático, diferentes condiciones de contorno y soluciones numéricas no convergidas. Esta parte de verificación ha sido presentada y aceptada para su publicación en el Journal of Computational Physics. Cap. 3 presenta un algoritmo de adaptación de malla basado en la estimación del error de truncación y compara los resultados con sensores de featured-based y adjointbased (en colaboración con Jorge Ponsín del INTA). Se consideran casos en dos y tres dimensiones, relevantes para la validación en la industria aeronáutica. Este trabajo ha sido presentado y aceptado en el AIAA Journal. También se incluye una extensión de estos métodos a las ecuaciones RANS (Reynolds Average Navier- Stokes), en donde adaptación de malla basada en _ y _ -extrapolación son aplicados a perfiles con viscosidad de alas. Este último trabajo se ha presentado en los Actas de la Institución de Ingenieros Mecánicos, Parte G: Journal of Aerospace Engineering. Palabras clave: adaptación de malla, predicción del error numérico, volúmenes finitos

Estudio numérico de flujo turbulento cargado con partículas sólidas a través de canales y tuberías de sección variable

La presente Tesis Doctoral tiene como objetivo el estudio de flujo turbulento cargado con partículas sólidas a través de canales y tuberías de sección constante usando un enfoque Euleriano-Lagrangiano. El campo de flujo de la fase de transporte (aire) se resuelve usando simulación de grandes escalas (LES), implementada en un programa de volúmenes finitos mientras que las ecuaciones gobernantes de la fase dispersa son resueltas por medio de un algoritmo de seguimiento Lagrangiano de partículas que ha sido desarrollado y acoplado al programa que resuelve el flujo. Se estudia de manera sistemática y progresiva la interacción fluido→partícula (one-way coupling), a través de diferentes configuraciones geométricas en coordenadas cartesianas (canales de sección constante y variable) y en coordenadas cilíndricas (tuberías de sección constante y sección variable) abarcando diferentes números de Reynolds y diferentes tamaños de partículas; todos los resultados obtenidos han sido comparados con datos publicados previamente. El estudio de flujo multifásico a través de, tuberías de sección variable, ha sido abordada en otras investigaciones mayoritariamente de forma experimental o mediante simulación usando modelos de turbulencia menos complejos y no mediante LES. El patrón de flujo que se verifica en una tubería con expansión es muy complejo y dicha configuración geométrica se halla en múltiples aplicaciones industriales que involucran el transporte de partículas sólidas, por ello es de gran interés su estudio. Como hecho innovador, en esta tesis no solo se resuelven las estadísticas de velocidad del fluido y las partículas en tuberías con diferentes tamaños de expansión y diferentes regímenes de flujo sino que se caracteriza, usando diversas formulaciones del número de Stokes y el parámetro de arrastre, el ingreso y acumulación de partículas dentro de la zona de recirculación, obteniéndose resultados coincidentes con datos experimentales. ABSTRACT The objective of this Thesis research is to study the turbulent flow laden with solid particles through channels and pipes with using Eulerian-Lagrangian approach. The flow field of the transport phase (air ) is solved using large eddy simulation ( LES ) implemented in a program of finite volume while the governing equations of the dispersed phase are resolved by means of a particle Lagrangian tracking algorithm which was developed and coupled to principal program flow solver . We studied systematically and progressively the fluid interaction → particle ( one- way coupling ) , through different geometric configurations in Cartesian coordinates ( channel with constant and variable section) and in cylindrical coordinates ( pipes with constant section and variable section ) covering different Reynolds numbers and different particle sizes, all results have been compared with previously published data . The study of multiphase flow through, pipes with variable section has been addressed in other investigations predominantly experimentally or by simulation using less complex models and no turbulence by LES. The flow pattern is verified in a pipe expansion is very complex and this geometry is found in many industrial applications involving the transport of solid particles, so it is of great interest to study. As an innovator fact , in this Thesis not only finds fluid velocity statistics and particles with different sizes of pipe expansion and different flow regimes but characterized, using various formulations of the Stokes number and the drag parameter are resolved, the entry and accumulation of particles within the recirculation zone , matching results obtained with experimental data.

Estudio de la respuesta dinámica transversal de viaductos altos de líneas de ferrocarril de alta velocidad bajo la acción de cargas de uso

Es conocido que las dimensiones de los puentes de ferrocarril han ido cambiando debido a las estrictas condiciones de trazado impuestas en las líneas de alta velocidad. Además, la creciente preocupación de la sociedad por cuidar y proteger el medio ambiente, reflejado en la correspondiente normativa, ha generado nuevos condicionantes en el diseño de estas infraestructuras. En concreto, se ha limitado el movimiento de grandes volúmenes de terreno particularmente en los espacios protegidos. Por estas razones, hoy en día se proyectan y construyen puentes de ferrocarril más altos y más largos en todo el mundo. En España se han construido varios viaductos de pilas altas para líneas de alta velocidad. Ejemplos de estas infraestructuras son el Viaducto O’Eixo y el Viaducto de Barbantiño, situados en la línea de alta velocidad Madrid-Galicia, Estos viaductos altos se caracterizan por tener una mayor flexibilidad lateral y una frecuencia fundamental de oscilación baja, de hasta 0.2 Hz. La respuesta dinámica de este tipo de estructura puede aumentar como consecuencia de la aproximación entre la frecuencias propias de la misma y las de excitación debidas al paso del tren y a la acción del viento. Por lo tanto, estas estructuras pueden presentar problemas a la hora de cumplir con las limitaciones impuestas en las normas de diseño de puentes de ferrocarril, y otras, para garantizar la seguridad del tráfico y el confort de los viajeros. La respuesta dinámica lateral de viaductos de pilas altas no ha sido suficientemente estudiada en la literatura científica. Se pueden intuir varios de los motivos para explicar esta carencia. El primero es la relativamente reciente aparición de este tipo de viaductos asociados al desarrollo de la alta velocidad. Por otro lado, se hace necesario, para estudiar este tema, construir nuevos modelos numéricos adecuados para el estudio de la interacción dinámica lateral del puente y del tren. La interacción entre el puente y un tren viajando sobre él es un problema dinámico no lineal, dependiente del tiempo y de acoplamiento entre los dos subsistemas que intervienen (vehículo y puente). Los dos subsistemas, que pueden ser modelados como estructuras elásticas, interaccionan el uno con el otro a través de las fuerzas de contacto, que tiene una marcada naturaleza no lineal por el rozamiento entre rueda y carril, y por la geometría de los perfiles de estos dos elementos en contacto. En esta tesis, se desarrolla la formulación completa de un modelo no lineal de interacción tren-vía-puente-viento que reproduce adecuadamente las fuerzas laterales de contacto rueda-carril, fuerzas que van a tener una gran influencia en los índices de seguridad del tráfico. Este modelo se ha validado a partir de casos resueltos en la literatura científica, y de medidas experimentales tomadas en eventos dinámicos ocurridos en los viaductos de Arroyo de Valle y Arroyo de las Piedras. Puentes altos que han estado monitorizados en servicio durante dos años. En los estudios realizados en este trabajo, se cuantifican, empleando el modelo construido, los niveles de seguridad del tráfico y de confort de los pasajeros de trenes ligeros de alta velocidad, como el tren articulado AVE S-100, que viajan sobre viaductos altos sometidos, o no, a fuertes vientos laterales racheados. Finalmente, se ha obtenido el grado de mejora de la seguridad del tráfico y del confort de los viajeros, cuando se emplean pantallas anti-viento en el tablero y amortiguadores de masa sintonizados en la cabeza de las pilas de un viaducto alto. Resultando, el uso simultaneo de estos dos dispositivos (pantallas y amortiguadores de masa), en puentes altos de líneas de alta velocidad, una opción a considerar en la construcción de estas estructuras para elevar significativamente el nivel de servicio de las mismas. It is known that dimensions of railway bridges have been changing due to the strict high-speed lines layout parameters. Moreover, the growing concern of society to take care of and protect the environment, reflected in the corresponding regulations, has created new environment requirements for the design of these infrastructures. Particularly, the mentioned regulations do not allow designers to move far from terrain to build these railway lines. Due to all these reasons, longer and higher railway bridges are being designed and built around the world. In Spain, several high pier railway viaducts have been built for high speed lines. Barbantiño Viaduct and Eixo Viaduct, belonging to the Madrid-Galicia high speed line, are examples of this kind of structures. These high viaducts have great lateral flexibility and a low fundamental vibration frequency of down to 0.2 Hz. The dynamic response of high speed railway bridges may increase because of the approximation between the natural viaduct frequencies and the excitation ones due to the train travel and the wind action. Therefore, this bridge response could not satisfy the serviceability limits states, for traffic safety and for passenger comfort, considered by the design standards of high speed bridges. It is difficult to find papers in the scientific literature about the lateral response of high-speed trains travel over long viaducts with high piers. Several reasons could explain this issue. On one hand, the construction of this kind of viaduct is relatively recent and it is associated to the development of the high speed railway. On the other hand, in order to study the dynamic lateral interaction between the train and the high bridge, it is necessary to build new numerical and complex models. The interaction between the bridge-track subsystem and the vehicle subsystem travelling over the bridge is a coupling, nonlinear and time dependent problem. Both subsystems, train and bridge, which can be modelled as elastic structures, interact each other through the contact forces. These forces have a strong nonlinear nature due to the friction and the geometry of rail and wheel profiles. In this thesis, the full formulation of a train-track-bridge-wind nonlinear interaction model is developed. This model can reproduce properly the lateral contact wheel-rail forces, which have a great influence on traffic safety indices. The validation of the model built has been reached through interaction solved cases found in the scientific literature and experimental measures taken in dynamic events which happened at Arroyo de las Piedras and Arroyo del Valle Viaducts. These high bridges have been controlled during two years of service by means of structural health monitoring. In the studies carried out for this thesis, the levels of traffic safety and passenger comfort are quantified using the interaction model built, in the cases of high speed and light trains, as AVE S-100, travelling over high pier bridges and with or without lateral turbulent winds acting. Finally, the improvement rate of the traffic safety and passenger comfort has been obtained, when wind barriers are used at the bridge deck and tuned mass dampers are installed at the pier heads of a high viaduct. The installation of both devices, wind barriers and tuned mass damper, at the same time, turned out to be a good option to be considered in the design of high pier railway viaducts, to improve significantly the serviceability level of this kind of structures.

Estudo numérico do efeito de blocagem hidrodinâmica em um túnel de cavitação sobre o escoamento ao redor de um submarino.

O projeto de submarinos é um tema que vem se desenvolvendo há muitos anos. No Brasil, vivemos um momento de pleno avanço na área, sendo encabeçado pela Marinha do Brasil com o desenvolvimento do primeiro submarino de propulsão nuclear brasileiro. No decorrer desse projeto, diversos estudos devem ser desenvolvidos, dentre eles, ensaios com modelos em escala, que serão realizados em um túnel de cavitação. Durante estes experimentos, espera-se que surjam diversas fontes de incerteza, que podem comprometer os resultados obtidos, destacando-se o efeito de blocagem hidrodinâmica. Nesse contexto, esta dissertação apresenta uma investigação do fenômeno de blocagem no modelo de submarino DARPA SUBOFF na seção de testes de um túnel de cavitação. Para isso, simulações tridimensionais de média de Reynolds (RANS) foram realizadas para o modelo de submarino posicionado no túnel (sob blocagem) e sob condição de águas profundas (referência), para diferentes ângulos de ataque e número de Reynolds (Re) constante. Coeficientes de força e momento hidrodinâmicos foram obtidos e os métodos de correção de blocagem clássico e WICS foram empregados para obter fatores que pudessem corrigir esses valores. A eficiência de cada método foi avaliada comparando os valores corrigidos com os de referência. Os resultados mostraram que ambos métodos de correção são eficientes na recuperação de coeficientes de força e momento hidrodinâmicos para razões de blocagem inferiores a 10%, mas ressalvas são feitas quanto à utilização de cada um desses métodos, sendo o método clássico indicado para o estudo de geometrias simples e o método WICS para modelos mais complexos. Paralelamente, a topologia do escoamento ao redor do submarino foi estudada através do método dos pontos críticos, para avaliar se a blocagem hidrodinâmica pode causar alterações nas estruturas presentes no escoamento. A análise topológica permitiu avaliar a evolução nas estruturas do escoamento para os ângulos de ataque e Re simulados. Foram capturadas as linhas de separação no corpo e avaliada sua relação com a tensão de cisalhamento ao longo do casco. A blocagem hidrodinâmica não causou alterações drásticas na topologia do escoamento.

A formal framework for modelling and analysing mobile systems

This paper presents a formal framework for modelling and analysing mobile systems. The framework comprises a collection of models of the dominant design paradigms which are readily extended to incorporate details of particular technologies, i.e., programming languages and their run-time support, and applications. The modelling language is Object-Z, an extension of the well-known Z specification language with explicit support for object-oriented concepts. Its support for object orientation makes Object-Z particularly suited to our task. The system structuring techniques offered by object-orientation are well suited to modelling mobile systems. In addition, inheritance and polymorphism allow us to exploit commonalities in mobile systems by defining more complex models in terms of simpler ones.

Flexible high speed machinery

The thesis describes an investigation into methods for the design of flexible high-speed product processing machinery, consisting of independent electromechanically actuated machine functions which operate under software coordination and control. An analysis is made of the elements of traditionally designed cam-actuated, mechanically coupled machinery, so that the operational functions and principal performance limitations of the separate machine elements may be identified. These are then used to define the requirements for independent actuators machinery, with a discussion of how this type of design approach is more suited to modern manufacturing trends. A distributed machine controller topology is developed which is a hybrid of hierarchical and pipeline control. An analysis is made, with the aid of dynamic simulation modelling, which confirms the suitability of the controller for flexible machinery control. The simulations include complex models of multiple independent actuators systems, which enable product flow and failure analyses to be performed. An analysis is made of high performance brushless d.c. servomotors and their suitability for actuating machine motions is assessed. Procedures are developed for the selection of brushless servomotors for intermittent machine motions. An experimental rig is described which has enabled the actuation and control methods developed to be implemented. With reference to this, an evaluation is made of the suitability of the machine design method and a discussion is given of the developments which are necessary for operational independent actuators machinery to be attained.

The Living Economy

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

Simulation modeling of phytoplankton dynamics in a large eutrophic river, Hungary – Danubian Phytoplankton Growth Model (DPGM)

Ecological models have often been used in order to answer questions that are in the limelight of recent researches such as the possible effects of climate change. The methodology of tactical models is a very useful tool comparison to those complex models requiring relatively large set of input parameters. In this study, a theoretical strategic model (TEGM ) was adapted to the field data on the basis of a 24-year long monitoring database of phytoplankton in the Danube River at the station of G¨od, Hungary (at 1669 river kilometer – hereafter referred to as “rkm”). The Danubian Phytoplankton Growth Model (DPGM) is able to describe the seasonal dynamics of phytoplankton biomass (mg L−1) based on daily temperature, but takes the availability of light into consideration as well. In order to improve fitting, the 24-year long database was split in two parts in accordance with environmental sustainability. The period of 1979–1990 has a higher level of nutrient excess compared with that of the 1991–2002. The authors assume that, in the above-mentioned periods, phytoplankton responded to temperature in two different ways, thus two submodels were developed, DPGM-sA and DPGMsB. Observed and simulated data correlated quite well. Findings suggest that linear temperature rise brings drastic change to phytoplankton only in case of high nutrient load and it is mostly realized through the increase of yearly total biomass.

A comprehensive study of bankruptcy prediction: Accounting ratios, market variables, and microstructure

Bankruptcy prediction has been a fruitful area of research. Univariate analysis and discriminant analysis were the first methodologies used. While they perform relatively well at correctly classifying bankrupt and nonbankrupt firms, their predictive ability has come into question over time. Univariate analysis lacks the big picture that financial distress entails. Multivariate discriminant analysis requires stringent assumptions that are violated when dealing with accounting ratios and market variables. This has led to the use of more complex models such as neural networks. While the accuracy of the predictions has improved with the use of more technical models, there is still an important point missing. Accounting ratios are the usual discriminating variables used in bankruptcy prediction. However, accounting ratios are backward-looking variables. At best, they are a current snapshot of the firm. Market variables are forward-looking variables. They are determined by discounting future outcomes. Microstructure variables, such as the bid-ask spread, also contain important information. Insiders are privy to more information that the retail investor, so if any financial distress is looming, the insiders should know before the general public. Therefore, any model in bankruptcy prediction should include market and microstructure variables. That is the focus of this dissertation. The traditional models and the newer, more technical models were tested and compared to the previous literature by employing accounting ratios, market variables, and microstructure variables. Our findings suggest that the more technical models are preferable, and that a mix of accounting and market variables are best at correctly classifying and predicting bankrupt firms. Multi-layer perceptron appears to be the most accurate model following the results. The set of best discriminating variables includes price, standard deviation of price, the bid-ask spread, net income to sale, working capital to total assets, and current liabilities to total assets.

Distributed Extremum-Seeking Control with Applications to High-Altitude Balloons

The real-time optimization of large-scale systems is a difficult problem due to the need for complex models involving uncertain parameters and the high computational cost of solving such problems by a decentralized approach. Extremum-seeking control (ESC) is a model-free real-time optimization technique which can estimate unknown parameters and can optimize nonlinear time-varying systems using only a measurement of the cost function to be minimized. In this thesis, we develop a distributed version of extremum-seeking control which allows large-scale systems to be optimized without models and with minimal computing power. First, we develop a continuous-time distributed extremum-seeking controller. It has three main components: consensus, parameter estimation, and optimization. The consensus provides each local controller with an estimate of the cost to be minimized, allowing them to coordinate their actions. Using this cost estimate, parameters for a local input-output model are estimated, and the cost is minimized by following a gradient descent based on the estimate of the gradient. Next, a similar distributed extremum-seeking controller is developed in discrete-time. Finally, we consider an interesting application of distributed ESC: formation control of high-altitude balloons for high-speed wireless internet. These balloons must be steered into a favourable formation where they are spread out over the Earth and provide coverage to the entire planet. Distributed ESC is applied to this problem, and is shown to be effective for a system of 1200 ballons subjected to realistic wind currents. The approach does not require a wind model and uses a cost function based on a Voronoi partition of the sphere. Distributed ESC is able to steer balloons from a few initial launch sites into a formation which provides coverage to the entire Earth and can maintain a similar formation as the balloons move with the wind around the Earth.

Directional genetic differentiation and relative migration

Understanding the population structure and patterns of gene flow within species is of fundamental importance to the study of evolution. In the fields of population and evolutionary genetics, measures of genetic differentiation are commonly used to gather this information. One potential caveat is that these measures assume gene flow to be symmetric. However, asymmetric gene flow is common in nature, especially in systems driven by physical processes such as wind or water currents. As information about levels of asymmetric gene flow among populations is essential for the correct interpretation of the distribution of contemporary genetic diversity within species, this should not be overlooked. To obtain information on asymmetric migration patterns from genetic data, complex models based on maximum-likelihood or Bayesian approaches generally need to be employed, often at great computational cost. Here, a new simpler and more efficient approach for understanding gene flow patterns is presented. This approach allows the estimation of directional components of genetic divergence between pairs of populations at low computational effort, using any of the classical or modern measures of genetic differentiation. These directional measures of genetic differentiation can further be used to calculate directional relative migration and to detect asymmetries in gene flow patterns. This can be done in a user-friendly web application called divMigrate-online introduced in this study. Using simulated data sets with known gene flow regimes, we demonstrate that the method is capable of resolving complex migration patterns under a range of study designs.

Artificial immune systems

The human immune system has numerous properties that make it ripe for exploitation in the computational domain, such as robustness and fault tolerance, and many different algorithms, collectively termed Artificial Immune Systems (AIS), have been inspired by it. Two generations of AIS are currently in use, with the first generation relying on simplified immune models and the second generation utilising interdisciplinary collaboration to develop a deeper understanding of the immune system and hence produce more complex models. Both generations of algorithms have been successfully applied to a variety of problems, including anomaly detection, pattern recognition, optimisation and robotics. In this chapter an overview of AIS is presented, its evolution is discussed, and it is shown that the diversification of the field is linked to the diversity of the immune system itself, leading to a number of algorithms as opposed to one archetypal system. Two case studies are also presented to help provide insight into the mechanisms of AIS; these are the idiotypic network approach and the Dendritic Cell Algorithm.

A NOVEL MODELING AND STATE OF CHARGE ESTIMATION SCHEME FOR LITHIUM-ION BATTERIES

Lithium Ion (Li-Ion) batteries have got attention in recent decades because of their undisputable advantages over other types of batteries. They are used in so many our devices which we need in our daily life such as cell phones, lap top computers, cameras, and so many electronic devices. They also are being used in smart grids technology, stand-alone wind and solar systems, Hybrid Electric Vehicles (HEV), and Plug in Hybrid Electric Vehicles (PHEV). Despite the rapid increase in the use of Lit-ion batteries, the existence of limited battery models also inadequate and very complex models developed by chemists is the lack of useful models a significant matter. A battery management system (BMS) aims to optimize the use of the battery, making the whole system more reliable, durable and cost effective. Perhaps the most important function of the BMS is to provide an estimate of the State of Charge (SOC). SOC is the ratio of available ampere-hour (Ah) in the battery to the total Ah of a fully charged battery. The Open Circuit Voltage (OCV) of a fully relaxed battery has an approximate one-to-one relationship with the SOC. Therefore, if this voltage is known, the SOC can be found. However, the relaxed OCV can only be measured when the battery is relaxed and the internal battery chemistry has reached equilibrium. This thesis focuses on Li-ion battery cell modelling and SOC estimation. In particular, the thesis, introduces a simple but comprehensive model for the battery and a novel on-line, accurate and fast SOC estimation algorithm for the primary purpose of use in electric and hybrid-electric vehicles, and microgrid systems. The thesis aims to (i) form a baseline characterization for dynamic modeling; (ii) provide a tool for use in state-of-charge estimation. The proposed modelling and SOC estimation schemes are validated through comprehensive simulation and experimental results.

Using Bayesian methods for the estimation of uncertainty in complex statistical models

The research objectives of this thesis were to contribute to Bayesian statistical methodology by contributing to risk assessment statistical methodology, and to spatial and spatio-temporal methodology, by modelling error structures using complex hierarchical models. Specifically, I hoped to consider two applied areas, and use these applications as a springboard for developing new statistical methods as well as undertaking analyses which might give answers to particular applied questions. Thus, this thesis considers a series of models, firstly in the context of risk assessments for recycled water, and secondly in the context of water usage by crops. The research objective was to model error structures using hierarchical models in two problems, namely risk assessment analyses for wastewater, and secondly, in a four dimensional dataset, assessing differences between cropping systems over time and over three spatial dimensions. The aim was to use the simplicity and insight afforded by Bayesian networks to develop appropriate models for risk scenarios, and again to use Bayesian hierarchical models to explore the necessarily complex modelling of four dimensional agricultural data. The specific objectives of the research were to develop a method for the calculation of credible intervals for the point estimates of Bayesian networks; to develop a model structure to incorporate all the experimental uncertainty associated with various constants thereby allowing the calculation of more credible credible intervals for a risk assessment; to model a single day’s data from the agricultural dataset which satisfactorily captured the complexities of the data; to build a model for several days’ data, in order to consider how the full data might be modelled; and finally to build a model for the full four dimensional dataset and to consider the timevarying nature of the contrast of interest, having satisfactorily accounted for possible spatial and temporal autocorrelations. This work forms five papers, two of which have been published, with two submitted, and the final paper still in draft. The first two objectives were met by recasting the risk assessments as directed, acyclic graphs (DAGs). In the first case, we elicited uncertainty for the conditional probabilities needed by the Bayesian net, incorporated these into a corresponding DAG, and used Markov chain Monte Carlo (MCMC) to find credible intervals, for all the scenarios and outcomes of interest. In the second case, we incorporated the experimental data underlying the risk assessment constants into the DAG, and also treated some of that data as needing to be modelled as an ‘errors-invariables’ problem [Fuller, 1987]. This illustrated a simple method for the incorporation of experimental error into risk assessments. In considering one day of the three-dimensional agricultural data, it became clear that geostatistical models or conditional autoregressive (CAR) models over the three dimensions were not the best way to approach the data. Instead CAR models are used with neighbours only in the same depth layer. This gave flexibility to the model, allowing both the spatially structured and non-structured variances to differ at all depths. We call this model the CAR layered model. Given the experimental design, the fixed part of the model could have been modelled as a set of means by treatment and by depth, but doing so allows little insight into how the treatment effects vary with depth. Hence, a number of essentially non-parametric approaches were taken to see the effects of depth on treatment, with the model of choice incorporating an errors-in-variables approach for depth in addition to a non-parametric smooth. The statistical contribution here was the introduction of the CAR layered model, the applied contribution the analysis of moisture over depth and estimation of the contrast of interest together with its credible intervals. These models were fitted using WinBUGS [Lunn et al., 2000]. The work in the fifth paper deals with the fact that with large datasets, the use of WinBUGS becomes more problematic because of its highly correlated term by term updating. In this work, we introduce a Gibbs sampler with block updating for the CAR layered model. The Gibbs sampler was implemented by Chris Strickland using pyMCMC [Strickland, 2010]. This framework is then used to consider five days data, and we show that moisture in the soil for all the various treatments reaches levels particular to each treatment at a depth of 200 cm and thereafter stays constant, albeit with increasing variances with depth. In an analysis across three spatial dimensions and across time, there are many interactions of time and the spatial dimensions to be considered. Hence, we chose to use a daily model and to repeat the analysis at all time points, effectively creating an interaction model of time by the daily model. Such an approach allows great flexibility. However, this approach does not allow insight into the way in which the parameter of interest varies over time. Hence, a two-stage approach was also used, with estimates from the first-stage being analysed as a set of time series. We see this spatio-temporal interaction model as being a useful approach to data measured across three spatial dimensions and time, since it does not assume additivity of the random spatial or temporal effects.