Optimal polygonal L1 linearization and fast interpolation of nonlinear systems

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using polygonal (continuous piecewise linear) models under the L1 norm. A thorough error analysis is developed to guide an optimal design of two kinds of polygonal approximations in the asymptotic case of a large budget of evaluation subintervals N. The method allows the user to obtain the level of linearization (N) for a target approximation error and vice versa. It is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), allowing real-time performance of computationally demanding applications. The quality and efficiency of the technique has been measured in detail on two nonlinear functions that are widely used in many areas of scientific computing and are expensive to evaluate.

Hybrid analysis of nonlinear circuits: DAE models with indices zero and one

We extend in this paper some previous results concerning the differential-algebraic index of hybrid models of electrical and electronic circuits. Specifically, we present a comprehensive index characterization which holds without passivity requirements, in contrast to previous approaches, and which applies to nonlinear circuits composed of uncoupled, one-port devices. The index conditions, which are stated in terms of the forest structure of certain digraph minors, do not depend on the specific tree chosen in the formulation of the hybrid equations. Additionally, we show how to include memristors in hybrid circuit models; in this direction, we extend the index analysis to circuits including active memristors, which have been recently used in the design of nonlinear oscillators and chaotic circuits. We also discuss the extension of these results to circuits with controlled sources, making our framework of interest in the analysis of circuits with transistors, amplifiers, and other multiterminal devices.

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

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

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

Computation of nonlinear streaky structures in boundary layer flow

En esta tesis se integran numéricamente las ecuaciones reducidas de Navier Stokes (RNS), que describen el flujo en una capa límite tridimensional que presenta también una escala característica espacial corta en el sentido transversal. La formulación RNS se usa para el cálculo de “streaks” no lineales de amplitud finita, y los resultados conseguidos coinciden con los existentes en la literatura, obtenidos típicamente utilizando simulación numérica directa (DNS) o nonlinear parabolized stability equations (PSE). El cálculo de los “streaks” integrando las RNS es mucho menos costoso que usando DNS, y no presenta los problemas de estabilidad que aparecen en la formulación PSE cuando la amplitud del “streak” deja de ser pequeña. El código de integración RNS se utiliza también para el cálculo de los “streaks” que aparecen de manera natural en el borde de ataque de una placa plana en ausencia de perturbaciones en la corriente uniforme exterior. Los resultados existentes hasta ahora calculaban estos “streaks” únicamente en el límite lineal (amplitud pequeña), y en esta tesis se lleva a cabo el cálculo de los mismos en el régimen completamente no lineal (amplitud finita). En la segunda parte de la tesis se generaliza el código RNS para incluir la posibilidad de tener una placa no plana, con curvatura en el sentido transversal que varía lentamente en el sentido de la corriente. Esto se consigue aplicando un cambio de coordenadas, que transforma el dominio físico en uno rectangular. La formulación RNS se integra también expresada en las correspondientes coordenadas curvilíneas. Este código generalizado RNS se utiliza finalmente para estudiar el flujo de capa límite sobre una placa con surcos que varían lentamente en el sentido de la corriente, y es usado para simular el flujo sobre surcos que crecen en tal sentido. Abstract In this thesis, the reduced Navier Stokes (RNS) equations are numerically integrated. This formulation describes the flow in a three-dimensional boundary layer that also presents a short characteristic space scale in the spanwise direction. RNS equations are used to calculate nonlinear finite amplitude “streaks”, and the results agree with those reported in the literature, typically obtained using direct numerical simulation (DNS) or nonlinear parabolized stability equations (PSE). “Streaks” simulations through the RNS integration are much cheaper than using DNS, and avoid stability problems that appear in the PSE when the amplitude of the “streak” is not small. The RNS integration code is also used to calculate the “streaks” that naturally emerge at the leading edge of a flat plate boundary layer in the absence of any free stream perturbations. Up to now, the existing results for these “streaks” have been only calculated in the linear limit (small amplitude), and in this thesis their calculation is carried out in the fully nonlinear regime (finite amplitude). In the second part of the thesis, the RNS code is generalized to include the possibility of having a non-flat plate, curved in the spanwise direction and slowly varying in the streamwise direction. This is achieved by applying a change of coordinates, which transforms the physical domain into a rectangular one. The RNS formulation expressed in the corresponding curvilinear coordinates is also numerically integrated. This generalized RNS code is finally used to study the boundary layer flow over a plate with grooves which vary slowly in the streamwise direction; and this code is used to simulate the flow over grooves that grow in the streamwise direction.

Coherent excitation of nonlinear oscillators

Coherently driven, dissipative nonlinear oscillators,(driving kept permanently in phase with the oscillators response) are proposed as systems with interesting dynamics. Results for simple, preliminary examples, which do not show chaotic behavior, are briefly discussed.

A modelling language for the resilience assessment of networked systems of systems

Systems of Systems (SoS) present challenging features and existing tools result often inadequate for their analysis, especially for heteregeneous networked infrastructures. Most accident scenarios in networked systems cannot be addressed by a simplistic black or white (i.e. functioning or failed) approach. Slow deviations from nominal operation conditions may cause degraded behaviours that suddenly end up into unexpected malfunctioning, with large portions of the network affected. In this paper,we present a language for modelling networked SoS. The language makes it possible to represent interdependencies of various natures, e.g. technical, organizational and human. The representation of interdependencies is based on control relationships that exchange physical quantities and related information. The language also makes it possible the identification of accident scenarios, by representing the propagation of failure events throughout the network. The results can be used for assessing the effectiveness of those mechanisms and measures that contribute to the overall resilience, both in qualitative and quantitative terms. The presented modelling methodology is general enough to be applied in combination with already existing system analysis techniques, such as risk assessment, dependability and performance evaluation

Resilience analysis of networked systems-of-systems based on structural and dynamic interdependencies

Critical infrastructures support everyday activities in modern societies, facilitating the exchange of services and quantities of various nature. Their functioning is the result of the integration of diverse technologies, systems and organizations into a complex network of interconnections. Benefits from networking are accompanied by new threats and risks. In particular, because of the increased interdependency, disturbances and failures may propagate and render unstable the whole infrastructure network. This paper presents a methodology of resilience analysis of networked systems of systems. Resilience generalizes the concept of stability of a system around a state of equilibrium, with respect to a disturbance and its ability of preventing, resisting and recovery. The methodology provides a tool for the analysis of off-equilibrium conditions that may occur in a single system and propagate through the network of dependencies. The analysis is conducted in two stages. The first stage of the analysis is qualitative. It identifies the resilience scenarios, i.e. the sequence of events, triggered by an initial disturbance, which include failures and the system response. The second stage is quantitative. The most critical scenarios can be simulated, for the desired parameter settings, in order to check if they are successfully handled, i.e recovered to nominal conditions, or they end into the network failure. The proposed methodology aims at providing an effective support to resilience-informed design.

Computation of nonlinear streaky structures in boundary layer flow

In this work, the Reduced Navier Stokes (RNS) are numerically integrated, and used to calculate nonlinear finite amplitude streaks. These structures are interesting since they can have a stabilizing effect and delay the transition to the turbulent regime. RNS formulation is also used to compute the family of nonlinear intrinsic streaks that emerge from the leading edge in absence of any external perturbation. Finally, this formulation is generalized to include the possibility of having a curved bottom wall

Differential resultants of super essential systems of linear OD-polynomials

The sparse differential resultant dres(P) of an overdetermined system P of generic nonhomogeneous ordinary differential polynomials, was formally defined recently by Li, Gao and Yuan (2011). In this note, a differential resultant formula dfres(P) is defined and proved to be nonzero for linear "super essential" systems. In the linear case, dres(P) is proved to be equal, up to a nonzero constant, to dfres(P*) for the supper essential subsystem P* of P.

Analysis of the railway track as a spatially periodic structure

This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartín [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de Nó and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given

Efficient computation of current collection in bare electrodynamic tethers in and beyond OML regime

One key issue in the simulation of bare electrodynamic tethers (EDTs) is the accurate and fast computation of the collected current, an ambient dependent operation necessary to determine the Lorentz force for each time step. This paper introduces a novel semianalytical solution that allows researchers to compute the current distribution along the tether efficient and effectively under orbital-motion-limited (OML) and beyond OML conditions, i.e., if tether radius is greater than a certain ambient dependent threshold. The method reduces the original boundary value problem to a couple of nonlinear equations. If certain dimensionless variables are used, the beyond OML effect just makes the tether characteristic length L ∗ larger and it is decoupled from the current determination problem. A validation of the results and a comparison of the performance in terms of the time consumed is provided, with respect to a previous ad hoc solution and a conventional shooting method.

New systems of management to improve the health and welfare of rabbits in farm conditions = Nuevos sistemas de cría y manejo para mejorar la salud y bienestar de conejos de granja

El objetivo general de esta Tesis Doctoral fue evaluar nuevos sistemas de alojamiento y cría de conejos de granja, estudiando tanto parámetros comportamentales (experimento 1) como productivos y reproductivos (experimento 3). Además, se evaluaron diferentes técnicas de muestreo con el fin de optimizar el tiempo empleado para el estudio del comportamiento animal (experimento 2). En el experimento 1, se estudió el comportamiento de conejas alojadas en dos tipos de jaulas (TJ), convencionales vs. alternativas con una plataforma elevada, en distintos estados fisiológicos (EF), lactantes y gestantes. Se observó el comportamiento de 12 conejas reproductoras con grabaciones de una duración de 24 h continuas. Independientemente del EF y TJ, las conejas pasaron gran parte de su tiempo sobre el reposapatas (57,7 %, de media). Sin embargo, debido al uso de la plataforma (23,0% del tiempo, de media), las conejas lactantes permanecieron un 36,6 % menos de tiempo (P<0,001) sobre el reposapatas y las gestantes un 27,0% menos (P<0,001) sobre el enrejillado en jaulas alternativas que en convencionales. En las jaulas alternativas, las conejas podían adoptar la postura “levantada”, sin embargo ésta fue observada solamente en conejas gestantes una media de 4,6 veces al día. Las conejas bebieron con mas frecuencia en jaulas convencionales que en alternativas (24,6 vs 19,1 veces al día; P<0,05). Se observó una mayor duración y frecuencia del comportamiento “interactuando con compañeras” en conejas gestantes alojadas en jaulas convencionales (276 s/d y 4,6 veces/d; P<0,05). La frecuencia de “interactuando con gazapos” fue menor en jaulas alternativas que en convencionales (2,4 vs 8,6 veces al día; P<0,01). La hora del día afectó al comportamiento de las conejas, teniendo un comportamiento menos activo durante las horas centrales del día. Durante las horas de oscuridad, las conejas estuvieron más inquietas realizando comportamientos como ‘encabritarse’ o amamantar, coincidiendo éstos en el tiempo en el cual las conejas pasaron más tiempo en la plataforma. Las conejas utilizaron frecuentemente la plataforma, independientemente del estado fisiológico. En la fase de lactación, las conejas utilizaron la plataforma para huir de los intentos de mamar por parte de los gazapos cuando éstas no estaban receptivas. El uso de la plataforma puede dar lugar a problemas higiénicos debidos tanto por la acumulación de heces sobre ella como por la caída de heces y orina sobre los animales que están en la parte inferior. La ausencia de estereotipias por parte de las conejas tanto en jaulas alternativas como en convencionales no sugiere una falta de bienestar debida al sistema de alojamiento. En el experimento 2, se compararon distintos métodos de observación simplificada con respecto un método de referencia usando grabaciones continuas de 24 h para la evaluación del comportamiento de conejas en distintos estados fisiológicos (gestantes y lactantes) alojadas en dos tipos de jaulas (convencionales y alternativas). Se analizaron un total de 576 h de grabaciones continuas de 24 h en 12 conejas reproductoras al final del periodo de lactación y en las mismas conejas después del destete. Los comportamientos observados se clasificaron en tres categorías independientes (localización en la jaula, postura y comportamientos funcionales). Se utilizaron grabaciones continuas de 24 h como método de referencia para validar otros cuatro métodos de observación simplificados, utilizando grabaciones de distinta duración y frecuencia a lo largo del día. Métodos regulares: corto y largo con 2.4 y 8 h de observación respectivamente, y métodos irregulares: corto y largo con 6 y 8 h de observación, respectivamente. Como resultado, se observó que independientemente del sistema de alojamiento, el mejor método para reducir el tiempo de observación necesario para evaluar el comportamiento de conejas reproductoras depende del tipo de variable a estudiar y del estado fisiológico de las conejas. En gestantes, los métodos irregulares no fueron adecuados para estimar comportamientos de larga duración tales como tumbada, sentada, descansando y acicalándose. Sin embargo, en ambos estados fisiológicos, los métodos regulares fueron precisos para los comportamientos de los grupos localización y postura y para comportamientos funcionales de larga duración. Por otro lado, los coeficientes de variación de los comportamientos poco frecuentes realizados principalmente durante el periodo de oscuridad fueron muy altos, y el método irregular largo obtuvo los menores errores de estimación para éstos comportamientos. En el experimento 3, se estudió el efecto de un uso combinado de lactaciones largas (hasta 46 días) con jaulas alternativas sobre los parámetros productivos y reproductivos de 104 conejas y sus camadas durante cinco ciclos reproductivos. La mitad de las conejas fueron alojadas en jaulas polivalentes convencionales (39 cm x 100 cm x 30 cm) y la otra mitad en jaulas polivalentes alternativas (39 cm x 100 cm x 60 cm), con una plataforma elevada. Dentro de cada grupo de alojamiento, la mitad de las conejas se destetaron a 32 días y la otra mitad a 46 días tras el parto. Las lactaciones más largas afectaron negativamente al peso (P<0,001), contenido en grasa y energía (P<0,05) de las conejas al final del periodo de lactación, pero éste efecto disminuyó con el número de partos. La fertilidad, prolificidad y la mortalidad de las conejas no fue afectada por la duración de la lactación. El destete tardío dio lugar a un mayor tamaño y peso de la camada al final del periodo de crecimiento (8,9 y 11,3 %, respectivamente) y a un menor índice de conversión por jaula durante el todo el periodo experimental (13,5 %) con respecto al destete convencional (P<0,001). Éstos resultados fueron paralelos a la menor mortalidad global (12,6 vs 17,6 %; P<0,05) observada en gazapos con destete tardío. Las diferencias en los parámetros productivos con las distintas edades al destete sólo fueron observadas en los ciclos con peor estado sanitario (tercer y quinto ciclo), en los cuales el destete tardío redujo la mortalidad. El tipo de jaula no afectó al peso de la coneja, condición corporal, mortalidad, fertilidad ni tamaño de camada durante los cinco primeros ciclos reproductivos. Sin embargo, el peso de la camada y el índice de conversión a los 21 días de edad fueron 4,2% mayor (P<0,001) y 5,0% menor (P<0,005) en animales alojados en jaulas alternativas que en jaulas convencionales. A día 59 las jaulas alternativas dieron lugar a camadas más pesadas (P<0,01); sin embargo, éste efecto fue influenciado por la densidad alcanzada en cada ciclo, ya que cuando la densidad de los animales fue menor que 40kg/m2 (tercer y quinto ciclo), el efecto del tipo de jaula sobre el peso de la camada no fue significativo. De los resultados obtenidos se puede concluir que el uso combinado de lactaciones más largas y jaulas con mayor superficie disponible con una plataforma elevada podría ser una alternativa para mejorar el bienestar animal en determinadas situaciones productivas. ABSTRACT The general aim of this PhD Thesis was to evaluate new housing and husbandry systems of farmed rabbits, studying behavioral (experiment 1), productive and reproductive (experiment 3) parameters. Moreover, different sampling techniques were evaluated in order to optimize the assessment of rabbit behaviour (experiment 2). In experiment 1, the behaviour of rabbit does housed in two different types of cage (TC), conventional vs. alternative with an elevated platform, at different physiological stages (PS), lactation and gestation was to study. Behavioural observations were carried out on 12 commercial rabbit does using continuous 24 hour video recording. Independently of PS and TC, rabbit does spent most of their time on foot mats (57.7 %, as average). However, due to the use of platforms (23.0% of time, as average), lactating does spent 36.6% less time (P<0.001) on foot mats and gestating does spent 27.0% less (P<0.001) time on wire mesh in alternative cages than in conventional cages. Alternative cages allowed for standing posture but this behaviour was only observed in gestating does (4.6 times a day, as average). Frequency of drinking was higher in conventional than in alternative cages (24.6 vs. 19.1 times a day; P<0.05). Gestating does housed in conventional cages reached the highest duration and frequency of interacting with neighbours (276 s/d and 4.6 times/d; P<0.05). The frequency of interacting with kits was lower in alternative than in conventional cages (2.4 vs. 8.6 times a day; P<0.01). Does’ behaviour was influenced by hour of day, being less active at the midday hours. During dark hours rabbit does more frequently performed restless behaviour such as hyperactivity or nursing, matching the time at which rabbit does spent more time on the platform. The platform was frequently used by rabbit does, independent of their physiological state, and during late lactation phase, when mothers were not receptive to nursing, does housed in alternative cages used the platform as a mean to flee from kids trying to suckle. The use of the platform might lead to hygienic problems due to retained faeces on the platform and faeces and urine falling onto animals located in the lower part of the cage. Stereotypies were not observed in any housing system, therefore conventional cages do not suggest lack of animal welfare. In experiment 2, it was compared the results of different simplified sampling methods of behavioural data with respect to reference records of 24-h in order to assess rabbit does behaviours at different physiological stages (gestation and lactation) in animals housed in two types of cages (conventional and alternative). A total of 576 h of continuous video of 12 rabbit does at the end of lactation and on the same females after weaning were analysed. The behavioural observations were studied using three independent categories of classification (location in the cage, posture and functional behaviours). Continuous behavioural recordings of 24 h were considered as the reference method to validate another 4 sampling methods of data collection by aggregated video recordings of different frequency and duration (regular short and long methods with 2.4 and 8 h of observation respectively, and irregular short and long methods with 6 and 8 h of observation, respectively). The current results showed that, independently of housing system, the best method to reduce the total observation time required to assess rabbit does behaviour depends on the trait studied and physiological stage of does. In gestating does, irregular methods were not suitable to estimate behaviours of long duration such as lying, sitting, resting and grooming. However, in both physiological stages, regular methods were accurate for location behaviours, postures and functional behaviours of long duration. Instead, for the study of infrequent behaviours performed mainly during dark period, where coefficients of variation were high, the irregular long method led to the lowest mean estimation errors. In experiment 3, the effects of the combined use of long lactation periods (46 days) with alternative cages on the reproductive and growth performance of 104 rabbit does and their litters during five consecutive reproductive cycles were studied. Half of does were housed in conventional polyvalent cages (39 cm x 100 cm x 30 cm) and the other half in alternative polyvalent cages (39 cm x 100 cm x 60 cm), with a raised platform. Half of the rabbit does in each type of cages were weaned at 32 and the other half at 46 days after parturition. Longer lactations affected negatively to body weight (P<0.001), fat and energy content (P<0.05) of rabbit does at the end of the lactation period, but this effect decreased with the number of parturitions. Fertility, prolificacy and doe mortality were not affected by lactation length. Late weaning led to higher litter size (by 8.9 %) and litter weight (by 11.3 %) at the end of growing period and lower feed conversion ratio per cage during the overall experimental period (13.5 %) than standard weaning (P<0.001). These results were parallels to a lower mortality (12.6 vs 17.6 %; P<0.05) of young rabbit weaned later during the overall experimental period. Differences in performances at different weaning ages were only observed during cycles with worst health status (third and fifth cycles) in which late weaning decreased mortality. Type of cage did not affect doe body weight and body condition, mortality, fertility, prolificacy and litter size during the five firsts reproductive cycles. Nevertheless, at day 21 litter weight and feed conversion ratio were 4.2 % higher (P<0.001) and 5.0 % lower (P<0.005) in animals housed in alternative than in conventional cages. Alternative cages also led to heavier litters at 59 days (P<0.01); however, this effect was influenced by density reached in each cycle, as when the density of animals was lower than 40 kg/m2 (cycles three and five), the difference of litter weight between alternative and conventional cages was not significant. From the results obtained it can be concluded that the combined use of longer lactations and cages with higher available surface with a raised platform could be an alternative to improve animal welfare in some productive situations.

On the application of meshfree methods to the nonlinear dynamics of multibody systems

Esta tesis propone una completa formulación termo-mecánica para la simulación no-lineal de mecanismos flexibles basada en métodos libres de malla. El enfoque se basa en tres pilares principales: la formulación de Lagrangiano total para medios continuos, la discretización de Bubnov-Galerkin, y las funciones de forma libres de malla. Los métodos sin malla se caracterizan por la definición de un conjunto de funciones de forma en dominios solapados, junto con una malla de integración de las ecuaciones discretas de balance. Dos tipos de funciones de forma se han seleccionado como representación de las familias interpolantes (Funciones de Base Radial) y aproximantes (Mínimos Cuadrados Móviles). Su formulación se ha adaptado haciendo sus parámetros compatibles, y su ausencia de conectividad predefinida se ha aprovechado para interconectar múltiples dominios de manera automática, permitiendo el uso de mallas de fondo no conformes. Se propone una formulación generalizada de restricciones, juntas y contactos, válida para sólidos rígidos y flexibles, siendo estos últimos discretizados mediante elementos finitos (MEF) o libres de malla. La mayor ventaja de este enfoque reside en que independiza completamente el dominio con respecto de las uniones y acciones externas a cada sólido, permitiendo su definición incluso fuera del contorno. Al mismo tiempo, también se minimiza el número de ecuaciones de restricción necesarias para la definición de uniones realistas. Las diversas validaciones, ejemplos y comparaciones detalladas muestran como el enfoque propuesto es genérico y extensible a un gran número de sistemas. En concreto, las comparaciones con el MEF indican una importante reducción del error para igual número de nodos, tanto en simulaciones mecánicas, como térmicas y termo-mecánicas acopladas. A igualdad de error, la eficiencia numérica de los métodos libres de malla es mayor que la del MEF cuanto más grosera es la discretización. Finalmente, la formulación se aplica a un problema de diseño real sobre el mantenimiento de estructuras masivas en el interior de un reactor de fusión, demostrando su viabilidad en análisis de problemas reales, y a su vez mostrando su potencial para su uso en simulación en tiempo real de sistemas no-lineales. A new complete formulation is proposed for the simulation of nonlinear dynamic of multibody systems with thermo-mechanical behaviour. The approach is founded in three main pillars: total Lagrangian formulation, Bubnov-Galerkin discretization, and meshfree shape functions. Meshfree methods are characterized by the definition of a set of shape functions in overlapping domains, and a background grid for integration of the Galerkin discrete equations. Two different types of shape functions have been chosen as representatives of interpolation (Radial Basis Functions), and approximation (Moving Least Squares) families. Their formulation has been adapted to use compatible parameters, and their lack of predefined connectivity is used to interconnect different domains seamlessly, allowing the use of non-conforming meshes. A generalized formulation for constraints, joints, and contacts is proposed, which is valid for rigid and flexible solids, being the later discretized using either finite elements (FEM) or meshfree methods. The greatest advantage of this approach is that makes the domain completely independent of the external links and actions, allowing to even define them outside of the boundary. At the same time, the number of constraint equations needed for defining realistic joints is minimized. Validation, examples, and benchmarks are provided for the proposed formulation, demonstrating that the approach is generic and extensible to further problems. Comparisons with FEM show a much lower error for the same number of nodes, both for mechanical and thermal analyses. The numerical efficiency is also better when coarse discretizations are used. A final demonstration to a real problem for handling massive structures inside of a fusion reactor is presented. It demonstrates that the application of meshfree methods is feasible and can provide an advantage towards the definition of nonlinear real-time simulation models.

Compensation of biased excitation effects for MLS-based nonlinear systems' identification

MLS-based identification of nonlinear systems is largely affected by deviations in the excitation signal amenable to the combined effect of DC-offset and an arbitrary gain. These induce orthogonality loss in the MLS filter bank output, thus invalidating the underlying identification construction. In this paper we present a correction algorithm to derive the corrected Volterra kernels from the biased estimations provided by the standard MLS-based procedure.