Advances in the Simultaneous Multiple Surface optical design method for imaging and non-imaging applications

Classical imaging optics has been developed over centuries in many areas, such as its paraxial imaging theory and practical design methods like multi-parametric optimization techniques. Although these imaging optical design methods can provide elegant solutions to many traditional optical problems, there are more and more new design problems, like solar concentrator, illumination system, ultra-compact camera, etc., that require maximum energy transfer efficiency, or ultra-compact optical structure. These problems do not have simple solutions from classical imaging design methods, because not only paraxial rays, but also non-paraxial rays should be well considered in the design process. Non-imaging optics is a newly developed optical discipline, which does not aim to form images, but to maximize energy transfer efficiency. One important concept developed from non-imaging optics is the “edge-ray principle”, which states that the energy flow contained in a bundle of rays will be transferred to the target, if all its edge rays are transferred to the target. Based on that concept, many CPC solar concentrators have been developed with efficiency close to the thermodynamic limit. When more than one bundle of edge-rays needs to be considered in the design, one way to obtain solutions is to use SMS method. SMS stands for Simultaneous Multiple Surface, which means several optical surfaces are constructed simultaneously. The SMS method was developed as a design method in Non-imaging optics during the 90s. The method can be considered as an extension to the Cartesian Oval calculation. In the traditional Cartesian Oval calculation, one optical surface is built to transform an input wave-front to an out-put wave-front. The SMS method however, is dedicated to solve more than 1 wave-fronts transformation problem. In the beginning, only 2 input wave-fronts and 2 output wave-fronts transformation problem was considered in the SMS design process for rotational optical systems or free-form optical systems. Usually “SMS 2D” method stands for the SMS procedure developed for rotational optical system, and “SMS 3D” method for the procedure for free-form optical system. Although the SMS method was originally employed in non-imaging optical system designs, it has been found during this thesis that with the improved capability to design more surfaces and control more input and output wave-fronts, the SMS method can also be applied to imaging system designs and possesses great advantage over traditional design methods. In this thesis, one of the main goals to achieve is to further develop the existing SMS-2D method to design with more surfaces and improve the stability of the SMS-2D and SMS-3D algorithms, so that further optimization process can be combined with SMS algorithms. The benefits of SMS plus optimization strategy over traditional optimization strategy will be explained in details for both rotational and free-form imaging optical system designs. Another main goal is to develop novel design concepts and methods suitable for challenging non-imaging applications, e.g. solar concentrator and solar tracker. This thesis comprises 9 chapters and can be grouped into two parts: the first part (chapter 2-5) contains research works in the imaging field, and the second part (chapter 6-8) contains works in the non-imaging field. In the first chapter, an introduction to basic imaging and non-imaging design concepts and theories is given. Chapter 2 presents a basic SMS-2D imaging design procedure using meridian rays. In this chapter, we will set the imaging design problem from the SMS point of view, and try to solve the problem numerically. The stability of this SMS-2D design procedure will also be discussed. The design concepts and procedures developed in this chapter lay the path for further improvement. Chapter 3 presents two improved SMS 3 surfaces’ design procedures using meridian rays (SMS-3M) and skew rays (SMS-1M2S) respectively. The major improvement has been made to the central segments selections, so that the whole SMS procedures become more stable compared to procedures described in Chapter 2. Since these two algorithms represent two types of phase space sampling, their image forming capabilities are compared in a simple objective design. Chapter 4 deals with an ultra-compact SWIR camera design with the SMS-3M method. The difficulties in this wide band camera design is how to maintain high image quality meanwhile reduce the overall system length. This interesting camera design provides a playground for the classical design method and SMS design methods. We will show designs and optical performance from both classical design method and the SMS design method. Tolerance study is also given as the end of the chapter. Chapter 5 develops a two-stage SMS-3D based optimization strategy for a 2 freeform mirrors imaging system. In the first optimization phase, the SMS-3D method is integrated into the optimization process to construct the two mirrors in an accurate way, drastically reducing the unknown parameters to only few system configuration parameters. In the second optimization phase, previous optimized mirrors are parameterized into Qbfs type polynomials and set up in code V. Code V optimization results demonstrates the effectiveness of this design strategy in this 2-mirror system design. Chapter 6 shows an etendue-squeezing condenser optics, which were prepared for the 2010 IODC illumination contest. This interesting design employs many non-imaging techniques such as the SMS method, etendue-squeezing tessellation, and groove surface design. This device has theoretical efficiency limit as high as 91.9%. Chapter 7 presents a freeform mirror-type solar concentrator with uniform irradiance on the solar cell. Traditional parabolic mirror concentrator has many drawbacks like hot-pot irradiance on the center of the cell, insufficient use of active cell area due to its rotational irradiance pattern and small acceptance angle. In order to conquer these limitations, a novel irradiance homogenization concept is developed, which lead to a free-form mirror design. Simulation results show that the free-form mirror reflector has rectangular irradiance pattern, uniform irradiance distribution and large acceptance angle, which confirm the viability of the design concept. Chapter 8 presents a novel beam-steering array optics design strategy. The goal of the design is to track large angle parallel rays by only moving optical arrays laterally, and convert it to small angle parallel output rays. The design concept is developed as an extended SMS method. Potential applications of this beam-steering device are: skylights to provide steerable natural illumination, building integrated CPV systems, and steerable LED illumination. Conclusion and future lines of work are given in Chapter 9. Resumen La óptica de formación de imagen clásica se ha ido desarrollando durante siglos, dando lugar tanto a la teoría de óptica paraxial y los métodos de diseño prácticos como a técnicas de optimización multiparamétricas. Aunque estos métodos de diseño óptico para formación de imagen puede aportar soluciones elegantes a muchos problemas convencionales, siguen apareciendo nuevos problemas de diseño óptico, concentradores solares, sistemas de iluminación, cámaras ultracompactas, etc. que requieren máxima transferencia de energía o dimensiones ultracompactas. Este tipo de problemas no se pueden resolver fácilmente con métodos clásicos de diseño porque durante el proceso de diseño no solamente se deben considerar los rayos paraxiales sino también los rayos no paraxiales. La óptica anidólica o no formadora de imagen es una disciplina que ha evolucionado en gran medida recientemente. Su objetivo no es formar imagen, es maximazar la eficiencia de transferencia de energía. Un concepto importante de la óptica anidólica son los “rayos marginales”, que se pueden utilizar para el diseño de sistemas ya que si todos los rayos marginales llegan a nuestra área del receptor, todos los rayos interiores también llegarán al receptor. Haciendo uso de este principio, se han diseñado muchos concentradores solares que funcionan cerca del límite teórico que marca la termodinámica. Cuando consideramos más de un haz de rayos marginales en nuestro diseño, una posible solución es usar el método SMS (Simultaneous Multiple Surface), el cuál diseña simultáneamente varias superficies ópticas. El SMS nació como un método de diseño para óptica anidólica durante los años 90. El método puede ser considerado como una extensión del cálculo del óvalo cartesiano. En el método del óvalo cartesiano convencional, se calcula una superficie para transformar un frente de onda entrante a otro frente de onda saliente. El método SMS permite transformar varios frentes de onda de entrada en frentes de onda de salida. Inicialmente, sólo era posible transformar dos frentes de onda con dos superficies con simetría de rotación y sin simetría de rotación, pero esta limitación ha sido superada recientemente. Nos referimos a “SMS 2D” como el método orientado a construir superficies con simetría de rotación y llamamos “SMS 3D” al método para construir superficies sin simetría de rotación o free-form. Aunque el método originalmente fue aplicado en el diseño de sistemas anidólicos, se ha observado que gracias a su capacidad para diseñar más superficies y controlar más frentes de onda de entrada y de salida, el SMS también es posible aplicarlo a sistemas de formación de imagen proporcionando una gran ventaja sobre los métodos de diseño tradicionales. Uno de los principales objetivos de la presente tesis es extender el método SMS-2D para permitir el diseño de sistemas con mayor número de superficies y mejorar la estabilidad de los algoritmos del SMS-2D y SMS-3D, haciendo posible combinar la optimización con los algoritmos. Los beneficios de combinar SMS y optimización comparado con el proceso de optimización tradicional se explican en detalle para sistemas con simetría de rotación y sin simetría de rotación. Otro objetivo importante de la tesis es el desarrollo de nuevos conceptos de diseño y nuevos métodos en el área de la concentración solar fotovoltaica. La tesis está estructurada en 9 capítulos que están agrupados en dos partes: la primera de ellas (capítulos 2-5) se centra en la óptica formadora de imagen mientras que en la segunda parte (capítulos 6-8) se presenta el trabajo del área de la óptica anidólica. El primer capítulo consta de una breve introducción de los conceptos básicos de la óptica anidólica y la óptica en formación de imagen. El capítulo 2 describe un proceso de diseño SMS-2D sencillo basado en los rayos meridianos. En este capítulo se presenta el problema de diseñar un sistema formador de imagen desde el punto de vista del SMS y se intenta obtener una solución de manera numérica. La estabilidad de este proceso se analiza con detalle. Los conceptos de diseño y los algoritmos desarrollados en este capítulo sientan la base sobre la cual se realizarán mejoras. El capítulo 3 presenta dos procedimientos para el diseño de un sistema con 3 superficies SMS, el primero basado en rayos meridianos (SMS-3M) y el segundo basado en rayos oblicuos (SMS-1M2S). La mejora más destacable recae en la selección de los segmentos centrales, que hacen más estable todo el proceso de diseño comparado con el presentado en el capítulo 2. Estos dos algoritmos representan dos tipos de muestreo del espacio de fases, su capacidad para formar imagen se compara diseñando un objetivo simple con cada uno de ellos. En el capítulo 4 se presenta un diseño ultra-compacto de una cámara SWIR diseñada usando el método SMS-3M. La dificultad del diseño de esta cámara de espectro ancho radica en mantener una alta calidad de imagen y al mismo tiempo reducir drásticamente sus dimensiones. Esta cámara es muy interesante para comparar el método de diseño clásico y el método de SMS. En este capítulo se presentan ambos diseños y se analizan sus características ópticas. En el capítulo 5 se describe la estrategia de optimización basada en el método SMS-3D. El método SMS-3D calcula las superficies ópticas de manera precisa, dejando sólo unos pocos parámetros libres para decidir la configuración del sistema. Modificando el valor de estos parámetros se genera cada vez mediante SMS-3D un sistema completo diferente. La optimización se lleva a cabo variando los mencionados parámetros y analizando el sistema generado. Los resultados muestran que esta estrategia de diseño es muy eficaz y eficiente para un sistema formado por dos espejos. En el capítulo 6 se describe un sistema de compresión de la Etendue, que fue presentado en el concurso de iluminación del IODC en 2010. Este interesante diseño hace uso de técnicas propias de la óptica anidólica, como el método SMS, el teselado de las lentes y el diseño mediante grooves. Este dispositivo tiene un límite teórica en la eficiencia del 91.9%. El capítulo 7 presenta un concentrador solar basado en un espejo free-form con irradiancia uniforme sobre la célula. Los concentradores parabólicos tienen numerosas desventajas como los puntos calientes en la zona central de la célula, uso no eficiente del área de la célula al ser ésta cuadrada y además tienen ángulos de aceptancia de reducido. Para poder superar estas limitaciones se propone un novedoso concepto de homogeneización de la irrandancia que se materializa en un diseño con espejo free-form. El análisis mediante simulación demuestra que la irradiancia es homogénea en una región rectangular y con mayor ángulo de aceptancia, lo que confirma la viabilidad del concepto de diseño. En el capítulo 8 se presenta un novedoso concepto para el diseño de sistemas afocales dinámicos. El objetivo del diseño es realizar un sistema cuyo haz de rayos de entrada pueda llegar con ángulos entre ±45º mientras que el haz de rayos a la salida sea siempre perpendicular al sistema, variando únicamente la posición de los elementos ópticos lateralmente. Las aplicaciones potenciales de este dispositivo son varias: tragaluces que proporcionan iluminación natural, sistemas de concentración fotovoltaica integrados en los edificios o iluminación direccionable con LEDs. Finalmente, el último capítulo contiene las conclusiones y las líneas de investigación futura.

Column Generation Algorithms for Nonlinear Optimization II: Numerical Investigations

García et al. present a class of column generation (CG) algorithms for nonlinear programs. Its main motivation from a theoretical viewpoint is that under some circumstances, finite convergence can be achieved, in much the same way as for the classic simplicial decomposition method; the main practical motivation is that within the class there are certain nonlinear column generation problems that can accelerate the convergence of a solution approach which generates a sequence of feasible points. This algorithm can, for example, accelerate simplicial decomposition schemes by making the subproblems nonlinear. This paper complements the theoretical study on the asymptotic and finite convergence of these methods given in [1] with an experimental study focused on their computational efficiency. Three types of numerical experiments are conducted. The first group of test problems has been designed to study the parameters involved in these methods. The second group has been designed to investigate the role and the computation of the prolongation of the generated columns to the relative boundary. The last one has been designed to carry out a more complete investigation of the difference in computational efficiency between linear and nonlinear column generation approaches. In order to carry out this investigation, we consider two types of test problems: the first one is the nonlinear, capacitated single-commodity network flow problem of which several large-scale instances with varied degrees of nonlinearity and total capacity are constructed and investigated, and the second one is a combined traffic assignment model

Bernstein polynomials in element-free Galerkin method

In the recent decades, meshless methods (MMs), like the element-free Galerkin method (EFGM), have been widely studied and interesting results have been reached when solving partial differential equations. However, such solutions show a problem around boundary conditions, where the accuracy is not adequately achieved. This is caused by the use of moving least squares or residual kernel particle method methods to obtain the shape functions needed in MM, since such methods are good enough in the inner of the integration domains, but not so accurate in boundaries. This way, Bernstein curves, which are a partition of unity themselves,can solve this problem with the same accuracy in the inner area of the domain and at their boundaries.

Simplified computational method for non-linear seismic analysis of bridges

After the experience gained during the past years it seems clear that nonlinear analysis of bridges are very important to compute ductility demands and to localize potential hinges. This is specially true for irregular bridges in which it is not clear weather or not it is possible to use a linear computation followed by a correction using a behaviour factor. To simplify the numerical effort several approximate methods have been proposed. Among them, the so-called Dynamic Plastic Hinge Method in which an evolutionary shape function is used to reduce the structure to a single degree of freedom system seems to mantein a good balance between accuracy and simplicity. This paper presents results obtained in a parametric study conducted under the auspicies of PREC-8 european research program.

Regularized model learning in EDAs for continuous and multi-objective optimization

Probabilistic modeling is the de�ning characteristic of estimation of distribution algorithms (EDAs) which determines their behavior and performance in optimization. Regularization is a well-known statistical technique used for obtaining an improved model by reducing the generalization error of estimation, especially in high-dimensional problems. `1-regularization is a type of this technique with the appealing variable selection property which results in sparse model estimations. In this thesis, we study the use of regularization techniques for model learning in EDAs. Several methods for regularized model estimation in continuous domains based on a Gaussian distribution assumption are presented, and analyzed from di�erent aspects when used for optimization in a high-dimensional setting, where the population size of EDA has a logarithmic scale with respect to the number of variables. The optimization results obtained for a number of continuous problems with an increasing number of variables show that the proposed EDA based on regularized model estimation performs a more robust optimization, and is able to achieve signi�cantly better results for larger dimensions than other Gaussian-based EDAs. We also propose a method for learning a marginally factorized Gaussian Markov random �eld model using regularization techniques and a clustering algorithm. The experimental results show notable optimization performance on continuous additively decomposable problems when using this model estimation method. Our study also covers multi-objective optimization and we propose joint probabilistic modeling of variables and objectives in EDAs based on Bayesian networks, speci�cally models inspired from multi-dimensional Bayesian network classi�ers. It is shown that with this approach to modeling, two new types of relationships are encoded in the estimated models in addition to the variable relationships captured in other EDAs: objectivevariable and objective-objective relationships. An extensive experimental study shows the e�ectiveness of this approach for multi- and many-objective optimization. With the proposed joint variable-objective modeling, in addition to the Pareto set approximation, the algorithm is also able to obtain an estimation of the multi-objective problem structure. Finally, the study of multi-objective optimization based on joint probabilistic modeling is extended to noisy domains, where the noise in objective values is represented by intervals. A new version of the Pareto dominance relation for ordering the solutions in these problems, namely �-degree Pareto dominance, is introduced and its properties are analyzed. We show that the ranking methods based on this dominance relation can result in competitive performance of EDAs with respect to the quality of the approximated Pareto sets. This dominance relation is then used together with a method for joint probabilistic modeling based on `1-regularization for multi-objective feature subset selection in classi�cation, where six di�erent measures of accuracy are considered as objectives with interval values. The individual assessment of the proposed joint probabilistic modeling and solution ranking methods on datasets with small-medium dimensionality, when using two di�erent Bayesian classi�ers, shows that comparable or better Pareto sets of feature subsets are approximated in comparison to standard methods.

Efficient design and optimization of bio-photonic sensing cells (BICELLs) for label free biosensing

In previous works we demonstrated the benefits of using micro–nano patterning materials to be used as bio-photonic sensing cells (BICELLs), referred as micro–nano photonic structures having immobilized bioreceptors on its surface with the capability of recognizing the molecular binding by optical transduction. Gestrinone/anti-gestrinone and BSA/anti-BSA pairs were proven under different optical configurations to experimentally validate the biosensing capability of these bio-sensitive photonic architectures. Moreover, Three-Dimensional Finite Difference Time Domain (FDTD) models were employed for simulating the optical response of these structures. For this article, we have developed an effective analytical simulation methodology capable of simulating complex biophotonic sensing architectures. This simulation method has been tested and compared with previous experimental results and FDTD models. Moreover, this effective simulation methodology can be used for efficiently design and optimize any structure as BICELL. In particular for this article, six different BICELL's types have been optimized. To carry out this optimization we have considered three figures of merit: optical sensitivity, Q-factor and signal amplitude. The final objective of this paper is not only validating a suitable and efficient optical simulation methodology but also demonstrating the capability of this method for analyzing the performance of a given number of BICELLs for label-free biosensing.

Cross-entropy optimization for scaling factors of a fuzzy controller: a see-and-avoid approach for unmanned aerial systems

The Cross-Entropy (CE) is an efficient method for the estimation of rare-event probabilities and combinatorial optimization. This work presents a novel approach of the CE for optimization of a Soft-Computing controller. A Fuzzy controller was designed to command an unmanned aerial system (UAS) for avoiding collision task. The only sensor used to accomplish this task was a forward camera. The CE is used to reach a near-optimal controller by modifying the scaling factors of the controller inputs. The optimization was realized using the ROS-Gazebo simulation system. In order to evaluate the optimization a big amount of tests were carried out with a real quadcopter.

Application of active heat pulse method with fiber optic temperature sensing for estimation of wetting bulbs and water distribution in drip emitters.

Through the use of the Distributed Fiber Optic Temperature Measurement (DFOT) method, it is possible to measure the temperature in small intervals (on the order of centimeters) for long distances (on the order of kilometers) with a high temporal frequency and great accuracy. The heat pulse method consists of applying a known amount of heat to the soil and monitoring the temperature evolution, which is primarily dependent on the soil moisture content. The use of both methods, which is called the active heat pulse method with fiber optic temperature sensing (AHFO), allows accurate soil moisture content measurements. In order to experimentally study the wetting patterns, i.e. shape, size, and the water distribution, from a drip irrigation emitter, a soil column of 0.5 m of diameter and 0.6 m high was built. Inside the column, a fiber optic cable with a stainless steel sheath was placed forming three concentric helixes of diameters 0.2 m, 0.4 m and 0.6 m, leading to a 148 measurement point network. Before, during, and after the irrigation event, heat pulses were performed supplying electrical power of 20 W/m to the steel. The soil moisture content was measured with a capacitive sensor in one location at depths of 0.1 m, 0.2 m, 0.3 m and 0.4 m during the irrigation. It was also determined by the gravimetric method in several locations and depths before and right after the irrigation. The emitter bulb dimensions and shape evolution was satisfactorily measured during infiltration. Furthermore, some bulb's characteristics difficult to predict (e.g. preferential flow) were detected. The results point out that the AHFO is a useful tool to estimate the wetting pattern of drip irrigation emitters in soil columns and show a high potential for its use in the field.

SMS-based optimization strategy for ultra-compact SWIR telephoto lens design

A new optical design strategy for rotational aspheres using very few parameters is presented. It consists of using the SMS method to design the aspheres embedded in a system with additional simpler surfaces (such as spheres, parabolas or other conics) and optimizing the free-parameters. Although the SMS surfaces are designed using only meridian rays, skew rays have proven to be well controlled within the optimization. In the end, the SMS surfaces are expanded using Forbes series and then a second optimization process is carried out with these SMS surfaces as a starting point. The method has been applied to a telephoto lens design in the SWIR band, achieving ultra-compact designs with an excellent performance.

Proyectando entre ruinas : lógicas de intervención continua en la arquitectura contemporánea

Los cambios percibidos hacia finales del siglo XX y a principios del nuevo milenio, nos ha mostrado que la crisis cultural de la que somos participes refleja también una crisis de los modelos universales. Nuestra situación contemporánea, parece indicar que ya no es posible formular un sistema estético para atribuirle una vigencia universal e intemporal más allá de su estricta eficacia puntual. La referencia organizada, delimitada, invariable y específica que ofrecía cualquier emplazamiento, en tanto preexistencia, reflejaba una jerarquía del sistema formal basado en lo extensivo: la medida, las normas, el movimiento, el tiempo, la modulación, los códigos y las reglas. Sin embargo, actualmente, algunos aspectos que permanecían latentes sobre lo construido, emergen bajo connotaciones intensivas, transgrediendo la simple manifestación visual y expresiva, para centrase en las propiedades del comportamiento de la materia y la energía como determinantes de un proceso de adaptación en el entorno. A lo largo del todo el siglo XX, el desarrollo de la relación del proyecto sobre lo construido ha sido abordado, casi en exclusiva, entre acciones de preservación o intervención. Ambas perspectivas, manifestaban esfuerzos por articular un pensamiento que diera una consistencia teórica, como soporte para la producción de la acción aditiva. No obstante, en las últimas décadas de finales de siglo, la teoría arquitectónica terminó por incluir pensamientos de otros campos que parecen contaminar la visión sesgada que nos refería lo construido. Todo este entramado conceptual previo, aglomeraba valiosos intentos por dar contenido a una teoría que pudiese ser entendida desde una sola posición argumental. Es así, que en 1979 Ignasi Solá-Morales integró todas las imprecisiones que referían una actuación sobre una arquitectura existente, bajo el termino de “intervención”, el cual fue argumentado en dos sentidos: El primero referido a cualquier tipo de actuación que se puede hacer en un edificio, desde la defensa, preservación, conservación, reutilización, y demás acciones. Se trata de un ámbito donde permanece latente el sentido de intensidad, como factor común de entendimiento de una misma acción. En segundo lugar, más restringido, la idea de intervención se erige como el acto crítico a las ideas anteriores. Ambos representan en definitiva, formas de interpretación de un nuevo discurso. “Una intervención, es tanto como intentar que el edificio vuelva a decir algo o lo diga en una determinada dirección”. A mediados de 1985, motivado por la corriente de revisión historiográfica y la preocupación del deterioro de los centros históricos que recorría toda Europa, Solá-Morales se propone reflexionar sobre “la relación” entre una intervención de nueva arquitectura y la arquitectura previamente existente. Relación condicionada estrictamente bajo consideraciones lingüísticas, a su entender, en sintonía con toda la producción arquitectónica de todo el siglo XX. Del Contraste a la Analogía, resumirá las transformaciones en la concepción discursiva de la intervención arquitectónica, como un fenómeno cambiante en función de los valores culturales, pero a su vez, mostrando una clara tendencia dialógica entres dos categorías formales: El Contraste, enfatizando las posibilidades de la novedad y la diferencia; y por otro lado la emergente Analogía, como una nueva sensibilidad de interpretación del edificio antiguo, donde la semejanza y la diversidad se manifiestan simultáneamente. El aporte reflexivo de los escritos de Solá-Morales podría ser definitivo, si en las últimas décadas antes del fin de siglo, no se hubiesen percibido ciertos cambios sobre la continuidad de la expresión lingüística que fomentaba la arquitectura, hacia una especie de hipertrofia figurativa. Entre muchos argumentos: La disolución de la consistencia compositiva y el estilo unitario, la incorporación volumétrica del proyecto como dispositivo reactivo, y el cambio de visión desde lo retrospectivo hacia lo prospectivo que sugiere la nueva conservación. En este contexto de desintegración, el proyecto, en tanto incorporación o añadido sobre un edificio construido, deja de ser considerado como un apéndice volumétrico subordinado por la reglas compositivas y formales de lo antiguo, para ser considerado como un organismo de orden reactivo, que produce en el soporte existente una alteración en su conformación estructural y sistémica. La extensión, antes espacial, se considera ahora una extensión sensorial y morfológica con la implementación de la tecnología y la hiper-información, pero a su vez, marcados por una fuerte tendencia de optimización energética en su rol operativo, ante el surgimiento del factor ecológico en la producción contemporánea. En una sociedad, como la nuestra, que se está modernizando intensamente, es difícil compartir una adecuada sintonía con las formas del pasado. Desde 1790, fecha de la primera convención francesa para la conservación de monumentos, la escala de lo que se pretende preservar es cada vez más ambiciosa, tanto es así, que al día de hoy el repertorio de lo que se conserva incluye prácticamente todas las tipologías del entorno construido. Para Koolhaas, el intervalo entre el objeto y el momento en el cual se decide su conservación se ha reducido, desde dos milenios en 1882 a unas décadas hoy en día. En breve este lapso desaparecerá, demostrando un cambio radical desde lo retrospectivo hacia lo prospectivo, es decir, que dentro de poco habrá que decidir que es lo que se conserva antes de construir. Solá-Morales, en su momento, distinguió la relación entre lo nuevo y lo antiguo, entre el contraste y la analogía. Hoy casi tres décadas después, el objetivo consiste en evaluar si el modelo de intervención arquitectónica sobre lo construido se ha mantenido desde entonces o si han aparecido nuevas formas de posicionamiento del proyecto sobre lo construido. Nuestro trabajo pretende demostrar el cambio de enfoque proyectual con la preexistencia y que éste tiene estrecha relación con la incorporación de nuevos conceptos, técnicas, herramientas y necesidades que imprimen el contexto cultural, producido por el cambio de siglo. Esta suposición nos orienta a establecer un paralelismo arquitectónico entre los modos de relación en que se manifiesta lo nuevo, entre una posición comúnmente asumida (Tópica), genérica y ortodoxa, fundamentada en lo visual y expresivo de las últimas décadas del siglo XX, y una realidad emergente (Heterotópica), extraordinaria y heterodoxa que estimula lo inmaterial y que parece emerger con creciente intensidad en el siglo XXI. Si a lo largo de todo el siglo XX, el proyecto de intervención arquitectónico, se debatía entre la continuidad y discontinuidad de las categorías formales marcadas por la expresión del edificio preexistente, la nueva intervención contemporánea, como dispositivo reactivo en el paisaje y en el territorio, demanda una absoluta continuidad, ya no visual, expresiva, ni funcional, sino una continuidad fisiológica de adaptación y cambio con la propia dinámica del territorio, bajo nuevas reglas de juego y desplegando planes y estrategias operativas (proyectivas) desde su propia lógica y contingencia. El objeto de esta investigación es determinar los nuevos modos de continuidad y las posibles lógicas de producción que se manifiestan dentro de la Intervención Arquitectónica, intentando superar lo aparente de su relación física y visual, como resultado de la incorporación del factor operativo desplegado por el nuevo dispositivo contemporáneo. Creemos que es acertado mantener la senda connotativa que marca la denominación intervención arquitectónica, por aglutinar conceptos y acercamientos teóricos previos que han ido evolucionando en el tiempo. Si bien el término adolece de mayor alcance operativo desde su formulación, una cualidad que infieren nuestras lógicas contemporáneas, podría ser la reformulación y consolidación de un concepto de intervención más idóneo con nuestros tiempos, anteponiendo un procedimiento lógico desde su propia necesidad y contingencia. Finalmente, nuestro planteamiento inicial aspira a constituir un nueva forma de reflexión que nos permita comprender las complejas implicaciones que infiere la nueva arquitectura sobre la preexistencia, motivada por las incorporación de factores externos al simple juicio formal y expresivo preponderante a finales del siglo XX. Del mismo modo, nuestro camino propuesto, como alternativa, permite proyectar posibles sendas de prospección, al considerar lo preexistente como un ámbito que abarca la totalidad del territorio con dinámicas emergentes de cambio, y con ellas, sus lógicas de intervención.Abstract The perceived changes towards the end of the XXth century and at the beginning of the new milennium have shown us that the cultural crisis in which we participate also reflects a crisis of the universal models. The difference between our contemporary situation and the typical situations of modern orthodoxy and post-modernistic fragmentation, seems to indicate that it is no longer possible to formulate a valid esthetic system, to assign a universal and eternal validity to it beyond its strictly punctual effectiveness; which is even subject to questioning because of the continuous transformations that take place in time and in the sensibility of the subject itself every time it takes over the place. The organised reference that any location offered, limited, invariable and specific, while pre-existing, reflected a hierarchy of the formal system based on the applicable: measure, standards, movement, time, modulation, codes and rules. Authors like Marshall Mc Luhan, Paul Virilio, or Marc Augé anticipated a reality where the conventional system already did not seem to respond to the new architectural requests in which information, speed, disappearance and the virtual had blurred the traditional limits of place; pre-existence did no longer possess a specific delimitation and, on the contrary, they expect to reach a global scale. Currently, some aspects that stayed latent relating to the constructed, surface from intensive connotations, transgressing the simple visual and expressive manifestation in order to focus on the traits of the behaviour of material and energy as determinants of a process of adaptation to the surroundings. Throughout the entire Century, the development of the relation of the project relating to the constructed has been addressed, almost exclusively, in preservational or interventianal actions. Both perspectives showed efforts in order to express a thought that would give a theoretical consistency as a base for the production of the additive action. Nevertheless, the last decades of the Century, architectural theory ended up including thoughts from other fields that seem to contaminate the biased vision 15 which the constructed related us. Ecology, planning, philosophy, global economy, etc, suggest new approaches to the construction of the contemporary city; but this time with a determined idea of change and continuous transformation, that enriches the panorama of thought and architectural practice, at the same time, according to some, it puts disciplinary specification at risk, given that there is no architecture without destruction, the constructed organism requires mutation in order to adjust to the change of shape. All of this previous conceptual framework gathered valuable intents to give importance to a theory that could be understood solely from an argumental position. Thusly, in 1979 Ignasi Solá-Morales integrated all of the imprecisions that referred to an action in existing architecture under the term of “Intervention”, which was explained in two ways: The first referring to any type of intervention that can be carried out in a building, regarding protection, conservation, reuse, etc. It is about a scope where the meaning of intensity stays latent as a common factor of the understanding of a single action. Secondly, more limitedly, the idea of intervention is established as the critical act to the other previous ideas such as restauration, conservation, reuse, etc. Both ultimately represent ways of interpretation of a new speech. “An intervention, is as much as trying to make the building say something again or that it be said in a certain direction”. Mid 1985, motivated by the current of historiographical revision and the concerns regarding the deterioration of historical centres that traversed Europe, Solá-Morales decides to reflect on “the relationship” between an intervention of the new architecture and the previously existing architecture. A relationship determined strictly by linguistic considerations, to his understanding, in harmony with all of the architectural production of the XXth century. From Contrast to Analogy would summarise transformations in the discursive perception of architectural intervention, as a changing phenomenon depending on cultural values, but at the same time, showing a clear dialogical tendency between two formal categories: Contrast, emphasising the possibilities of novelty and difference; and on the other hand the emerging Analogy, as a new awareness of interpretation of the ancient building, where the similarity and diversity are manifested simultaneously. For Solá-Morales the analogical procedure is not based on the visible simultaneity of formal orders, but on associations that the subject establishes throughout time. Through analogy it is tried to overcome the simple visual relationship with the antique, to focus on its spacial, physical and geographical nature. If the analogical attempt guides an opening towards a new continuity; it still persists in the connection of dimensional, typological and figurative factors, subordinate to the formal hierarchy of the preexisting subjects. 16 The reflexive contribution of Solá-Morales’ works could be final, if in the last decades before the end of the century there had not been certain changes regarding linguistic expression, encouraged by architecture, towards a kind of figurative hypertrophy, amongst many arguments we are in this case interested in three moments: The dissolution of the compositional consistency and the united style, the volumetric incorporation of the project as a reactive mechanism, and the change of the vision from retrospective towards prospective that the new conservation suggests. The recurrence to the history of architecture and its recognisable forms, as a way of perpetuating memory and establishing a reference, dissolved any instinct of compositive unity and style, provoking permanent relationships to tend to disappear. The composition and coherence lead to suppose a type of discontinuity of isolated objects in which only possible relationships could appear; no longer as an order of certain formal and compositive rules, but as a special way of setting elements in a specific work. The new globalised field required new forms of consistency between the project and the pre-existent subject, motivated amongst others by the higher pace of market evolution, increase of consumer tax and the level of information and competence between different locations; aspects which finally made stylistic consistence inefficient. In this context of disintegration, the project, in incorporation as well as added to a constructed building, stops being considered as a volumetric appendix subordinate to compositive and formal rules of old, to be considered as an organism of reactive order, that causes a change in the structural and systematic configuration of the existing foundation. The extension, previsouly spatial, is now considered a sensorial and morphological extension, with the implementation of technology and hyper-information, but at the same time, marked by a strong tendency of energetic optimization in its operational role, facing the emergence of the ecological factor in contemporary production. The technological world turns into a new nature, a nature that should be analysed from ecological terms; in other words, as an event of transition in the continuous redistribution of energy. In this area, effectiveness is not only determined by the capacity of adaptation to changing conditions, but also by its transforming capacity “expressly” in order to change an environment. In a society, like ours, that is modernising intensively, it is difficult to share an adecuate agreement with the forms of the past. From 1790, the date of the first French convention for the conservation of monuments, the scale of what is expexted to be preserved is more and more ambitious, so much so that nowadays the repertoire of that what is conserved includes practically all typologies of the constructed surroundings. For Koolhaas, the ínterval between the object and the moment when its conservation is decided has been reduced, from two 17 milennia in 1882 to a few decades nowadays. Shortly this lapse will disappear, showing a radical change of retrospective towards prospective, that is to say, that soon it will be necessary to decide what to conserve before constructing. The shapes of cities are the result of the continuous incorporation of architecture, and perhaps that only through architecture the response to the universe can be understood, the continuity of what has already been constructed. Our work is understood also within that system, modifying the field of action and leaving the road ready for the next movement of those that will follow after us. Continuity does not mean conservatism, continuity means being conscient of the transitory value of our answers to specific needs, accepting the change that we have received. That what has been constructed to remain and last, should cause future interventions to be integrated in it. It is necessary to accept continuity as a rule. Solá-Morales, in his time, distinguished between the relationship with new and old, between contrast and analogy. Today, almost three decades later, the objective consists of evaluating whether the model of architectural intervention in the constructed has been maintained since then or if new ways of positioning the project regarding the constructed have appeared. Our work claims to show the change of the approach of projects with pre-existing subjects and that this has got a close relation to the incorporation of new concepts, techniques, tools and necessities that impress the cultural context, caused by the change of centuries. This assumption guides us to establish a parallelism between the forms of connection where that what is new is manifested between a commonly assumed (topical), generic and orthodox position, based on that what is visual and expressive in the last decades of the XXth century, and an emerging (heterotopical), extraordinary and heterodox reality that stimulates the immaterial and that seems to emerge with growing intensity in the XXIst century. If throughout the XXth century the project of architectural intervention was considered from the continuity and discontinuity of formal categories, marked by the expression of the pre-existing building, the new contemporary intervention, as a reactive device in the landscape and territory, demands an absolute continuity. No longer a visual, expressive or functional one but a morphological continuity of adaptation and change with its own territorial dynamics, under new game rules and unfolding new operative (projective) strategies from its own logic and contingency. 18 The aim of this research is to determine new forms of continuity and the possible logic of production that are expressed in the Architectural Intervention, trying to overcome the obviousness of its physical and visual relationship, at the beginning of this new century, as a result of the incorporation of the operative factor that the new architectural device unfolds. We think it is correct to maintain the connotative path that marks the name architectural intervention by bringing previous concepts and theorical approaches that have been evolving through time together. If the name suffers from a wider operational range because of its formulation, a quality that our contemporary logic provokes, the reformulation and consolidation of an interventional concept could be more suitable for our times, giving preference to a logical method from its own necessity and contingency. It seems that now time shapes the topics, it is no longer about materialising a certain time but about expressing the changes that its new temporality generates. Finally, our initial approach aspires to form a new way of reflection that permits us to understand the complex implications that the new architecture submits the pre-existing subject to, motivated by the incorporation of factors external to simple formal and expressive judgement, prevailing at the end of the XXth century. In the same way, our set road, as an alternative, permits the contemplation of possible research paths, considering that what is pre-existing as an area that spans the whole territory with emerging changing dynamics and, with them, their interventional logics.

Optical systems design using the SMS method and optimizations

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

Contribución al desarrollo de técnicas CAD para el diseño de antenas impresas y dispositivos pasivos de microondas basadas en el método de elementos finitos

El objetivo principal de esta tesis es el desarrollo de herramientas numéricas basadas en técnicas de onda completa para el diseño asistido por ordenador (Computer-Aided Design,‘CAD’) de dispositivos de microondas. En este contexto, se desarrolla una herramienta numérica basada en el método de los elementos finitos para el diseño y análisis de antenas impresas mediante algoritmos de optimización. Esta técnica consiste en dividir el análisis de una antena en dos partes. Una parte de análisis 3D que se realiza sólo una vez en cada punto de frecuencia de la banda de funcionamiento donde se sustituye una superficie que contiene la metalización del parche por puertas artificiales. En una segunda parte se inserta entre las puertas artificiales en la estructura 3D la superficie soportando una metalización y se procede un análisis 2D para caracterizar el comportamiento de la antena. La técnica propuesta en esta tesis se puede implementar en un algoritmo de optimización para definir el perfil de la antena que permite conseguir los objetivos del diseño. Se valida experimentalmente dicha técnica empleándola en el diseño de antenas impresas de banda ancha para diferentes aplicaciones mediante la optimización del perfil de los parches. También, se desarrolla en esta tesis un procedimiento basado en el método de descomposición de dominio y el método de los elementos finitos para el diseño de dispositivos pasivos de microonda. Se utiliza este procedimiento en particular para el diseño y sintonía de filtros de microondas. En la primera etapa de su aplicación se divide la estructura que se quiere analizar en subdominios aplicando el método de descomposición de dominio, este proceso permite analizar cada segmento por separado utilizando el método de análisis adecuado dado que suele haber subdominios que se pueden analizar mediante métodos analíticos por lo que el tiempo de análisis es más reducido. Se utilizan métodos numéricos para analizar los subdominios que no se pueden analizar mediante métodos analíticos. En esta tesis, se utiliza el método de los elementos finitos para llevar a cabo el análisis. Además de la descomposición de dominio, se aplica un proceso de barrido en frecuencia para reducir los tiempos del análisis. Como método de orden reducido se utiliza la técnica de bases reducidas. Se ha utilizado este procedimiento para diseñar y sintonizar varios ejemplos de filtros con el fin de comprobar la validez de dicho procedimiento. Los resultados obtenidos demuestran la utilidad de este procedimiento y confirman su rigurosidad, precisión y eficiencia en el diseño de filtros de microondas. ABSTRACT The main objective of this thesis is the development of numerical tools based on full-wave techniques for computer-aided design ‘CAD’ of microwave devices. In this context, a numerical technique based on the finite element method ‘FEM’ for the design and analysis of printed antennas using optimization algorithms has been developed. The proposed technique consists in dividing the analysis of the antenna in two stages. In the first stage, the regions of the antenna which do not need to be modified during the CAD process are initially characterized only once from their corresponding matrix transfer function (Generalized Admittance matrix, ‘GAM’). The regions which will be modified are defined as artificial ports, precisely the regions which will contain the conducting surfaces of the printed antenna. In a second stage, the contour shape of the conducting surfaces of the printed antenna is iteratively modified in order to achieve a desired electromagnetic performance of the antenna. In this way, a new GAM of the radiating device which takes into account each printed antenna shape is computed after each iteration. The proposed technique can be implemented with a genetic algorithm to achieve the design objectives. This technique is validated experimentally and applied to the design of wideband printed antennas for different applications by optimizing the shape of the radiating device. In addition, a procedure based on the domain decomposition method and the finite element method has been developed for the design of microwave passive devices. In particular, this procedure can be applied to the design and tune of microwave filters. In the first stage of its implementation, the structure to be analyzed is divided into subdomains using the domain decomposition method; this process allows each subdomains can be analyzed separately using suitable analysis method, since there is usually subdomains that can be analyzed by analytical methods so that the time of analysis is reduced. For analyzing the subdomains that cannot be analyzed by analytical methods, we use the numerical methods. In this thesis, the FEM is used to carry out the analysis. Furthermore the decomposition of the domain, a frequency sweep process is applied to reduce analysis times. The reduced order model as the reduced basis technique is used in this procedure. This procedure is applied to the design and tune of several examples of microwave filters in order to check its validity. The obtained results allow concluding the usefulness of this procedure and confirming their thoroughness, accuracy and efficiency for the design of microwave filters.

Dynamic Response Optimization of Vehicles through Efficient Multibody Formulations and Automatic Differentiation Techniques

El diseño y desarrollo de sistemas de suspensión para vehículos se basa cada día más en el diseño por ordenador y en herramientas de análisis por ordenador, las cuales permiten anticipar problemas y resolverlos por adelantado. El comportamiento y las características dinámicas se calculan con precisión, bajo coste, y recursos y tiempos de cálculo reducidos. Sin embargo, existe una componente iterativa en el proceso, que requiere la definición manual de diseños a través de técnicas “prueba y error”. Esta Tesis da un paso hacia el desarrollo de un entorno de simulación eficiente capaz de simular, analizar y evaluar diseños de suspensiones vehiculares, y de mejorarlos hacia la solución optima mediante la modificación de los parámetros de diseño. La modelización mediante sistemas multicuerpo se utiliza aquí para desarrollar un modelo de autocar con 18 grados de libertad, de manera detallada y eficiente. La geometría y demás características de la suspensión se ajustan a las del vehículo real, así como los demás parámetros del modelo. Para simular la dinámica vehicular, se utiliza una formulación multicuerpo moderna y eficiente basada en las ecuaciones de Maggi, a la que se ha incorporado un visor 3D. Así, se consigue simular maniobras vehiculares en tiempos inferiores al tiempo real. Una vez que la dinámica está disponible, los análisis de sensibilidad son cruciales para una optimización robusta y eficiente. Para ello, se presenta una técnica matemática que permite derivar las variables dinámicas dentro de la formulación, de forma algorítmica, general, con la precisión de la maquina, y razonablemente eficiente: la diferenciación automática. Este método propaga las derivadas con respecto a las variables de diseño a través del código informático y con poca intervención del usuario. En contraste con otros enfoques en la bibliografía, generalmente particulares y limitados, se realiza una comparación de librerías, se desarrolla una formulación híbrida directa-automática para el cálculo de sensibilidades, y se presentan varios ejemplos reales. Finalmente, se lleva a cabo la optimización de la respuesta dinámica del vehículo citado. Se analizan cuatro tipos distintos de optimización: identificación de parámetros, optimización de la maniobrabilidad, optimización del confort y optimización multi-objetivo, todos ellos aplicados al diseño del autocar. Además de resultados analíticos y gráficos, se incluyen algunas consideraciones acerca de la eficiencia. En resumen, se mejora el comportamiento dinámico de vehículos por medio de modelos multicuerpo y de técnicas de diferenciación automática y optimización avanzadas, posibilitando un ajuste automático, preciso y eficiente de los parámetros de diseño. ABSTRACT Each day, the design and development of vehicle suspension systems relies more on computer-aided design and computer-aided engineering tools, which allow anticipating the problems and solving them ahead of time. Dynamic behavior and characteristics are thus simulated accurately and inexpensively with moderate computational times and resources. There is, however, an iterative component in the process, which involves the manual definition of designs in a trialand-error manner. This Thesis takes a step towards the development of an efficient simulation framework capable of simulating, analyzing and evaluating vehicle suspension designs, and automatically improving them by varying the design parameters towards the optimal solution. The multibody systems approach is hereby used to model a three-dimensional 18-degrees-of-freedom coach in a comprehensive yet efficient way. The suspension geometry and characteristics resemble the ones from the real vehicle, as do the rest of vehicle parameters. In order to simulate vehicle dynamics, an efficient, state-of-the-art multibody formulation based on Maggi’s equations is employed, and a three-dimensional graphics viewer is developed. As a result, vehicle maneuvers can be simulated faster than real-time. Once the dynamics are ready, a sensitivity analysis is crucial for a robust optimization. To that end, a mathematical technique is introduced, which allows differentiating the dynamic variables within the multibody formulation in a general, algorithmic, accurate to machine precision, and reasonably efficient way: automatic differentiation. This method propagates the derivatives with respect to the design parameters throughout the computer code, with little user interaction. In contrast with other attempts in the literature, mostly not generalpurpose, a benchmarking of libraries is carried out, a hybrid direct-automatic differentiation approach for the computation of sensitivities is developed, and several real-life examples are analyzed. Finally, a design optimization process of the aforementioned vehicle is carried out. Four different types of dynamic response optimization are presented: parameter identification, handling optimization, ride comfort optimization and multi-objective optimization; all of which are applied to the design of the coach example. Together with analytical and visual proof of the results, efficiency considerations are made. In summary, the dynamic behavior of vehicles is improved by using the multibody systems approach, along with advanced differentiation and optimization techniques, enabling an automatic, accurate and efficient tuning of design parameters.

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.

Modeling and optimization of frequencies on congested bus lines

In this paper some mathematical programming models are exposed in order to set the number of services on a specified system of bus lines, which are intended to assist high demand levels which may arise because of the disruption of Rapid Transit services or during the celebration of massive events. By means of this model two types of basic magnitudes can be determined, basically: a) the number of bus units assigned to each line and b) the number of services that should be assigned to those units. In these models, passenger flow assignment to lines can be considered of the system optimum type, in the sense that the assignment of units and of services is carried out minimizing a linear combination of operation costs and total travel time of users. The models consider delays experienced by buses as a consequence of the get in/out of the passengers, queueing at stations and the delays that passengers experience waiting at the stations. For the case of a congested strategy based user optimal passenger assignment model with strict capacities on the bus lines, the use of the method of successive averages is shown.