Fuzzy min-max neural networks for categorical data: application to missing data imputation

The fuzzy min–max neural network classifier is a supervised learning method. This classifier takes the hybrid neural networks and fuzzy systems approach. All input variables in the network are required to correspond to continuously valued variables, and this can be a significant constraint in many real-world situations where there are not only quantitative but also categorical data. The usual way of dealing with this type of variables is to replace the categorical by numerical values and treat them as if they were continuously valued. But this method, implicitly defines a possibly unsuitable metric for the categories. A number of different procedures have been proposed to tackle the problem. In this article, we present a new method. The procedure extends the fuzzy min–max neural network input to categorical variables by introducing new fuzzy sets, a new operation, and a new architecture. This provides for greater flexibility and wider application. The proposed method is then applied to missing data imputation in voting intention polls. The micro data—the set of the respondents’ individual answers to the questions—of this type of poll are especially suited for evaluating the method since they include a large number of numerical and categorical attributes.

Experimental study on the effective width of flat slab structures under dynamic seismic loading

This paper investigates the effective width of reinforced concrete flat slab structures subjected to seismic loading on the basis of dynamic shaking table tests. The study is focussed on the behavior of corner slab? column connections with structural steel I- or channel-shaped sections (shearheads) as shear punching reinforcement. To this end, a 1/2 scale test model consisting of a flat slab supported on four box-type steel columns was subjected to several seismic simulations of increasing intensity. It is found from the test results that the effective width tends to increase with the intensity of the seismic simulation, and this increase is limited by the degradation of adherence between reinforcing steel and concrete induced by the strain reversals caused by the earthquake. Also, significant differences are found between the effective width obtained from the tests and the values predicted by formula proposed in the literature. These differences are attributed to the stiffening effect provided by the steel profiles that constitute the punching shear reinforcement.

Maximum Likelihood Estimation of Modal Parameters in Structures Using the Expectation Maximization Algorithm

This paper presents a time-domain stochastic system identification method based on maximum likelihood estimation (MLE) with the expectation maximization (EM) algorithm. The effectiveness of this structural identification method is evaluated through numerical simulation in the context of the ASCE benchmark problem on structural health monitoring. The benchmark structure is a four-story, two-bay by two-bay steel-frame scale model structure built in the Earthquake Engineering Research Laboratory at the University of British Columbia, Canada. This paper focuses on Phase I of the analytical benchmark studies. A MATLAB-based finite element analysis code obtained from the IASC-ASCE SHM Task Group web site is used to calculate the dynamic response of the prototype structure. A number of 100 simulations have been made using this MATLAB-based finite element analysis code in order to evaluate the proposed identification method. There are several techniques to realize system identification. In this work, stochastic subspace identification (SSI)method has been used for comparison. SSI identification method is a well known method and computes accurate estimates of the modal parameters. The principles of the SSI identification method has been introduced in the paper and next the proposed MLE with EM algorithm has been explained in detail. The advantages of the proposed structural identification method can be summarized as follows: (i) the method is based on maximum likelihood, that implies minimum variance estimates; (ii) EM is a computational simpler estimation procedure than other optimization algorithms; (iii) estimate more parameters than SSI, and these estimates are accurate. On the contrary, the main disadvantages of the method are: (i) EM algorithm is an iterative procedure and it consumes time until convergence is reached; and (ii) this method needs starting values for the parameters. Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using both the SSI method and the proposed MLE + EM method. The numerical results show that the proposed method identifies eigenfrequencies, damping ratios and mode shapes reasonably well even in the presence of 10% measurement noises. These modal parameters are more accurate than the SSI estimated modal parameters.

Multi-dimensional classification using Bayesian networks for stationary and evolving streaming data

Hoy en día, con la evolución continua y rápida de las tecnologías de la información y los dispositivos de computación, se recogen y almacenan continuamente grandes volúmenes de datos en distintos dominios y a través de diversas aplicaciones del mundo real. La extracción de conocimiento útil de una cantidad tan enorme de datos no se puede realizar habitualmente de forma manual, y requiere el uso de técnicas adecuadas de aprendizaje automático y de minería de datos. La clasificación es una de las técnicas más importantes que ha sido aplicada con éxito a varias áreas. En general, la clasificación se compone de dos pasos principales: en primer lugar, aprender un modelo de clasificación o clasificador a partir de un conjunto de datos de entrenamiento, y en segundo lugar, clasificar las nuevas instancias de datos utilizando el clasificador aprendido. La clasificación es supervisada cuando todas las etiquetas están presentes en los datos de entrenamiento (es decir, datos completamente etiquetados), semi-supervisada cuando sólo algunas etiquetas son conocidas (es decir, datos parcialmente etiquetados), y no supervisada cuando todas las etiquetas están ausentes en los datos de entrenamiento (es decir, datos no etiquetados). Además, aparte de esta taxonomía, el problema de clasificación se puede categorizar en unidimensional o multidimensional en función del número de variables clase, una o más, respectivamente; o también puede ser categorizado en estacionario o cambiante con el tiempo en función de las características de los datos y de la tasa de cambio subyacente. A lo largo de esta tesis, tratamos el problema de clasificación desde tres perspectivas diferentes, a saber, clasificación supervisada multidimensional estacionaria, clasificación semisupervisada unidimensional cambiante con el tiempo, y clasificación supervisada multidimensional cambiante con el tiempo. Para llevar a cabo esta tarea, hemos usado básicamente los clasificadores Bayesianos como modelos. La primera contribución, dirigiéndose al problema de clasificación supervisada multidimensional estacionaria, se compone de dos nuevos métodos de aprendizaje de clasificadores Bayesianos multidimensionales a partir de datos estacionarios. Los métodos se proponen desde dos puntos de vista diferentes. El primer método, denominado CB-MBC, se basa en una estrategia de envoltura de selección de variables que es voraz y hacia delante, mientras que el segundo, denominado MB-MBC, es una estrategia de filtrado de variables con una aproximación basada en restricciones y en el manto de Markov. Ambos métodos han sido aplicados a dos problemas reales importantes, a saber, la predicción de los inhibidores de la transcriptasa inversa y de la proteasa para el problema de infección por el virus de la inmunodeficiencia humana tipo 1 (HIV-1), y la predicción del European Quality of Life-5 Dimensions (EQ-5D) a partir de los cuestionarios de la enfermedad de Parkinson con 39 ítems (PDQ-39). El estudio experimental incluye comparaciones de CB-MBC y MB-MBC con los métodos del estado del arte de la clasificación multidimensional, así como con métodos comúnmente utilizados para resolver el problema de predicción de la enfermedad de Parkinson, a saber, la regresión logística multinomial, mínimos cuadrados ordinarios, y mínimas desviaciones absolutas censuradas. En ambas aplicaciones, los resultados han sido prometedores con respecto a la precisión de la clasificación, así como en relación al análisis de las estructuras gráficas que identifican interacciones conocidas y novedosas entre las variables. La segunda contribución, referida al problema de clasificación semi-supervisada unidimensional cambiante con el tiempo, consiste en un método nuevo (CPL-DS) para clasificar flujos de datos parcialmente etiquetados. Los flujos de datos difieren de los conjuntos de datos estacionarios en su proceso de generación muy rápido y en su aspecto de cambio de concepto. Es decir, los conceptos aprendidos y/o la distribución subyacente están probablemente cambiando y evolucionando en el tiempo, lo que hace que el modelo de clasificación actual sea obsoleto y deba ser actualizado. CPL-DS utiliza la divergencia de Kullback-Leibler y el método de bootstrapping para cuantificar y detectar tres tipos posibles de cambio: en las predictoras, en la a posteriori de la clase o en ambas. Después, si se detecta cualquier cambio, un nuevo modelo de clasificación se aprende usando el algoritmo EM; si no, el modelo de clasificación actual se mantiene sin modificaciones. CPL-DS es general, ya que puede ser aplicado a varios modelos de clasificación. Usando dos modelos diferentes, el clasificador naive Bayes y la regresión logística, CPL-DS se ha probado con flujos de datos sintéticos y también se ha aplicado al problema real de la detección de código malware, en el cual los nuevos ficheros recibidos deben ser continuamente clasificados en malware o goodware. Los resultados experimentales muestran que nuestro método es efectivo para la detección de diferentes tipos de cambio a partir de los flujos de datos parcialmente etiquetados y también tiene una buena precisión de la clasificación. Finalmente, la tercera contribución, sobre el problema de clasificación supervisada multidimensional cambiante con el tiempo, consiste en dos métodos adaptativos, a saber, Locally Adpative-MB-MBC (LA-MB-MBC) y Globally Adpative-MB-MBC (GA-MB-MBC). Ambos métodos monitorizan el cambio de concepto a lo largo del tiempo utilizando la log-verosimilitud media como métrica y el test de Page-Hinkley. Luego, si se detecta un cambio de concepto, LA-MB-MBC adapta el actual clasificador Bayesiano multidimensional localmente alrededor de cada nodo cambiado, mientras que GA-MB-MBC aprende un nuevo clasificador Bayesiano multidimensional. El estudio experimental realizado usando flujos de datos sintéticos multidimensionales indica los méritos de los métodos adaptativos propuestos. ABSTRACT Nowadays, with the ongoing and rapid evolution of information technology and computing devices, large volumes of data are continuously collected and stored in different domains and through various real-world applications. Extracting useful knowledge from such a huge amount of data usually cannot be performed manually, and requires the use of adequate machine learning and data mining techniques. Classification is one of the most important techniques that has been successfully applied to several areas. Roughly speaking, classification consists of two main steps: first, learn a classification model or classifier from an available training data, and secondly, classify the new incoming unseen data instances using the learned classifier. Classification is supervised when the whole class values are present in the training data (i.e., fully labeled data), semi-supervised when only some class values are known (i.e., partially labeled data), and unsupervised when the whole class values are missing in the training data (i.e., unlabeled data). In addition, besides this taxonomy, the classification problem can be categorized into uni-dimensional or multi-dimensional depending on the number of class variables, one or more, respectively; or can be also categorized into stationary or streaming depending on the characteristics of the data and the rate of change underlying it. Through this thesis, we deal with the classification problem under three different settings, namely, supervised multi-dimensional stationary classification, semi-supervised unidimensional streaming classification, and supervised multi-dimensional streaming classification. To accomplish this task, we basically used Bayesian network classifiers as models. The first contribution, addressing the supervised multi-dimensional stationary classification problem, consists of two new methods for learning multi-dimensional Bayesian network classifiers from stationary data. They are proposed from two different points of view. The first method, named CB-MBC, is based on a wrapper greedy forward selection approach, while the second one, named MB-MBC, is a filter constraint-based approach based on Markov blankets. Both methods are applied to two important real-world problems, namely, the prediction of the human immunodeficiency virus type 1 (HIV-1) reverse transcriptase and protease inhibitors, and the prediction of the European Quality of Life-5 Dimensions (EQ-5D) from 39-item Parkinson’s Disease Questionnaire (PDQ-39). The experimental study includes comparisons of CB-MBC and MB-MBC against state-of-the-art multi-dimensional classification methods, as well as against commonly used methods for solving the Parkinson’s disease prediction problem, namely, multinomial logistic regression, ordinary least squares, and censored least absolute deviations. For both considered case studies, results are promising in terms of classification accuracy as well as regarding the analysis of the learned MBC graphical structures identifying known and novel interactions among variables. The second contribution, addressing the semi-supervised uni-dimensional streaming classification problem, consists of a novel method (CPL-DS) for classifying partially labeled data streams. Data streams differ from the stationary data sets by their highly rapid generation process and their concept-drifting aspect. That is, the learned concepts and/or the underlying distribution are likely changing and evolving over time, which makes the current classification model out-of-date requiring to be updated. CPL-DS uses the Kullback-Leibler divergence and bootstrapping method to quantify and detect three possible kinds of drift: feature, conditional or dual. Then, if any occurs, a new classification model is learned using the expectation-maximization algorithm; otherwise, the current classification model is kept unchanged. CPL-DS is general as it can be applied to several classification models. Using two different models, namely, naive Bayes classifier and logistic regression, CPL-DS is tested with synthetic data streams and applied to the real-world problem of malware detection, where the new received files should be continuously classified into malware or goodware. Experimental results show that our approach is effective for detecting different kinds of drift from partially labeled data streams, as well as having a good classification performance. Finally, the third contribution, addressing the supervised multi-dimensional streaming classification problem, consists of two adaptive methods, namely, Locally Adaptive-MB-MBC (LA-MB-MBC) and Globally Adaptive-MB-MBC (GA-MB-MBC). Both methods monitor the concept drift over time using the average log-likelihood score and the Page-Hinkley test. Then, if a drift is detected, LA-MB-MBC adapts the current multi-dimensional Bayesian network classifier locally around each changed node, whereas GA-MB-MBC learns a new multi-dimensional Bayesian network classifier from scratch. Experimental study carried out using synthetic multi-dimensional data streams shows the merits of both proposed adaptive methods.

Properties and applications of high electron density structures based on InN and related compounds

El objetivo principal del presente trabajo es estudiar y explotar estructuras que presentan un gas bidimensional de electrones (2DEG) basadas en compuestos nitruros con alto contenido de indio. Existen muchas preguntas abiertas, relacionadas con el nitruro de indio y sus aleaciones, algunas de las cuales se han abordado en este estudio. En particular, se han investigado temas relacionados con el análisis y la tecnología del material, tanto para el InN y heteroestructuras de InAl(Ga)N/GaN como para sus aplicaciones a dispositivos avanzados. Después de un análisis de la dependencia de las propiedades del InN con respecto a tratamientos de procesado de dispositivos (plasma y térmicos), el problema relacionado con la formación de un contacto rectificador es considerado. Concretamente, su dificultad es debida a la presencia de acumulación de electrones superficiales en la forma de un gas bidimensional de electrones, debido al pinning del nivel de Fermi. El uso de métodos electroquímicos, comparados con técnicas propias de la microelectrónica, ha ayudado para la realización de esta tarea. En particular, se ha conseguido lamodulación de la acumulación de electrones con éxito. En heteroestructuras como InAl(Ga)N/GaN, el gas bidimensional está presente en la intercara entre GaN y InAl(Ga)N, aunque no haya polarización externa (estructuras modo on). La tecnología relacionada con la fabricación de transistores de alta movilidad en modo off (E-mode) es investigada. Se utiliza un método de ataque húmedo mediante una solución de contenido alcalino, estudiando las modificaciones estructurales que sufre la barrera. En este sentido, la necesidad de un control preciso sobre el material atacado es fundamental para obtener una estructura recessed para aplicaciones a transistores, con densidad de defectos e inhomogeneidad mínimos. La dependencia de la velocidad de ataque de las propiedades de las muestras antes del tratamiento es observada y comentada. Se presentan también investigaciones relacionadas con las propiedades básicas del InN. Gracias al uso de una puerta a través de un electrolito, el desplazamiento de los picos obtenidos por espectroscopia Raman es correlacionado con una variación de la densidad de electrones superficiales. En lo que concierne la aplicación a dispositivos, debido al estado de la tecnología actual y a la calidad del material InN, todavía no apto para dispositivos, la tesis se enfoca a la aplicación de heteroestructuras de InAl(Ga)N/GaN. Gracias a las ventajas de una barrera muy fina, comparada con la tecnología de AlGaN/GaN, el uso de esta estructura es adecuado para aplicaciones que requieren una elevada sensibilidad, estando el canal 2DEG más cerca de la superficie. De hecho, la sensibilidad obtenida en sensores de pH es comparable al estado del arte en términos de variaciones de potencial superficial, y, debido al poco espesor de la barrera, la variación de la corriente con el pH puede ser medida sin necesidad de un electrodo de referencia externo. Además, estructuras fotoconductivas basadas en un gas bidimensional presentan alta ganancia debida al elevado campo eléctrico en la intercara, que induce una elevada fuerza de separación entre hueco y electrón generados por absorción de luz. El uso de metalizaciones de tipo Schottky (fotodiodos Schottky y metal-semiconductormetal) reduce la corriente de oscuridad, en comparación con los fotoconductores. Además, la barrera delgada aumenta la eficiencia de extracción de los portadores. En consecuencia, se obtiene ganancia en todos los dispositivos analizados basados en heteroestructuras de InAl(Ga)N/GaN. Aunque presentando fotoconductividad persistente (PPC), los dispositivos resultan más rápidos con respeto a los valores que se dan en la literatura acerca de PPC en sistemas fotoconductivos. ABSTRACT The main objective of the present work is to study and exploit the two-dimensionalelectron- gas (2DEG) structures based on In-related nitride compounds. Many open questions are analyzed. In particular, technology and material-related topics are the focus of interest regarding both InNmaterial and InAl(Ga)N/GaNheterostructures (HSs) as well as their application to advanced devices. After the analysis of the dependence of InN properties on processing treatments (plasma-based and thermal), the problemof electrical blocking behaviour is taken into consideration. In particular its difficulty is due to the presence of a surface electron accumulation (SEA) in the form of a 2DEG, due to Fermi level pinning. The use of electrochemical methods, compared to standard microelectronic techniques, helped in the successful realization of this task. In particular, reversible modulation of SEA is accomplished. In heterostructures such as InAl(Ga)N/GaN, the 2DEGis present at the interface between GaN and InAl(Ga)N even without an external bias (normally-on structures). The technology related to the fabrication of normally off (E-mode) high-electron-mobility transistors (HEMTs) is investigated in heterostructures. An alkali-based wet-etching method is analysed, standing out the structural modifications the barrier underwent. The need of a precise control of the etched material is crucial, in this sense, to obtain a recessed structure for HEMT application with the lowest defect density and inhomogeneity. The dependence of the etch rate on the as-grown properties is observed and commented. Fundamental investigation related to InNis presented, related to the physics of this degeneratematerial. With the help of electrolyte gating (EG), the shift in Raman peaks is correlated to a variation in surface eletron density. As far as the application to device is concerned, due to the actual state of the technology and material quality of InN, not suitable for working devices yet, the focus is directed to the applications of InAl(Ga)N/GaN HSs. Due to the advantages of a very thin barrier layer, compared to standard AlGaN/GaN technology, the use of this structure is suitable for high sensitivity applications being the 2DEG channel closer to the surface. In fact, pH sensitivity obtained is comparable to the state-of-the-art in terms of surface potential variations, and, due to the ultrathin barrier, the current variation with pH can be recorded with no need of the external reference electrode. Moreover, 2DEG photoconductive structures present a high photoconductive gain duemostly to the high electric field at the interface,and hence a high separation strength of photogenerated electron and hole. The use of Schottky metallizations (Schottky photodiode and metal-semiconductor-metal) reduce the dark current, compared to photoconduction, and the thin barrier helps to increase the extraction efficiency. Gain is obtained in all the device structures investigated. The devices, even if they present persistent photoconductivity (PPC), resulted faster than the standard PPC related decay values.

The time variable in the calculation of building structures. How to extend the working life until the 100 years?

The idea that a building and consequently its structure is for a lifetime has stopped being a reference. CTE establishes that the life utility of a normal construction structure should be of 50years. If the time variable is introduced in the calculation of actions on structures, seems evident thatdifferent values can be used for a standard building, for a provisional structure with ≤ 10 years of life utility or for a monumental building with a life utility of 100 years. The present presentation follows at all moment, the directives and formulations given in the different structural Eurocodes, till the moment not included in the CTE. Finally the values of the actions that must be used to extend the life utility of a building until. 100 years will be deduced, also it suitability and e conomic feasibility will be discuss.

A review of load models for the prediction of footfall-induced vibration in structures

Crowd induced dynamic loading in large structures, such as gymnasiums or stadium, is usually modelled as a series of harmonic loads which are defined in terms of their Fourier coefficients. Different values of these coefficients that were obtained from full scale measurements can be found in codes. Recently, an alternative has been proposed, based on random generation of load time histories that take into account phase lag among individuals inside the crowd. This paper presents the testing done on a structure designed to be a gymnasium. Two series of dynamic test were performed on the gym slab. For the first test an electrodynamic shaker was placed at several locations and during the second one people located inside a marked area bounced and jumped guided by different metronome rates. A finite element model (FEM) is presented and a comparison of numerically predicted and experimentally observed vibration modes and frequencies has been used to assess its validity. The second group of measurements will be compared with predictions made using the FEM model and three alternatives for crowd induced load modelling.

Model of human rhythmic activities on structures

Crowd induced dynamic loading in large structures, such as gymnasiums or stadiums, is usually modelled as a series of harmonic loads which are defined in terms of their Fourier coefficients. Different values of these Fourier coefficients that were obtained from full scale measurements can be found in codes. Recently, an alternative has been proposed, based on random generation of load time histories that take into account phase lags among individuals inside the crowd. Generally the testing is performed on platforms or structures that can be considered rigid because their natural frequencies are higher than the excitation frequencies associated with crowd loading. In this paper we shall present the testing done on a structure designed to be a gymnasium, which has natural frequencies within that range. In this test the gym slab was instrumented with acceleration sensors and different people jumped on a force plate installed on the floor. Test results have been compared with predictions based on the two abovementioned load modelling alternatives and a new methodology for modelling jumping loads has been proposed in order to reduce the difference between experimental and numerical results at high frequency range.

Novel educational assessment for building structures: Automatic evaluation of on-line graphics

This article presents a new automatic evaluation for on-line graphics, its application and the numerous advantages achieved applying this developed correcting method. The software application developed by the Innovation in Education Group “E4”, from the Technical University of Madrid, is oriented for the online self-assessment of the graphic drawings that students carry out as continuous training. The adaptation to the European Higher Educational Area is an important opportunity to research about the possibilities of on-line education assessment. In this way, a new software tool has been developed for continuous self-testing by undergraduates. Using this software it is possible to evaluate the graphical answer of the students. Thus, the drawings made on-line by students are automatically corrected according to the geometry (straight lines, sloping lines or second order curves) and by sizes (depending on the specific values which define the graphics).

Modified Gutenberg-Richter coefficient for damage evaluation in reinforced concrete structures subjected to seismic simulations on a shaking table

This paper presents analysis and discussion of the b- and ib-values calculated from the acoustic emission (AE) signals recorded during dynamic shake-table tests conducted on a reinforced concrete (RC) frame subjected to several uniaxial seismic simulations of increasing intensity until collapse. The intensity of shaking was controlled by the peak acceleration applied to the shake-table in each seismic simulation, and it ranged from 0.08 to 0.47 times the acceleration of gravity. The numerous spurious signals not related to concrete damage that inevitably contaminate AE measurements obtained from complex dynamic shake-table tests were properly filtered with an RMS filter and the use of guard sensors. Comparing the b- and ib-values calculated through the tests with the actual level of macro-cracking and damage observed during testing, it was concluded that the limit value of 0.05 proposed in previous research to determine the onset of macro-cracks should be revised in the case of earthquake-type dynamic loading. Finally, the b- and ibvalues were compared with the damage endured by the RC frame evaluated both visually and quantitatively in terms of the inter-story drift index.

Proposal of a new indicator to define ductility applied to corroded steel reinforcement on concrete structures = Propuesta de un nuevo indicador para definir la ductilidad aplicada a la corrosión del acero de refuerzo en estructuras de hormigón

The carbonation of concrete or the chlorides ingress in such quantity to reach the level of bars is triggers of reinforcement corrosion. One of the most significant effects of reinforcing steel corrosion on reinforced concrete structures is the decline in the ductility-related properties of the steel. Reinforcement ductility has a decisive effect on the overall ductility of reinforced concrete structures. Different Codes classify the type of steel depending on their ductility defined by the minimum values of several parameters. Using indicators of ductility associating different properties can be advantageous on many occasions. It is considered necessary to define the ductility by means of a single parameter that considers strength values and deformation simultaneously. There are a number of criteria for defining steel ductility by a single parameter. The present experimental study addresses the variation in the ductility of concrete-embedded steel bars when exposed to accelerated corrosion. This paper analyzes the suitability of a new indicator of ductility used in corroded bars.

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.

Two near-optimal layouts for trusslike bridge structures bearing uniform weight between supports

Although the primary objective on designing a structure is to support the external loads, the achievement of an optimal layout that reduces all costs associated with the structure is an aspect of increasing interest. The problem of finding the optimal layout for bridgelike structures subjected to a uniform load is considered. The problem is formulated following a theory on economy of frame structures, using the stress volume as the objective function and including the selection of appropriate values for statically indeterminate reactions. It is solved in a function space of finite dimension instead of using a general variational approach, obtaining near-optimal solutions. The results obtained with this profitable strategy are very close to the best layouts known to date, with differences of less than 2% for the stress volume, but with a simpler layout that can be recognized in some real bridges. This strategy could be a guide to preliminary design of bridges subject to a wide class of costs.