Maximum likelihood estimation of new state space models for operational modal analysis

The modal analysis of a structural system consists on computing its vibrational modes. The experimental way to estimate these modes requires to excite the system with a measured or known input and then to measure the system output at different points using sensors. Finally, system inputs and outputs are used to compute the modes of vibration. When the system refers to large structures like buildings or bridges, the tests have to be performed in situ, so it is not possible to measure system inputs such as wind, traffic, . . .Even if a known input is applied, the procedure is usually difficult and expensive, and there are still uncontrolled disturbances acting at the time of the test. These facts led to the idea of computing the modes of vibration using only the measured vibrations and regardless of the inputs that originated them, whether they are ambient vibrations (wind, earthquakes, . . . ) or operational loads (traffic, human loading, . . . ). This procedure is usually called Operational Modal Analysis (OMA), and in general consists on to fit a mathematical model to the measured data assuming the unobserved excitations are realizations of a stationary stochastic process (usually white noise processes). Then, the modes of vibration are computed from the estimated model. The first issue investigated in this thesis is the performance of the Expectation- Maximization (EM) algorithm for the maximum likelihood estimation of the state space model in the field of OMA. The algorithm is described in detail and it is analysed how to apply it to vibration data. After that, it is compared to another well known method, the Stochastic Subspace Identification algorithm. The maximum likelihood estimate enjoys some optimal properties from a statistical point of view what makes it very attractive in practice, but the most remarkable property of the EM algorithm is that it can be used to address a wide range of situations in OMA. In this work, three additional state space models are proposed and estimated using the EM algorithm: • The first model is proposed to estimate the modes of vibration when several tests are performed in the same structural system. Instead of analyse record by record and then compute averages, the EM algorithm is extended for the joint estimation of the proposed state space model using all the available data. • The second state space model is used to estimate the modes of vibration when the number of available sensors is lower than the number of points to be tested. In these cases it is usual to perform several tests changing the position of the sensors from one test to the following (multiple setups of sensors). Here, the proposed state space model and the EM algorithm are used to estimate the modal parameters taking into account the data of all setups. • And last, a state space model is proposed to estimate the modes of vibration in the presence of unmeasured inputs that cannot be modelled as white noise processes. In these cases, the frequency components of the inputs cannot be separated from the eigenfrequencies of the system, and spurious modes are obtained in the identification process. The idea is to measure the response of the structure corresponding to different inputs; then, it is assumed that the parameters common to all the data correspond to the structure (modes of vibration), and the parameters found in a specific test correspond to the input in that test. The problem is solved using the proposed state space model and the EM algorithm. Resumen El análisis modal de un sistema estructural consiste en calcular sus modos de vibración. Para estimar estos modos experimentalmente es preciso excitar el sistema con entradas conocidas y registrar las salidas del sistema en diferentes puntos por medio de sensores. Finalmente, los modos de vibración se calculan utilizando las entradas y salidas registradas. Cuando el sistema es una gran estructura como un puente o un edificio, los experimentos tienen que realizarse in situ, por lo que no es posible registrar entradas al sistema tales como viento, tráfico, . . . Incluso si se aplica una entrada conocida, el procedimiento suele ser complicado y caro, y todavía están presentes perturbaciones no controladas que excitan el sistema durante el test. Estos hechos han llevado a la idea de calcular los modos de vibración utilizando sólo las vibraciones registradas en la estructura y sin tener en cuenta las cargas que las originan, ya sean cargas ambientales (viento, terremotos, . . . ) o cargas de explotación (tráfico, cargas humanas, . . . ). Este procedimiento se conoce en la literatura especializada como Análisis Modal Operacional, y en general consiste en ajustar un modelo matemático a los datos registrados adoptando la hipótesis de que las excitaciones no conocidas son realizaciones de un proceso estocástico estacionario (generalmente ruido blanco). Posteriormente, los modos de vibración se calculan a partir del modelo estimado. El primer problema que se ha investigado en esta tesis es la utilización de máxima verosimilitud y el algoritmo EM (Expectation-Maximization) para la estimación del modelo espacio de los estados en el ámbito del Análisis Modal Operacional. El algoritmo se describe en detalle y también se analiza como aplicarlo cuando se dispone de datos de vibraciones de una estructura. A continuación se compara con otro método muy conocido, el método de los Subespacios. Los estimadores máximo verosímiles presentan una serie de propiedades que los hacen óptimos desde un punto de vista estadístico, pero la propiedad más destacable del algoritmo EM es que puede utilizarse para resolver un amplio abanico de situaciones que se presentan en el Análisis Modal Operacional. En este trabajo se proponen y estiman tres modelos en el espacio de los estados: • El primer modelo se utiliza para estimar los modos de vibración cuando se dispone de datos correspondientes a varios experimentos realizados en la misma estructura. En lugar de analizar registro a registro y calcular promedios, se utiliza algoritmo EM para la estimación conjunta del modelo propuesto utilizando todos los datos disponibles. • El segundo modelo en el espacio de los estados propuesto se utiliza para estimar los modos de vibración cuando el número de sensores disponibles es menor que vi Resumen el número de puntos que se quieren analizar en la estructura. En estos casos es usual realizar varios ensayos cambiando la posición de los sensores de un ensayo a otro (múltiples configuraciones de sensores). En este trabajo se utiliza el algoritmo EM para estimar los parámetros modales teniendo en cuenta los datos de todas las configuraciones. • Por último, se propone otro modelo en el espacio de los estados para estimar los modos de vibración en la presencia de entradas al sistema que no pueden modelarse como procesos estocásticos de ruido blanco. En estos casos, las frecuencias de las entradas no se pueden separar de las frecuencias del sistema y se obtienen modos espurios en la fase de identificación. La idea es registrar la respuesta de la estructura correspondiente a diferentes entradas; entonces se adopta la hipótesis de que los parámetros comunes a todos los registros corresponden a la estructura (modos de vibración), y los parámetros encontrados en un registro específico corresponden a la entrada en dicho ensayo. El problema se resuelve utilizando el modelo propuesto y el algoritmo EM.

State space models for multi-setup operational modal analysis

Operational Modal Analysis consists on estimate the modal parameters of a structure (natural frequencies, damping ratios and modal vectors) from output-only vibration measurements. The modal vectors can be only estimated where a sensor is placed, so when the number of available sensors is lower than the number of tested points, it is usual to perform several tests changing the position of the sensors from one test to the following (multiple setups of sensors): some sensors stay at the same position from setup to setup, and the other sensors change the position until all the tested points are covered. The permanent sensors are then used to merge the mode shape estimated at each setup (or partial modal vectors) into global modal vectors. Traditionally, the partial modal vectors are estimated independently setup by setup, and the global modal vectors are obtained in a postprocess phase. In this work we present two state space models that can be used to process all the recorded setups at the same time, and we also present how these models can be estimated using the maximum likelihood method. The result is that the global mode shape of each mode is obtained automatically, and subsequently, a single value for the natural frequency and damping ratio of the mode is computed. Finally, both models are compared using real measured data.

Modal contribution and state space order selection in operational modal analysis

The estimation of modal parameters of a structure from ambient measurements has attracted the attention of many researchers in the last years. The procedure is now well established and the use of state space models, stochastic system identification methods and stabilization diagrams allows to identify the modes of the structure. In this paper the contribution of each identified mode to the measured vibration is discussed. This modal contribution is computed using the Kalman filter and it is an indicator of the importance of the modes. Also the variation of the modal contribution with the order of the model is studied. This analysis suggests selecting the order for the state space model as the order that includes the modes with higher contribution. The order obtained using this method is compared to those obtained using other well known methods, like Akaike criteria for time series or the singular values of the weighted projection matrix in the Stochastic Subspace Identification method. Finally, both simulated and measured vibration data are used to show the practicability of the derived technique. Finally, it is important to remark that the method can be used with any identification method working in the state space model.

Hardware-Based Particle Filter with Evolutionary Resampling Stage

Autonomous systems require, in most of the cases, reasoning and decision-making capabilities. Moreover, the decision process has to occur in real time. Real-time computing means that every situation or event has to have an answer before a temporal deadline. In complex applications, these deadlines are usually in the order of milliseconds or even microseconds if the application is very demanding. In order to comply with these timing requirements, computing tasks have to be performed as fast as possible. The problem arises when computations are no longer simple, but very time-consuming operations. A good example can be found in autonomous navigation systems with visual-tracking submodules where Kalman filtering is the most extended solution. However, in recent years, some interesting new approaches have been developed. Particle filtering, given its more general problem-solving features, has reached an important position in the field. The aim of this thesis is to design, implement and validate a hardware platform that constitutes itself an embedded intelligent system. The proposed system would combine particle filtering and evolutionary computation algorithms to generate intelligent behavior. Traditional approaches to particle filtering or evolutionary computation have been developed in software platforms, including parallel capabilities to some extent. In this work, an additional goal is fully exploiting hardware implementation advantages. By using the computational resources available in a FPGA device, better performance results in terms of computation time are expected. These hardware resources will be in charge of extensive repetitive computations. With this hardware-based implementation, real-time features are also expected.

Two-layer particle filter for multiple target detection and tracking

This paper deals with the detection and tracking of an unknown number of targets using a Bayesian hierarchical model with target labels. To approximate the posterior probability density function, we develop a two-layer particle filter. One deals with track initiation, and the other with track maintenance. In addition, the parallel partition method is proposed to sample the states of the surviving targets.

Computational Methods for Identification of Vibrating Structures

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

Estimating the modal parameters from multiple measurement setups using a joint state space model

Computing the modal parameters of structural systems often requires processing data from multiple non-simultaneously recorded setups of sensors. These setups share some sensors in common, the so-called reference sensors, which are fixed for all measurements, while the other sensors change their position from one setup to the next. One possibility is to process the setups separately resulting in different modal parameter estimates for each setup. Then, the reference sensors are used to merge or glue the different parts of the mode shapes to obtain global mode shapes, while the natural frequencies and damping ratios are usually averaged. In this paper we present a new state space model that processes all setups at once. The result is that the global mode shapes are obtained automatically, and only a value for the natural frequency and damping ratio of each mode is estimated. We also investigate the estimation of this model using maximum likelihood and the Expectation Maximization algorithm, and apply this technique to simulated and measured data corresponding to different structures.

Using the EM algorithm to estimate the state space model for OMAX

This paper presents a time-domain stochastic system identification method based on Maximum Likelihood Estimation and the Expectation Maximization algorithm that is applied to the estimation of modal parameters from system input and output data. The effectiveness of this structural identification method is evaluated through numerical simulation. Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the simulated structure are estimated applying the proposed identification method to a set of 100 simulated cases. The numerical results show that the proposed method estimates the modal parameters with precision in the presence of 20% measurement noise even. Finally, advantages and disadvantages of the method have been discussed.

An approach to operational modal analysis using the expectation maximization algorithm

This paper presents the Expectation Maximization algorithm (EM) applied to operational modal analysis of structures. The EM algorithm is a general-purpose method for maximum likelihood estimation (MLE) that in this work is used to estimate state space models. As it is well known, the MLE enjoys some optimal properties from a statistical point of view, which make it very attractive in practice. However, the EM algorithm has two main drawbacks: its slow convergence and the dependence of the solution on the initial values used. This paper proposes two different strategies to choose initial values for the EM algorithm when used for operational modal analysis: to begin with the parameters estimated by Stochastic Subspace Identification method (SSI) and to start using random points. The effectiveness of the proposed identification method has been evaluated through numerical simulation and measured vibration data in the context of a benchmark problem. Modal parameters (natural frequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using SSI and the EM algorithm. On the whole, the results show that the application of the EM algorithm starting from the solution given by SSI is very useful to identify the vibration modes of a structure, discarding the spurious modes that appear in high order models and discovering other hidden modes. Similar results are obtained using random starting values, although this strategy allows us to analyze the solution of several starting points what overcome the dependence on the initial values used.

Operational modal analisys using joint statistical analysis of multiple records

In Operational Modal Analysis (OMA) of a structure, the data acquisition process may be repeated many times. In these cases, the analyst has several similar records for the modal analysis of the structure that have been obtained at di�erent time instants (multiple records). The solution obtained varies from one record to another, sometimes considerably. The differences are due to several reasons: statistical errors of estimation, changes in the external forces (unmeasured forces) that modify the output spectra, appearance of spurious modes, etc. Combining the results of the di�erent individual analysis is not straightforward. To solve the problem, we propose to make the joint estimation of the parameters using all the records. This can be done in a very simple way using state space models and computing the estimates by maximum-likelihood. The method provides a single result for the modal parameters that combines optimally all the records.

Parallel Computer Vision Algorithms for Graphics Processing Units

La evolución de los teléfonos móviles inteligentes, dotados de cámaras digitales, está provocando una creciente demanda de aplicaciones cada vez más complejas que necesitan algoritmos de visión artificial en tiempo real; puesto que el tamaño de las señales de vídeo no hace sino aumentar y en cambio el rendimiento de los procesadores de un solo núcleo se ha estancado, los nuevos algoritmos que se diseñen para visión artificial han de ser paralelos para poder ejecutarse en múltiples procesadores y ser computacionalmente escalables. Una de las clases de procesadores más interesantes en la actualidad se encuentra en las tarjetas gráficas (GPU), que son dispositivos que ofrecen un alto grado de paralelismo, un excelente rendimiento numérico y una creciente versatilidad, lo que los hace interesantes para llevar a cabo computación científica. En esta tesis se exploran dos aplicaciones de visión artificial que revisten una gran complejidad computacional y no pueden ser ejecutadas en tiempo real empleando procesadores tradicionales. En cambio, como se demuestra en esta tesis, la paralelización de las distintas subtareas y su implementación sobre una GPU arrojan los resultados deseados de ejecución con tasas de refresco interactivas. Asimismo, se propone una técnica para la evaluación rápida de funciones de complejidad arbitraria especialmente indicada para su uso en una GPU. En primer lugar se estudia la aplicación de técnicas de síntesis de imágenes virtuales a partir de únicamente dos cámaras lejanas y no paralelas—en contraste con la configuración habitual en TV 3D de cámaras cercanas y paralelas—con información de color y profundidad. Empleando filtros de mediana modificados para la elaboración de un mapa de profundidad virtual y proyecciones inversas, se comprueba que estas técnicas son adecuadas para una libre elección del punto de vista. Además, se demuestra que la codificación de la información de profundidad con respecto a un sistema de referencia global es sumamente perjudicial y debería ser evitada. Por otro lado se propone un sistema de detección de objetos móviles basado en técnicas de estimación de densidad con funciones locales. Este tipo de técnicas es muy adecuada para el modelado de escenas complejas con fondos multimodales, pero ha recibido poco uso debido a su gran complejidad computacional. El sistema propuesto, implementado en tiempo real sobre una GPU, incluye propuestas para la estimación dinámica de los anchos de banda de las funciones locales, actualización selectiva del modelo de fondo, actualización de la posición de las muestras de referencia del modelo de primer plano empleando un filtro de partículas multirregión y selección automática de regiones de interés para reducir el coste computacional. Los resultados, evaluados sobre diversas bases de datos y comparados con otros algoritmos del estado del arte, demuestran la gran versatilidad y calidad de la propuesta. Finalmente se propone un método para la aproximación de funciones arbitrarias empleando funciones continuas lineales a tramos, especialmente indicada para su implementación en una GPU mediante el uso de las unidades de filtraje de texturas, normalmente no utilizadas para cómputo numérico. La propuesta incluye un riguroso análisis matemático del error cometido en la aproximación en función del número de muestras empleadas, así como un método para la obtención de una partición cuasióptima del dominio de la función para minimizar el error. ABSTRACT The evolution of smartphones, all equipped with digital cameras, is driving a growing demand for ever more complex applications that need to rely on real-time computer vision algorithms. However, video signals are only increasing in size, whereas the performance of single-core processors has somewhat stagnated in the past few years. Consequently, new computer vision algorithms will need to be parallel to run on multiple processors and be computationally scalable. One of the most promising classes of processors nowadays can be found in graphics processing units (GPU). These are devices offering a high parallelism degree, excellent numerical performance and increasing versatility, which makes them interesting to run scientific computations. In this thesis, we explore two computer vision applications with a high computational complexity that precludes them from running in real time on traditional uniprocessors. However, we show that by parallelizing subtasks and implementing them on a GPU, both applications attain their goals of running at interactive frame rates. In addition, we propose a technique for fast evaluation of arbitrarily complex functions, specially designed for GPU implementation. First, we explore the application of depth-image–based rendering techniques to the unusual configuration of two convergent, wide baseline cameras, in contrast to the usual configuration used in 3D TV, which are narrow baseline, parallel cameras. By using a backward mapping approach with a depth inpainting scheme based on median filters, we show that these techniques are adequate for free viewpoint video applications. In addition, we show that referring depth information to a global reference system is ill-advised and should be avoided. Then, we propose a background subtraction system based on kernel density estimation techniques. These techniques are very adequate for modelling complex scenes featuring multimodal backgrounds, but have not been so popular due to their huge computational and memory complexity. The proposed system, implemented in real time on a GPU, features novel proposals for dynamic kernel bandwidth estimation for the background model, selective update of the background model, update of the position of reference samples of the foreground model using a multi-region particle filter, and automatic selection of regions of interest to reduce computational cost. The results, evaluated on several databases and compared to other state-of-the-art algorithms, demonstrate the high quality and versatility of our proposal. Finally, we propose a general method for the approximation of arbitrarily complex functions using continuous piecewise linear functions, specially formulated for GPU implementation by leveraging their texture filtering units, normally unused for numerical computation. Our proposal features a rigorous mathematical analysis of the approximation error in function of the number of samples, as well as a method to obtain a suboptimal partition of the domain of the function to minimize approximation error.

Space-state robust control of a Buck converter with amorphous core coil and variable load

Pulse-width modulation is widely used to control electronic converters. One of the most frequently used topologies for high DC voltage/low DC voltage conversion is the Buck converter. These converters are described by a second order system with an LC filter between the switching subsystem and the load. The use of a coil with an amorphous magnetic material core rather than an air core permits the design of smaller converters. If high switching frequencies are used to obtain high quality voltage output, then the value of the auto inductance L is reduced over time. Robust controllers are thus needed if the accuracy of the converter response must be preserved under auto inductance and payload variations. This paper presents a robust controller for a Buck converter based on a state space feedback control system combined with an additional virtual space variable which minimizes the effects of the inductance and load variations when a switching frequency that is not too high is applied. The system exhibits a null steady-state average error response for the entire range of parameter variations. Simulation results and a comparison with a standard PID controller are also presented.

Video analysis based vehicle detection and tracking using an MCMC sampling framework

This article presents a probabilistic method for vehicle detection and tracking through the analysis of monocular images obtained from a vehicle-mounted camera. The method is designed to address the main shortcomings of traditional particle filtering approaches, namely Bayesian methods based on importance sampling, for use in traffic environments. These methods do not scale well when the dimensionality of the feature space grows, which creates significant limitations when tracking multiple objects. Alternatively, the proposed method is based on a Markov chain Monte Carlo (MCMC) approach, which allows efficient sampling of the feature space. The method involves important contributions in both the motion and the observation models of the tracker. Indeed, as opposed to particle filter-based tracking methods in the literature, which typically resort to observation models based on appearance or template matching, in this study a likelihood model that combines appearance analysis with information from motion parallax is introduced. Regarding the motion model, a new interaction treatment is defined based on Markov random fields (MRF) that allows for the handling of possible inter-dependencies in vehicle trajectories. As for vehicle detection, the method relies on a supervised classification stage using support vector machines (SVM). The contribution in this field is twofold. First, a new descriptor based on the analysis of gradient orientations in concentric rectangles is dened. This descriptor involves a much smaller feature space compared to traditional descriptors, which are too costly for real-time applications. Second, a new vehicle image database is generated to train the SVM and made public. The proposed vehicle detection and tracking method is proven to outperform existing methods and to successfully handle challenging situations in the test sequences.

Applications for wireless sensor networks : tracking with binary proximity sensors

El interés cada vez mayor por las redes de sensores inalámbricos pueden ser entendido simplemente pensando en lo que esencialmente son: un gran número de pequeños nodos sensores autoalimentados que recogen información o detectan eventos especiales y se comunican de manera inalámbrica, con el objetivo final de entregar sus datos procesados a una estación base. Los nodos sensores están densamente desplegados dentro del área de interés, se pueden desplegar al azar y tienen capacidad de cooperación. Por lo general, estos dispositivos son pequeños y de bajo costo, de modo que pueden ser producidos y desplegados en gran numero aunque sus recursos en términos de energía, memoria, velocidad de cálculo y ancho de banda están enormemente limitados. Detección, tratamiento y comunicación son tres elementos clave cuya combinación en un pequeño dispositivo permite lograr un gran número de aplicaciones. Las redes de sensores proporcionan oportunidades sin fin, pero al mismo tiempo plantean retos formidables, tales como lograr el máximo rendimiento de una energía que es escasa y por lo general un recurso no renovable. Sin embargo, los recientes avances en la integración a gran escala, integrado de hardware de computación, comunicaciones, y en general, la convergencia de la informática y las comunicaciones, están haciendo de esta tecnología emergente una realidad. Del mismo modo, los avances en la nanotecnología están empezando a hacer que todo gire entorno a las redes de pequeños sensores y actuadores distribuidos. Hay diferentes tipos de sensores tales como sensores de presión, acelerómetros, cámaras, sensores térmicos o un simple micrófono. Supervisan las condiciones presentes en diferentes lugares tales como la temperatura, humedad, el movimiento, la luminosidad, presión, composición del suelo, los niveles de ruido, la presencia o ausencia de ciertos tipos de objetos, los niveles de tensión mecánica sobre objetos adheridos y las características momentáneas tales como la velocidad , la dirección y el tamaño de un objeto, etc. Se comprobara el estado de las Redes Inalámbricas de Sensores y se revisaran los protocolos más famosos. Así mismo, se examinara la identificación por radiofrecuencia (RFID) ya que se está convirtiendo en algo actual y su presencia importante. La RFID tiene un papel crucial que desempeñar en el futuro en el mundo de los negocios y los individuos por igual. El impacto mundial que ha tenido la identificación sin cables está ejerciendo fuertes presiones en la tecnología RFID, los servicios de investigación y desarrollo, desarrollo de normas, el cumplimiento de la seguridad y la privacidad y muchos más. Su potencial económico se ha demostrado en algunos países mientras que otros están simplemente en etapas de planificación o en etapas piloto, pero aun tiene que afianzarse o desarrollarse a través de la modernización de los modelos de negocio y aplicaciones para poder tener un mayor impacto en la sociedad. Las posibles aplicaciones de redes de sensores son de interés para la mayoría de campos. La monitorización ambiental, la guerra, la educación infantil, la vigilancia, la micro-cirugía y la agricultura son solo unos pocos ejemplos de los muchísimos campos en los que tienen cabida las redes mencionadas anteriormente. Estados Unidos de América es probablemente el país que más ha investigado en esta área por lo que veremos muchas soluciones propuestas provenientes de ese país. Universidades como Berkeley, UCLA (Universidad de California, Los Ángeles) Harvard y empresas como Intel lideran dichas investigaciones. Pero no solo EE.UU. usa e investiga las redes de sensores inalámbricos. La Universidad de Southampton, por ejemplo, está desarrollando una tecnología para monitorear el comportamiento de los glaciares mediante redes de sensores que contribuyen a la investigación fundamental en glaciología y de las redes de sensores inalámbricos. Así mismo, Coalesenses GmbH (Alemania) y Zurich ETH están trabajando en diversas aplicaciones para redes de sensores inalámbricos en numerosas áreas. Una solución española será la elegida para ser examinada más a fondo por ser innovadora, adaptable y polivalente. Este estudio del sensor se ha centrado principalmente en aplicaciones de tráfico, pero no se puede olvidar la lista de más de 50 aplicaciones diferentes que ha sido publicada por la firma creadora de este sensor específico. En la actualidad hay muchas tecnologías de vigilancia de vehículos, incluidos los sensores de bucle, cámaras de video, sensores de imagen, sensores infrarrojos, radares de microondas, GPS, etc. El rendimiento es aceptable, pero no suficiente, debido a su limitada cobertura y caros costos de implementación y mantenimiento, especialmente este ultimo. Tienen defectos tales como: línea de visión, baja exactitud, dependen mucho del ambiente y del clima, no se puede realizar trabajos de mantenimiento sin interrumpir las mediciones, la noche puede condicionar muchos de ellos, tienen altos costos de instalación y mantenimiento, etc. Por consiguiente, en las aplicaciones reales de circulación, los datos recibidos son insuficientes o malos en términos de tiempo real debido al escaso número de detectores y su costo. Con el aumento de vehículos en las redes viales urbanas las tecnologías de detección de vehículos se enfrentan a nuevas exigencias. Las redes de sensores inalámbricos son actualmente una de las tecnologías más avanzadas y una revolución en la detección de información remota y en las aplicaciones de recogida. Las perspectivas de aplicación en el sistema inteligente de transporte son muy amplias. Con este fin se ha desarrollado un programa de localización de objetivos y recuento utilizando una red de sensores binarios. Esto permite que el sensor necesite mucha menos energía durante la transmisión de información y que los dispositivos sean más independientes con el fin de tener un mejor control de tráfico. La aplicación se centra en la eficacia de la colaboración de los sensores en el seguimiento más que en los protocolos de comunicación utilizados por los nodos sensores. Las operaciones de salida y retorno en las vacaciones son un buen ejemplo de por qué es necesario llevar la cuenta de los coches en las carreteras. Para ello se ha desarrollado una simulación en Matlab con el objetivo localizar objetivos y contarlos con una red de sensores binarios. Dicho programa se podría implementar en el sensor que Libelium, la empresa creadora del sensor que se examinara concienzudamente, ha desarrollado. Esto permitiría que el aparato necesitase mucha menos energía durante la transmisión de información y los dispositivos sean más independientes. Los prometedores resultados obtenidos indican que los sensores de proximidad binarios pueden formar la base de una arquitectura robusta para la vigilancia de áreas amplias y para el seguimiento de objetivos. Cuando el movimiento de dichos objetivos es suficientemente suave, no tiene cambios bruscos de trayectoria, el algoritmo ClusterTrack proporciona un rendimiento excelente en términos de identificación y seguimiento de trayectorias los objetos designados como blancos. Este algoritmo podría, por supuesto, ser utilizado para numerosas aplicaciones y se podría seguir esta línea de trabajo para futuras investigaciones. No es sorprendente que las redes de sensores de binarios de proximidad hayan atraído mucha atención últimamente ya que, a pesar de la información mínima de un sensor de proximidad binario proporciona, las redes de este tipo pueden realizar un seguimiento de todo tipo de objetivos con la precisión suficiente. Abstract The increasing interest in wireless sensor networks can be promptly understood simply by thinking about what they essentially are: a large number of small sensing self-powered nodes which gather information or detect special events and communicate in a wireless fashion, with the end goal of handing their processed data to a base station. The sensor nodes are densely deployed inside the phenomenon, they deploy random and have cooperative capabilities. Usually these devices are small and inexpensive, so that they can be produced and deployed in large numbers, and so their resources in terms of energy, memory, computational speed and bandwidth are severely constrained. Sensing, processing and communication are three key elements whose combination in one tiny device gives rise to a vast number of applications. Sensor networks provide endless opportunities, but at the same time pose formidable challenges, such as the fact that energy is a scarce and usually non-renewable resource. However, recent advances in low power Very Large Scale Integration, embedded computing, communication hardware, and in general, the convergence of computing and communications, are making this emerging technology a reality. Likewise, advances in nanotechnology and Micro Electro-Mechanical Systems are pushing toward networks of tiny distributed sensors and actuators. There are different sensors such as pressure, accelerometer, camera, thermal, and microphone. They monitor conditions at different locations, such as temperature, humidity, vehicular movement, lightning condition, pressure, soil makeup, noise levels, the presence or absence of certain kinds of objects, mechanical stress levels on attached objects, the current characteristics such as speed, direction and size of an object, etc. The state of Wireless Sensor Networks will be checked and the most famous protocols reviewed. As Radio Frequency Identification (RFID) is becoming extremely present and important nowadays, it will be examined as well. RFID has a crucial role to play in business and for individuals alike going forward. The impact of ‘wireless’ identification is exerting strong pressures in RFID technology and services research and development, standards development, security compliance and privacy, and many more. The economic value is proven in some countries while others are just on the verge of planning or in pilot stages, but the wider spread of usage has yet to take hold or unfold through the modernisation of business models and applications. Possible applications of sensor networks are of interest to the most diverse fields. Environmental monitoring, warfare, child education, surveillance, micro-surgery, and agriculture are only a few examples. Some real hardware applications in the United States of America will be checked as it is probably the country that has investigated most in this area. Universities like Berkeley, UCLA (University of California, Los Angeles) Harvard and enterprises such as Intel are leading those investigations. But not just USA has been using and investigating wireless sensor networks. University of Southampton e.g. is to develop technology to monitor glacier behaviour using sensor networks contributing to fundamental research in glaciology and wireless sensor networks. Coalesenses GmbH (Germany) and ETH Zurich are working in applying wireless sensor networks in many different areas too. A Spanish solution will be the one examined more thoroughly for being innovative, adaptable and multipurpose. This study of the sensor has been focused mainly to traffic applications but it cannot be forgotten the more than 50 different application compilation that has been published by this specific sensor’s firm. Currently there are many vehicle surveillance technologies including loop sensors, video cameras, image sensors, infrared sensors, microwave radar, GPS, etc. The performance is acceptable but not sufficient because of their limited coverage and expensive costs of implementation and maintenance, specially the last one. They have defects such as: line-ofsight, low exactness, depending on environment and weather, cannot perform no-stop work whether daytime or night, high costs for installation and maintenance, etc. Consequently, in actual traffic applications the received data is insufficient or bad in terms of real-time owed to detector quantity and cost. With the increase of vehicle in urban road networks, the vehicle detection technologies are confronted with new requirements. Wireless sensor network is the state of the art technology and a revolution in remote information sensing and collection applications. It has broad prospect of application in intelligent transportation system. An application for target tracking and counting using a network of binary sensors has been developed. This would allow the appliance to spend much less energy when transmitting information and to make more independent devices in order to have a better traffic control. The application is focused on the efficacy of collaborative tracking rather than on the communication protocols used by the sensor nodes. Holiday crowds are a good case in which it is necessary to keep count of the cars on the roads. To this end a Matlab simulation has been produced for target tracking and counting using a network of binary sensors that e.g. could be implemented in Libelium’s solution. Libelium is the enterprise that has developed the sensor that will be deeply examined. This would allow the appliance to spend much less energy when transmitting information and to make more independent devices. The promising results obtained indicate that binary proximity sensors can form the basis for a robust architecture for wide area surveillance and tracking. When the target paths are smooth enough ClusterTrack particle filter algorithm gives excellent performance in terms of identifying and tracking different target trajectories. This algorithm could, of course, be used for different applications and that could be done in future researches. It is not surprising that binary proximity sensor networks have attracted a lot of attention lately. Despite the minimal information a binary proximity sensor provides, networks of these sensing modalities can track all kinds of different targets classes accurate enough.

A unified framework for linear function approximation of value functions in stochastic control

This paper contributes with a unified formulation that merges previ- ous analysis on the prediction of the performance ( value function ) of certain sequence of actions ( policy ) when an agent operates a Markov decision process with large state-space. When the states are represented by features and the value function is linearly approxi- mated, our analysis reveals a new relationship between two common cost functions used to obtain the optimal approximation. In addition, this analysis allows us to propose an efficient adaptive algorithm that provides an unbiased linear estimate. The performance of the pro- posed algorithm is illustrated by simulation, showing competitive results when compared with the state-of-the-art solutions.