Diseño y fabricación de un equipo de prácticas para el aprendizaje del proceso de sincronización de generadores síncronos a la red

La finalidad del proyecto es el diseño y la fabricación de un equipo de prácticas que permita a los alumnos ensayar el proceso de sincronización real de un generador síncrono a la red. El diseño consiste en un equipo de prácticas con el cual el alumno deberá acoplar el generador, previa verificación de la tensión, frecuencia y ángulo de fase con un sincronoscopio monofásico. Durante el proceso, el profesor podrá ir provocando errores de fase en las tensiones que el alumno deberá corregir. Al término del proceso, el alumno, si ha conseguido acoplar el generador, recibirá una calificación sobre diez en una pantalla LCD. Posteriormente se llevaran a cabo ensayos con alumnos voluntarios. ABSTRACT The purpose of the project is the design and manufacture of an equipment which allows students to perform the process of synchronization of a synchronous generator to the grid. The design consists of an equipment with which students must synchronize the generator to the grid, after checking voltage, frequency or phase angle with a single-phase synchronoscope. During that process, the teacher can cause phase angle errors in the voltage which students must solve. At the end of the process, if students have been able to synchronize the generator to the grid, they will receive a mark on an LCD screen. Afterwards a testing is going to be run by volunteers.

Synchronizing sound from different devices over a TCP network

Nowadays, we can send audio on the Internet for multiples uses like telephony, broadcast audio or teleconferencing. The issue comes when you need to synchronize the sound from different sources because the network where we are going to work could lose packets and introduce delay in the delivery. This can also come because the sound cards could be work in different speeds. In this project, we will work with two computers emitting sound (one will simulate the left channel (mono) of a stereo signal, and the other the right channel) and connected with a third computer by a TCP network. The last computer must get the sound from both computers and reproduce it in a speaker properly (without delay). So, basically, the main goal of the project is to synchronize multi-track sound over a network. TCP networks introduce latency into data transfers. Streaming audio suffers from two problems: a delay and an offset between the channels. This project explores the causes of latency, investigates the affect of the inter-channel offset and proposes a solution to synchronize the received channels. In conclusion, a good synchronization of the sound is required in a time when several audio applications are being developed. When two devices are ready to send audio over a network, this multi-track sound will arrive at the third computer with an offset giving a negative effect to the listener. This project has dealt with this offset achieving a good synchronization of the multitrack sound getting a good effect on the listener. This was achieved thanks to the division of the project into several steps having constantly a good vision of the problem, a good scalability and having controlled the latency at all times. As we can see in the chapter 4 of the project, a lack of synchronization over c. 100μs is audible to the listener. RESUMEN. A día de hoy, podemos transmitir audio a través de Internet por varios motivos como pueden ser: una llamada telefónica, una emisión de audio o una teleconferencia. El problema viene cuando necesitas sincronizar ese sonido producido por los diferentes orígenes ya que la red a la que nos vamos a conectar puede perder los paquetes y/o introducir un retardo en las entregas de los mismos. Así mismo, estos retardos también pueden venir producidos por las diferentes velocidades a las que trabajan las tarjetas de sonido de cada dispositivo. En este proyecto, se ha trabajado con dos ordenadores emitiendo sonido de manera intermitente (uno se encargará de simular el canal izquierdo (mono) de la señal estéreo emitida, y el otro del canal derecho), estando conectados a través de una red TCP a un tercer ordenador, el cual debe recibir el sonido y reproducirlo en unos altavoces adecuadamente y sin retardo (deberá juntar los dos canales y reproducirlo como si de estéreo de tratara). Así, el objetivo principal de este proyecto es el de encontrar la manera de sincronizar el sonido producido por los dos ordenadores y escuchar el conjunto en unos altavoces finales. Las redes TCP introducen latencia en la transferencia de datos. El streaming de audio emitido a través de una red de este tipo puede sufrir dos grandes contratiempos: retardo y offset, los dos existentes en las comunicaciones entre ambos canales. Este proyecto se centra en las causas de ese retardo, investiga el efecto que provoca el offset entre ambos canales y propone una solución para sincronizar los canales en el dispositivo receptor. Para terminar, una buena sincronización del sonido es requerida en una época donde las aplicaciones de audio se están desarrollando continuamente. Cuando los dos dispositivos estén preparados para enviar audio a través de la red, la señal de sonido multi-canal llegará al tercer ordenador con un offset añadido, por lo que resultará en una mala experiencia en la escucha final. En este proyecto se ha tenido que lidiar con ese offset mencionado anteriormente y se ha conseguido una buena sincronización del sonido multi-canal obteniendo un buen efecto en la escucha final. Esto ha sido posible gracias a una división del proyecto en diversas etapas que proporcionaban la facilidad de poder solucionar los errores en cada paso dando una importante visión del problema y teniendo controlada la latencia en todo momento. Como se puede ver en el capítulo 4 del proyecto, la falta de sincronización sobre una diferencia de 100μs entre dos canales (offset) empieza a ser audible en la escucha final.

Cifrado de imágenes digitales basado en teoría del caos: mapas logísticos

Las nuevas tendencias de compartir archivos multimedia a través de redes abiertas, demanda el uso de mejores técnicas de encriptación que garanticen la integridad, disponibilidad y confidencialidad, manteniendo y/o mejorando la eficiencia del proceso de cifrado sobre estos archivos. Hoy en día es frecuente la transferencia de imágenes a través de medios tecnológicos, siendo necesario la actualización de las técnicas de encriptación existentes y mejor aún, la búsqueda de nuevas alternativas. Actualmente los algoritmos criptográficos clásicos son altamente conocidos en medio de la sociedad informática lo que provoca mayor vulnerabilidad, sin contar los altos tiempos de procesamiento al momento de ser utilizados, elevando la probabilidad de ser descifrados y minimizando la disponibilidad inmediata de los recursos. Para disminuir estas probabilidades, el uso de la teoría de caos surge como una buena opción para ser aplicada en un algoritmo que tome partida del comportamiento caótico de los sistemas dinámicos, y aproveche las propiedades de los mapas logísticos para elevar el nivel de robustez en el cifrado. Es por eso que este trabajo propone la creación de un sistema criptográfico basado sobre una arquitectura dividida en dos etapas de confusión y difusión. Cada una de ellas utiliza una ecuación logística para generar números pseudoaleatorios que permitan desordenar la posición del píxel y cambiar su intensidad en la escala de grises. Este proceso iterativo es determinado por la cantidad total de píxeles de una imagen. Finalmente, toda la lógica de cifrado es ejecutada sobre la tecnología CUDA que permite el procesamiento en paralelo. Como aporte sustancial, se propone una nueva técnica de encriptación vanguardista de alta sensibilidad ante ruidos externos manteniendo no solo la confidencialidad de la imagen, sino también la disponibilidad y la eficiencia en los tiempos de proceso.---ABSTRACT---New trends to share multimedia files over open networks, demand the best use of encryption techniques to ensure the integrity, availability and confidentiality, keeping and/or improving the efficiency of the encryption process on these files. Today it is common to transfer pictures through technological networks, thus, it is necessary to update existing techniques encryption, and even better, the searching of new alternatives. Nowadays, classic cryptographic algorithms are highly known in the midst of the information society which not only causes greater vulnerability, but high processing times when this algorithms are used. It raise the probability of being deciphered and minimizes the immediate availability of resources. To reduce these odds, the use of chaos theory emerged as a good option to be applied on an algorithm that takes advantage of chaotic behavior of dynamic systems, and take logistic maps’ properties to raise the level of robustness in the encryption. That is why this paper proposes the creation of a cryptographic system based on an architecture divided into two stages: confusion and diffusion. Each stage uses a logistic equation to generate pseudorandom numbers that allow mess pixel position and change their intensity in grayscale. This iterative process is determined by the total number of pixels of an image. Finally, the entire encryption logic is executed on the CUDA technology that enables parallel processing. As a substantial contribution, it propose a new encryption technique with high sensitivity on external noise not only keeping the confidentiality of the image, but also the availability and efficiency in processing times.

Transiciones irreversibles en redes complejas

En esta tesis se aborda la emergencia de sincronización en sistemas de osciladores acoplados. En particular, nos centraremos en la emergencia de un tipo de transición discontinua entre el estado incoherente y el estado síncrono, llamada transición explosiva. Este fenómeno es análogo al de las transiciones de fase de primer orden asociadas a los cambios de agregación de la materia, cuya importancia abarca diversos campos, desde la sincronización espontánea de redes neuronales al riesgo de desincronización súbita entre los osciladores que componen la red de suministro de potencia eléctrica. Para analizar el problema, se introducen varios métodos de creciente generalidad cuyo efecto es inducir una transición explosiva al imponer una serie condiciones sobre la topología y las frecuencias naturales de cada oscilador. Así mismo, se aborda el estudio de un modelo algo más complejo con características similares para entender en mayor profundidad las características asociadas a este tipo de transiciones, siendo la histéresis una de las más destacadas. Finalmente, se propone un método cuantitativo para describir la importancia de cada nodo en el proceso de sincronización con el objetivo de estudiar y caracterizar el efecto sobre los nodos del sistema de los diversos métodos que inducen una transición explosiva. Este nuevo enfoque permite descubrir un proceso de frustración de la sincronización local en redes de osciladores acoplados, siendo el responsable de la emergencia de la sincronización explosiva. ABSTRACT In this thesis we address the emergence of synchronization in systems of coupled oscillators in complex networks. We focus our attention on a particular kind of discontinuous transitions, named explosive synchronization, where the system changes abruptly from an incoherent state to a synchronous state. This emergent phenomena is analogous to those first order transitions typically associated with changes among the aggregate states of matter, and it is important in many different fields, such as spontaneous synchronization of neurons or spontaneous desynchronization in power grids. To analyze it, we introduce some methods of increasing generality in order to induce such a discontinuous transition by acting over the topology and the natural frequencies in several different ways. Likewise, we address the study of a more complex model in order to acquire deeper knowledge on the properties of this kind of transitions, where a hysteretic behavior is specially relevant. Finally, we propose a new quantitative approach in order to find the importance of each node in the route to synchronization, aiming to provide a characterization of the effects over the network’s units of the different methods able to induce an explosive transition. This approach allows us to show the inner mechanisms behind such explosive behavior in networks of coupled oscillators, being rooted by a frustration of the local synchronization process previous to the emergence of global coherence.

Digital chaos synchronization in optical networks

A new method to obtain digital chaos synchronization between two systems is reported. It is based on the use of Optically Programmable Logic Cells as chaos generators. When these cells are feedbacked, periodic and chaotic behaviours are obtained. They depend on the ratio between internal and external delay times. Chaos synchronization is obtained if a common driving signal feeds both systems. A control to impose the same boundary conditions to both systems is added to the emitter. New techniques to analyse digital chaos are presented. The main application of these structures is to obtain secure communications in optical networks.

Experimental evidence of a hard transition to chaos

A generic, sudden transition to chaos has been experimentally verified using electronic circuits. The particular system studied involves the near resonance of two coupled oscillators at 2:1 frequency ratio when the damping of the first oscillator becomes negative. We identified in the experiment all types of orbits described by theory. We also found that a theoretical, ID limit map fits closely a map of the experimental attractor which, however, could be strongly disturbed by noise. In particular, we found noisy periodic orbits, in good agreement with noise theory.

Geometric diagnostics of complex patterns: Spiral defect chaos

Motivated by the observation of spiral patterns in a wide range of physical, chemical, and biological systems, we present an automated approach that aims at characterizing quantitatively spiral-like elements in complex stripelike patterns. The approach provides the location of the spiral tip and the size of the spiral arms in terms of their arc length and their winding number. In addition, it yields the number of pattern components (Betti number of order 1), as well as their size and certain aspects of their shape. We apply the method to spiral defect chaos in thermally driven Rayleigh- Bénard convection and find that the arc length of spirals decreases monotonically with decreasing Prandtl number of the fluid and increasing heating. By contrast, the winding number of the spirals is nonmonotonic in the heating. The distribution function for the number of spirals is significantly narrower than a Poisson distribution. The distribution function for the winding number shows approximately an exponential decay. It depends only weakly on the heating, but strongly on the Prandtl number. Large spirals arise only for larger Prandtl numbers. In this regime the joint distribution for the spiral length and the winding number exhibits a three-peak structure, indicating the dominance of Archimedean spirals of opposite sign and relatively straight sections. For small Prandtl numbers the distribution function reveals a large number of small compact pattern components.

Sequences of bifurcations and transition to chaos in an optical processing element

Digital chaotic behaviour in an Optical-Processing Element is reported. It is obtained as the result of processing two fixed trains of bits. Period doublings in a Feigenbaum-like scenario have been obtained. A new method to characterize digital chaos is reported

Determination of critical slip surfaces using mutative scale chaos optimization

Limit equilibrium is a common method used to analyze the stability of a slope, and minimization of the factor of safety or identification of critical slip surfaces is a classical geotechnical problem in the context of limit equilibrium methods for slope stability analyses. A mutative scale chaos optimization algorithm is employed in this study to locate the noncircular critical slip surface with Spencer’s method being employed to compute the factor of safety. Four examples from the literature—one homogeneous slope and three layered slopes—are employed to identify the efficiency and accuracy of this approach. Results indicate that the algorithm is flexible and that although it does not generally provide the minimum FS, it provides results that are close to the minimum, an improvement over other solutions proposed in the literature and with small relative errors with respect to other minimum factor of safety (FS) values reported in the literature.

Characterizing chaos in a type of fractional duffing's equation

We characterize the chaos in a fractional Duffing’s equation computing the Lyapunov exponents and the dimension of the strange attractor in the effective phase space of the system. We develop a specific analytical method to estimate all Lyapunov exponents and check the results with the fiduciary orbit technique and a time series estimation method.

Correction of systematic errors in Wide Area Multilateration

This work presents a method to estimate and correct slow time-dependent position errors due to non perfect ground station synchronization and tropospheric propagation. It uses opportunity traffic emissions, i.e. signals transmitted from the aircrafts within the coverage zone. This method is used to overcome the difficulty of installing reference beacons simultaneously visible by all the base stations in a given Wide Area Multilateration (WAM) system.

Reduced order adaptive models for systems of PDEs using POD

In this work we propose a method to accelerate time dependent numerical solvers of systems of PDEs that require a high cost in computational time and memory. The method is based on the combined use of such numerical solver with a proper orthogonal decomposition, from which we identify modes, a Galerkin projection (that provides a reduced system of equations) and the integration of the reduced system, studying the evolution of the modal amplitudes. We integrate the reduced model until our a priori error estimator indicates that our approximation in not accurate. At this point we use again our original numerical code in a short time interval to adapt the POD manifold and continue then with the integration of the reduced model. Application will be made to two model problems: the Ginzburg-Landau equation in transient chaos conditions and the two-dimensional pulsating cavity problem, which describes the motion of liquid in a box whose upper wall is moving back and forth in a quasi-periodic fashion. Finally, we will discuss a way of improving the performance of the method using experimental data or information from numerical simulations

Mixing Snapshots and Fast Time Integration of PDEs

A local proper orthogonal decomposition (POD) plus Galerkin projection method was recently developed to accelerate time dependent numerical solvers of PDEs. This method is based on the combined use of a numerical code (NC) and a Galerkin sys- tem (GS) in a sequence of interspersed time intervals, INC and IGS, respectively. POD is performed on some sets of snapshots calculated by the numerical solver in the INC inter- vals. The governing equations are Galerkin projected onto the most energetic POD modes and the resulting GS is time integrated in the next IGS interval. The major computa- tional e®ort is associated with the snapshots calculation in the ¯rst INC interval, where the POD manifold needs to be completely constructed (it is only updated in subsequent INC intervals, which can thus be quite small). As the POD manifold depends only weakly on the particular values of the parameters of the problem, a suitable library can be con- structed adapting the snapshots calculated in other runs to drastically reduce the size of the ¯rst INC interval and thus the involved computational cost. The strategy is success- fully tested in (i) the one-dimensional complex Ginzburg-Landau equation, including the case in which it exhibits transient chaos, and (ii) the two-dimensional unsteady lid-driven cavity problem

Reduced synchronization persistence in neural networks derived from atm-deficient mice

Many neurodegenerative diseases are characterized by malfunction of the DNA damage response. Therefore, it is important to understand the connection between system level neural network behavior and DNA. Neural networks drawn from genetically engineered animals, interfaced with micro-electrode arrays allowed us to unveil connections between networks’ system level activity properties and such genome instability. We discovered that Atm protein deficiency, which in humans leads to progressive motor impairment, leads to a reduced synchronization persistence compared to wild type synchronization, after chemically imposed DNA damage. Not only do these results suggest a role for DNA stability in neural network activity, they also establish an experimental paradigm for empirically determining the role a gene plays on the behavior of a neural network.

Analytical properties of horizontal visibility graphs in the Feigenbaum scenario

Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [B. Luque et al., PLoS ONE 6, 9 (2011)] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here, we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree distributions, mean distances, clustering coefficients, etc., associated to the bifurcation cascades and their accumulation points. We describe how the resultant families of graphs can be framed into a renormalization group scheme in which fixed-point graphs reveal their scaling properties. These fixed points are then re-derived from an entropy optimization process defined for the graph sets, confirming a suggested connection between renormalization group and entropy optimization. Finally, we provide analytical and numerical results for the graph entropy and show that it emulates the Lyapunov exponent of the map independently of its sign.