Dissertations / Theses on the topic 'Nonlinear Data processing'

In this abstract, we present a nonlinear curvelet-based sparsity promoting formulation of a seismic processing flow, consisting of the following steps: seismic data regularization and the restoration of migration amplitudes. We show that the curvelet’s wavefront detection capability and invariance under the migration-demigration operator lead to a formulation that is stable under noise and missing data.

In this abstract, we present a nonlinear curvelet-based sparsity-promoting formulation of a seismic processing flow, consisting of the following steps: seismic data regularization and the restoration of migration amplitudes. We show that the curvelet's wavefront detection capability and invariance under the migration-demigration operator lead to a formulation that is stable under noise and missing data.

This dissertation describes our recent results in the study of various types of photonic switches. Special attention is given to the devices with Fabry-Perot etalon or planar waveguide structures based on dispersive optical nonlinearities. Basic optical logic functions, such as digital pattern recognition, symbolic substitution, and all-optical compare-and-exchange operation are demonstrated using ZnS and ZnSe nonlinear interference filters. Differential gain, cascading, and optical latching circuits are demonstrated using GaAs/AlGaAs multiple-quantum-well nonlinear etalons that are compatible with diode-laser sources, and the relationship between differential gain and device response time is established through a thorough investigation of the switching dynamics. Preliminary results also indicate that optical fibers can be used as interconnects between optical logic gates. Picosecond all-optical switching with good (> 3:1) contrast is demonstrated for the first time in single-mode strip-loaded GaAs/AlGaAs nonlinear directional couplers (NLDC's). The anisotropy of quantum-well structure to light polarization is used to achieve polarization-dependent two-beam switching, and the optical Stark effect is used to demonstrate all-optical modulation in an NLDC with subpicosecond recovery time.

Nonlinear phenomena originating from the distributed coupling process were observed when distributed couplers, such as prisms and gratings, were used to couple light into nonlinear ZnS thin film waveguides. The efficiency of the nonlinear distributed coupling process was found to depend on two independent parameters, the angle of the incident beam and the power of the incident beam. Depending on the detuning of the incident angle, from the optimum incident angle at low powers, either optical limiting, power-dependent switching, or power-dependent bistability of the coupling efficiency, and thereby of the in-coupled power, was observed. At zero detuning, a twenty-fold decrease of the coupling efficiency with increasing powers was measured. At a nonzero detuning of the incident angle, power-dependent switching at milliwatt powers was observed. At larger angular detunings, corresponding to the angular width. FWHM, of the coupling peak at low powers, power-dependent bistability was observed, and the width of the bistability loop was found to increase with increasing detunings. All-optical beam scanning via a nonlinear grating coupler was also demonstrated, utilizing a control-signal beam configuration, where the signal beam scanned through an angle of 0.5° when the power of the control beam was varied. The observed nonlinearity in ZnS was positive and of thermal origin. The power-induced change in the refractive index was found to be 0.01 and a relaxation time of 10 μsec was measured. Problems with the long-term stability of the nonlinear distributed coupling process were traced to the occurrence of desorption and adsorption of water vapor in the ZnS films.

Thesis submitted in fulfilment of the requirements for the degree Doctor of Technology: Electrical Engineering in the Faculty of Engineering at the Cape Peninsula University of Technology 2014
This thesis focuses on the design, development and real-time simulation of a robust nonlinear networked control for the dissolved oxygen concentration as part of the wastewater distributed systems. This concept differs from previous methods of wastewater control in the sense that the controller and the wastewater treatment plants are separated by a wide geographical distance and exchange data through a communication medium. The communication network introduced between the controller and the DO process creates imperfections during its operation, as time delays which are an object of investigation in the thesis. Due to the communication network imperfections, new control strategies that take cognisance of the network imperfections in the process of the controller design are needed to provide adequate robustness for the DO process control system. This thesis first investigates the effects of constant and random network induced time delays and the effects of controller parameters on the DO process behaviour with a view to using the obtained information to design an appropriate controller for the networked closed loop system. On the basis of the above information, a Smith predictor delay compensation controller is developed in the thesis to eliminate the deadtime, provide robustness and improve the performance of the DO process. Two approaches are adopted in the design of the Smith predictor compensation scheme. The first is the transfer function approach that allows a linearized model of the DO process to be described in the frequency domain. The second one is the nonlinear linearising approach in the time domain. Simulation results reveal that the developed Smith predictor controllers out-performed the nonlinear linearising controller designed for the DO process without time delays by compensating for the network imperfections and maintaining the DO concentration within a desired acceptable level. The transfer function approach of designing the Smith predictor is found to perform better under small time delays but the performance deteriorates under large time delays and disturbances. It is also found to respond faster than the nonlinear approach. The nonlinear feedback linearisig approach is slower in response time but out-performs the transfer function approach in providing robustness and performance for the DO process under large time delays and disturbances. The developed Smith predictor compensation schemes were later simulated in a real-time platform using LabVIEW. The Smith predictor controllers developed in this thesis can be applied to other process control plants apart from the wastewater plants, where distributed control is required. It can also be applied in the nuclear reactor plants where remote control is required in hazardous conditions. The developed LabVIEW real-time simulation environment would be a valuable tool for researchers and students in the field of control system engineering. Lastly, this thesis would form the basis for further research in the field of distributed wastewater control.

Solving nonlinear systems of equations is a central problem in numerical analysis, with enormous significance for science and engineering. A special case, sparse systems of equations, occurs frequently in various applications. Sparsity occurs in the analysis of many types of complex systems because of the local nature of the dependence or connectivity among system components. One such system which may be modeled by a nonlinear sparse set of equations is the power system load flow analysis. This is a mathematical study performed by electrical utilities to monitor the electrical power system. The data from system components are used to create a set of nonlinear equations. These equations are then solved to find the voltage profile of the power network. With these data, control and security of the power system are achieved. Solving problems of this type is very time consuming when the system is large. This dissertation proposes a highly parallel computer architecture for solving large sets of nonlinear sparse equations. The goal of this architecture is to reduce the processing time required to solve this type of problem. In particular, the load flow problem is analyzed and implemented on this architecture. For the FPL network, the speed is increased by a factor of about 2000.

Since the discovery of optical bistability a considerable amount of research activity has been aimed toward the realization of general-purpose all-optical computers. The basic premise for most of this work is the widely held notion that a reliable optical switch can be fabricated from a piece of optically bistable material. To date only a very small number of published articles have addressed the subject of the engineering issues (that is, the optimization and tolerancing) of these optical switches. This dissertation is a systematic treatment of these issues. From the starting point of Maxwell's equations a simple model of optically bistable Fabry-Perot etalons is outlined, in which the material is assumed to be a pure Kerr medium having linear absorption. This model allows for a relatively straightforward optical switch optimization procedure. The procedure is applicable for optimizing any number of switch parameters. The emphasis in this dissertation is on the optimization of the contrast of the switch's output signals, with the other parameters (switching energy, tolerance sensitivity) assuming a secondary yet critical role. Following the optimization of the optical switch is a tolerance analysis which addresses the manufacturability and noise immunity of the optimized switch. In the first part of this analysis equations describing the propagation of errors through a large scale system of like devices are derived from the truth tables of the switches themselves. From these equations worst case tolerances are established on the optical switch's transfer function parameters. In the second part of the tolerance analysis the bistability model is used to arrive at tolerances on the physical parameters of the switch. These tolerances are what determine the manufacturability of the optical switches. The major conclusion of the dissertation is that, within the range of validity of the model and the other simplifying assumptions, optically bistable Fabry-Perot etalons cannot be used reliably as logic gates in large-scale computing systems.

A finite element program is developed to depict the behavior of a sheet pile interlock connection in an axial pull test. Two types of sheet piles, PS32 and PSX32, are considered. The thumb and finger in the interlock of a sheet pile will provide three contact points for connection with another sheet pile. The problem is highly nonlinear in nature which involves large deflections and rotations, elastic-plastic material response, and a nonlinear boundary effect due to multi-contact surfaces. The Updated Lagrangian formulation is adopted in this study. When the response is in elastic range the Updated Lagrangian with Transformation is used while the Updated Lagrangian with Jaumann stress rate is employed when the element starts to yield. An elastic-plastic with isotropic strain hardening material model is used. The yielding of an element is detected by the Von Mises yield criterion. The finite element formulation also includes a moving contact algorithm to incorporate with both geometric and material nonlinearities. Incremental potential of contact forces for a discretized system is constructed such that geometric compatibilities are maintained between contacting bodies. A method to calculate contact tractions from residual load of internal element stresses is employed. The incremental equilibrium equation is solved by a Newton-Raphson technique. Convergence criteria based on incremental displacement, incremental internal energy of the system, and the changes in contact forces can be chosen to advance or terminate the iteration process.
Ph. D.

The effect of structural optimization on control of stiffened laminated composite structures is considered. The structural optimization considered here, is the maximization of structural frequencies of the structure subject to maximum weight and frequency separation constraints and an upper bound on weight. The number of plies with a given orientation and the stiffener areas form the two sets of design variables. As the number of plies is restricted to integer values, the optimization problem considered belongs to the class of nonlinear mixed integer problems (NMIP). Several efficiency measures are proposed to reduce the computational cost for solution of the optimization problem. Savings in computer time due to each of the measures is discussed. The control problem is solved using the independent modal space control technique. This technique greatly simplifies the evaluation of the sensitivity of the performance index with respect to the individual frequencies. The effect of different optimization schemes on the control performance is considered. To reduce the probability, that conclusions drawn from numerical results, are purely coincidental, a large number of cases has been studied. It has been concluded that sufficient improvement in control performance can be achieved through structural optimization.
Ph. D.

Thesis (M. S.)--Aerospace Engineering, Georgia Institute of Technology, 2008.
Committee Chair: Eric N. Johnson; Committee Co-Chair: Allen R. Tannenbaum; Committee Member: Anthony J. Calise; Committee Member: Eric Feron; Committee Member: Patricio A. Vela.

Estimation of the ground motion parameters is extremely important for engineers to make the structures safer and more economical, so it is one of the main issues of Earthquake Engineering. Peak values of the ground motions obtained either from existing records or with the help of attenuation relationships, have been used as a useful parameter to estimate the effect of an earthquake on a specific location. Peak Ground Velocities (PGV) of a ground motion is used extensively in the recent years as a measure of intensity and as the primary source of energy-related analysis of structures. Consequently, PGV values are used to construct emergency response systems like Shake Maps or to determine the deformation demands of structures. Despite the importance of the earthquakes for Turkey, there is a lack of suitable attenuation relationships for velocity developed specifically for the country. The aim of this study is to address this deficiency by developing an attenuation relationship for the Peak Ground Velocities of the chosen database based on the strong ground motion records of Turkey. A database is processed with the established techniques and corrected database for the chosen ground motions is formed. Five different forms of equations that were used in the previous studies are selected to be used as models and by using nonlinear regression analysis, best fitted mathematical relation for attenuation is obtained. The result of this study can be used as an effective tool for seismic hazard assessment studies for Turkey. Besides, being a by-product of this study, a corrected database of strong ground motion recordings of Turkey may prone to be a valuable source for the future researchers.

Im Mittelpunkt dieser Arbeit stehen virtuelle 3D-Stadtmodelle, die Objekte, Phänomene und Prozesse in urbanen Räumen in digitaler Form repräsentieren. Sie haben sich zu einem Kernthema von Geoinformationssystemen entwickelt und bilden einen zentralen Bestandteil geovirtueller 3D-Welten. Virtuelle 3D-Stadtmodelle finden nicht nur Verwendung als Mittel für Experten in Bereichen wie Stadtplanung, Funknetzplanung, oder Lärmanalyse, sondern auch für allgemeine Nutzer, die realitätsnah dargestellte virtuelle Städte in Bereichen wie Bürgerbeteiligung, Tourismus oder Unterhaltung nutzen und z. B. in Anwendungen wie GoogleEarth eine räumliche Umgebung intuitiv erkunden und durch eigene 3D-Modelle oder zusätzliche Informationen erweitern. Die Erzeugung und Darstellung virtueller 3D-Stadtmodelle besteht aus einer Vielzahl von Prozessschritten, von denen in der vorliegenden Arbeit zwei näher betrachtet werden: Texturierung und Visualisierung. Im Bereich der Texturierung werden Konzepte und Verfahren zur automatischen Ableitung von Fototexturen aus georeferenzierten Schrägluftbildern sowie zur Speicherung oberflächengebundener Daten in virtuellen 3D-Stadtmodellen entwickelt. Im Bereich der Visualisierung werden Konzepte und Verfahren für die multiperspektivische Darstellung sowie für die hochqualitative Darstellung nichtlinearer Projektionen virtueller 3D-Stadtmodelle in interaktiven Systemen vorgestellt. Die automatische Ableitung von Fototexturen aus georeferenzierten Schrägluftbildern ermöglicht die Veredelung vorliegender virtueller 3D-Stadtmodelle. Schrägluftbilder bieten sich zur Texturierung an, da sie einen Großteil der Oberflächen einer Stadt, insbesondere Gebäudefassaden, mit hoher Redundanz erfassen. Das Verfahren extrahiert aus dem verfügbaren Bildmaterial alle Ansichten einer Oberfläche und fügt diese pixelpräzise zu einer Textur zusammen. Durch Anwendung auf alle Oberflächen wird das virtuelle 3D-Stadtmodell flächendeckend texturiert. Der beschriebene Ansatz wurde am Beispiel des offiziellen Berliner 3D-Stadtmodells sowie der in GoogleEarth integrierten Innenstadt von München erprobt. Die Speicherung oberflächengebundener Daten, zu denen auch Texturen zählen, wurde im Kontext von CityGML, einem international standardisierten Datenmodell und Austauschformat für virtuelle 3D-Stadtmodelle, untersucht. Es wird ein Datenmodell auf Basis computergrafischer Konzepte entworfen und in den CityGML-Standard integriert. Dieses Datenmodell richtet sich dabei an praktischen Anwendungsfällen aus und lässt sich domänenübergreifend verwenden. Die interaktive multiperspektivische Darstellung virtueller 3D-Stadtmodelle ergänzt die gewohnte perspektivische Darstellung nahtlos um eine zweite Perspektive mit dem Ziel, den Informationsgehalt der Darstellung zu erhöhen. Diese Art der Darstellung ist durch die Panoramakarten von H. C. Berann inspiriert; Hauptproblem ist die Übertragung des multiperspektivischen Prinzips auf ein interaktives System. Die Arbeit stellt eine technische Umsetzung dieser Darstellung für 3D-Grafikhardware vor und demonstriert die Erweiterung von Vogel- und Fußgängerperspektive. Die hochqualitative Darstellung nichtlinearer Projektionen beschreibt deren Umsetzung auf 3D-Grafikhardware, wobei neben der Bildwiederholrate die Bildqualität das wesentliche Entwicklungskriterium ist. Insbesondere erlauben die beiden vorgestellten Verfahren, dynamische Geometrieverfeinerung und stückweise perspektivische Projektionen, die uneingeschränkte Nutzung aller hardwareseitig verfügbaren, qualitätssteigernden Funktionen wie z.~B. Bildraumgradienten oder anisotroper Texturfilterung. Beide Verfahren sind generisch und unterstützen verschiedene Projektionstypen. Sie ermöglichen die anpassungsfreie Verwendung gängiger computergrafischer Effekte wie Stilisierungsverfahren oder prozeduraler Texturen für nichtlineare Projektionen bei optimaler Bildqualität. Die vorliegende Arbeit beschreibt wesentliche Technologien für die Verarbeitung virtueller 3D-Stadtmodelle: Zum einen lassen sich mit den Ergebnissen der Arbeit Texturen für virtuelle 3D-Stadtmodelle automatisiert herstellen und als eigenständige Attribute in das virtuelle 3D-Stadtmodell einfügen. Somit trägt diese Arbeit dazu bei, die Herstellung und Fortführung texturierter virtueller 3D-Stadtmodelle zu verbessern. Zum anderen zeigt die Arbeit Varianten und technische Lösungen für neuartige Projektionstypen für virtueller 3D-Stadtmodelle in interaktiven Visualisierungen. Solche nichtlinearen Projektionen stellen Schlüsselbausteine dar, um neuartige Benutzungsschnittstellen für und Interaktionsformen mit virtuellen 3D-Stadtmodellen zu ermöglichen, insbesondere für mobile Geräte und immersive Umgebungen.
This thesis concentrates on virtual 3D city models that digitally encode objects, phenomena, and processes in urban environments. Such models have become core elements of geographic information systems and constitute a major component of geovirtual 3D worlds. Expert users make use of virtual 3D city models in various application domains, such as urban planning, radio-network planning, and noise immision simulation. Regular users utilize virtual 3D city models in domains, such as tourism, and entertainment. They intuitively explore photorealistic virtual 3D city models through mainstream applications such as GoogleEarth, which additionally enable users to extend virtual 3D city models by custom 3D models and supplemental information. Creation and rendering of virtual 3D city models comprise a large number of processes, from which texturing and visualization are in the focus of this thesis. In the area of texturing, this thesis presents concepts and techniques for automatic derivation of photo textures from georeferenced oblique aerial imagery and a concept for the integration of surface-bound data into virtual 3D city model datasets. In the area of visualization, this thesis presents concepts and techniques for multiperspective views and for high-quality rendering of nonlinearly projected virtual 3D city models in interactive systems. The automatic derivation of photo textures from georeferenced oblique aerial imagery is a refinement process for a given virtual 3D city model. Our approach uses oblique aerial imagery, since it provides a citywide highly redundant coverage of surfaces, particularly building facades. From this imagery, our approach extracts all views of a given surface and creates a photo texture by selecting the best view on a pixel level. By processing all surfaces, the virtual 3D city model becomes completely textured. This approach has been tested for the official 3D city model of Berlin and the model of the inner city of Munich accessible in GoogleEarth. The integration of surface-bound data, which include textures, into virtual 3D city model datasets has been performed in the context of CityGML, an international standard for the exchange and storage of virtual 3D city models. We derive a data model from a set of use cases and integrate it into the CityGML standard. The data model uses well-known concepts from computer graphics for data representation. Interactive multiperspective views of virtual 3D city models seamlessly supplement a regular perspective view with a second perspective. Such a construction is inspired by panorama maps by H. C. Berann and aims at increasing the amount of information in the image. Key aspect is the construction's use in an interactive system. This thesis presents an approach to create multiperspective views on 3D graphics hardware and exemplifies the extension of bird's eye and pedestrian views. High-quality rendering of nonlinearly projected virtual 3D city models focuses on the implementation of nonlinear projections on 3D graphics hardware. The developed concepts and techniques focus on high image quality. This thesis presents two such concepts, namely dynamic mesh refinement and piecewise perspective projections, which both enable the use of all graphics hardware features, such as screen space gradients and anisotropic texture filtering under nonlinear projections. Both concepts are generic and customizable towards specific projections. They enable the use of common computer graphics effects, such as stylization effects or procedural textures, for nonlinear projections at optimal image quality and interactive frame rates. This thesis comprises essential techniques for virtual 3D city model processing. First, the results of this thesis enable automated creation of textures for and their integration as individual attributes into virtual 3D city models. Hence, this thesis contributes to an improved creation and continuation of textured virtual 3D city models. Furthermore, the results provide novel approaches to and technical solutions for projecting virtual 3D city models in interactive visualizations. Such nonlinear projections are key components of novel user interfaces and interaction techniques for virtual 3D city models, particularly on mobile devices and in immersive environments.

For the first time in human history, large volumes of spoken audio are being broadcast, made available on the internet, archived, and monitored for surveillance every day. New technologies are urgently required to unlock these vast and powerful stores of information. Spoken Term Detection (STD) systems provide access to speech collections by detecting individual occurrences of specified search terms. The aim of this work is to develop improved STD solutions based on phonetic indexing. In particular, this work aims to develop phonetic STD systems for applications that require open-vocabulary search, fast indexing and search speeds, and accurate term detection. Within this scope, novel contributions are made within two research themes, that is, accommodating phone recognition errors and, secondly, modelling uncertainty with probabilistic scores. A state-of-the-art Dynamic Match Lattice Spotting (DMLS) system is used to address the problem of accommodating phone recognition errors with approximate phone sequence matching. Extensive experimentation on the use of DMLS is carried out and a number of novel enhancements are developed that provide for faster indexing, faster search, and improved accuracy. Firstly, a novel comparison of methods for deriving a phone error cost model is presented to improve STD accuracy, resulting in up to a 33% improvement in the Figure of Merit. A method is also presented for drastically increasing the speed of DMLS search by at least an order of magnitude with no loss in search accuracy. An investigation is then presented of the effects of increasing indexing speed for DMLS, by using simpler modelling during phone decoding, with results highlighting the trade-off between indexing speed, search speed and search accuracy. The Figure of Merit is further improved by up to 25% using a novel proposal to utilise word-level language modelling during DMLS indexing. Analysis shows that this use of language modelling can, however, be unhelpful or even disadvantageous for terms with a very low language model probability. The DMLS approach to STD involves generating an index of phone sequences using phone recognition. An alternative approach to phonetic STD is also investigated that instead indexes probabilistic acoustic scores in the form of a posterior-feature matrix. A state-of-the-art system is described and its use for STD is explored through several experiments on spontaneous conversational telephone speech. A novel technique and framework is proposed for discriminatively training such a system to directly maximise the Figure of Merit. This results in a 13% improvement in the Figure of Merit on held-out data. The framework is also found to be particularly useful for index compression in conjunction with the proposed optimisation technique, providing for a substantial index compression factor in addition to an overall gain in the Figure of Merit. These contributions significantly advance the state-of-the-art in phonetic STD, by improving the utility of such systems in a wide range of applications.

Dans le monde industriel comme dans le monde scientifique, le développement de capteurs a toujours répondu à la volonté d’observer l’inobservable. La caméra rapide fait partie de ceux-là puisqu’elle permet de dévoiler des dynamiques invisibles, de la formation de fissure au vol du moustique. Dans un environnement extrêmement concurrentiel, ces caméras sont principalement limitées par le nombre d’images acquises par seconde. Le but de cette thèse est d’augmenter la capacité de dévoiler la dynamique invisible en enrichissant l’acquisition initiale par des modèles dynamiques. La problématique consiste alors à élaborer des méthodes permettant de relier en temps réel un modèle et la perception d’un système réel. Les bénéfices de cette utilisation offrent ainsi la possibilité de faire de l’interpolation, de la prédiction et de l’identification. Cette thèse est composée de trois parties. La première est axée sur la philosophie du traitement vidéo et propose d’utiliser des modèles élémentaires et génériques. Un algorithme d’estimation de grands mouvements est proposé mais l’approche actuellement proposée n’est pas assez générique pour être exploitée dans un contexte industriel. La deuxième partie propose d’utiliser des méthodes d’assimilation de données séquentielle basées sur la famille des filtres de Kalman afin d’associer un modèle avec des observations par caméras rapides pour des systèmes mécaniques. La troisième partie est une application à l’analyse modale expérimentale non linéaire. Deux schémas d’assimilation temps réel multicapteurs sont présentés et leur mise en œuvre est illustrée pour de la reconstruction 3D et de la magnification
The development of sensors has always followed the ambition of industrial and scientific people to observe the unobservable. High speed cameras are part of this adventure, revealing invisible dynamics such as cracks formation or subtle mosquito flight. Industrial high speed vision is a very competitive domain in which cameras stand out through their acquisition speed. This thesis aims to broaden their capacity by augmenting the initial acquisition with dynamic models. This work proposes to develop methods linking in real time a model with a real system. Aimed benefits are interpolation, prediction and identification. Three parts are developed. The first one is based on video processing and submits to use kinematic elementary and generic models. An algorithm of motion estimation for large movements is proposed but the generic nature does not allow a sufficient knowledge to be conclusive. The second part proposes using sequential data assimilation methods known as Kalman filters. A scheme to assimilate video data with a mechanical model is successfully implemented. An application of data assimilation in modal analysis is developed. Two multi sensors real time assimilation schemes for nonlinear modal identification are proposed. These schemes are integrated in two applications on 3D reconstruction and motion magnification

Thesis (Ph. D.)--Aerospace Engineering, Georgia Institute of Technology, 2008.
Committee Chair: Johnson, Eric; Committee Co-Chair: Calise, Anthony; Committee Member: Prasad, J.V.R.; Committee Member: Tannenbaum, Allen; Committee Member: Tsiotras, Panagiotis.

Cette thèse propose des solutions aux problématiques inhérentes au contrôle de formations aériennes de type leader­-suiveur pour des flottes de quadrirotors. Au regard des travaux existants, les stratégies qui sont proposés dans notre travail, considère que le(s) leader{s) a une interaction avec les suiveurs. En outre, les rôles de leader et de suiveur sont interchangeables lors de la formation. Dans un premier temps, la modélisation mathématique d'un seul quadrirotor et celle de la formation de quadrirotors est développée. Ensuite, le problème de suivi de trajectoire pour un seul quadrirotor est étudié. Au travers de l'analyse de 1, dynamique du système pour la conception d'une commande par platitude, il apparait que le suivi de trajectoire pour chaque quadrirotor équivaut à déterminer les sorties plates désirées. Un contrôleur pour système plats permettant l'asservissement des drones pour le suivi de trajectoire est donc proposé. Étant donné la propriété de double-boucle de la dynamique du quadrirotor en boucle fermée, un contrôleur d'attitude avec des grands gains est conçu, selon la théorie « singular perturbation system ». Puisque la dynamique du quadrirotor en boucle fermée fonctionne sur deux échelles de temps, la dynamique de rotation (boundary-layer mode) est contrôlée sur l'échelle de temps la plus rapide. La conception du contrôleur de formation dépend seulement de la dynamique de translation (modèle réduit dans une échelle de temps lente). Ce résultat a simplifié la conception du contrôleur de formation, de telle sorte que le modèle réduit du quadrirotor est utilisé au lieu du modèle complet. Étant donné que le modèle réduit du quadrirotor a une caractéristique de double-intégrateur, un algorithme de consensus pour des systèmes caractérisés par de multiple double-intégrateurs est proposé. Pour traiter le problème de la formation leader-suiveur, une matrice d'interaction est initialement proposée basée sur la matrice de Laplacienne. Nous montrons que la condition de convergence et la vitesse de convergence de l'erreur de formation dépendent de la plus petite valeur propre de la matrice d'interaction. Trois stratégies de contrôle de la formation avec une topologie fixe sont ensuite proposées. Le contrôle de formation par platitude est proposé pour obtenir une formation agressive, tandis que les dérivées de grands ordres de la trajectoire désirée pour chaque UAV sont estimées en utilisant un observateur; la méthode Lyapunov redesign est implémentée pour traiter les non-linéarités de la dynamique de la translation des quadrotors; une loi de commande bornée par l'utilisation, entre autre, de la fonction tangente hyperbolique est développée avec un feedback composite non linéaire, afin d'améliorer les performances de la formation. De plus, une commande de commutation saturée de la formation est étudiée, car la topologie de la formation est variable. La stabilité du système est obtenue grâce aux théories “convex hull » et « common Lyapunov function ». Cette stratégie de commande de commutation permet le changement des leaders dans la formation. Inspirée par certains travaux existants, tels que le contrôle de la formation avec des voisins anonymes, nous proposons, finalement, une loi de commande avec des voisins pondérés, qui montre une meilleure robustesse que le contrôle avec des voisins anonymes. Les résultats de simulation obtenus avec Matlab illustrent premièrement nos stratégies de contrôle que nous proposons De plus, en utilisant le langage de programmation C ++, nos stratégies sont mises en œuvre dans un framework de simulation et d'expérimentation développé au laboratoire Heudiasyc. Grâce aux nombreux tests variés que nous avons réalisés en simulation et en temps-réel, l'efficacité et les avantages de nos stratégies de contrôle de la formation proposées sont présentés
In this thesis, we address a leader-follower (L-F) formation control problem for multiple UAVs, especially quadrotors. Different from existing works, the strategies, which are proposed in our work, consider that the leader(s) have interaction with the followers. Additionally, the leader(s) are changeable during the formation. First, the mathematical modeling of a single quadrotor and of the formation of quadrotors is developed. The trajectory tracking problem for a single quadrotor is investigated. Through the analysis of the flatness of the quadrotor dynamical model, the desired trajectory for each quadrotor is transferred to the design of the desired at outputs. A flatness-based trajectory tracking controller is, then, proposed. Considering the double-loop property of the closed-loop quadrotor dynamics, a high-gain attitude controller is designed, according to the singular perturbation system theory. Since the closed-loop quadrotor dynamics performs in two time scales, the rotational dynamics (boundary-layer model) is controlled in a fast time scale. The formation controller design is then only considered for the translational dynamics: reduced model in a slow time scale. This result has simplified the formation controller design such that the reduced model of the quadrotor is considered instead of the complete model. Since the reduced model of the quadrotor has a double-integrator characteristic, consensus algorithm for multiple double-integrator systems is proposed. Dealing with the leader-follower formation problem, an interaction matrix is originally proposed based on the Laplacian matrix. We prove that the convergence condition and convergence speed of the formation error are in terms of the smallest eigenvalue of the interaction matrix. Three formation control strategies with fixed formation topology are then proposed. The flatness-based formation control is proposed to deal with the aggressive formation problem, while the high-order derivatives of the desired trajectory for each UAV are estimated by using an observer; the Lyapunov redesign is developed to deal with the nonlinearities of the translational dynamics of the quadrotors; the hyperbolic tangent-based bounded control with composite nonlinear feedback is developed in order to improve the performance of the formation. In an additional way, a saturated switching control of the formation is investigated, where the formation topology is switching. The stability of the system is obtained by introducing the convex hull theory and the common Lyapunov function. This switching control strategy permits the change of the leaders in the formation. Inspired by some existing works, such as the anonymous neighbor-based formation control, we finally propose a weighted neighbor-based control, which shows better robustness than the anonymous neighbor-based control. Simulation results using Matlab primarily illustrate our proposed formation control strategies. Furthermore, using C++ programming, our strategies are implemented on the simulator-experiment framework, developed at Heudiasyc laboratory. Through a variety of tests on the simulator and real-time experiments, the efficiency and the advantages of our proposed formation control strategies are shown. Finally, a vision-based inter-distance detection system is developed. This system is composed by an on-board camera, infrared LEDs and an infrared filter. The idea is to detect the UAVs and calculate the inter-distance by calculating the area of the special LEDs patterns. This algorithm is validated on a PC, with a webcam and primarily implemented on a real quadrotor

Nous nous intéressons à la phénoménologie des villes en nous limitant à la géométrie induite par le squelette de leur réseau de rues. C'est une étude à volonté synthétique, fonctionnelle et interdisciplinaire qui vient s'ajouter aux travaux qui ont été menés à grande cadence depuis le début du XXème siècle par des urbanistes, sociologues, géographes, statisticiens, physiciens. Nous cherchons à montrer que la rue, en tant qu'alignement cohérent de segments de rues peut être considérée comme structure élémentaire de la ville. Quelle quantité d'information est donnée par la géométrie du réseau routier ? Dans quelle mesure contraint-il nos échanges ? Comment le paysage urbain actuel est-il déterminé par son évolution le long d'axes de circulation et d'éléments structurants ? Nous présentons un cadre mathématique permettant de considérer la carte d'une ville comme un continuum géométrique défi ni par la topologie d'un graphe planaire. Nous superposons à ce graphe une structure d'hypergraphe pour manipuler aisément la notion d'axes ainsi qu'une représentation multi-échelles de la ville. En dépit d'une grande diversité apparente de formes, nous montrons que le réseau de rues d'une ville se soumet à un certain nombre de lois générales qui laissent des traces sur le plan de la ville. Nous proposons des modèles de croissance et de morphogénèse de la ville, implé- mentant l'idée que l'évolution de la ville suit une logique d'extension / division structurée de l'espace et reproduisant les signatures observées sur les plans de villes réelles. La compréhension des mécanismes régulateurs de la ville nous permet de proposer des algorithmes fonctionnels dont le temps de calcul est très intéressant. Ainsi nous présentons un algorithme reconstituant les rues à partir de segments de rues ; la notion de centralité simple dont le calcul sur une carte permet une analyse hiérarchique de celle-ci, met en valeur les axes de trafic principaux et en évidence les zones mal desservies ; un algorithme permettant d'approximer rapidement le plus court chemin entre deux points aléatoires ; un algorithme prenant appui sur le Spectral Clustering pour produire des segmentations morphologiques de cartes et retravaillons l'identi cation de modèles de mosaïques aléatoires pour les substituer à un réseau urbain particulier dans la résolution par équivalents statistiques de grands problèmes d'optimisation.

The reported results are direct applications of nonlinear dynamics to information processing or are relevant for the applications. In the second chapter we describe a simple method for estimating the embedding dimension that can be used as a first step in constructing nonlinear models. The method for the reduction of measurement noise in chaotic systems that is presented in the third chapter is attractive in the cases where high accuracy is necessary. Next we propose how to overcome some problems encountered in constructing models of complex nonlinear systems. Finally, the behaviour of one-dimensional cellular automata useful for the detection of velocities of patterns is shown and explained in the last chapter. The method of estimating the embedding dimension is based on the idea that when the observed dynamical system is deterministic and smooth and the embedding dimension is correctly chosen, the relationship between the successive reconstructed state vectors should be described as a continuous mapping. To check if the given embedding dimension is a good one we search for pairs of state vectors whose distance is smaller than some number. For each pair we compute the distance between the successors of the elements of pairs and represent this distance graphically. When the embedding dimension is equal or larger than the minimum correct dimension, all distances are small in comparison to distances for incorrect dimensions. The method for noise reduction is developed assuming that the map of the system is known and the noise is bounded. The closer the initial condition is to the true state of the system, the longer the computed trajectory follows the observed trajectory. To reduce the uncertainty in knowing the given state we recursively search for the state for which the computed trajectory follows the observed trajectory as long as possible. The method is demonstrated on several twodimensional invertible and noninvertible chaotic maps. When the map is known exactly an arbitrary level of noise reduction can be achieved. With the increase of the complexity of a nonlinear system it is harder to construct its model. We propose to discover first how to construct a model of a similar but simple system. Discovered heuristics can be useful in modeling more complex systems. We demonstrate the approach by constructing a deterministic feed-forward neural network that can extract velocities of onedimensional patterns. Analysing simpler models we discovered how to estimate the necessary numbers of neurons; what are the useful ranges of the parameters of the network and what are the potential functional dependencies between the parameters. The class of one-dimensional cellular automata whose state is a function of both the previous state and a time-dependant input is described. As inputs we considered the sequences of binary strings that represent black-and-white objects moving in front of a white background. As outputs we considered the trajectory of the automaton. For some rules the automaton will evolve to the zero state for all velocities of the object except for the velocities in specific narrow range. The phenomenon is persistent even when a strong noise is present in input patterns but unreliable units of the automaton or having a more complex input break it down.

Cheng, Lap Kei.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.
Includes bibliographical references.
Abstracts in English and Chinese.
ABSTRACT --- p.I
摘要 --- p.II
ACKNOWLEDGEMENTS --- p.V
TABLE OF CONTENTS --- p.IV
INTRODUCTION --- p.0
Chapter 1.1 --- Different ways to achieve all-optical tunable delay --- p.2
Chapter 1.1.1 --- Optical buffer realized with optical switching --- p.2
Chapter 1.1.2 --- Slow light technique --- p.3
Chapter (i) --- Basics of slow light --- p.4
Chapter (ii) --- Slow light via electromagnetically induced transparency (EIT) --- p.6
Chapter (iii) --- Slow light via coherent population oscillation (CPO) --- p.7
Chapter (iv) --- Slow light via optical parametric amplification (OPA) --- p.8
Chapter (v) --- Slow light via stimulated Raman and Brillouin scattering --- p.8
Chapter 1.1.3 --- Tunable delay using wavelength conversion together with chromatic dispersion --- p.10
Chapter 1.1.4 --- Comparison of different schemes for constructing all-optical delay line --- p.11
Chapter 1.2 --- Overview of the thesis --- p.12
References --- p.14
ALL-OPTICAL SWITCHING OF DPSK SIGNAL IN AN SOA USING NONLINEAR POLARIZATION ROTATION --- p.18
Chapter 2.1 --- Introduction --- p.19
Chapter 2.2 --- Birefringence and nonlinear polarization rotation --- p.20
Chapter 2.3 --- Differential-phase-shift keying (DPSK) modulation format --- p.22
Chapter 2.4 --- Experimental setup --- p.23
Chapter 2.5 --- Experimental results --- p.25
Chapter 2.6 --- Conclusion --- p.29
References --- p.30
WIDEBAND SLOW LIGHT VIA STIMULATED BRILLOUIN SCATTERING IN AN OPTICAL FIBER USING A PHASE-MODULATED PUMP --- p.32
Chapter 3.1 --- Introduction --- p.33
Chapter 3.2 --- Stimulated Brillouin scattering (SBS) --- p.34
Chapter 3.3 --- Slow light via SBS --- p.35
Chapter 3.4 --- Experimental setup --- p.37
Chapter 3.5 --- Experimental result --- p.39
Conclusion --- p.42
References --- p.43
SIGNAL WAVELENGTH TRANSPARENT SBS SLOW LIGHT USING XGM BASED WAVELENGTH CONVERTER AND BRILLOUIN FIBER LASER --- p.45
Chapter 4.1 --- Introduction --- p.46
Chapter 4.2 --- Brillouin fiber laser and XGM wavelength converter --- p.47
Chapter 4.3 --- Operating principle --- p.50
Chapter 4.4 --- Experimental setup and results --- p.51
Conclusion --- p.56
References --- p.57
ALL-OPTICAL TUNABLE DELAY LINE FOR CHANNEL SELECTION IN A 40-GB/S OPTICAL TIME DIVISION MULTIPLEXING SYSTEM --- p.59
Chapter 5.1 --- Introduction --- p.60
Chapter 5.2 --- Principle of four-wave mixing --- p.61
Chapter 5.3 --- Channel selection in an OTDM system --- p.63
Chapter 5.4 --- Experimental setup --- p.64
Chapter 5.5 --- Experimental results --- p.67
Conclusion --- p.70
References --- p.71
TUNABLE OPTICAL DELAY WITH CSRZ-OOK TO RZ-OOK OPTICAL DATA FORMAT CONVERSION USING FOUR-WAVE MIXING WAVELENGTH CONVERSION AND GROUP VELOCITY DISPERSION --- p.73
Chapter 6.1 --- Introduction --- p.74
Chapter 6.2 --- Carrier-Suppressed Return-to-Zero --- p.76
Chapter 6.3 --- Operating Principle --- p.77
Chapter 6.4 --- Experimental setup --- p.79
Chapter 6.5 --- Experimental result --- p.81
Conclusion --- p.86
References --- p.87
CONCLUSION --- p.90
Chapter 7.1 --- Summary of work --- p.90
Chapter 7.2 --- Prospects of future work --- p.92
APPENDIX: LIST OF PUBLICATIONS A

by Long Mei.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.
Includes bibliographical references (leaves 73-77).
Abstracts in English and Chinese.
Acknowledgements --- p.iv
Abstract --- p.v
Table of Contents --- p.vii
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Nonlinear Factor Analysis Model --- p.1
Chapter 1.2 --- Main Objectives --- p.2
Chapter 1.2.1 --- Investigation of the performance of the ML approach with MCECM algorithm in NFA model --- p.2
Chapter 1.2.2 --- Investigation of the Robustness of the ML approach with MCECM algorithm --- p.3
Chapter 1.3 --- Structure of the Thesis --- p.3
Chapter 2 --- Theoretical Background of the MCECM Algorithm --- p.5
Chapter 2.1 --- Introduction of the EM algorithm --- p.5
Chapter 2.2 --- Monte Carlo integration --- p.7
Chapter 2.3 --- Markov Chains --- p.7
Chapter 2.4 --- The Metropolis-Hastings algorithm --- p.8
Chapter 3 --- Maximum Likelihood Estimation of a Nonlinear Factor Analysis Model --- p.10
Chapter 3.1 --- MCECM Algorithm --- p.10
Chapter 3.1.1 --- Motivation of Using MCECM algorithm --- p.11
Chapter 3.1.2 --- Introduction of the Realization of the MCECM algorithm --- p.12
Chapter 3.1.3 --- Implementation of the E-step via the MH Algorithm --- p.13
Chapter 3.1.4 --- Maximization Step --- p.15
Chapter 3.2 --- Monitoring Convergence of MCECM --- p.17
Chapter 3.2.1 --- Bridge Sampling Method --- p.17
Chapter 3.2.2 --- Average Batch Mean Method --- p.18
Chapter 4 --- Simulation Studies --- p.20
Chapter 4.1 --- The First Simulation Study with the Normal Distribution --- p.20
Chapter 4.1.1 --- Model Specification --- p.20
Chapter 4.1.2 --- The Selection of System Parameters --- p.22
Chapter 4.1.3 --- Monitoring the Convergence --- p.22
Chapter 4.1.4 --- Simulation Results for the ML Estimates --- p.25
Chapter 4.2 --- The Second Simulation Study with the Normal Distribution --- p.34
Chapter 4.2.1 --- Model Specification --- p.34
Chapter 4.2.2 --- Monitoring the Convergence --- p.35
Chapter 4.2.3 --- Simulation Results for the ML Estimates --- p.38
Chapter 4.3 --- The Third Simulation Study on Robustness --- p.47
Chapter 4.3.1 --- Model Specification --- p.47
Chapter 4.3.2 --- Monitoring the Convergence --- p.48
Chapter 4.3.3 --- Simulation Results for the ML Estimates --- p.51
Chapter 4.4 --- The Fourth Simulation Study on Robustness --- p.59
Chapter 4.4.1 --- Model Specification --- p.59
Chapter 4.4.2 --- Monitoring the Convergence --- p.59
Chapter 4.4.3 --- Simulation Results for the ML Estimates --- p.62
Chapter 5 --- Conclusion --- p.71
Bibliography --- p.73

In the first part of the dissertation, a novel stochastic averaging technique based on a Hilbert transform definition of the oscillator response displacement amplitude is developed. In comparison to standard stochastic averaging, the requirement of “a priori” determination of an equivalent natural frequency is bypassed, yielding flexibility in the ensuing analysis and potentially higher accuracy. Further, the herein proposed Hilbert transform based stochastic averaging is adapted for determining the time-dependent survival probability and first-passage time probability density function of stochastically excited nonlinear oscillators, even endowed with fractional derivative terms. To this aim, a Galerkin scheme is utilized to solve approximately the backward Kolmogorov partial differential equation governing the survival probability of the oscillator response. Next, the potential of the stochastic averaging technique to be used in conjunction with performance-based engineering design applications is demonstrated by proposing a stochastic version of the widely used incremental dynamic analysis (IDA). Specifically, modeling the excitation as a non-stationary stochastic process possessing an evolutionary power spectrum (EPS), an approximate closed-form expression is derived for the parameterized oscillator response amplitude probability density function (PDF). In this regard, IDA surfaces are determined providing the conditional PDF of the engineering demand parameter (EDP) for a given intensity measure (IM) value. In contrast to the computationally expensive Monte Carlo simulation, the methodology developed herein determines the IDA surfaces at minimal computational cost. In the second part of the dissertation, a novel multiple-input/single-output (MISO) system identification technique is developed for parameter identification of nonlinear and time-variant oscillators with fractional derivative terms subject to incomplete non-stationary data. The technique utilizes a representation of the nonlinear restoring forces as a set of parallel linear sub-systems. Next, a recently developed L1-norm minimization procedure based on compressive sensing theory is applied for determining the wavelet coefficients of the available incomplete non-stationary input-output (excitation-response) data. Several numerical examples are considered for assessing the reliability of the technique, even in the presence of incomplete and corrupted data. These include a 2-DOF time-variant Duffing oscillator endowed with fractional derivative terms, as well as a 2-DOF system subject to flow-induced forces where the non-stationary sea state possesses a recently proposed evolutionary version of the JONSWAP spectrum. In the third part of this dissertation, a joint time-frequency analysis technique based on generalized harmonic wavelets (GHWs) is developed for dynamic cerebral autoregulation (DCA) performance quantification. DCA is the continuous counter-regulation of the cerebral blood flow by the active response of cerebral blood vessels to the spontaneous or induced blood pressure fluctuations. Specifically, various metrics of the phase shift and magnitude of appropriately defined GHW-based transfer functions are determined based on data points over the joint time-frequency domain. The potential of these metrics to be used as a diagnostics tool for indicating healthy versus impaired DCA function is assessed by considering both healthy individuals and patients with unilateral carotid artery stenosis. Next, another application in biomedical engineering is pursued related to the Pulse Wave Imaging (PWI) technique. This relies on ultrasonic signals for capturing the propagation of pressure pulses along the carotid artery, and eventually for prognosis of focal vascular diseases (e.g., atherosclerosis and abdominal aortic aneurysm). However, to obtain a high spatio-temporal resolution the data are acquired at a high rate, in the order of kilohertz, yielding large datasets. To address this challenge, an efficient data compression technique is developed based on the multiresolution wavelet decomposition scheme, which exploits the high correlation of adjacent RF-frames generated by the PWI technique. Further, a sparse matrix decomposition is proposed as an efficient way to identify the boundaries of the arterial wall in the PWI technique.