Vibration analysis is a method that studies patterns in vibration data and measures vibration levels. It is usually performed on time waveforms of the vibration signal directly and on thefrequency spectrum derived by applying the Fourier Transform on the time waveform. Conventional vibration analysis methods are either expensive, need a complicated setup, or both. Non-contact measurement systems, such as high-speed cameras coupled with computer vision and motion magnification methods, are suitable options for monitoring vibrations of any system. In this work, many classic and state-of-the-art computer vision tracking algorithms were compared. Low and high frame rate videos are used to evaluate their ability to track the oscillatory movement that characterizes vibrations. The trackers are benchmarked with literature and experimental study. Two sets of experiments were carried out in this work, one using a cantilever and another using a robot. The resonance frequencies obtained from the vision camera method are compared to the Laser vibrometer method, which is industry standard. The results show that the resonance frequencies of both methods are closer to each other. The limitations of the tracking algorithm-based approach used for vibration analysis were discussed at the end. Since the methods provided are generic, they may be easily modified for other relevant applications. / Vibrationsanalys är en metod som studerar mönster i vibrationsdata och mäter vibrationsnivåer. Det utförs vanligtvis på tidvågformer av vibrationssignalen direkt och på frekvensen, spektrum som härleds genom att applicera Fourier Transform på tidvågform. Konventionella vibrationsanalysmetoder är antingen dyra, kräver en komplicerad installation eller båda. Beröringsfria mätsystem, till exempel höghastighetskameror i kombination med datorsyn och rörelseförstoringsmetoder, är lämpliga alternativ för att övervaka vibrationer i alla system. I detta arbete jämfördes många klassiska och toppmoderna datorsynsspårningsalgoritmer. Videor med låg och hög bildhastighet används för att utvärdera deras förmåga att spåra den oscillerande rörelsen som kännetecknar vibrationer. Spårarna jämförs med litteratur och experimentell studie. I detta arbete utfördes två uppsättningar experiment, ett med en fribärare och ett annat med en robot. De resonans frekvenser som erhålls från visionkamerametoden jämförs med Laservibrometer metoden, som är branschstandard. Resultaten visar att resonansfrekvenserna för båda metoderna ligger närmare varandra. Begränsningarna av det spårningsalgoritmbaserade tillvägagångssättet som används för vibrationsanalys diskuterades i slutet. Eftersom de angivna metoderna är generiska kan de enkelt modifieras för andra relevanta applikationer.

<p>Основни допринос дисертације су дефинисани методи истовременог<br />формирања више снопова код пријемника мултистатичког радара. Тиме<br />иста пријемна антена прима сигнале из целе хемисфере уз појачања<br />адекватна величини антене. Показано је да дефинисане методе,<br />примењене на конформне антене омогућавају формирање више<br />стотина снопова са само једним FPGA колом. Приказане су и<br />могућности паралелне обраде оволиког броја примљених радарских<br />сигнала. У пријемнику су обједињене функције претраживања простора<br />и праћења циљева. Процењене су величине простора који се може<br />покрити оваквим системом уз искључиву примену комерцијалне<br />технологије. Дате су методе синхронизације предајника и пријемника<br />засноване на технологији ултраширокопојасних комуникација.<br />&nbsp;</p> / <p>Osnovni doprinos disertacije su definisani metodi istovremenog<br />formiranja više snopova kod prijemnika multistatičkog radara. Time<br />ista prijemna antena prima signale iz cele hemisfere uz pojačanja<br />adekvatna veličini antene. Pokazano je da definisane metode,<br />primenjene na konformne antene omogućavaju formiranje više<br />stotina snopova sa samo jednim FPGA kolom. Prikazane su i<br />mogućnosti paralelne obrade ovolikog broja primljenih radarskih<br />signala. U prijemniku su objedinjene funkcije pretraživanja prostora<br />i praćenja ciljeva. Procenjene su veličine prostora koji se može<br />pokriti ovakvim sistemom uz isključivu primenu komercijalne<br />tehnologije. Date su metode sinhronizacije predajnika i prijemnika<br />zasnovane na tehnologiji ultraširokopojasnih komunikacija.<br />&nbsp;</p> / <p>Main contribution of this dissertation are the new digital beam forming<br />methods, suitable for applicable in multibeam conformal antenna. These<br />methods maintain antenna gain independently of beam positions in whole<br />hemisphere, scanned by the radar. Few hundred beams could be formed by<br />the only one FPGA. Parallel digital signal processing of these beams can be<br />also performed by the only one FPGA. Functions of surveillance and tracking<br />radar are joint in the one receiver. High accuracy in time and frequency<br />synchronization between receiver and transmitter is enabled by UWB.</p>

We consider the problem of numerical integration, where one aims to approximate an integral of a given continuous function from the function values at given sampling points, also known as quadrature points. A useful framework for such an approximation process is provided by the theory of reproducing kernel Hilbert spaces and the concept of the worst case quadrature error. However, the computation of optimal quadrature points, which minimize the worst case quadrature error, is in general a challenging task and requires efficient algorithms, in particular for large numbers of points. The focus of this thesis is on the efficient computation of optimal quadrature points on the torus T^d, the sphere S^d, and the rotation group SO(3). For that reason we present a general framework for the minimization of the worst case quadrature error on Riemannian manifolds, in order to construct numerically such quadrature points. Therefore, we consider, for N quadrature points on a manifold M, the worst case quadrature error as a function defined on the product manifold M^N. For the optimization on such high dimensional manifolds we make use of the method of steepest descent, the Newton method, and the conjugate gradient method, where we propose two efficient evaluation approaches for the worst case quadrature error and its derivatives. The first evaluation approach follows ideas from computational physics, where we interpret the quadrature error as a pairwise potential energy. These ideas allow us to reduce for certain instances the complexity of the evaluations from O(M^2) to O(M log(M)). For the second evaluation approach we express the worst case quadrature error in Fourier domain. This enables us to utilize the nonequispaced fast Fourier transforms for the torus T^d, the sphere S^2, and the rotation group SO(3), which reduce the computational complexity of the worst case quadrature error for polynomial spaces with degree N from O(N^k M) to O(N^k log^2(N) + M), where k is the dimension of the corresponding manifold. For the usual choice N^k ~ M we achieve the complexity O(M log^2(M)) instead of O(M^2). In conjunction with the proposed conjugate gradient method on Riemannian manifolds we arrive at a particular efficient optimization approach for the computation of optimal quadrature points on the torus T^d, the sphere S^d, and the rotation group SO(3). Finally, with the proposed optimization methods we are able to provide new lists with quadrature formulas for high polynomial degrees N on the sphere S^2, and the rotation group SO(3). Further applications of the proposed optimization framework are found due to the interesting connections between worst case quadrature errors, discrepancies and potential energies. Especially, discrepancies provide us with an intuitive notion for describing the uniformity of point distributions and are of particular importance for high dimensional integration in quasi-Monte Carlo methods. A generalized form of uniform point distributions arises in applications of image processing and computer graphics, where one is concerned with the problem of distributing points in an optimal way accordingly to a prescribed density function. We will show that such problems can be naturally described by the notion of discrepancy, and thus fit perfectly into the proposed framework. A typical application is halftoning of images, where nonuniform distributions of black dots create the illusion of gray toned images. We will see that the proposed optimization methods compete with state-of-the-art halftoning methods.

We consider the problem of numerical integration, where one aims to approximate an integral of a given continuous function from the function values at given sampling points, also known as quadrature points. A useful framework for such an approximation process is provided by the theory of reproducing kernel Hilbert spaces and the concept of the worst case quadrature error. However, the computation of optimal quadrature points, which minimize the worst case quadrature error, is in general a challenging task and requires efficient algorithms, in particular for large numbers of points. The focus of this thesis is on the efficient computation of optimal quadrature points on the torus T^d, the sphere S^d, and the rotation group SO(3). For that reason we present a general framework for the minimization of the worst case quadrature error on Riemannian manifolds, in order to construct numerically such quadrature points. Therefore, we consider, for N quadrature points on a manifold M, the worst case quadrature error as a function defined on the product manifold M^N. For the optimization on such high dimensional manifolds we make use of the method of steepest descent, the Newton method, and the conjugate gradient method, where we propose two efficient evaluation approaches for the worst case quadrature error and its derivatives. The first evaluation approach follows ideas from computational physics, where we interpret the quadrature error as a pairwise potential energy. These ideas allow us to reduce for certain instances the complexity of the evaluations from O(M^2) to O(M log(M)). For the second evaluation approach we express the worst case quadrature error in Fourier domain. This enables us to utilize the nonequispaced fast Fourier transforms for the torus T^d, the sphere S^2, and the rotation group SO(3), which reduce the computational complexity of the worst case quadrature error for polynomial spaces with degree N from O(N^k M) to O(N^k log^2(N) + M), where k is the dimension of the corresponding manifold. For the usual choice N^k ~ M we achieve the complexity O(M log^2(M)) instead of O(M^2). In conjunction with the proposed conjugate gradient method on Riemannian manifolds we arrive at a particular efficient optimization approach for the computation of optimal quadrature points on the torus T^d, the sphere S^d, and the rotation group SO(3). Finally, with the proposed optimization methods we are able to provide new lists with quadrature formulas for high polynomial degrees N on the sphere S^2, and the rotation group SO(3). Further applications of the proposed optimization framework are found due to the interesting connections between worst case quadrature errors, discrepancies and potential energies. Especially, discrepancies provide us with an intuitive notion for describing the uniformity of point distributions and are of particular importance for high dimensional integration in quasi-Monte Carlo methods. A generalized form of uniform point distributions arises in applications of image processing and computer graphics, where one is concerned with the problem of distributing points in an optimal way accordingly to a prescribed density function. We will show that such problems can be naturally described by the notion of discrepancy, and thus fit perfectly into the proposed framework. A typical application is halftoning of images, where nonuniform distributions of black dots create the illusion of gray toned images. We will see that the proposed optimization methods compete with state-of-the-art halftoning methods.

A partir de dados obtidos do modelo do geopotencial EGM96, da gravimetria, do GPS e do nivelamento geométrico, e aplicando harmônicos esféricos e FFT como técnicas de determinação geoidal, foram utilizadas neste trabalho redes neurais artificiais como ferramenta alternativa na determinação de um modelo geoidal. Procurou-se uma determinação geoidal de forma mais rápida, com precisão adequada e com menor esforço na determinação de parâmetros importantes na obtenção da referida superfície. Foram utilizados modelos de redes neurais do tipo MLP, algoritmo de treinamento backpropagation, variando o número de camadas, o número de neurônios, a função de ativação, a taxa de aprendizado e o termo momento. Os dados dos modelos mencionados foram tratados de forma a serem utilizados pelos modelos de redes neurais. Foram executadas a normalização, a análise de componentes principais e a definição dos atributos de entrada e saída para treinamento do modelo de rede neural. Foram Realizadas comparações entre os modelos geoidais existentes, os quais foram utilizados nesta pesquisa, com os resultados obtidos pelo modelo de rede neural. Tais comparações resultaram na obtenção dos erros entre as superfícies, justificando dessa forma a possibilidade de uso do referido método, com a conseqüente demonstração de suas vantagens e desvantagens. / Applying data from EGM96 geopotential model, gravimetric, GPS and geometric leveling data and using spherical harmonics and FFT as techniques of geoidal determination, this thesis has the goal to find a fast alternative tool to define a geoidal undulation model considering precision and a small effort to estimate important parameters to obtain the mentioned model. MLP neural networks, backpropagation algorithm changing the numbers of layers, neurons numbers, activation function, learning rate and momentum term have been applied. The data of the mentioned models were handling aiming to be used by the neural networks models. Normalization, analysis of the main components, definition of the input and output attributes to training the neural network model, have been also used. Comparison among existing models and the models used in this research with results obtained by the neural network have been done, showing the errors between the created surfaces. At the end, it is presented a positive argument to use the MLP neural network to generate a geoidal model with advantages and disadvantages.

A partir de dados obtidos do modelo do geopotencial EGM96, da gravimetria, do GPS e do nivelamento geométrico, e aplicando harmônicos esféricos e FFT como técnicas de determinação geoidal, foram utilizadas neste trabalho redes neurais artificiais como ferramenta alternativa na determinação de um modelo geoidal. Procurou-se uma determinação geoidal de forma mais rápida, com precisão adequada e com menor esforço na determinação de parâmetros importantes na obtenção da referida superfície. Foram utilizados modelos de redes neurais do tipo MLP, algoritmo de treinamento backpropagation, variando o número de camadas, o número de neurônios, a função de ativação, a taxa de aprendizado e o termo momento. Os dados dos modelos mencionados foram tratados de forma a serem utilizados pelos modelos de redes neurais. Foram executadas a normalização, a análise de componentes principais e a definição dos atributos de entrada e saída para treinamento do modelo de rede neural. Foram Realizadas comparações entre os modelos geoidais existentes, os quais foram utilizados nesta pesquisa, com os resultados obtidos pelo modelo de rede neural. Tais comparações resultaram na obtenção dos erros entre as superfícies, justificando dessa forma a possibilidade de uso do referido método, com a conseqüente demonstração de suas vantagens e desvantagens. / Applying data from EGM96 geopotential model, gravimetric, GPS and geometric leveling data and using spherical harmonics and FFT as techniques of geoidal determination, this thesis has the goal to find a fast alternative tool to define a geoidal undulation model considering precision and a small effort to estimate important parameters to obtain the mentioned model. MLP neural networks, backpropagation algorithm changing the numbers of layers, neurons numbers, activation function, learning rate and momentum term have been applied. The data of the mentioned models were handling aiming to be used by the neural networks models. Normalization, analysis of the main components, definition of the input and output attributes to training the neural network model, have been also used. Comparison among existing models and the models used in this research with results obtained by the neural network have been done, showing the errors between the created surfaces. At the end, it is presented a positive argument to use the MLP neural network to generate a geoidal model with advantages and disadvantages.

Cette thèse s'inscrit dans la thématique classique de l'homogénéisation des milieux hétérogènes linéaires et a pour but l'étude et la prédiction du comportement optique de couches de peintures. L'objectif est double : d'une part caractériser et modéliser la microstructure hétérogène des matériaux utilisés dans les revêtements de peinture, d'autre part prédire le comportement optique de ces matériaux par des moyens numériques, et étudier l'influence de la morphologie sur les propriétés optiques. Ces travaux ont été faits dans le cadre du projet LIMA (Lumière Interaction Matière Aspect), soutenu par l'Agence Nationale de la Recherche et en partenariat avec le groupe PSA. Des images acquises par microscopie électronique à balayage (MEB) sont obtenues de différentes couches de peintures. On y distingue différentes échelles pigmentaires : microscopique et nanoscopique. Des images représentatives des échelles sont alors sélectionnées et segmentées, pour permettre la prise de mesures morphologiques. Ces mesures permettent l'élaboration de modèles aléatoires propres à chacune des échelles. Ces modèles sont ensuite validés, et optimisés pour le cas du modèle nanoscopique à deux échelles. La prédiction du comportement optique des modèles aléatoires de matériaux hétérogènes se fait ici avec l'utilisation de méthodes utilisant les transformées de Fourier rapides (FFT). La théorie de l'optique des milieux composites est rappelée, ainsi que les contraintes et limites des méthodes FFT. L'approximation quasi-statique est une contrainte, impliquant l'application de la méthode FFT au seul modèle nanoscopique. Le comportement optique du modèle nanoscopique optimisé est calculé numériquement, et comparé à celui mesuré de la peinture qui a servi de référence. Les fonctions diélectriques des matériaux constituants de la peinture ont été mesurées à l'ellipsomètre spectroscopique au Musée de Minéralogie des Mines de Paris. Les réponses mesurée et calculées sont comparées entre elles et à des estimations analytiques. Une caractérisation statistique est également faite sur le modèle aléatoire et sur les champs locaux de déplacement diélectrique, par le calcul du volume élémentaire représentatif (VER). / This work presents a numerical and theoretical study of the optical properties of paint layers, in the classical framework of homogenization of heterogeneous media. Objectives are : describing and modeling the heterogenous microstructures used in paint coatings, and predicting the optical response of such materials by numerical ways, depending of the pigments morphology. This work was carried out as part of the LIMA project (Light Interaction Materials Aspect), in partnership with the Agence Nationale de la Recherche and the PSA company. Images of differents paint layers are acquired by scanning electron microscopy (SEM). Different length scales are considered for the microstructures and pigments : microscopic and nanoscopic. Representatives images of these scales are chosen and segmented in order to estimate morphological measurements. Using these measurements, random models are developed depending on the scales. These models, of a multiscale nature, are optimized and validated. The prediction of the optical behaviour of random models describing heterogenous materials is carried out using numerical process based on fast Fourier transforms (FFT). Optics of composite materials theory is introduced, as well as the limits of FFT methods. The quasi-static approximation is a constraint which implies the use of the FFT method on the nanoscopic model only. Dielectric functions of the components of the paint have been measured on macroscopic samples at the Museum of Mineralogy of Mines de Paris by spectroscopic ellipsometry. The optical response of the optimized nanoscopic model is computed and compared to ellipsometry measurements carried out on a reference paint layer. The computed and measured responses are also compared with analytical estimates. In addition, a statistical characterization is made on the random model and the local dielectrical displacement fields, by using the representative volume element (RVE).

We present a MPI based software library for computing the fast Fourier transforms on massively parallel, distributed memory architectures. Similar to established transpose FFT algorithms, we propose a parallel FFT framework that is based on a combination of local FFTs, local data permutations and global data transpositions. This framework can be generalized to arbitrary multi-dimensional data and process meshes. All performance relevant building blocks can be implemented with the help of the FFTW software library. Therefore, our library offers great flexibility and portable performance. Likewise FFTW, we are able to compute FFTs of complex data, real data and even- or odd-symmetric real data. All the transforms can be performed completely in place. Furthermore, we propose an algorithm to calculate pruned FFTs more efficiently on distributed memory architectures. For example, we provide performance measurements of FFTs of size 512^3 and 1024^3 up to 262144 cores on a BlueGene/P architecture.

<p>There is a lot of applications for DSPs (Digital Signal Processor) in the most rapidly growing areas in the industry right now as wireless communication along with audio and video products are getting more and more popular. In this report, a DSP, developed at the division of Computer Engineering at the University of Linköping, is optimized and verified.</p><p>Register Forwarding was implemented on a general architecture level to avoiddata hazards that may arise when implementing instruction pipelining in a processor.</p><p>The very common FFT algorithm is also optimized but on instruction setlevel. That means the algorithm is carefully analyzed to find operations that mayexecute in parallel and then create new instructions for these parallel operations.The optimization is concentrated on the butterfly operation as it is such a majorpart of the FFT computation. Comparing the accelerated butterfly with the unaccelerated gives an improvement of 30% in terms of clock cycles needed for thecomputation.</p><p>In the report there are also some discussions about the benefits and drawbacksof changing from a hardware to a software stack, mostly in terms of interrupts andthe return instruction.</p><p>Another important property of the processor is scalability. That is, it is possibleto attach extra peripherals to the core, which accelerates certain tasks. Aninterface towards these peripherals is developed along with two template designsthat may be used to develop other peripherals.</p><p>After all these modifications, a new test bench is developed to verify the functionality.</p>

Syftet med denna studie är att undersöka hur familjebehandlare upplever det att arbeta med FFT-metoden samt de faktorerna som gör den funktionell. Eftersom FFT är anpassad till den amerikanska kulturen som skiljer sig ganska mycket från den svenska, båda i kultur och socialsystem är det viktigt att inte bara utvärdera utifrån modellen men också hur implementering och anpassning av modellen har gått. För att kunna besvara syftet och frågeställningar har fem kvalitativa intervjuer genomförts av semistrukturerad karaktär. Urvalet av respondenter gjordes utifrån snöbollsmetoden där de intervjuade arbetar inom socialtjänstens öppenvård. Resultaten visade att det finns många saker som ska tas hänsyn till vid anpassning till andra kulturer, bland annat utbildningar, målgrupper och ekonomi. FFT är en behandlingsmetod och en påbyggnadsutbildning där gränsen mellan det som är klientens behandling och det som är FFT-terapeuternas utbildning är diffus. Studien kan bidra med tankar om hur man skulle kunna göra vidare studier rörande utbildning och implementering av evidensbaserade modeller.