On considère des méthodes de Galerkin stochastiques pour des systèmes hyperboliques faisant intervenir des données en entrée incertaines de lois de distribution connues paramétrées par des variables aléatoires. On s'intéresse à des problèmes où un choc apparaît presque sûrement en temps fini. Dans ce cas, la solution peut développer des discontinuités dans les domaines spatial et stochastique. On utilise un schéma de Volumes Finis pour la discrétisation spatiale et une projection de Galerkin basée sur une approximation polynomiale par morceaux pour la discrétisation stochastique. On propose un solveur de type Roe avec correcteur entropique pour le système de Galerkin, utilisant une technique originale pour approcher la valeur absolue de la matrice de Roe et une adaptation du correcteur entropique de Dubois et Mehlmann. La méthode proposée reste coûteuse car une discrétisation stochastique très fine est nécessaire pour représenter la solution au voisinage des discontinuités. Il est donc nécessaire de faire appel à des stratégies adaptatives. Comme les discontinuités sont localisées en espace et évoluent en temps, on propose des représentations stochastiques dépendant de l'espace et du temps. On formule cette méthodologie dans un contexte multi-résolution basé sur le concept d'arbres binaires pour décrire la discrétisation stochastique. Les étapes d'enrichissement et d'élagage adaptatifs sont réalisées en utilisant des critères d'analyse multi-résolution. Dans le cas multidimensionnel, une anisotropie de la procédure adaptative est proposée. La méthodologie est évaluée sur le système des équations d'Euler dans un tube à choc et sur l'équation de Burgers en une et deux dimensions stochastiques / This work is concerned with stochastic Galerkin methods for hyperbolic systems involving uncertain data with known distribution functions parametrized by random variables. We are interested in problems where a shock appears almost surely in finite time. In this case, the solution exhibits discontinuities in the spatial and in the stochastic domains. A Finite Volume scheme is used for the spatial discretization and a Galerkin projection based on piecewise poynomial approximation is used for the stochastic discretization. A Roe-type solver with an entropy correction is proposed for the Galerkin system, using an original technique to approximate the absolute value of the Roe matrix and an adaptation of the Dubois and Mehlman entropy corrector. Although this method deals with complex situations, it remains costly because a very fine stochastic discretization is needed to represent the solution in the vicinity of discontinuities. This fact calls for adaptive strategies. As discontinuities are localized in space and time, stochastic representations depending on space and time are proposed. This methodology is formulated in a multiresolution context based on the concept of binary trees for the stochastic discretization. The adaptive enrichment and coarsening steps are based on multiresolution analysis criteria. In the multidimensional case, an anisotropy of the adaptive procedure is proposed. The method is tested on the Euler equations in a shock tube and on the Burgers equation in one and two stochastic dimensions

Este trabalho apresenta um estudo sobre transformada Wavelet aplicada à qualidade da energia elétrica com o intuito de detectar, localizar e classificar eventuais distúrbios que ocorrem no sistema elétrico. Inicialmente é apresentada uma introdução sobre qualidade da energia, mostrando fatos, evoluções e explicando o conceito dos principais fenômenos que interferem na qualidade da energia do sistema elétrico brasileiro, devido, principalmente, à grande demanda de aparelhos eletrônicos produzidos atualmente. Em seguida é mostrada uma revisão dos principais métodos e modelos aplicados atualmente no mundo a respeito do assunto. A transformada Wavelet vem como uma grande ajuda nesta área de análise de sinais, já que é capaz de extrair simultaneamente informações de tempo e freqüência, diferentemente da transformada de Fourier. A simulação dos diversos distúrbios ocorridos no sistema foi realizada através do software ATP (Alternative Transients Program), cujas características seguem corretamente um sistema de distribuição real da concessionária CPFL. Os distúrbios de tensão gerados e analisados foram detectados e localizados através da técnica de Análise Multiresolução e, posteriormente, classificados, utilizando para isto o método da Curva de Desvio Padrão / This dissertation presents a study of Wavelet transform applied to power quality in order to detect, locate and classify disturbances that may occur in the power system. Initially an introduction of power quality is presented, showing facts, evolutions and explaining the concept of the main phenomena that interfere the on power quality of the brazilian power system, due to, mainly, a great demand for electronic devices produced nowadays. A revision of the main methods and models currently applied in the world regarding this subject is also show. The Wavelet transform comes as a great support in the area of signal assessment, as it can extract information about time and frequency simultaneously, differently from the Fourier transform. The simulation of the diverse disturbances occurred in the system was accomplished through ATP software (Alternative Transients Program), whose characteristics correctly follow a system of real distribution of CPFL eletric utility. The generated and analyzed voltage disturbances were detected and located by Multiresolution Analysis technique and later classified by the method of the Standard Deviation

A Qualidade da energia elétrica é caracterizada pela disponibilidade da energia através de uma forma de onda senoidal pura, sem alterações na amplitude e freqüência. No entanto situações transitórias em sistemas de potência são comuns e estas podem provocar inúmeras interferências indesejáveis. Neste contexto, este trabalho tem como objetivo desenvolver um algoritmo para detectar, localizar no tempo e classificar diversos distúrbios que ocorrem no sistema elétrico através da aplicação da transformada wavelet (TW). Foi realizado um estudo teórico desde a origem até os recentes avanços sobre a TW. Para a detecção e localização no tempo foi utilizada apenas a TW. Com relação à classificação foram comparadas três ferramentas matemáticas: TW, TRF (Transformada Rápida de Fourier) e RNA (Redes Neurais Artificiais). Através do software ATP (Alternative Transients Program) foi modelado um sistema de distribuição, cujas características seguem um sistema real. Todos os distúrbios de tensão gerados e analisados puderam ser detectados e localizados no tempo através da técnica de análise multiresolução. Em relação à classificação, foi realizada uma comparação entre a TW, a TRF e RNA com resultados satisfatórios, destacando dentre elas a TRF e a RNA. Pode-se concluir que os resultados obtidos através do algoritmo mostraram-se eficientes tanto no aspecto da detecção, localização e classificação, assim como na estimação da amplitude do distúrbio e da duração do distúrbio. / A perfect power supply would be one that is always available, maintaining the supply voltage and frequency within certain limits, and supplying pure noise free sinusoidal waveform. Nevertheless, transient events are usual in power systems, resulting in several interferences. The purpose of this study is for detecting, locating in time and to classifying with wavelet transform (WT) several disturbances that occur on power systems. A WT theoretical revision, referring to the first mention in wavelet up to the recent research advances is presented. Only WT was used in order to detect and locate in time the power system disturbances. For classification, three mathematical tools were compared: WT, FFT (Fast Fourier Transform) and ANN (Artificial Neural Networks). A distribution System, with identical characteristics as the real distribution system, was performed with ATP software (Alternative Transients Program). The results showed that multiresolution analysis technique is able to detect and locate all the generated and analyzed voltage disturbances. For classification the results were similar for the WT, FFT and ANN, however FFT and ANN results presented a better performance. The results conclude that the WT algorithm is efficient at detecting, localizing and classifying power system disturbances, as well as, at estimating the amplitude and duration of the voltage disturbance.

A Qualidade da energia elétrica é caracterizada pela disponibilidade da energia através de uma forma de onda senoidal pura, sem alterações na amplitude e freqüência. No entanto situações transitórias em sistemas de potência são comuns e estas podem provocar inúmeras interferências indesejáveis. Neste contexto, este trabalho tem como objetivo desenvolver um algoritmo para detectar, localizar no tempo e classificar diversos distúrbios que ocorrem no sistema elétrico através da aplicação da transformada wavelet (TW). Foi realizado um estudo teórico desde a origem até os recentes avanços sobre a TW. Para a detecção e localização no tempo foi utilizada apenas a TW. Com relação à classificação foram comparadas três ferramentas matemáticas: TW, TRF (Transformada Rápida de Fourier) e RNA (Redes Neurais Artificiais). Através do software ATP (Alternative Transients Program) foi modelado um sistema de distribuição, cujas características seguem um sistema real. Todos os distúrbios de tensão gerados e analisados puderam ser detectados e localizados no tempo através da técnica de análise multiresolução. Em relação à classificação, foi realizada uma comparação entre a TW, a TRF e RNA com resultados satisfatórios, destacando dentre elas a TRF e a RNA. Pode-se concluir que os resultados obtidos através do algoritmo mostraram-se eficientes tanto no aspecto da detecção, localização e classificação, assim como na estimação da amplitude do distúrbio e da duração do distúrbio. / A perfect power supply would be one that is always available, maintaining the supply voltage and frequency within certain limits, and supplying pure noise free sinusoidal waveform. Nevertheless, transient events are usual in power systems, resulting in several interferences. The purpose of this study is for detecting, locating in time and to classifying with wavelet transform (WT) several disturbances that occur on power systems. A WT theoretical revision, referring to the first mention in wavelet up to the recent research advances is presented. Only WT was used in order to detect and locate in time the power system disturbances. For classification, three mathematical tools were compared: WT, FFT (Fast Fourier Transform) and ANN (Artificial Neural Networks). A distribution System, with identical characteristics as the real distribution system, was performed with ATP software (Alternative Transients Program). The results showed that multiresolution analysis technique is able to detect and locate all the generated and analyzed voltage disturbances. For classification the results were similar for the WT, FFT and ANN, however FFT and ANN results presented a better performance. The results conclude that the WT algorithm is efficient at detecting, localizing and classifying power system disturbances, as well as, at estimating the amplitude and duration of the voltage disturbance.

Fluidized bed dryers are used in the pharmaceutical industry for the batch drying of pharmaceutical granulate. Maintaining optimal hydrodynamic conditions throughout the drying process is essential to product quality. Due to the complex interactions inherent in the fluidized bed drying process, mechanistic models capable of identifying these optimal modes of operation are either unavailable or limited in their capabilities. Therefore, empirical models based on experimentally generated data are relied upon to study these systems.<p> Principal Component Analysis (PCA) and Partial Least Squares (PLS) are multivariate statistical techniques that project data onto linear subspaces that are the most descriptive of variance in a dataset. By modeling data in terms of these subspaces, a more parsimonious representation of the system is possible. In this study, PCA and PLS are applied to data collected from a fluidized bed dryer containing pharmaceutical granulate. <p>System hydrodynamics were quantified in the models using high frequency pressure fluctuation measurements. These pressure fluctuations have previously been identified as a characteristic variable of hydrodynamics in fluidized bed systems. As such, contributions from the macroscale, mesoscale, and microscales of motion are encoded into the signals. A multiresolutional decomposition using a discrete wavelet transformation was used to resolve these signals into components more representative of these individual scales before modeling the data. <p>The combination of multiresolutional analysis with PCA and PLS was shown to be an effective approach for modeling the conditions in the fluidized bed dryer. In this study, datasets from both steady state and transient operation of the dryer were analyzed. The steady state dataset contained measurements made on a bed of dry granulate and the transient dataset consisted of measurements taken during the batch drying of granulate from approximately 33 wt.% moisture to 5 wt.%. Correlations involving several scales of motion were identified in both studies.<p> In the steady state study, deterministic behavior related to superficial velocity, pressure sensor position, and granulate particle size distribution was observed in PCA model parameters. It was determined that these properties could be characterized solely with the use of the high frequency pressure fluctuation data. Macroscopic hydrodynamic characteristics such as bubbling frequency and fluidization regime were identified in the low frequency components of the pressure signals and the particle scale interactions of the microscale were shown to be correlated to the highest frequency signal components. PLS models were able to characterize the effects of superficial velocity, pressure sensor position, and granulate particle size distribution in terms of the pressure signal components. Additionally, it was determined that statistical process control charts capable of monitoring the fluid bed hydrodynamics could be constructed using PCA<p>In the transient drying experiments, deterministic behaviors related to inlet air temperature, pressure sensor position, and initial bed mass were observed in PCA and PLS model parameters. The lowest frequency component of the pressure signal was found to be correlated to the overall temperature effects during the drying cycle. As in the steady state study, bubbling behavior was also observed in the low frequency components of the pressure signal. PLS was used to construct an inferential model of granulate moisture content. The model was found to be capable of predicting the moisture throughout the drying cycle. Preliminary statistical process control models were constructed to monitor the fluid bed hydrodynamics throughout the drying process. These models show promise but will require further investigation to better determine sensitivity to process upsets.<p> In addition to PCA and PLS analyses, Multiway Principal Component Analysis (MPCA) was used to model the drying process. Several key states related to the mass transfer of moisture and changes in temperature throughout the drying cycle were identified in the MPCA model parameters. It was determined that the mass transfer of moisture throughout the drying process affects all scales of motion and overshadows other hydrodynamic behaviors found in the pressure signals.

Fluidized bed dryers are used in the pharmaceutical industry for the batch drying of pharmaceutical granulate. Maintaining optimal hydrodynamic conditions throughout the drying process is essential to product quality. Due to the complex interactions inherent in the fluidized bed drying process, mechanistic models capable of identifying these optimal modes of operation are either unavailable or limited in their capabilities. Therefore, empirical models based on experimentally generated data are relied upon to study these systems.<p> Principal Component Analysis (PCA) and Partial Least Squares (PLS) are multivariate statistical techniques that project data onto linear subspaces that are the most descriptive of variance in a dataset. By modeling data in terms of these subspaces, a more parsimonious representation of the system is possible. In this study, PCA and PLS are applied to data collected from a fluidized bed dryer containing pharmaceutical granulate. <p>System hydrodynamics were quantified in the models using high frequency pressure fluctuation measurements. These pressure fluctuations have previously been identified as a characteristic variable of hydrodynamics in fluidized bed systems. As such, contributions from the macroscale, mesoscale, and microscales of motion are encoded into the signals. A multiresolutional decomposition using a discrete wavelet transformation was used to resolve these signals into components more representative of these individual scales before modeling the data. <p>The combination of multiresolutional analysis with PCA and PLS was shown to be an effective approach for modeling the conditions in the fluidized bed dryer. In this study, datasets from both steady state and transient operation of the dryer were analyzed. The steady state dataset contained measurements made on a bed of dry granulate and the transient dataset consisted of measurements taken during the batch drying of granulate from approximately 33 wt.% moisture to 5 wt.%. Correlations involving several scales of motion were identified in both studies.<p> In the steady state study, deterministic behavior related to superficial velocity, pressure sensor position, and granulate particle size distribution was observed in PCA model parameters. It was determined that these properties could be characterized solely with the use of the high frequency pressure fluctuation data. Macroscopic hydrodynamic characteristics such as bubbling frequency and fluidization regime were identified in the low frequency components of the pressure signals and the particle scale interactions of the microscale were shown to be correlated to the highest frequency signal components. PLS models were able to characterize the effects of superficial velocity, pressure sensor position, and granulate particle size distribution in terms of the pressure signal components. Additionally, it was determined that statistical process control charts capable of monitoring the fluid bed hydrodynamics could be constructed using PCA<p>In the transient drying experiments, deterministic behaviors related to inlet air temperature, pressure sensor position, and initial bed mass were observed in PCA and PLS model parameters. The lowest frequency component of the pressure signal was found to be correlated to the overall temperature effects during the drying cycle. As in the steady state study, bubbling behavior was also observed in the low frequency components of the pressure signal. PLS was used to construct an inferential model of granulate moisture content. The model was found to be capable of predicting the moisture throughout the drying cycle. Preliminary statistical process control models were constructed to monitor the fluid bed hydrodynamics throughout the drying process. These models show promise but will require further investigation to better determine sensitivity to process upsets.<p> In addition to PCA and PLS analyses, Multiway Principal Component Analysis (MPCA) was used to model the drying process. Several key states related to the mass transfer of moisture and changes in temperature throughout the drying cycle were identified in the MPCA model parameters. It was determined that the mass transfer of moisture throughout the drying process affects all scales of motion and overshadows other hydrodynamic behaviors found in the pressure signals.

As the tick-by-tick data of financial transactions become easier to reach, processing that much of information in an efficient and correct way to estimate the integrated volatility gains importance. However, empirical findings show that, this much of data may become unusable due to microstructure effects. Most common way to get over this problem is to sample the data in equidistant intervals of calendar, tick or business time scales. The comparative researches on that subject generally assert that, the most successful sampling scheme is a calendar time sampling which samples the data every 5 to 20 minutes. But this generally means throwing out more than 99 percent of the data. So it is obvious that a more efficient sampling method is needed. Although there are some researches on using alternative techniques, none of them is proven to be the best. Our study is concerned with a sampling scheme that uses the information in different scales of frequency and is less prone to microstructure effects. We introduce a new concept of business intensity, the sampler of which is named Optimizable Multiresolution Quadratic Variation Filter. Our filter uses multiresolution analysis techniques to decompose the data into different scales and quadratic variation to build up the new business time scale. Our empirical findings show that our filter is clearly less prone to microstructure effects than any other common sampling method. We use the classified tick-by-tick data for Turkish Interbank FX market. The market is closed for nearly 14 hours of the day, so big jumps occur between closing and opening prices. We also propose a new smoothing algorithm to reduce the effects of those jumps.

In this thesis, we introduce a new approach to wavefront phase reconstruction in Adaptive Optics (AO) from the low-resolution gradient measurements provided by a wavefront sensor, using a non-linear approach derived from the Microcanonical Multiscale Formalism (MMF). MMF comes from established concepts in statistical physics, it is naturally suited to the study of multiscale properties of complex natural signals, mainly due to the precise numerical estimate of geometrically localized critical exponents, called the singularity exponents. These exponents quantify the degree of predictability, locally, at each point of the signal domain, and they provide information on the dynamics of the associated system. We show that multiresolution analysis carried out on the singularity exponents of a high-resolution turbulent phase (obtained by model or from data) allows a propagation along the scales of the gradients in low-resolution (obtained from the wavefront sensor), to a higher resolution. We compare our results with those obtained by linear approaches, which allows us to offer an innovative approach to wavefront phase reconstruction in Adaptive Optics.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Turbulent flow high complexity makes it difficult to describe complex phenomena, such as the transport of vector and scalar quantities at the lower atmosphere, making the analysis of experimental data, such as time series, largely employed. The method mostly used by the micrometeorological community to quantify such turbulent transport is associated with the determination of the statistical covariance between two variables. It is known that the determination of statistical quantities for very long temporal windows leads to a large flux uncertainty. At the same time, the theory indicates that the association between fluxes and statistical covariance is only valid for temporally stationary series. The aim of the present study is to test the hypothesis that the estimate uncertainty is directly related to the series non-stationarity. To better understand this issue, we use a methodology based on a group of parametric and nonparametric statistical tests. The tests considered here are the T-test, F-test, median test, U-test and run test. Furthermore, the test results are compared with the outputs of two signal decomposition procedures: multiresolution analysis and empirical mode decomposition. The results suggest that the flux variability over large temporal scales characterizes the existence of temporal trends and low frequency components in the time series considered, so that it is more associated with an observational limitation of the analysis than with non-stationarity, as this concept should be the property of an ensemble, rather than of a single realization. Such limitation suggests the definition of a practical single order stationarity, associated with temporal trends and low frequency components whose energy is similar or larger to that of the turbulent fluctuations. For that reason, we affirm that the interactions test is, among all considered, the best suited for analyzing atmospheric data, because it is the most sensible to the existence of temporal trends. Furthermore, such test allows obtaining a temporal scale beyond which mesoscale events become important. / A complexidade de escoamentos turbulentos causa dificuldade para a descrição de fenômenos complexos, como o transporte de grandezas vetoriais e escalares na baixa atmosfera, fazendo com que a análise de dados experimentais, principalmente séries temporais, seja amplamente utilizada. O método mais utilizado pela comunidade micrometeorológica para quantificar esse transporte pela turbulência está associado à determinação da covariância entre duas variáveis. Sabe-se que a determinação de quantidades estatísticas para janelas temporais muito longas resulta em uma grande incerteza nos valores dos fluxos obtidos através desse método. Ao mesmo tempo, a teoria indica que o procedimento de associar fluxos a covariâncias estatísticas só vale para séries temporalmente estacionárias. O objetivo deste trabalho é testar a hipótese de que a incerteza das estimativas esteja relacionada diretamente com a não-estacionariedade das séries temporais. Para entendermos melhor isso, usamos uma metodologia baseada em um conjunto de testes estatísticos paramétricos e não-paramétricos de hipótese nula. Os testes considerados são o teste-T, teste-F, teste da mediana, teste-U e o teste das interações. Os resultados dos testes são ainda comparados com os obtidos com dois métodos de decomposição de sinais: a análise de multiresolução e a Decomposição Empírica de Modos. Os resultados sugerem que a variabilidade dos fluxos nas grandes escalas temporais está associada diretamente com a presença de tendências e componentes de baixa frequência nas séries analisadas, e que este fato está mais ligado à limitação observacional em que a análise é realizada do que propriamente com a não-estacionariedade, já que esta última é uma propriedade de ensemble e não de apenas uma realização. Esta limitação sugere a definição de um conceito mais prático de estacionariedade de primeira ordem, que seja associado à presença de tendências ou componentes de baixa frequência com energias da ordem ou maiores que a energia das escalas turbulentas. Por esse motivo podemos afirmar que na análise de dados atmosféricos o teste das interações mostrou-se, entre todos os considerados, o mais sensível à presença de tendências, permitindo inclusive a obtenção de uma escala temporal na qual os eventos de meso/submesoescala ganham importância.

Este trabalho apresenta um estudo sobre transformada Wavelet aplicada à qualidade da energia elétrica com o intuito de detectar, localizar e classificar eventuais distúrbios que ocorrem no sistema elétrico. Inicialmente é apresentada uma introdução sobre qualidade da energia, mostrando fatos, evoluções e explicando o conceito dos principais fenômenos que interferem na qualidade da energia do sistema elétrico brasileiro, devido, principalmente, à grande demanda de aparelhos eletrônicos produzidos atualmente. Em seguida é mostrada uma revisão dos principais métodos e modelos aplicados atualmente no mundo a respeito do assunto. A transformada Wavelet vem como uma grande ajuda nesta área de análise de sinais, já que é capaz de extrair simultaneamente informações de tempo e freqüência, diferentemente da transformada de Fourier. A simulação dos diversos distúrbios ocorridos no sistema foi realizada através do software ATP (Alternative Transients Program), cujas características seguem corretamente um sistema de distribuição real da concessionária CPFL. Os distúrbios de tensão gerados e analisados foram detectados e localizados através da técnica de Análise Multiresolução e, posteriormente, classificados, utilizando para isto o método da Curva de Desvio Padrão / This dissertation presents a study of Wavelet transform applied to power quality in order to detect, locate and classify disturbances that may occur in the power system. Initially an introduction of power quality is presented, showing facts, evolutions and explaining the concept of the main phenomena that interfere the on power quality of the brazilian power system, due to, mainly, a great demand for electronic devices produced nowadays. A revision of the main methods and models currently applied in the world regarding this subject is also show. The Wavelet transform comes as a great support in the area of signal assessment, as it can extract information about time and frequency simultaneously, differently from the Fourier transform. The simulation of the diverse disturbances occurred in the system was accomplished through ATP software (Alternative Transients Program), whose characteristics correctly follow a system of real distribution of CPFL eletric utility. The generated and analyzed voltage disturbances were detected and located by Multiresolution Analysis technique and later classified by the method of the Standard Deviation