Multiresolution and Wavelet Analysis

Este trabalho apresenta o desenvolvimento de um localizador de faltas em linhas de transmissao que utiliza a plataforma de desenvolvimento Beagleboard. O sistema implementado usa registros de oscilografia em padrao COMTRADE como dados de entrada. Ele e composto por quatro modulos basicos, programados em linguagem Python, e tambem por uma interface grafica para entrada de dados e apresentacao de resultados. Sao adotados tres casos de faltas reais e um caso de falta simulada com o software ATP em testes de avaliacao. Os resultados obtidos comprovam a eficiencia do localizador de faltas desenvolvido.

Resumo: Este trabalho apresenta o desenvolvimento de um localizador de faltas em linhas de transmissão que utiliza a plataforma de desenvolvimento Beagleboard. O sistema implementado usa registros de oscilografia em padrão COMTRADE como dados de entrada. Ele é composto por quatro módulos básicos, programados em linguagem Python, e também por uma interface gráfica para entrada de dados e apresentação de resultados. São adotados três casos de faltas reais e um caso de falta simulada com o software ATP em testes de avaliação. Os resultados obtidos comprovam a eficiência do localizador de faltas desenvolvido.

In this paper, systems of Fredholm integral equations of the second kind have been studied. A numerical method for solving these systems is presented. The method is based upon Legendre wavelet approximations. Some examples are presented to illustrate the ability of the method.

-L'objectif de cet article est de proposer l'analyse multirésolution en ondelettes en tant qu'outil efficace permettant d'améliorer la sensibilité des indicateurs scalaires (kurtosis et facteur de crête) pour l'identification des défauts mécaniques induisant des forces impulsives. En effet, ces indicateurs sont très sensibles aux variations dans le signal temporel dues aux chocs périodiques causés par le défaut. Néanmoins, leur fiabilité est immédiatement limitée en présence de niveaux intenses de bruit aléatoire associésà de faibles gravités du défaut. L'analyse Multirésolution en Ondelettes (AMRO) est proposée comme solutionà ce problème. Adaptée pour un tel objectif, plusieurs de ses paramètres d'analyse sont choisis, voire optimisés. Initialement la méthode proposée est appliquée sur un signal simulé. Pour la validation expérimentale, plusieurs séries d'expériences ontété réalisées sur des roulementsà billes età rouleaux cylindriques, sur lesquels différents défauts ontété provoqués. Les mesures ontété prises dans différentes configurations, 210 signaux ontété mesurés dans plusieurs fréquences d'échantillonnage et vitesses de rotation sur un banc d'essais, l'application industrielle est faite sur un groupe turbo-alternateur. Mots clés : Signaux de choc / analyse multirésolution en ondelettes / kurtosis / facteur de crête / détection des défauts Abstract-Optimization of wavelet multiresolution analysis of shock signals. Application to the signals generated by defective rolling bearings. The aim of this paper is to propose the wavelet analysis as an effective tool allowing to improve the sensitivity of scalar indicators (Kurtosis and crest factor) for the identification of mechanical faults inducing impulsive forces. Indeed, these indicators are very sensitive to the variations in temporal signal due to the periodic shocks caused by the defect. Nevertheless, their reliability is immediately limited by the presence of high level of random noise associated to a small gravity of the defect. Wavelet Multiresolution Analysis (WMRA) is proposed as a solution to this problem. Adapted for such objective, several of its parameters were chosen, even optimized. Initially, the proposed method is applied to simulated signal. For the experimental validation, several series of experiments were realized on ball and cylindrical roller bearings, on which various defects were caused. Measurements were taken with various configurations, 210 signals were measured at different sampling rates and rotation speeds on a laboratory test rig, the industrial application is carried out on a turbo alternator.

Subdivision schemes are special multi-resolution analysis (MRA) methods that have become prevalent in computer-aided geometric design. This paper draws useful analogies between the mathematics of subdivision schemes and the hierarchical structures of music compositions. Based on these analogies, we propose new methods for music synthesis and analysis through MRA, which provide a different perspective on music composition, representation and analysis. We demonstrate that the structure and recursive nature of the recently proposed subdivision models [S. Hed and D. Levin, Subdivision models for varying-resolution and generalized perturbations, Int. J. Comput. Math. 88(17) (2011), pp. 3709-3749; S. Hed and D. Levin, A 'subdivision regression' model for data analysis, 2012, in preparation] are well suited to the synthesis and analysis of monophonic and polyphonic musical patterns, doubtless due in large part to the strongly hierarchical nature of traditional musical structures. The analysis methods demonstrated enable the compression and decompression (reconstruction) of selected musical pieces and derive useful features of the pieces, laying groundwork for music classification.

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In this work, we present a collocation method based on the Legendre wavelet combined with the Gauss-Jacobi quadrature formula for solving a class of fractional delay-type integro-differential equations. The problem is considered with either initial or boundary conditions and the fractional derivative is described in the Caputo sense. First, an approximation of the unknown solution is considered in terms of the Legendre wavelet basis functions. Then, we substitute this approximation and its derivatives into the considered equation. The Caputo derivative of the unknown function is approximated using the Gauss-Jacobi quadrature formula. By collocating the obtained residual at the well-known shifted Chebyshev points, we get a system of nonlinear algebraic equations. In order to obtain a continuous solution, some conditions are added to the resulting system. Some error bounds are given for the Legendre wavelet approximation of an arbitrary function. Finally, some examples are included to show the efficiency and accuracy of this new technique.

-L'objectif de cet article est de proposer l'analyse multirésolution en ondelettes en tant qu'outil efficace permettant d'améliorer la sensibilité des indicateurs scalaires (kurtosis et facteur de crête) pour l'identification des défauts mécaniques induisant des forces impulsives. En effet, ces indicateurs sont très sensibles aux variations dans le signal temporel dues aux chocs périodiques causés par le défaut. Néanmoins, leur fiabilité est immédiatement limitée en présence de niveaux intenses de bruit aléatoire associésà de faibles gravités du défaut. L'analyse Multirésolution en Ondelettes (AMRO) est proposée comme solutionà ce problème. Adaptée pour un tel objectif, plusieurs de ses paramètres d'analyse sont choisis, voire optimisés. Initialement la méthode proposée est appliquée sur un signal simulé. Pour la validation expérimentale, plusieurs séries d'expériences ontété réalisées sur des roulementsà billes età rouleaux cylindriques, sur lesquels différents défauts ontété provoqués. Les mesures ontété prises dans différentes configurations, 210 signaux ontété mesurés dans plusieurs fréquences d'échantillonnage et vitesses de rotation sur un banc d'essais, l'application industrielle est faite sur un groupe turbo-alternateur. Mots clés : Signaux de choc / analyse multirésolution en ondelettes / kurtosis / facteur de crête / détection des défauts Abstract-Optimization of wavelet multiresolution analysis of shock signals. Application to the signals generated by defective rolling bearings. The aim of this paper is to propose the wavelet analysis as an effective tool allowing to improve the sensitivity of scalar indicators (Kurtosis and crest factor) for the identification of mechanical faults inducing impulsive forces. Indeed, these indicators are very sensitive to the variations in temporal signal due to the periodic shocks caused by the defect. Nevertheless, their reliability is immediately limited by the presence of high level of random noise associated to a small gravity of the defect. Wavelet Multiresolution Analysis (WMRA) is proposed as a solution to this problem. Adapted for such objective, several of its parameters were chosen, even optimized. Initially, the proposed method is applied to simulated signal. For the experimental validation, several series of experiments were realized on ball and cylindrical roller bearings, on which various defects were caused. Measurements were taken with various configurations, 210 signals were measured at different sampling rates and rotation speeds on a laboratory test rig, the industrial application is carried out on a turbo alternator.

УДК 624.014 АЛГОРИТМ УПРАВЛІННЯ СПЕКТРОМ ВЛАСНИХ ЧАСТОТ І ФОРМ КОЛИВАНЬ ЗА РАХУНОК ЗМІНИ ГЕОМЕТРИЧНИХ ПАРАМЕТРІВ ЩОГЛОВИХ СИСТЕМ Д-р техн. наук В. Б. Гриньов, асист. В. В. Виноградов ALGORITHM FOR CONTROLLING THE SPECTRUM OF EIGENFREQUENCIES AND VIBRATION MODES BY CHARDING THE GEOMETRIC PARAMETERS OF MAST SESTEMS D. Sc. (Tech.) V. B. Grinyov, аssistant V. V. Vynogradov Анотація. У статті розглядається модель щогли з шістьма рівнями закріплення вант. Головну увагу в роботі приділено розгляду методів управління спектром власних частот. Автоматизація процесів обчислення забезпечується за рахунок програмування вбудованого модуля в програмі Revit. У роботі проведено аналіз чутливості для першої та другої власних частот. Наведено співвідношення на випадок завдання пошуку екстремуму власної частоти з заданим номером за умови, що загальний обсяг варійованих поясів фіксований. Ключові слова: щогли з вантовим закріпленням, управління спектром власних коливань, розподіл геометричних характеристик, варійовані величини.

The article considers the problems of managing the efficiency of use of production and technological potential of rolling stock. It is investigated that in order to improve the efficiency of functioning it is necessary to determine the conceptual approaches of the components of the processes of maintenance and operation of rolling stock. This requires the use of technical means and methods of monitoring the technical condition of the wheelsets of the rolling stock. It is investigated that the possibility of successful solution of one of the important tasks of the railway industry risk of improving the quality of repair and restoration works and prolonging the life cycle of rolling stock is possible by ensuring control over finished products and improving process management. It is determined that the form of the concept of conceptual approaches to determining the essence of production and technological potential of maintenance and operation of traction rolling stock is a model of the...

Реферат. Проаналізовано вплив Північноатлантичної осциляції (NAO) на часові зміни опадів над Україною за допомогою методу вейвлет-розкладання. Показано, що найбільші коефіцієнти кореляції між індексами NAO та місячними сумами опадів відзначаються для заходу України і для періоду тривалого домінування однієї фази NAO.

A necessidade de detecção e localização de faltas em linhas de transmissão de maneira rápida e precisa tem crescido de maneira significativa no setor elétrico em âmbito global, principalmente nas últimas décadas. Alterações no modelo de mercado tem feito com que companhias de transmissão alterem a maneira a qual gerenciam e operam seus ativos, uma vez que, em diversas situações, as mesmas são remuneradas não pela potência transmitida, mas sim pela disponibilidade da linha que opera [1]. Assim, sistemas de proteção ou localização de faltas baseado em novas técnicas que sejam mais rápidas e mais precisas que as tradicionais, essencialmente baseadas em fasores, têm, desde o início do desenvolvimento dos sistemas de potência, atraído o interesse de diversas  empresas de energia em experimentar esta nova técnica em aplicações reais em campo.

Esse artigo possui a finalidade de apresentar uma breve revisão da história de ondas viajantes em sistemas de potência até aplicações atuais da tecnologia, bem como apresentar algumas aplicações e experiência no uso desta tecnologia, com ênfase em resultados reais de aplicação.

We present an adaptive graph filtering approach to semi-supervised classification. Adaptive graph filters combine decisions from multiple graph filters using a weighting function that is optimized in a semi-supervised manner. We also demonstrate the multiresolution property of adaptive graph filters by connecting them to the diffusion wavelets. In our experiments, we apply the adaptive graph filters to the classification of online blogs and damage identification in indirect bridge structural health monitoring.

The analysis and processing of sequence of the data presented in the form of time series, is one of the prevalent methodologies in studying of various processes and the phenomena which are concerned to different fields of activity and researches. As a practice shows, the most of investigated time series have a property of self-similarity. At the same time, among existing variety of different ways and methods for the data processing which are presented in the form of a time series, it is possible to allocate the ideology of a multiresolution wavelet-analysis. The essence of such ideology consists in carrying out of wavelet-expansion of investigated data and the subsequent analysis of corresponding coefficients of such expansion-wavelets coefficients. Thus, necessity in answer to a question about properties of such wavelet coefficients is objective. It makes a basis of the given research. Hence, the basic properties of wavelet coefficients of self-similar time series are formulated and proved on theoretical level in this work. Also, there are presented the results of experiments which have confirmed a theoretical substantiation of the basic properties of wavelet coefficients of self-similar time series. They have shown that the considered properties are characteristic for time series with different correlation structure.

This paper presents a block based digital image watermarking scheme that is dependent on the mathematical technique of singular value decomposition (SVD). Traditional SVD watermarking already exists for watermark embedding on the image as a whole. In the proposed approach, the original image is divided into blocks, and then the watermark is embedded in the singular values (SVs) of each block separately. This segmentation and watermarking process makes the watermark much more robust to the attacks such as noise, compression, cropping. Watermark detection is implemented by extracting the watermark from the SVs of the watermarked blocks. Experiments show that extracting the watermark from one block at least is enough to ensure the existence of the watermark.

Resumo-A principal contribuição deste trabalhoé a introdução do Algoritmo de Berlekamp-Massey (BMA) naárea de testes de circuitos integrados. Embora o BMA tenha sido inicialmente proposto para a localização de erros em sistemas de comunicações, de fato, esse provê uma solução geral para a síntese do mais curto registrador de deslocamento com realimentação linear (LFSR) capaz de gerar uma dada seqüência finita. Neste trabalho, mostra-se que com uma ligeira modificação no BMA, pode-se projetar um esquema de teste de circuitos integrados baseado totalmente em umúnico LFSR como gerador de testes no qualé capaz de obter cobertura de falha total e tendo tanto consumo deárea de silício como tempo de teste reduzido.

Технологія вейвлет-фільтрації профілів експресій генів з метою видалення фонового шуму Представлена технология вейвлет-фильтрации профилей экспрессий генов для удаления фонового «белого» шума на основе критерия энтропия Шеннона, который рассчитан посредством использования метода оценки Джеймса и Стейна. Предложена структурная блок-схема процесса определения параметров вейвлет-фильтра, предполагающая расчет энтропии Шеннона как для фильтрованного сигнала, так и для удаленной шумовой компоненты. Ключевые слова: профили экспрессий генов, вейвлеты, трешолдинг, фильтрация. Подано технологію вейвлет-фільтрації профілів експресій генів для видалення фонового «білого» шуму на основі критерію ентропія Шеннона, розрахованого з використанням методу оцінки Джеймса та Стейна. Запропоновано структурну блок-схему процесу визначення параметрів вейвлет-фільтру, яка передбачає розрахунок ентропії Шеннона як для фільтрованого сигналу, так і для видаленої шумової компоненти. Ключові слова: профілі експресій генів, вейвлети, трешолдінг, фільтрація.

Identification and Verification of person on the basis of biometric features has become known in our society. When the biometric systems are connected to a person’s body remarkably decreases the possibility of fraud. A biometric system basically is a pattern recognition system and to recognize the pattern or the image is not an easy task. From the various biometric techniques, recognisation done by fingerprint technique is best. Due to various qualities of fingerprint technique like easy to use, reliabilty, high stability, high acceptance in indentification and authentification, fingerprint technique is used mostly. The use of such technique ensures that the facilities provided are used by a authenticated user and no one else. Examples of such applications include secure access to buildings, computer systems, laptops, cellular phones, and ATMs. In security applications, biometrics are most often used to verify a person’s identity for the purpose of granting access to property or inf...

Esse trabalho apresenta um algoritmo de localização de faltas usando a Teoria das Ondas Viajantes - TOV e Transformada Wavelet Discreta – TWD, através do Python. A linguagem Python é apresentada como uma linguagem de programação para extração de características de dados de sinais de faltas modeladas em linhas de transmissão usando o Kit Smart Grid. Os resultados encontrados neste artigo apresentaram uma boa acurácia na localização da falta com erros abaixo de 1% para faltas fase-terra.

Este trabalho apresenta um estudo comparativo entre diferentes famílias de Transformada Wavelet aplicadas à análise cepstral de sinais digitais de fala humana, com o objetivo específico de determinar o período de pitch dos mesmos e, ao final, propõe um algoritmo diferencial para realizar tal operação, levando-se em consideração aspectos importantes do ponto de vista computacional, tais como: desempenho, complexidade do algoritmo, plataforma utilizada, dentre outros. São apresentados também, os resultados obtidos através da implementação da nova técnica (baseada na transformada wavelet) em comparação com a abordagem tradicional (baseada na transformada de Fourier). A implementação da técnica foi testada em linguagem C++ padrão ANSI sob as plataformas Windows XP Professional SP3, Windows Vista Business SP1, Mac OSX Leopard e Linux Mandriva 10.

Subdivision schemes are special multi-resolution analysis (MRA) methods that have become prevalent in computer-aided geometric design. This paper draws useful analogies between the mathematics of subdivision schemes and the hierarchical structures of music compositions. Based on these analogies, we propose new methods for music synthesis and analysis through MRA, which provide a different perspective on music composition, representation and analysis. We demonstrate that the structure and recursive nature of the recently proposed subdivision models [S. Hed and D. Levin, Subdivision models for varying-resolution and generalized perturbations, Int. J. Comput. Math. 88(17) (2011), pp. 3709-3749; S. Hed and D. Levin, A 'subdivision regression' model for data analysis, 2012, in preparation] are well suited to the synthesis and analysis of monophonic and polyphonic musical patterns, doubtless due in large part to the strongly hierarchical nature of traditional musical structures. The analysis methods demonstrated enable the compression and decompression (reconstruction) of selected musical pieces and derive useful features of the pieces, laying groundwork for music classification.

Este trabalho apresenta uma aplicação da Transformada Wavelet (TW) para analisar os transitórios de alta freqüência em um sistema de transmissão gerados por uma situação de falta, tendo como principal objetivo, a determinação do ponto de ocorrência da mesma, o mais precisamente possível. A abordagem baseia-se na teoria de ondas viajantes, onde, em função do tempo de propagação do sinal entre o ponto de falta e os terminais da linha, revelados pela TW, a localização da falta é estimada. Desta tomada de tempo, obtém-se a indicação da localização de uma determinada situação de falta pela implementação prática de um algoritmo computacional, dispondo-se do software MatLab?. Nesta implementação, o usuário pode escolher dentre as técnicas de localização a ser utilizada, de modo a trabalhar com dados registrados em um ou em ambos os terminais da linha, conforme sua necessidade e/ou disponibilidade dos recursos requeridos. Independente da técnica de localização utilizada, o algoritmo desenvo...

We present a fully adaptive numerical scheme for evolutionary PDEs in Cartesian geometry based on a second-order finite volume discretization. A multiresolution strategy allows local grid refinement while controlling the approximation error in space. For time discretization we use an explicit Runge-Kutta scheme of second-order with a scale-dependent time step. On the finest scale the size of the time step is imposed by the stability condition of the explicit scheme. On larger scales, the time step can be increased without violating the stability requirement of the explicit scheme. The implementation uses a dynamic tree data structure. Numerical validations for test problems in one space dimension demonstrate the efficiency and accuracy of the local time-stepping scheme with respect to both multiresolution scheme with global time stepping and finite volume scheme on a regular grid. Fully adaptive three-dimensional computations for reaction-diffusion equations illustrate the additional speed-up of the local time stepping for a thermo-diffusive flame instability.

Adaptive strategies in space and time allow considerable speed-up of finite volume schemes for conservation laws, while controlling the accuracy of the discretization. In this paper, a multiresolution technique for finite volume schemes with explicit time discretization is presented. An adaptive grid is introduced by suitable thresholding of the wavelet coefficients, which maintains the accuracy of the finite volume scheme of the regular grid. Further speed-up is obtained by local scale-dependent time stepping, i.e., on large scales larger time steps can be used without violating the stability condition of the explicit scheme. Furthermore, an estimation of the truncation error in time, using embedded Runge-Kutta type schemes, guarantees a control of the time step for a given precision. The accuracy and efficiency of the fully adaptive method is illustrated with applications for compressible Euler equations in one and two space dimensions.

Apresenta-se nesse trabalho uma análise sobre o impacto de diferentes tipos de modelos de linhas de transmissão (LTs) disponíveis em programas Electromagnetic Transients Program (EMTP) sobre estudos relacionados à propagação de ondas viajantes (OVs). Os modelos considerados são: Bergeron e J. Martí, os quais são implementados assumindo LTs perfeitamente transpostas, transpostas e não transpostas. No estudo proposto, consideram-se transitórios induzidos por faltas monofásicas, os quais são avaliados por meio de um método típico de filtragem de OVs. Em cada caso, sinais nos domínios de fases e modal são avaliados, revelando diferenças do ponto de vista da propagação de OVs quando diferentes modelos de LT são utilizados. Dos resultados obtidos, conclui-se que cada modelo de LT resulta em diferentes padrões de propagação das OVs, especialmente nas ondas de modo terra.

We present a multiresolution classification framework with semi-supervised learning on graphs with application to the indirect bridge structural health monitoring. Classification in real-world applications faces two main challenges: reliable features can be hard to extract and few labeled signals are available for training. We propose a novel classification framework to address these problems: we use a multiresolution framework to deal with nonstationarities in the signals and extract features in each localized time-frequency region and semi-supervised learning to train on both labeled and unlabeled signals. We further propose an adaptive graph filter for semi-supervised classification that allows for classifying unlabeled as well as unseen signals and for correcting mislabeled signals. We validate the proposed framework on indirect bridge structural health monitoring and show that it performs significantly better than previous approaches. Index Terms-Multiresolution classification, semi-supervised learning, discrete signal processing on graphs, adaptive graph filter, indirect bridge structural health monitoring. I. INTRODUCTION C LASSIFICATION is a signal processing task whose goal is to design a map that associates each input signal with a predefined class label. It is widely used in a number of realworld applications, such as geophysical waveform classification Manuscript

Digital images have an inherent amount Deepika Sharma of noise introduced either by the imaging process or manual creation. Singular value decomposition (SVD) is one of the most important and useful factorizations in linear algebra. We describe how SVD is applied to problems involving image processing—in particular, how SVD removes the noise from digital images using linear calculations. In this paper, we proposed an efficient model of noise removal. Further the results have been compared with that of existing noise removal median filter to investigate the extent of removal of unwanted noise from digital images.

In the article, an economic and mathematical model is constructed for the optimal distribution of the state order for the training of specialists, based on the ranking of specialties of universities. By the hypothetical example, the distribution of the government procurement for the training of specialists has been figured on using the proposed mathematical model. According to the results of the analysis, the expediency of using the proposed model in domestic practice is substantiated.

Технологія вейвлет-фільтрації профілів експресій генів з метою видалення фонового шуму Представлена технология вейвлет-фильтрации профилей экспрессий генов для удаления фонового «белого» шума на основе критерия энтропия Шеннона, который рассчитан посредством использования метода оценки Джеймса и Стейна. Предложена структурная блок-схема процесса определения параметров вейвлет-фильтра, предполагающая расчет энтропии Шеннона как для фильтрованного сигнала, так и для удаленной шумовой компоненты. Ключевые слова: профили экспрессий генов, вейвлеты, трешолдинг, фильтрация. Подано технологію вейвлет-фільтрації профілів експресій генів для видалення фонового «білого» шуму на основі критерію ентропія Шеннона, розрахованого з використанням методу оцінки Джеймса та Стейна. Запропоновано структурну блок-схему процесу визначення параметрів вейвлет-фільтру, яка передбачає розрахунок ентропії Шеннона як для фільтрованого сигналу, так і для видаленої шумової компоненти. Ключові слова: профілі експресій генів, вейвлети, трешолдінг, фільтрація.

We present an adaptive graph filtering approach to semi-supervised classification. Adaptive graph filters combine decisions from multiple graph filters using a weighting function that is optimized in a semi-supervised manner. We also demonstrate the multiresolution property of adaptive graph filters by connecting them to the diffusion wavelets. In our experiments, we apply the adaptive graph filters to the classification of online blogs and damage identification in indirect bridge structural health monitoring.

Esta pesquisa apresenta um método para a estimação da freqüência em sistemas elétricos de potência utilizando filtros adaptativos baseados no método dos mínimos quadrados (MMQ). A análise do sistema de potência é realizada através da conversão das tensões trifásicas em um sinal complexo pela aplicação da transformada α β, sendo este direcionado ao algoritmo de filtragem adaptativa. As simulações computacionais, assim como a modelagem dos equipamentos, foram realizadas utilizando-se do software ATP (Alternative Transients Program). Este teve por objetivo, gerar dados das mais diversas e distintas situações para a verificação e análise da metodologia proposta, em comparação a resultados obtidos de um determinado relé comercial, habilitado à supervisão da freqüência do sistema.

A space-time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value multiresolution analysis using Hermite interpolation. Thus locally refined dyadic spatial grids are introduced which are efficiently implemented with dynamic quadtree data structures. For adaptive time integration, an embedded Runge-Kutta method is employed. The precision of the new fully adaptive method is analysed and speed up of CPU time and memory compression with respect to the uniform grid discretization are reported.

The analysis and processing of sequence of the data presented in the form of time series, is one of the prevalent methodologies in studying of various processes and the phenomena which are concerned to different fields of activity and researches. As a practice shows, the most of investigated time series have a property of self-similarity. At the same time, among existing variety of different ways and methods for the data processing which are presented in the form of a time series, it is possible to allocate the ideology of a multiresolution wavelet-analysis. The essence of such ideology consists in carrying out of wavelet-expansion of investigated data and the subsequent analysis of corresponding coefficients of such expansion-wavelets coefficients. Thus, necessity in answer to a question about properties of such wavelet coefficients is objective. It makes a basis of the given research. Hence, the basic properties of wavelet coefficients of self-similar time series are formulated and proved on theoretical level in this work. Also, there are presented the results of experiments which have confirmed a theoretical substantiation of the basic properties of wavelet coefficients of self-similar time series. They have shown that the considered properties are characteristic for time series with different correlation structure.

In this paper, we study the existence of weak solutions for a class of nonlinear parabolic equations with regular data in the setting of variable exponent Sobolev spaces. We prove a "version" of a weak Lebesgue space estimate that goes back to "Lions J. L. Quelques méthodes de résolution des problèmes aux limites. Dunod, Paris (1969)" for parabolic equations with anisotropic constant exponents (pi(⋅)=pi).

The transmission line is the equipment of the electrical system most conducive to an electrical fault. Based on the difficult conditions of access to these lines, such as the distance from cities and because of its large dimensions, it is essential to locate an electrical fault accurately and quickly. The objective of this work is to carry out a comparative analysis between two aspects of the Girgis, Hart, and Peterson (1992) Algorithm to locate an electrical fault: the complete and the simplified model. To simulate the transmission line, the ATP® software was used and the algorithms were developed in software aimed at numerical calculations. The simulation scenarios took into account variations in the resistive and inductive parameters of some sections of the transmission line, in search of the location of the fault point and the respective location error due to these changes.

In this paper we consider a specific way of organizing 1D signals or 2D image databases, such that a more efficient storage and faster querying is achieved. A multiresolution technique of data processing is used in order of saving the most significant processed data.

Aos meus pais Hermínio e Marta que desde minha infância me ensinaram, me apoiaram e me valorizaram. Que estiveram ao meu lado em todo o decorrer deste trabalho, que sempre acreditaram em mim. À meu esposo Everaldo, pelo constante incentivo e compreensão. À meu irmão Igor, pelos momentos de descontração enquanto escrevia este texto. Em especial ao Prof. Dr. Petrônio Vieira Junior, pela sua sábia orientação, apoio e amizade. Aos colegas de pós-graduação Lucélio e Klaus, pelo fornecimento de dados e modelos de linhas de transmissão. Ao Programa de Pós-graduação em Engenharia Elétrica, pela oportunidade de usufruir espaços, livros, equipamentos, em suma, por toda a estrutura a mim proporcionada. À Universidade Federal do Pará, pelo suporte desde minha graduação. Aos professores e colegas, pela colaboração e paciência. v SUMÁRIO AGRADECIMENTOS .

The necessity in image compression continuously grows during the last decade. A number of image compression techniques have been developed in the past different kind of application. But, majority of the image compression approaches available in the literature have poor visual quality and low PSNR (Peak Signal to Noise Ratio) value. In recent years, discrete time wavelet transform (DWT) is observed to be very efficient for image compression techniques. The existing work implemented with SPIHT (Set Partitioning in Hierarchical Tress) compression scheme. This paper introduce a proposed method of implementation wavelet family which is combine with SPIHT compression scheme using PSO (Particle Swarm Optimization) which gives significant improvement in image visual quality such as PSNR value than existing work.

Multispectral satellite images are tools that allow the analysis of phenomena developed on the Earth's surface without being in contact. It is a raster model so it is possible to decompose it into a digital signal. There is a certain data that presents alterations (noise) due to errors caused by the sensors, atmospheric conditions, among others. Such examples affect its use and its derived products. Satellite images by their nature present difficulty in their processing and handling due to the considerable weight they have; whose problem justified the present work. The objective is to minimize white noise and to compress the image with the least possible loss of information through the Multiresolution Analysis (MRA) technique and Wavelet transformation. The images worked belong to the National Recreation Area "El Boliche" (Ecuador) that is next to the Cotopaxi volcano. Through a standard deviation evaluation of the obtained wavelet coefficients, the order of the "Discrete Wavelet Transform" (DWT) was established in the Daubechies (db) and Haar families. With db3 level 4, obtained a compression of 11.268% in respect to the original weight and with Haar level 4 11.288% as the best results. The wavelet db is more effective than the Haar type for the treatment of multispectral satellite images in the elimination of white noise and compression by means of the MRA, with a reconstruction of the signal without loss of information due to the type of wavelet used, which is evidenced in the image.

The representation of transmission lines in modal domain is widely known. However, there is nothing in the literature regarding the behavior of loads in the modal domain connected to the receiver of a transmission line. In this article we will show how the transmission lines are represented in the modal domain, considering the presence of connected loads in their terminals. The results show that balanced loads with or without mutual coupling can be represented in the modal domain as uncoupled single-phase loads that are connected at the receiving terminal of each line propagation mode. When it comes to unbalanced loads it is found that they are also represented by single phase loads. However, in the case of unbalanced loads, there is a coupling between these single-phase loads. The study allows the understanding of how transmission lines with loads are represented, in the modal domain, in software that performs simulations of electromagnetic transients in electrical power systems (A...

We present two versions of third order accurate jet schemes, which achieve high order accuracy by tracking derivative information of the solution along characteristic curves. For a benchmark linear advection problem, the efficiency of jet schemes is compared with WENO and Discontinuous Galerkin methods of the same order. Moreover, the performance of various schemes in tracking solution contours is investigated. It is demonstrated that jet schemes possess the simplicity and speed of WENO schemes, while showing several of the advantages as well as the accuracy of DG methods.

A comparison between two different ways of extracting coherent vortices in three-dimensional (3D) homogeneous isotropic turbulence is performed, using either orthogonal or biorthogonal wavelets. The method is based on a wavelet decomposition of the vorticity field and a subsequent thresholding of the wavelet coefficients. The coherent vorticity is reconstructed from a few strong wavelet coefficients, while the incoherent vorticity is reconstructed from the remaining weak coefficients. The choice of the threshold, which has no adjustable parameters, is motivated for the orthogonal case from the denoising theory. Using only 3% of the coefficients we show that both decompositions, that is orthogonal and biorthogonal, extract the coherent vortices. They contain most of the energy (around 99% in both cases) and retain 74% and 68% of the enstrophy in the orthogonal and biorthogonal cases, respectively. The incoherent background flow for the orthogonal decomposition, which corresponds to 97% of the wavelet coefficients, is structureless, decorrelated, and has a Gaussian velocity probability distribution function (PDF). In contrast, for the biorthogonal decomposition, the background flow exhibits quasitwo-dimensional (2D) structures and yields an exponential velocity PDF. Moreover, the biorthogonal decomposition loses 3.7% of both enstrophy and helicity, while they are conserved by the orthogonal decomposition.

Este trabalho apresenta o uso da transformada wavelet para quantificar variações de tensão de curta duração a partir de oscilografias gravadas obtidas dos registradores de perturbações do sistema de análise pó-despacho das concessionárias de energia elétrica, com o objetivo de obter uma base de dados com as características de fenômenos de curta duração, que permita o uso de procedimentos de análise e avaliação,para se obter informações sobre o comportamento e desempenho do sistema elétrico.