Transformadores de potência são dispositivos que requerem atenção especial devido a sua grande importância ao sistema elétrico de potência no qual ele está conectado. Geralmente relés diferenciais são utilizados como proteção primária em transformadores de potência. Nestes relés, a corrente diferencial é comparada com um nível de ajuste e caso ocorra uma falta interna, o transformador deverá ser desconectado do restante do sistema. Entretanto, a simples detecção da presença de uma corrente diferencial não é suficiente para distinguir faltas internas de outras situações que também podem produzir tal corrente. Tais situações surgem durante a energização dos transformadores, devido a saturação dos transformadores de corrente, entre outras, as quais podem resultar em uma incorreta atuação da proteção. Uma rápida e correta discriminação entre faltas internas e outras situações é um dos desafios da moderna proteção de transformadores de potência. A respeito da identificação de faltas internas ou situações de energização, além da mencionada lógica diferencial é acrescentado uma subrotina baseada na restrição de harmônicas. Neste método, a corrente de energização é reconhecida através da presença de uma segunda harmônica obtida por filtros de Fourier. No entanto, o método de filtragem pode algumas vezes retardar a operação da proteção. Além disto, uma componente de segunda harmônica pode também estar presente durante uma falta interna. Este trabalho propõe a utilização da transformada Wavelet - uma poderosa ferramenta matemática - empregada como um meio rápido e eficiente de analisar as formas de onda de transformadores de potência e como uma alternativa a tradicional transformada de Fourier. Os sinais das correntes diferenciais são processados pelas transformadas discretas Wavelet, visando obter uma discriminação entre ambas situações (energização e falta). Um nível de limiar é utilizado após a decomposição Wavelet do sinal para discriminar entre as situações descritas. A janela de dados utilizada para este propósito pode ser variada. Para testar o algoritmo proposto, as simulações de energização e falta foram implementadas, utilizando o programa ATP (\"Alternative Transient Program\"). Em situações onde a janela de dados é reduzida para 1/4 de ciclo o critério de discriminação pode ser otimizado utilizando a transformada discreta de Wavelet auxiliada com técnicas de reconhecimento de padrões. Este trabalho apresenta a utilização de redes neurais artificiais para tal finalidade como exemplo. Resultados encorajadores são apresentados sobre a capacidade de discriminação para as situações descritas assim como a rapidez de resposta quando comparados aos métodos tradicionais. / Power transformers are devices that require special maintenance and care due to their importance to the electrical system to which they are connected. Generally, differential relays are used for the primary protection of large transformers. In such relays, differential currents are compared to a threshold and in the case of an internal fault, the transformer should be disconnected from the rest of the system. However, a simple detection of a differential current is not sufficient to distinguish internal faults from other situations that also produce such a current. Some of these situations appear during transformer energization (inrush currents), CT (current transformer) saturation, among others, which can result in an incorrect trip. A correct and fast distinction of internal faults from the other situations mentioned is one of the challenges for modern protection of power transformers. Concerning the identification of internal faults as opposed to inrush currents, the approach tarditionally used is the aforementioned differential logic together with harmonic restraint. In this method, transformer inrush current due to energization is recognized on the basis of second harmonic components obtained by Fourier filters. However, the filtering method can sometimes delay the protection process. In addition to this, a second harmonic component can also be present during internal faults. This work proposes Wavelet transform - a powerful mathematical tool - employed as a fast and effective means of analyzing waveforms from power transformers, as an alternative to the traditional Fourier transform. The differential signals are processed by discrete Wavelet transform to obtain the discrimination between both situations (inrush and fault). A threshold level is utilized after the Wavelet decomposition to discriminate the situations describeb. The time window used for such purpose can be varied. In order to test proposed algorithm, simulations of fault and inrush currents in a power transformer were implemented using ATP ( \"Alternative Transient Program\") software. When the time window is reduced to only 1/4 of the cycle the discrimination criteria should be optimized using a pattern recognition technique to aid the Discrete Wavelet transform. This study shows as a sample for this purpose the use of artificial neural networks. Very encouraging results are presented concerning the capacity of discrimination of the described situations as well as the speed of response when compared to the traditional method.

O choque hipovolêmico foi induzido em 14 ratos machos através de sucessivos sangramentos de 3,1 ml de sangue para cada 100 g de peso. Após o período de sangrias, foi iniciado o tratamento com solução salina isotônica (7,5 % NaCl por 0,4 ml/g de peso) ou hipertônica (0,9 % NaCl por 0,4 ml/g de peso). Iniciando com o sinal basal, a aquisição de dados da pressão arterial foi feita durante todo o experimento que durou aproximadamente 30 minutos. O objetivo deste trabalho é analisar a variabilidade do débito cardíaco durante a indução do choque e identificar se o mecanismo de compensação de perda de volume está funcionando. A análise está focada no débito cardíaco porque ele depende linearmente do volume sistólico e da freqüência cardíaca. Um método não invasivo foi implementado para calcular o volume sistólico diretamente do sinal da pressão arterial. A análise wavelet foi usada para encontrar as freqüências principais do sinal da pressão arterial e também suas variabilidades durante cada estágio. Durante o experimento, a estabilidade do débito cardíaco era esperada, pois a freqüência cardíaca deve aumentar para compensar a perda de volume. Na maioria dos casos foi observado que a freqüência aumenta nos dois primeiros estágios, seguida de uma queda significativa. Como conseqüência o débito cardíaco diminuiu durante os estágios intermediários, mostrando que o mecanismo de compensação não estava funcionando apropriadamente. Em três casos, as freqüências aumentaram somente no estágio final. Esta anomalia sugere uma investigação mais profunda incluindo resposta ao tratamento e acompanhamento da evolução do choque / Hypovolemic shock was induced in fourteen male rats by successive bleeding. During 30 minutes, after base signal acquisition, 3.1ml of blood for each 100g of weight was collected. After this period, a treatment was initiated with isotonic saline solution (7.5 % NaCl each 0.4 ml/g of weight) or hypertonic (0.9 % NaCl each 0.4 ml/g of weight). The arterial pressure signal was captured during all the experiment. The goal of this work is to analise the variability of the cardiac debit during the induction of shock and identify whether the physiological mechanism to compensate the loss of volume is working. The analysis is focused on the cardiac debit because it depends linearly on systolic volume and cardiac frequency. A non-invasive method was implemented to calculate the systolic volume directly from the arterial pressure signal. Wavelet analysis was used to find the main frequencies and also their variability during each stage. The cardiac debit stability was expected, during experiment because the cardiac frequency must increase to compensate the lost of volume. In most cases was observed that the frequency increases in the first two stages followed by a significant decrease. As a consequence the cardiac debit decreases during the intermediate stages, showing that the compensation mechanism was not working properly. In three cases the frequencies increased only in the final stage. This anomalie suggests a deeper investigation including response to treatment and shock evolution

Medical image is a core step of medical diagnosis and has been diffusely applied in modern medical domain. The technology of modern medical image is more and more mature which could present images in different modes and features. Medical image fusion is the technology that could compound two mutual images into one according to certain rules to achieve clear visual effect. By observing medical fusion image, doctor could easily confirm the position of illness. According to the mutual features of CT medical image and MRI medical image, based on the technology of wavelet transform, the paper presents twp effective and applied medical image fusion methods. The first method is based on the features of certain area. The principle is to construct weighted factor and matching degree with certain related parameters to compound the area of high frequency which presents the detailed information. To the area of low frequency, principle of maximum absolute value is selected. Finally we get the fusion image by wavelet reconfiguration. By estimate of subjectivity and objectivity, the method is applied that could export excellent visual effect and good parameters. The other method is based on lifting wavelet. It decomposes the original image to area of low frequency and high frequency, and then transforms them with different fusion rules. To area of low frequency, weighted fusion is applied and to area of high frequency, rule of maximum standard deviation is chosen. Finally we get fusion image from wavelet reconstruction. By the estimate of subjectivity and objectivity, the method is an applied and excellent way that keeps the detailed information effectively and presents clear profile. At the same time, the executed time is shorter than others.

This paper presents a wavelet Galerkin scheme for the fast solution of boundary integral equations. Wavelet Galerkin schemes employ appropriate wavelet bases for the discretization of boundary integral operators. This yields quasi-sparse system matrices which can be compressed to O(N_J) relevant matrix entries without compromising the accuracy of the underlying Galerkin scheme. Herein, O(N_J) denotes the number of unknowns. The assembly of the compressed system matrix can be performed in O(N_J) operations. Therefore, we arrive at an algorithm which solves boundary integral equations within optimal complexity. By numerical experiments we provide results which corroborate the theory.

The wavelet Galerkin scheme for the fast solution of boundary integral equations produces approximate solutions within discretization error accuracy offered by the underlying Galerkin method at a computational expense that stays proportional to the number of unknowns. In this paper we present an adaptive version of the scheme which preserves the super-convergence of the Galerkin method.

In this paper we consider the fully discrete wavelet Galerkin scheme for the fast solution of boundary integral equations in three dimensions. It produces approximate solutions within discretization error accuracy offered by the underlying Galerkin method at a computational expense that stays proportional to the number of unknowns. We focus on implementational details of the scheme, in particular on numerical integration of relevant matrix coefficients. We illustrate the proposed algorithms by numerical results.

The Wavelet Finite Element Method (WFEM) involves combining the versatile wavelet analysis with the classical Finite Element Method (FEM) by utilizing the wavelet scaling functions as interpolating functions; providing an alternative to the conventional polynomial interpolation functions used in classical FEM. Wavelet analysis as a tool applied in WFEM has grown in popularity over the past decade and a half and the WFEM has demonstrated potential prowess to overcome some difficulties and limitations of FEM. This is particular for problems with regions of the solution domain where the gradient of the field variables are expected to vary fast or suddenly, leading to higher computational costs and/or inaccurate results. The properties of some of the various wavelet families such as compact support, multiresolution analysis (MRA), vanishing moments and the “two-scale” relations, make the use of wavelets in WFEM advantageous, particularly in the analysis of problems with strong nonlinearities, singularities and material property variations present. The wavelet based finite elements (WFEs) presented in this study, conceptually based on previous works, are constructed using the Daubechies and B-spline wavelet on the interval (BSWI) wavelet families. These two wavelet families possess the desired properties of multiresolution, compact support, the “two scale” relations and vanishing moments. The rod, beam and planar bar WFEs are used to study structural static and dynamic problems (moving load) via numerical examples. The dynamic analysis of functionally graded materials (FGMs) is further carried out through a new modified wavelet based finite element formulation using the Daubechies and BSWI wavelets, tailored for such classes of composite materials that have their properties varying spatially. Consequently, a modified algorithm of the multiscale Daubechies connection coefficients used in the formulation of the FGM elemental matrices and load vectors in wavelet space is presented and implemented in the formulation of the WFEs. The approach allows for the computation of the integral of the products of the Daubechies functions, and/or their derivatives, for different Daubechies function orders. The effects of varying the material distribution of a functionally graded (FG) beam on the natural frequency and dynamic response when subjected to a moving load for different velocity profiles are analysed. The dynamic responses of a FG beam resting on a viscoelastic foundation are also analysed for different material distributions, velocity and viscous damping profiles. The approximate solutions of the WFEM converge to the exact solution when the order and/or multiresolution scale of the WFE are increased. The results demonstrate that the Daubechies and B-spline based WFE solutions are highly accurate and require less number of elements than FEM due to the multiresolution property of WFEM. Furthermore, the applied moving load velocities and viscous damping influence the effects of varying the material distribution of FG beams on the dynamic response. Additional aspects of WFEM such as, the effect of altering the layout of the WFE and selection of the order of wavelet families to analyse static problems, are also presented in this study.

Orientadores: Rangel Arthur, Francisco José Arnold / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Tecnologia / Made available in DSpace on 2018-08-26T23:50:19Z (GMT). No. of bitstreams: 1 Pedrosa_JezerOliveira_M.pdf: 1689446 bytes, checksum: fa812fba987c6c905ee50de809f6f732 (MD5) Previous issue date: 2015 / Resumo: Neste trabalho é criada uma base de dados de sinais de corrente de cargas domésticas e é proposta uma técnica para a identificação dessas cargas, etapa necessária para a desagregação das cargas dentro do contexto SMART GRID. A técnica de desagregação proposta baseia-se no uso de redes neurais e na transformada wavelet. A identificação das cargas elétricas tem como objetivo a descoberta de qual equipamento está ligado na rede elétrica. Dessa forma é possível calcular separadamente quanto cada equipamento está consumindo de energia elétrica. Os resultados obtidos a partir das informações extraídas com o emprego dos algoritmos propostos são discutidos e apresentados. Os algoritmos de processamento e identificação das cargas via redes neurais e transformada wavelet foram desenvolvidos no ambiente do MATLAB. Os resultados encontrados comprovam a eficácia da técnica proposta / Abstract: This work aims to create a current signal database of domestic loads and proposes a technique for identifying such loads, necessary step for the disaggregation of loads in the Smart-grid context. The disaggregation of the proposed technique is based on the use of neural networks and wavelet transform. The identification of electrical loads aims to discover what equipment is connected to utility power. Thus it is possible to calculate separately for each device is consuming electricity. The results obtained from the information derived from the proposed algorithms are discussed and presented. The algorithms processing and load identification by wavelet and neural networks were developed using MATLAB environment. The results prove the efficiency of the proposed technique / Mestrado / Tecnologia e Inovação / Mestre em Tecnologia

Esta dissertação apresenta o desenvolvimento e avaliação de um método para a segmentação de vasos sangüíneos em imagens de retina, em que se usa a transformada wavelet contínua bidimensional combinada com classificação supervisionada. A segmentação dos vasos é a etapa inicial para a análise automática das imagens, cujo objetivo é auxiliar a comunidade médica na detecção de doenças. Entre outras doenças, as imagens podem revelar sinais da retinopatia diabética, uma das principais causas de cegueira em adultos, que pode ser prevenida se detectada em um diagnóstico precoce. A abordagem apresentada consiste na geração de segmentações pela classificação supervisionada de pixels nas classes \"vaso\" e \"não vaso\". As características usadas para classificação são obtidas através da transformada wavelet contínua bidimensional usando a wavelet de Gabor. Resultados são avaliados nos bancos públicos DRIVE e STARE de imagens coloridas através da análise ROC (\"receiver operating characteristic\", ou característica de operação do receptor). O método atinge áreas sob curvas ROC de 0.9614 e 0.9671 nos bancos DRIVE e STARE, respectivamente, ligeiramente superiores àquelas apresentadas por outros métodos do estado da arte. Apesar de bons resultados ROC, a análise visual revela algumas dificuldades do método, como falsos positivos ao redor do disco óptico e de patologias. A wavelet de Gabor mostra-se eficiente na detecção dos vasos, superando outros filtros lineares. Bons resultados e uma classificação rápida são obtidos usando o classificador bayesiano em que as funções de densidade de probabilidade condicionais às classes são descritas por misturas de gaussianas. A implementação do método está disponível na forma de \"scripts\" código aberto em MATLAB para pesquisadores interessados em detalhes de implementação, avaliação ou desenvolvimento de métodos. / This dissertation presents the development and evaluation of a method for blood vessel segmentation in retinal images which combines the use of the two-dimensional continuous wavelet transform with supervised classification. Segmentation of the retinal vasculature is the first step towards automatic analysis of the images, aiming at helping the medical community in detecting diseases. Among other diseases, the images may reveal signs of diabetic retinopathy, a leading cause of adult blindness, which can be prevented if identified early enough. The presented approach produces segmentations by supervised classification of each image pixel as \"vessel\" or \"nonvessel\", with pixel features derived using the two-dimensional continuous Gabor wavelet transform. Results are evaluated on publicly available DRIVE and STARE color image databases using ROC (receiver operating characteristic) analysis. The method achieves areas under ROC curves of 0.9614 and 0.9671 on the DRIVE and STARE databases, respectively, being slightly superior than that presented by state-of-the-art approaches. Though good ROC results are presented, visual inspection shows some typical difficulties of the method, such as false positives on the borders of the optic disc and pathologies. The Gabor wavelet shows itself efficient for vessel enhancement, outperforming other linear filters. Good segmentation results and a fast classification phase are obtained using the Bayesian classifier with class-conditional probability density functions described as Gaussian mixtures. The method\'s implementation is available as open source MATLAB scripts for researchers interested in implementation details, evaluation, or development of methods.

Tato práce se zabývá možností využití vlnkové transformace v aplikacích, které se zabývají potlačením šumu. Především se jedná o oblast filtrace signálu EKG. Úkolem je zhodnotit vliv různých parametrů nastavení samotné filtrace a zjistit jaký vliv má různé nastavení prahování wavelet koeficientů. Výsledkem práce je také stanovení hodnot prahů, stanovení nejlepšího způsobu rozkladu signálu a volba rekonstrukčních bank filtrů. Text obsahuje výsledky Wienerovy filtrace, při které byly testovány různé banky rozkladových a rekonstrukčních filtrů.Všechny popsané filtrační metody byly testovány na reálných záznamech EKG s aditivním myopotenciálním šumem. Algoritmy byly realizovány v prostředí MATLAB.