O presente trabalho visa a utilização da transformada Wavelet no monitoramento do sistema elétrico no que diz respeito a problemas de qualidade da energia com o intuito de detectar, localizar e classificar os mesmos. A transformada Wavelet tem surgido na literatura como uma nova ferramenta para análise de sinais, utilizando funções chamadas Wavelet mãe para mapear sinais em seu domínio, fornecendo informações simultâneas nos domínios tempo e freqüência. A transformada Wavelet é realizada através de filtros decompondo-se um dado sinal em análise multiresolução. Por esta, obtém-se a detecção e a localização de distúrbios relacionados com a qualidade da energia decompondo-se o sinal em dois outros que representam uma versão de detalhes (correspondente as altas freqüências do sinal) e uma versão de aproximação (correspondente as baixas freqüências do sinal). A versão de aproximação é novamente decomposta obtendo-se novos sinais de detalhes e aproximações e assim sucessivamente. Sendo assim, os distúrbios podem ser detectados e localizados no tempo em função do seu conteúdo de freqüência. Estas informações fornecem também características únicas pertinentes a cada distúrbio, permitindo classificá-los. Desta forma, propõe-se neste trabalho o desenvolvimento de um algoritmo classificador automático de distúrbios relacionados com a qualidade da energia baseado unicamente nas decomposições obtidas da análise multiresolução. / The aim of the present dissertation is to apply the Wavelet transform to analyze power quality problems, detecting, localizing and classifying them. The topic Wavelet transform, has appeared in the literature as a new tool for the analysis of signals, using functions called mother Wavelet to map signals in its domain, supplying information in the time and frequency domain, simultaneously. Wavelet transform is accomplished through filters decomposing a provided signal in multiresolution analysis. The detection and localization of disturbances are obtained by decomposing a signal into two other signals that represent, a detailed version (high frequency signals) and a smoothed version (low frequency signals). The smoothed version is decomposed again, and new detailed and smoothed signals are obtained. This process is repeated as many times as necessary and the disturbances can be detected and localized in the time as a function of its level frequency. This information also supplies characteristics to each disturbance, allowing classifying them. Thus, this research presents a way to develop an automatic classifying algorithm of power quality disturbances, based only on multiresolution analysis.

Wavelets are functions used to approximate data and can be traced back to several different areas, including seismic geology and quantum mechanics. Wavelets are applicable in many areas, including fingerprint and data compression, earthquake prediction, speech discrimination, and human vision. In this paper, we first give a brief history on the origins of wavelet theory. We will then discuss the work of Daubechies, whose construction of continuous, compactly supported scaling functions resulted in an explosion in the study of wavelets in the 1990's. These scaling functions allow for the construction of Daubechies' wavelets. Next, we shall use the algorithm to construct the Daubechies D4 scaling filters associated with the D4 scaling function. We then explore the Cascade Algorithm, which is a process that uses approximations to get possible representations for the D2N scaling function of Daubechies. Lastly, we will use the Cascade Algorithm to get a visual representation of the D4 scaling function.

Cette thèse introduit un cadre d’analyse multirésolution pour les données de classements. Initiée au 18e siècle dans le contexte d’élections, l’analyse des données de classements a attiré un intérêt majeur dans de nombreux domaines de la littérature scientifique : psychométrie, statistiques, économie, recherche opérationnelle, apprentissage automatique ou choix social computationel entre autres. Elle a de plus été revitalisée par des applications modernes comme les systèmes de recommandation, où le but est d’inférer les préférences des utilisateurs pour leur proposer les meilleures suggestions personnalisées. Dans ces contextes, les utilisateurs expriment leurs préférences seulement sur des petits sous-ensembles d’objets variant au sein d’un large catalogue. L’analyse de tels classements incomplets pose cependant un défi important, tant du point de vue statistique que computationnel, poussant les acteurs industriels à utiliser des méthodes qui n’exploitent qu’une partie de l’information disponible. Cette thèse introduit une nouvelle représentation pour les données, qui surmonte par construction ce double défi. Bien qu’elle repose sur des résultats de combinatoire et de topologie algébrique, ses nombreuses analogies avec l’analyse multirésolution en font un cadre naturel et efficace pour l’analyse des classements incomplets. Ne faisant aucune hypothèse sur les données, elle mène déjà à des estimateurs au-delà de l’état-de-l’art pour des petits catalogues d’objets et peut être combinée avec de nombreuses procédures de régularisation pour des larges catalogues. Pour toutes ces raisons, nous croyons que cette représentation multirésolution ouvre la voie à de nombreux développements et applications futurs. / This thesis introduces a multiresolution analysis framework for ranking data. Initiated in the 18th century in the context of elections, the analysis of ranking data has attracted a major interest in many fields of the scientific literature : psychometry, statistics, economics, operations research, machine learning or computational social choice among others. It has been even more revitalized by modern applications such as recommender systems, where the goal is to infer users preferences in order to make them the best personalized suggestions. In these settings, users express their preferences only on small and varying subsets of a large catalog of items. The analysis of such incomplete rankings poses however both a great statistical and computational challenge, leading industrial actors to use methods that only exploit a fraction of available information. This thesis introduces a new representation for the data, which by construction overcomes the two aforementioned challenges. Though it relies on results from combinatorics and algebraic topology, it shares several analogies with multiresolution analysis, offering a natural and efficient framework for the analysis of incomplete rankings. As it does not involve any assumption on the data, it already leads to overperforming estimators in small-scale settings and can be combined with many regularization procedures for large-scale settings. For all those reasons, we believe that this multiresolution representation paves the way for a wide range of future developments and applications

Scientific visualization is an essential and indispensable tool for the systematic study of computational (CFD) datasets. There are numerous methods currently used for the unwieldy task of processing and visualizing the characteristically large datasets. Feature extraction is one such technique and has become a significant means for enabling effective visualization. This thesis proposes different modules to refine the maps which are generated from a feature detection on a dataset. The specific example considered in this work is the vortical flow in a two-dimensional oceanographic dataset. This thesis focuses on performing feature extraction by detecting the features and processing the feature maps in three different modules, namely, denoising, segmenting and ranking. The denoising module exploits a wavelet-based multiresolution analysis (MRA). Although developed for two-dimensional datasets, these techniques are directly extendable to three-dimensional cases. A comparative study of the performance of Optimal Feature-Preserving (OFP) filters and non-OFP filters for denoising is presented. A computationally economical implementation for segmenting the feature maps as well as different algorithms for ranking the regions of interest (ROI's) are also discussed in this work.

No description available.

A height field is a set of height distance values sampled at a finite set of sample points in a two-dimensional parameter domain. A height field usually contains a lot of redundant information, much of which can be removed without a substantial degradation of its quality. A common approach to reducing the size of a height field representation is to use a piecewise polygonal surface approximation. This consists of a mesh of polygons that approximates the surfaces of the original data at a desired level of accuracy. Polygonal surface approximation of height fields has numerous applications in the fields of computer graphics and computer vision. Triangular mesh approximations are a popular means of representing three-dimensional surfaces, and multiresolution analysis (MRA) is often used to obtain compact representations of dense input data, as well as to allow surface approximations at varying spatial resolution. Multiresolution approaches, particularly those moving from coarse to fine resolutions, can often improve the computational efficiency of mesh generation as well as can provide easy control of level of details for approximations. This dissertation concerns the use of wavelet-based MRA methods to produce a triangular-mesh surface approximation from a single height field dataset. The goal of this study is to obtain a fast surface approximation for a set of height data, using a small number of approximating elements to satisfy a given error criterion. Typically, surface approximation techniques attempt to balance error of fit, number of approximating elements, and speed of computation. A novel aspect of this approach is the direct evaluation of wavelet coefficients to assess surface shape characteristics within each triangular element at a given scale. Our approach hierarchically subdivides and refines triangles as the resolution level increases. / Ph. D.

A expressividade é um elemento chave para o transporte de emoções em música, e seu modelamento, vital para a concepção de sistemas de síntese mais realistas. Gestos musicais executados durante a interpretação usualmente portam a informação responsável pela expressividade percebida, e podem ser rastreados por meio de padrões sônicos a eles associados em diversas escalas de resolução. Um conjunto relevante de gestos musicais expressivos foi estudado através de uma análise em multiresolução utilizando-se a transformada wavelet. A escolha deve-se principalmente à capacidade natural desta ferramenta em realizar análises de tempo-escala/frequência, e suas semelhanças com o processamento dos estágios primários do sistema auditivo. Vinte e sete eventos musicais foram capturados em interpretações de violino e flauta, e analisados com o objetivo de avaliar a aplicabilidade desta ferramenta na identificação e segregação de padrões sônicos associados a gestos musicais expressivos. Os algoritmos wavelet foram implementados na plataforma MATLAB utilizando-se bancos de filtros organizados em esquema piramidal. Rotinas para análises gráfica e sônica e uma interface ao usuário foram também implementadas. Verificou-se que as wavelets permitem a identificação de padrões sônicos associados a gestos expressivos exibindo diferentes propriedades em níveis diferentes da análise. A técnica mostrou-se útil para isolar ruídos oriundos de fontes diversas, extrair transientes associados a gestos súbitos e/ou intensos, e para segregar a estrutura harmônica de tons musicais, entre outras potencialidades não menos importantes. Particularidades da técnica e efeitos secundários observados são discutidos, e os padrões sônicos observados nos níveis wavelets são correlacionados com os gestos musicais que lhes deram origem. São propostos trabalhos futuros objetivando a investigação de certos eventos musicais e fenômenos verificados, bem como o estudo de implementações alternativas. / Expressiveness is a key element for emotion transportation in music, and its modeling necessary to conceive more realistic synthesis systems. Musical gestures executed during a performance carry the information answering for expressiveness, and may be tracked by means of sonic patterns associated to them within several resolution scales. A relevant set of musical gestures was studied through a multiresolution analysis using the wavelet transform. The choice for this tool is mainly due to its natural ability to perform time-scale/frequency analysis, and for its similarities with early auditory processing stages. Twenty seven musical events were captured from violin and flute performances, and analyzed in order to evaluate the applicability of this tool for identification and segregation of sonic patterns associated with expressive musical gestures. The wavelet algorithms were implemented on the MATLAB platform, employing filter banks organized in a pyramidal scheme. Graphical and sonic analysis routines and a user interface were carried out over the same platform. It was verified that wavelets enable the identification of sonic patterns associated to musical gestures revealing different properties on different levels of the analysis. The technique showed up useful to isolate noise from different sources, extract transients associated to sudden and/or intense gestures, and segregate the tonal harmonic structure, among other important features. Particularities of the technique and secondary effects observed are discussed, and sonic patterns on wavelet levels are correlated with the musical gestures which produced them. Future works are proposed addressing further investigation of certain musical events and phenomena observed, as well as the study of alternative implementations.

A expressividade é um elemento chave para o transporte de emoções em música, e seu modelamento, vital para a concepção de sistemas de síntese mais realistas. Gestos musicais executados durante a interpretação usualmente portam a informação responsável pela expressividade percebida, e podem ser rastreados por meio de padrões sônicos a eles associados em diversas escalas de resolução. Um conjunto relevante de gestos musicais expressivos foi estudado através de uma análise em multiresolução utilizando-se a transformada wavelet. A escolha deve-se principalmente à capacidade natural desta ferramenta em realizar análises de tempo-escala/frequência, e suas semelhanças com o processamento dos estágios primários do sistema auditivo. Vinte e sete eventos musicais foram capturados em interpretações de violino e flauta, e analisados com o objetivo de avaliar a aplicabilidade desta ferramenta na identificação e segregação de padrões sônicos associados a gestos musicais expressivos. Os algoritmos wavelet foram implementados na plataforma MATLAB utilizando-se bancos de filtros organizados em esquema piramidal. Rotinas para análises gráfica e sônica e uma interface ao usuário foram também implementadas. Verificou-se que as wavelets permitem a identificação de padrões sônicos associados a gestos expressivos exibindo diferentes propriedades em níveis diferentes da análise. A técnica mostrou-se útil para isolar ruídos oriundos de fontes diversas, extrair transientes associados a gestos súbitos e/ou intensos, e para segregar a estrutura harmônica de tons musicais, entre outras potencialidades não menos importantes. Particularidades da técnica e efeitos secundários observados são discutidos, e os padrões sônicos observados nos níveis wavelets são correlacionados com os gestos musicais que lhes deram origem. São propostos trabalhos futuros objetivando a investigação de certos eventos musicais e fenômenos verificados, bem como o estudo de implementações alternativas. / Expressiveness is a key element for emotion transportation in music, and its modeling necessary to conceive more realistic synthesis systems. Musical gestures executed during a performance carry the information answering for expressiveness, and may be tracked by means of sonic patterns associated to them within several resolution scales. A relevant set of musical gestures was studied through a multiresolution analysis using the wavelet transform. The choice for this tool is mainly due to its natural ability to perform time-scale/frequency analysis, and for its similarities with early auditory processing stages. Twenty seven musical events were captured from violin and flute performances, and analyzed in order to evaluate the applicability of this tool for identification and segregation of sonic patterns associated with expressive musical gestures. The wavelet algorithms were implemented on the MATLAB platform, employing filter banks organized in a pyramidal scheme. Graphical and sonic analysis routines and a user interface were carried out over the same platform. It was verified that wavelets enable the identification of sonic patterns associated to musical gestures revealing different properties on different levels of the analysis. The technique showed up useful to isolate noise from different sources, extract transients associated to sudden and/or intense gestures, and segregate the tonal harmonic structure, among other important features. Particularities of the technique and secondary effects observed are discussed, and sonic patterns on wavelet levels are correlated with the musical gestures which produced them. Future works are proposed addressing further investigation of certain musical events and phenomena observed, as well as the study of alternative implementations.

Submitted by Maike Costa (maiksebas@gmail.com) on 2017-05-24T12:51:24Z No. of bitstreams: 1 arquivototal.pdf: 2705219 bytes, checksum: cb06011410866630871a99b2788703f1 (MD5) / Made available in DSpace on 2017-05-24T12:51:24Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2705219 bytes, checksum: cb06011410866630871a99b2788703f1 (MD5) Previous issue date: 2015-10-26 / The three-phase induction motors are the most important way for electromechanical conversion, being present in almost every industrial process. Because of their importance, it is crucial that these devices have a proper predictive maintenance, avoiding lost production and operational accidents in the event of unexpected failures. In this scenario several researchers have conducted studies to detect incipient faults. About the sensing method used, the most common techniques are related to measuring the vibration levels using accelerometers and measuring electrical motor signals. The choice of technique involves factors such as invasiveness, drive motor type and the sensitivity to failure. The purpose of this work involves the development of a hybrid system that uses data collected by vibration and current sensors for fault detection in induction motors, earlier and more efficiently. The current and vibration signals were processed in the frequency domain and through the multiresolution analysis, serving as inputs of a fuzzy logic system, allowing to increase the sensitivity and efficiency in fault detection techniques in relation to the individual. The unbalance failure was investigated on a workbench with the motor coupled to a propeller and broken bars with another bench with DC motor to apply the load, the best methods being chosen in each case. The system was developed in Matlab software and was validated with correct detection for both failures, being able to detect the unbalance failure on the shaft or propeller as broken bars in different load conditions. / O motor de indução trifásico é o principal meio de conversão eletromecânica existente, estando presente em praticamente todos os processos industriais. Devido à sua importância, é fundamental que estes equipamentos tenham uma correta manutenção preditiva, evitando perda de produção e acidentes operacionais em caso de falhas inesperadas. Diante deste cenário vários pesquisadores têm realizado estudos para detecção de falhas incipientes. Quanto ao método sensor utilizado, as técnicas mais comuns estão relacionadas a medição dos níveis de vibração utilizando acelerômetros e medição de sinais elétricos do motor. A escolha da técnica envolve fatores como a invasividade, tipo de acionamento do motor e a sensibilidade à falha. A proposta deste trabalho envolve o desenvolvimento de um sistema híbrido que utilize dados coletados por sensores de vibração e de corrente para detecção de falhas incipientes em motores de indução trifásicos de maneira mais precoce e eficiente. Os sinais de corrente e de vibração foram processados no domínio da frequência pela transformada de Fourier e através da análise multiresolução, servindo como entrada para sistemas de lógica Fuzzy, permitindo que se aumente a eficiência na detecção da falha em relação às técnicas individuais. Foi investigada a falha de desbalanceamento em uma bancada com o motor acoplado a uma hélice e barras quebradas em outra bancada com motor de corrente contínua acoplado para aplicar a carga, sendo escolhidos os melhores métodos em cada caso. O sistema foi desenvolvido no software Matlab e foi validado através de diagnósticos corretos para ambas as falhas, sendo capaz de detectar a falha de desbalanceamento tanto na hélice quanto no eixo e de barras quebradas em diferentes condições de carga.

<p style="text-align: justify;">In this doctoral dissertation several integral transforms are discussed.The first one is the Short time Fourier transform (STFT). We present continuity theorems for the STFT and its adjoint on the test function space <em>K</em>₁(ℝⁿ) and the topological tensor product <em>K</em>₁(ℝⁿ) &otimes; <em>U</em>(<strong>ℂ</strong>ⁿ), where <em>U</em>(<strong>ℂ</strong>ⁿ) is the space of entirerapidly decreasing functions in any horizontal band of&nbsp;<strong>ℂ</strong>ⁿ. We then use such continuity results to develop a framework for the STFT on K&#39;₁(ℝⁿ). Also, we devote one section to the characterization of <em>K</em>&rsquo;₁(ℝⁿ) and related spaces via modulation spaces. We also obtain various Tauberian theorems for the short-time Fourier transform.</p><p style="text-align: justify;">Part of the thesis is dedicated to the ridgelet and the Radon transform. We define and study the ridgelet transform of (Lizorkin) distributions and we show that the ridgelet transform and the ridgelet synthesis operator can be extended as continuous mappings <em>R</em>_{<em>&psi;&nbsp;</em>}: <em>S</em>&rsquo;₀(ℝⁿ) &rarr; <em>S</em>&rsquo;(<strong>Y</strong>ⁿ⁺¹) and <em>R^t</em>_{<span style="vertical-align: sub;">&psi;</span>}: <em>S</em>&rsquo;(<strong>Y</strong>ⁿ⁺¹) &rarr; <em>S</em>&rsquo;₀(ℝⁿ). We then use our results to develop a distributional framework for the ridgelet transform that is, we treat the ridgelet transform on <em>S</em>&rsquo;₀(ℝⁿ) via a duality approach. Then, the continuity theorems for the ridgelet transform are applied to discuss the continuity of the Radon transform on these spaces and their duals. Finally, we deal with some Abelian and Tauberian theorems relating the quasiasymptotic behavior of distributions with the quasiasymptotics of the its Radon and ridgelet transform.</p><p style="text-align: justify;">The last chapter is dedicated to the MRA of M-exponential distributions. We study the convergence of multiresolution expansions in various test function and distribution spaces and we discuss the pointwise convergence of multiresolution expansions to the distributional point values of a distribution. We also provide a characterization of the quasiasymptotic behavior in terms of multiresolution expansions and give an MRA sufficient condition for the existence of &alpha;-density points of positive measures.</p> / <p>U ovoj doktorskoj disertaciji razmotreno je nekoliko integralnih transformacija. Prva je short time Fourier transform (STFT). Date su i dokazane teoreme o neprekidnosti STFT i njena sinteza na prostoru test funkcije <em>K</em>₁(ℝⁿ) i na prostoru <em>K</em>₁(ℝⁿ) &otimes; <em>U</em>(ℂⁿ), gde je&nbsp;<em>U</em>(ℂⁿ) prostor od celih brzo opadajućih funkcija u proizvoljnom horizontalnom opsegu na ℂⁿ. Onda, ovi rezultati neprekidnosti su iskori&scaron;teni za razvijanje teorije STFT na prostoru <em>K</em>&rsquo;₁(ℝⁿ). Jedno poglavlje je posvećeno karakterizaciji&nbsp;<em>K</em>&rsquo;₁(ℝⁿ) sa srodnih modulaciskih prostora. Dokazani su i različiti Tauberovi rezultata za STFT. Deo teze je posvećen na ridglet i Radon transformacije. Ridgelet transformacija je definisana na (Lizorkin) distribucije i pokazano je da ridgelet transformacija i njen operator sinteze mogu da se pro&scaron;ire kako neprekidna preslikava <em>R</em>_&psi; : <em>S</em>&rsquo;₀(ℝⁿ) &rarr; <em>S</em>&rsquo;(<strong>Y</strong>ⁿ⁺¹) and <em>R</em>^t_&Psi;: <em>S</em>&rsquo;(<strong>Y</strong>ⁿ⁺¹) &rarr; <em>S</em>&rsquo;₀(ℝⁿ).&nbsp;Ridgelet transformacija na <em>S</em>&rsquo;₀(ℝⁿ) je data preko dualnog pristupa. Na&scaron;e teoreme neprekidnosti ridgelet transformacije su primenjene u dokazivanju neprekidnosti Radonove transformacije na Lizorkin test prostorima i njihovim dualima. Na kraju, dajemo Abelovih i Tauberovih teorema koji daju veze izmedju kvaziasimptotike distribucija i kvaziasimptotike rigdelet i Radonovog transfomaciju.<br />Zadnje poglavje je posveceno multirezolucijskog analizu M - eksponencijalnih distrubucije. Proucavamo konvergenciju multirezolucijkog razvoja u razlicitih prostori test funkcije i distribucije i razmotrena je tackasta konvergencija multirezolucijkog razvoju u tacku u distributivnog smislu. Obezbedjena je i karakterizacija kvaziasimptotike u pogled multirezolucijskog razvoju i dat dovoljni uslov za postojanje &alpha;-tacka gustine za pozitivne mere.</p>