Petrophysical properties are fundamental to understanding fluid flow processes in hydrocarbon reservoirs. Special Core Analysis (SCAL) routinely used in industry are time-consuming, expensive, and often destructive. Alternatively, easily available thin section data is lacking the representation of pore space in 3D, which is a requisite for generating pore network models (PNM) and computing petrophysical properties. In this study, these challenges were addressed using a numerical SCAL workflow that employs pore volume reconstruction from thin section images obtained from confocal laser scanning microscopy (CLSM). A key objective is to investigate methods capable of 2D to 3D reconstruction, to obtain PNM used for the estimation of transport properties. Representative thin sections from a well-known Middle-Eastern carbonate formation were used to obtain CLSM images. The thin-sections were specially prepared by spiking the resin with UV dye, enabling high-resolution imaging. The grayscale images obtained from CLSM were preprocessed and segmented into binary images. Generative Adversarial Networks (GAN) and Two-Point Statistics (TPS) were applied, and PNM were extracted from these binary datasets. Porosity, Permeability, and Mercury Injection Porosimetry (MIP) on the corresponding core plugs were conducted and an assessment of the properties computed from the PNM obtained from the reconstructed 3D pore volume is presented. Moreover, the results from the artificial pore networks were corroborated using 3D confocal images of etched pore casts (PCE). The results showed that based on visual inspection only, GAN outperformed TPS in mimicking the 3D distribution of pore scale heterogeneity, additionally, GAN and PCE outperformed the results of MIP obtained by TPS on the Skeletal-Oolitic facies, without providing a major improvement on more heterogeneous samples. All methods captured successfully the porosity while absolute permeability was not captured. Formation resistivity factor and thermal conductivity showcased their strong correlation with porosity. The study thus provides valuable insights into the application of 2D to 3D reconstruction to obtain pore network models of heterogeneous carbonate rocks for petrophysical characterization for quick decision. The study addresses the following important questions: 1) how legacy thin sections can be leveraged to petrophysically characterize reservoir rocks 2) how reliable are 2D to 3D reconstruction methods when predicting petrophysical properties of carbonates.

Phase Space Reconstruction is a method that allows to reconstruct the phase space of a system using only an one dimensional time series as input. It can be used for calculating Lyapunov-exponents and detecting chaos. It helps to understand complex dynamics and their behavior. And it can reproduce datasets which were not measured. There are many different methods which produce correct reconstructions such as time-delay, Hilbert-transformation, derivation and integration. The most used one is time-delay but all methods have special properties which are useful in different situations. Hence, every reconstruction method has some situations where it is the best choice. Looking at all these different methods the questions are: Why can all these different looking methods be used for the same purpose? Is there any connection between all these functions? The answer is found in the frequency domain : Performing a Fourier transformation all these methods getting a similar shape: Every presented reconstruction method can be described as a multiplication in the frequency domain with a frequency-depending reconstruction function. This structure is also known as a filter. From this point of view every reconstructed dimension can be seen as a filtered version of the measured time series. It contains the original data but applies just a new focus: Some parts are amplified and other parts are reduced. Furthermore I show, that not every function can be used for reconstruction. In the thesis three characteristics are identified, which are mandatory for the reconstruction function. Under consideration of these restrictions one gets a whole bunch of new reconstruction functions. So it is possible to reduce noise within the reconstruction process itself or to use some advantages of already known reconstructions methods while suppressing unwanted characteristics of it. / Attraktorrekonstruktion („Phase Space Reconstruction“) ist eine Technik, die es ermöglicht, aus einer einzelnen Zeitreihe den vollständigen Phasenraum eines Systems zu rekonstruieren und somit Rückschlüsse auf topologische Eigenschaften dieses dynamischen Systems zu ziehen. Sie findet Verwendung in der Bestimmung von Lyapunov-Exponenten und zur Reproduktion von unbeobachteten Systemgrößen. Es gibt viele verschiedene Methoden zur Attraktorrekonstruktion wie z.B. die Time-Delay-Methode or Rekonstruktion durch Ableitung, Integration oder mithilfe einer Hilbert-Transformation. Zumeist wird der Time-Delay-Ansatz verwendet, es gibt jedoch auch diverse Problemstellungen, in welchen die alternativen Methoden bessere Ergebnisse liefern. Die Kernfragen, die beim Vergleich dieser Methoden entsteht, sind: Wie kommt es, dass alle Ansätze, trotz ihrer teilweise sehr unterschiedlichen Struktur, denselben Zweck erfüllen? Gibt es Übereinstimmungen zwischen all diesen Methoden? Die Antwort lässt sich im Frequenzraum finden: Nach einer Fourier-Transformation besitzen alle genannten Methoden plötzlich eine sehr ähnliche Struktur. Jede Methode transformiert sich im Frequenzraum zu einer einfachen Multiplikation des Eingangssignals mit einer frequenzabhängigen Rekonstruktionsfunktion. Diese Struktur ist in der Datenanalyse auch bekannt als Filter. Aus dieser Perspektive lässt sich jede Rekonstruktionsdimension als gefilterte Zeitreihe der ursprünglichen Zeitreihe interpretieren: Sie enthält den Originaldatensatz, allerdings mit einem verschobenen Fokus: Einige Eigenschaften der Originalzeitreihe werden unterdrückt, während andere Teile verstärkt wiedergegeben werden. Des weiteren zeige ich in der Diplomarbeit, dass nicht jede beliebige Funktion im Frequenzraum zur Rekonstruktion verwendet werden kann. Ich stelle drei Eigenschaften vor, welche jede Rekonstruktionsfunktion erfüllen muss. Unter Beachtung dieser Bedingungen ergeben sich nun diverse Möglichkeiten für neue Rekonstruktionsfunktionen. So ist es z.B. möglich gleichzeitig mit der Rekonstruktion das Ursprungssignal auch zu filtern, oder man kann bereits bestehende Rekonstruktionsfunktionen so abwandeln, dass unerwünschte Nebeneffekte der Rekonstruktion abgemildert oder gar ganz unterdrückt werden.

Earthquakes, floods, rainfall represent a class of nonlinear systems termed chaotic, in which the relationships between variables in a system are dynamic and disproportionate, however completely deterministic. Classical linear time series models have proved inadequate in analysis and prediction of complex geophysical phenomena. Nonlinear approaches such as Artificial Neural Networks, Hidden Markov Models and Nonlinear Prediction are useful in forecasting of daily discharge values in a river. The focus of these methods is on forecasting magnitudes of future discharge values and not the prediction of floods. Chaos theory provides a structured explanation for irregular behavior and anomalies in systems that are not inherently stochastic. Time Series Data Mining methodology combines chaos theory and data mining to characterize and predict complex, nonperiodic and chaotic time series. Time Series Data Mining focuses on the prediction of events.

The problem of accurately simulating light transport using Monte Carlo integration can be very difficult. In particular, scenes with complex illumination effects or complex materials can cause a scene to converge very slowly and demand a lot of computational time. To overcome this problem, image denoising algorithms have become popular in recent years. In this work we first review known approaches to denoising and adaptive rendering. We implement one of the promising algorithm by Moon et al. [2014] in a commercial rendering system Corona Standalone Renderer, evaluate its performance, strengths and weaknesses on 14 test scenes. These include difficult to denoise and converge rendering effects such as fine sub-pixel geometry, participating media, extreme depth of field of highlights, motion blur, and others. We propose corrections which make the algorithm more stable and robust. We show that it is possible to denoise renderings with Linear Weighted Regression only using a CPU. However, still even after our propositions, it is not possible to filter scenes in a consistent manner without over-blurring or not filtering where desired.

O objetivo deste trabalho foi avaliar vozes saudáveis e com alterações patológicas aplicando análise de Padrões Visuais de Dinâmica Vocal (PVDV) em conjunto com análise acústica e análise perceptivo-auditiva. Foram avaliadas 91 vozes da vogal sustentada /a/ do português do Brasil, de sujeitos de ambos os gêneros com idades entre 21 e 88 anos. As vozes foram gravadas com taxa de amostragem de 22.050 Hz, 16 bits, mono canal e formato WAV. Foram obtidos valores de jitter, shimmer e freqüência fundamental. Para análise perceptivo-auditiva foram avaliadas rugosidade, soprosidade, tensão e instabilidade. Para descrever a dinâmica dos sinais de voz dos PVDV foi utilizada a técnica de reconstrução de espaço de fase e foram analisados qualitativamente os parâmetros de loops, regularidade e convergência de traçados. Foram aplicados testes estatísticos paramétricos e não paramétricos. Os resultados demonstram que jitter apresenta uma correlação negativa com loop, regularidade e convergência dos traçados; e que shimmer tem correlação negativa com convergência e loops. As características de rugosidade e soprosidade estão correlacionadas negativamente com os três parâmetros dinâmicos. A análise qualitativa dos PVDV é uma técnica promissora, por considerar os componentes caótico e determinístico da voz. É sugerido que não substitui as técnicas existentes, embora possa aperfeiçoar e complementar os métodos usados por profissionais fonoaudiólogos e otorrinolaringologistas. / The aim of this research was to analyze healthy and pathologic voices using Vocal Dynamic Visual Patterns (VDVP) in combination with acoustical and perceptual analysis. Ninety one voice signals of sustained vowel /a/ from Brazilian Portuguese, from male and female patients, were analyzed using acoustical analysis, perceptual analysis and Vocal Dynamic Visual Patterns (VDVP) analysis. All voice samples were quantized in amplitude with 16 bits and recorded in mono-channel WAV format. The sampling frequency was 22050 Hz. Acoustical values for jitter, shimmer and fundamental frequency were obtained. Roughness, breathiness, strain and irregularity were analyzed for perceptual analysis. Phase space reconstruction technique was performed in order to describe the voice signal nonlinear characteristics by Vocal Dynamic Visual Patterns. Results showed negative correlation for jitter and the 3 dynamic parameters, as well as, for shimmer with convergence and loops. Roughness and breathiness were negative correlated with dynamical parameters. Vocal Dynamic Visual Pattern analysis is a promising technique for voice evaluation; including voice chaotic and deterministic components. It is suggested that visual pattern analysis do not replace the existing voice analysis techniques, although it complements and improves the voice evaluation methods available for speech therapist and laryngologists.

Analisar fenômenos aeroelásticos não-lineares através de dados experimentais é uma poderosa ferramenta para a identificação e controle de comportamentos aeroelásticos adversos. A modelagem matemática de sistemas aeroelásticos não-lineares não é trivial, fato que muitas vezes leva a admissão de simplificações, afastando o modelo da realidade. Desta forma, a análise de sistemas dinâmicos sem a necessidade de um modelo, feita através da análise de séries temporais obtidas de experimentos, pode fornecer melhores resultados. Alguns métodos de análise de séries temporais, como o método da defasagem, para reconstrução do espaço de estados, são sensíveis ao ruído, inevitavelmente presente em qualquer série temporal experimental. Este trabalho apresenta a técnica da decomposição em valores singulares (SVD), que reconstrói o espaço de estados eliminando o ruído presente na série temporal em um único processo. O método SVD é aplicado em séries temporais aeroelásticas, obtidas experimentalmente de um modelo de asa ensaiado em túnel de vento. Com os espaços de estados reconstruídos, é feita uma análise qualitativa do sistema aeroelástico, a evolução dos atratores obtidos com a variação de alguns parâmetros é apresentada. Comparações com o método da defasagem são realizadas com a aplicação dos métodos a uma série temporal aeroelástica do experimento. Os resultados mostram que a técnica (SVD) é mais confiável que o método da defasagem, os atratores obtidos revelam a ocorrência de bifurcações e comportamentos complexos, possivelmente caóticos. / Nonlinear aeroelastic phenomena analysis by using experimental data is a powerful tool for identification and control of adverse aeroelastic behaviors. Mathematical models for nonlinear aeroelastic systems are not trivial, by this, simplifications are assumed, thereby deviating from reality. Then, the analysis of dynamic systems without the need of a mathematical model, done by the analysis of experimental time series, may provide better results. However, methods of time series analysis, like the method of delays, for state space reconstruction are sensitive to noise, unavoidably present in experimental data. This work presents the application of singular value decomposition (SVD) that reconstructs the state space, eliminating noise present in the time series. The SVD method is applied in experimental aeroelastic time series, obtained from a wind tunnel wing model. With the reconstructed state spaces, qualitative analyses are done and the evolutions of the obtained attractors with parametric variation are presented. Comparisons with the method of delays are realized by applying MOD and SVD in a same experimental aeroelastic time series. The results show that the SVD method is more reliable than MOD and the obtained attractors reveal the occurrence of bifurcations and complex behavior, possibly chaotic.

O objetivo deste trabalho foi avaliar vozes saudáveis e com alterações patológicas aplicando análise de Padrões Visuais de Dinâmica Vocal (PVDV) em conjunto com análise acústica e análise perceptivo-auditiva. Foram avaliadas 91 vozes da vogal sustentada /a/ do português do Brasil, de sujeitos de ambos os gêneros com idades entre 21 e 88 anos. As vozes foram gravadas com taxa de amostragem de 22.050 Hz, 16 bits, mono canal e formato WAV. Foram obtidos valores de jitter, shimmer e freqüência fundamental. Para análise perceptivo-auditiva foram avaliadas rugosidade, soprosidade, tensão e instabilidade. Para descrever a dinâmica dos sinais de voz dos PVDV foi utilizada a técnica de reconstrução de espaço de fase e foram analisados qualitativamente os parâmetros de loops, regularidade e convergência de traçados. Foram aplicados testes estatísticos paramétricos e não paramétricos. Os resultados demonstram que jitter apresenta uma correlação negativa com loop, regularidade e convergência dos traçados; e que shimmer tem correlação negativa com convergência e loops. As características de rugosidade e soprosidade estão correlacionadas negativamente com os três parâmetros dinâmicos. A análise qualitativa dos PVDV é uma técnica promissora, por considerar os componentes caótico e determinístico da voz. É sugerido que não substitui as técnicas existentes, embora possa aperfeiçoar e complementar os métodos usados por profissionais fonoaudiólogos e otorrinolaringologistas. / The aim of this research was to analyze healthy and pathologic voices using Vocal Dynamic Visual Patterns (VDVP) in combination with acoustical and perceptual analysis. Ninety one voice signals of sustained vowel /a/ from Brazilian Portuguese, from male and female patients, were analyzed using acoustical analysis, perceptual analysis and Vocal Dynamic Visual Patterns (VDVP) analysis. All voice samples were quantized in amplitude with 16 bits and recorded in mono-channel WAV format. The sampling frequency was 22050 Hz. Acoustical values for jitter, shimmer and fundamental frequency were obtained. Roughness, breathiness, strain and irregularity were analyzed for perceptual analysis. Phase space reconstruction technique was performed in order to describe the voice signal nonlinear characteristics by Vocal Dynamic Visual Patterns. Results showed negative correlation for jitter and the 3 dynamic parameters, as well as, for shimmer with convergence and loops. Roughness and breathiness were negative correlated with dynamical parameters. Vocal Dynamic Visual Pattern analysis is a promising technique for voice evaluation; including voice chaotic and deterministic components. It is suggested that visual pattern analysis do not replace the existing voice analysis techniques, although it complements and improves the voice evaluation methods available for speech therapist and laryngologists.

Diversos estudos foram realizados para detecção de patologias na laringe. Essas patologias causam alteração na frequência, amplitude e formato de onda do sinal de voz e podem ser estudadas através dos parâmetros convencionais de análise como jitter e shimmer, ou sob o enfoque da dinâmica não linear. Essas técnicas são não invasivas e servem de apoio ao especialista da área de fonoaudiologia para o diagnóstico de patologias nas pregas vocais. As técnicas de análise acústica baseiam-se no formato de onda vocal no domínio do tempo e domínio da frequência, enquanto que a técnica de análise não linear utilizada nesse trabalho baseia-se no atrator reconstruído do sinal de voz. O objetivo dessa tese é diferenciar vozes normais e patológicas e entre patologias usando a técnica de análise não linear conhecida como Seção de Poincaré. Foram analisados 48 sinais de vozes humanas, divididos em 3 grupos (16 normais, 16 com nódulo e 16 com edema de Reinke). Em seguida foram selecionados 3 trechos de 500 ms nos intervalos 0.5s-1.0s, 2.0s-2.5s e 4.0s-4.5s chamado de primeiro critério e um trecho 500ms no trecho de maior variação de pitch, chamado de segundo critério. Em seguida, o atrator foi reconstruído em 3 dimensões, determinado o atrator médio, e de cada ponto do atrator médio foi extraída a seção de Poincaré. De cada seção de Poincaré foi calculada a dispersão dos pontos do atrator no plano através da média e desvio padrão das dispersão dos pontos da seção de Poincaré em relação ao ponto médio da seção. A validação da ferramenta desenvolvida para essa tese foi realizada utilizando um sinal senoidal inserindo jitter gradativamente, onde verificou-se uma variação proporcional da média da dispersão. Os resultados obtidos mostraram que não foi possível diferenciar patologias mas foi possível classificar vozes normais das patológicas. O melhor intervalo para classificar as vozes normais das patológicas utilizando o primeiro critério foi entre 0.5s-1.0s pois nesse intervalo todas as vozes normais foram classificadas corretamente. No entanto, 6 vozes patológicas foram classificadas como normais com 2 vozes patológicas na fronteira que separa as vozes normais das patológicas. O segundo critério classificou todas as vozes normais corretamente e apenas uma voz patológica foi classificada como patológica. Concluiu-se que a ferramenta proposta utilizando o segundo critério mostrou-se superior em relação ao primeiro critério para diferenciar vozes normais das patológicas. / Several studies have been performed to detect pathologies of the larynx. These pathologies cause changes in the frequency, amplitude, and waveform of the voice signal. They can be studied by means of conventional analysis parameters such as jitter and shimmer, or from nonlinear dynamics concepts. These techniques are noninvasive and can help the speech therapist to better diagnose the pathologies in the vocal folds. The acoustic analysis techniques are based on the voice waveform in the time and frequency domains, while the non-linear analysis techniques are based on the attractor reconstructed from the speech signal.The aim of this thesis is to differentiate normal and pathological voices using a nonlinear analysis technique named Poincaré section. We analyzed 48 human voice signals divided into 3 groups (16 normal, 16 nodule and 16 Reinke\'s edema). Then, we analyzed 3 stretches of 500ms in the intervals 0.5s-1.0s, 2.0s-2.5s e 4.0-4.5s, denominated first criteria, and a stretch of 500ms in a higher variation in pitch, denominated second criteria. The attractor was then reconstructed in three dimensions, the average attractor was determined, and at each point of the average attractor, a Poincaré section was extracted. From each Poincaré section, the dispersion of the points of the attractor was calculated in the plane by means of the statistical average and standard deviation related to the medium point of the section. The validation of the tool developed for this thesis was achieved by inserting jitter gradually in a sinusoidal wave, where there was a proportional variation of average\'s dispersion was observed. The results obtained for this set of voices showed that the average and standard deviation of dispersion of the points in the Poincaré section differentiate the groups of voices, but not the pathological groups. The Statistical tests of Anova and Tukey were used to analyze the 3 groups and all group pairings, two by two, with a statistical significance of 5%. The best interval to classify normal voices from pathological voices by means of the first criteria was between 0.5s-1.0s, given the fact that in this interval, all normal voices were correctly classified. However, 6 pathological voices were classified as normal voices, with 2 voices border lining the frontier between normal voices from pathological voices. The second criteria classified all normal voices correctly, with only one pathological voice incorrectly classified. In conclusion, the second criteria tool proposed by this thesis was proven superior to differentiate normal voices from pathological ones.

Analisar fenômenos aeroelásticos não-lineares através de dados experimentais é uma poderosa ferramenta para a identificação e controle de comportamentos aeroelásticos adversos. A modelagem matemática de sistemas aeroelásticos não-lineares não é trivial, fato que muitas vezes leva a admissão de simplificações, afastando o modelo da realidade. Desta forma, a análise de sistemas dinâmicos sem a necessidade de um modelo, feita através da análise de séries temporais obtidas de experimentos, pode fornecer melhores resultados. Alguns métodos de análise de séries temporais, como o método da defasagem, para reconstrução do espaço de estados, são sensíveis ao ruído, inevitavelmente presente em qualquer série temporal experimental. Este trabalho apresenta a técnica da decomposição em valores singulares (SVD), que reconstrói o espaço de estados eliminando o ruído presente na série temporal em um único processo. O método SVD é aplicado em séries temporais aeroelásticas, obtidas experimentalmente de um modelo de asa ensaiado em túnel de vento. Com os espaços de estados reconstruídos, é feita uma análise qualitativa do sistema aeroelástico, a evolução dos atratores obtidos com a variação de alguns parâmetros é apresentada. Comparações com o método da defasagem são realizadas com a aplicação dos métodos a uma série temporal aeroelástica do experimento. Os resultados mostram que a técnica (SVD) é mais confiável que o método da defasagem, os atratores obtidos revelam a ocorrência de bifurcações e comportamentos complexos, possivelmente caóticos. / Nonlinear aeroelastic phenomena analysis by using experimental data is a powerful tool for identification and control of adverse aeroelastic behaviors. Mathematical models for nonlinear aeroelastic systems are not trivial, by this, simplifications are assumed, thereby deviating from reality. Then, the analysis of dynamic systems without the need of a mathematical model, done by the analysis of experimental time series, may provide better results. However, methods of time series analysis, like the method of delays, for state space reconstruction are sensitive to noise, unavoidably present in experimental data. This work presents the application of singular value decomposition (SVD) that reconstructs the state space, eliminating noise present in the time series. The SVD method is applied in experimental aeroelastic time series, obtained from a wind tunnel wing model. With the reconstructed state spaces, qualitative analyses are done and the evolutions of the obtained attractors with parametric variation are presented. Comparisons with the method of delays are realized by applying MOD and SVD in a same experimental aeroelastic time series. The results show that the SVD method is more reliable than MOD and the obtained attractors reveal the occurrence of bifurcations and complex behavior, possibly chaotic.

Diversos estudos foram realizados para detecção de patologias na laringe. Essas patologias causam alteração na frequência, amplitude e formato de onda do sinal de voz e podem ser estudadas através dos parâmetros convencionais de análise como jitter e shimmer, ou sob o enfoque da dinâmica não linear. Essas técnicas são não invasivas e servem de apoio ao especialista da área de fonoaudiologia para o diagnóstico de patologias nas pregas vocais. As técnicas de análise acústica baseiam-se no formato de onda vocal no domínio do tempo e domínio da frequência, enquanto que a técnica de análise não linear utilizada nesse trabalho baseia-se no atrator reconstruído do sinal de voz. O objetivo dessa tese é diferenciar vozes normais e patológicas e entre patologias usando a técnica de análise não linear conhecida como Seção de Poincaré. Foram analisados 48 sinais de vozes humanas, divididos em 3 grupos (16 normais, 16 com nódulo e 16 com edema de Reinke). Em seguida foram selecionados 3 trechos de 500 ms nos intervalos 0.5s-1.0s, 2.0s-2.5s e 4.0s-4.5s chamado de primeiro critério e um trecho 500ms no trecho de maior variação de pitch, chamado de segundo critério. Em seguida, o atrator foi reconstruído em 3 dimensões, determinado o atrator médio, e de cada ponto do atrator médio foi extraída a seção de Poincaré. De cada seção de Poincaré foi calculada a dispersão dos pontos do atrator no plano através da média e desvio padrão das dispersão dos pontos da seção de Poincaré em relação ao ponto médio da seção. A validação da ferramenta desenvolvida para essa tese foi realizada utilizando um sinal senoidal inserindo jitter gradativamente, onde verificou-se uma variação proporcional da média da dispersão. Os resultados obtidos mostraram que não foi possível diferenciar patologias mas foi possível classificar vozes normais das patológicas. O melhor intervalo para classificar as vozes normais das patológicas utilizando o primeiro critério foi entre 0.5s-1.0s pois nesse intervalo todas as vozes normais foram classificadas corretamente. No entanto, 6 vozes patológicas foram classificadas como normais com 2 vozes patológicas na fronteira que separa as vozes normais das patológicas. O segundo critério classificou todas as vozes normais corretamente e apenas uma voz patológica foi classificada como patológica. Concluiu-se que a ferramenta proposta utilizando o segundo critério mostrou-se superior em relação ao primeiro critério para diferenciar vozes normais das patológicas. / Several studies have been performed to detect pathologies of the larynx. These pathologies cause changes in the frequency, amplitude, and waveform of the voice signal. They can be studied by means of conventional analysis parameters such as jitter and shimmer, or from nonlinear dynamics concepts. These techniques are noninvasive and can help the speech therapist to better diagnose the pathologies in the vocal folds. The acoustic analysis techniques are based on the voice waveform in the time and frequency domains, while the non-linear analysis techniques are based on the attractor reconstructed from the speech signal.The aim of this thesis is to differentiate normal and pathological voices using a nonlinear analysis technique named Poincaré section. We analyzed 48 human voice signals divided into 3 groups (16 normal, 16 nodule and 16 Reinke\'s edema). Then, we analyzed 3 stretches of 500ms in the intervals 0.5s-1.0s, 2.0s-2.5s e 4.0-4.5s, denominated first criteria, and a stretch of 500ms in a higher variation in pitch, denominated second criteria. The attractor was then reconstructed in three dimensions, the average attractor was determined, and at each point of the average attractor, a Poincaré section was extracted. From each Poincaré section, the dispersion of the points of the attractor was calculated in the plane by means of the statistical average and standard deviation related to the medium point of the section. The validation of the tool developed for this thesis was achieved by inserting jitter gradually in a sinusoidal wave, where there was a proportional variation of average\'s dispersion was observed. The results obtained for this set of voices showed that the average and standard deviation of dispersion of the points in the Poincaré section differentiate the groups of voices, but not the pathological groups. The Statistical tests of Anova and Tukey were used to analyze the 3 groups and all group pairings, two by two, with a statistical significance of 5%. The best interval to classify normal voices from pathological voices by means of the first criteria was between 0.5s-1.0s, given the fact that in this interval, all normal voices were correctly classified. However, 6 pathological voices were classified as normal voices, with 2 voices border lining the frontier between normal voices from pathological voices. The second criteria classified all normal voices correctly, with only one pathological voice incorrectly classified. In conclusion, the second criteria tool proposed by this thesis was proven superior to differentiate normal voices from pathological ones.