Orientador: Marco Aurélio Cremasco / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Química / Made available in DSpace on 2018-08-18T08:24:24Z (GMT). No. of bitstreams: 1 Castilho_GuilhermeJosede_D.pdf: 4727634 bytes, checksum: 262e7551887344a4d33739e6ac52ca97 (MD5) Previous issue date: 2011 / Resumo: Stringer (1989) sugeriu que um leito fluidizado gás-sólido pode ser um sistema caótico no qual seu comportamento irregular, entretanto determinístico, é causado por suas propriedades não-lineares. Desde então, surgiu uma nova forma de analisar flutuações de sinais em sistemas fluidizados: a análise não linear de séries temporais, comumente referida como análise de caos. A análise de caos é uma técnica muito utilizada no processamento de sinais em sistemas fluidizados, porém pouco difundida a nível nacional. Este tipo de análise baseia-se na reconstrução de atratores imersos em um espaço de fase e no estudo das propriedades deste atrator. Nesta Tese de Doutorado, avalia-se o comportamento fluidodinâmico em leito fluidizado circulante (LFC) operando sob condição de transporte pneumático diluído utilizando a análise de caos e também outras análises no domínio do tempo, como a distribuição de frequência e desvio médio absoluto. Os sinais avaliados foram obtidos por uma sonda de fibras ópticas, gerando séries temporais de flutuação de sinais elétricos que representam concentração de sólidos. A análise de caos demonstrou que os sistemas estudados apresentam comportamento caótico, por apresentar entropia de Kolmogorov positiva para todas as situações. A vantagem deste tipo de análise em comparação com as ferramentas usuais no domínio do tempo e no domínio da frequência (espectro de Fourier) é que a mesma considera o comportamento não-linear que existe neste tipo de reator multifásico. A partir de seus resultados, pôde-se descrever detalhadamente a fluidodinâmica do LFC, permitindo relacionar os parâmetros encontrados com fenômenos físicos como formação e repartição de clusters, turbulência do gás, interações partícula-partícula e partícula-parede e má alimentação. Tal análise permitiu, inclusive, a identificação de três regimes distintos: diluído, resultante de um escoamento mais complexo devido à turbulência da fase gasosa; concentrado, onde a presença de clusters diminui o caminho médio das partículas e por conseqüência reduz o grau de complexidade do sistema; e um terceiro regime ainda não publicado em trabalhos anteriores, referente às condições extremamente diluídas, onde o aumento do fluxo de sólidos provocou o aumento da complexidade. Neste regime, a fase gasosa predomina e o escoamento é mais previsível quando há presença de poucas partículas. Pretende-se, com esta Tese de Doutorado, incentivar a utilização deste método para, pelo menos, servir como complementação da técnica usualmente utilizada na análise de sinais nesta área de pesquisa, que são os espectros de potência de Fourier / Abstract: Stringer (1989) was the first to suggest that a gas-solid fluidized bed may be a chaotic system, in which the irregular, yet deterministic, behavior is caused by its nonlinear properties. Since then, another way to analyze signals fluctuations in fluidized systems came to light: the nonlinear time series analysis commonly referred to as chaos analysis. It is a technique widely used in the signal analysis in fluidized systems, but not very common at national level. This type of analysis is based on the reconstruction of attractors embedded in a phase space and the study of the properties of this attractor. This Ph.D. Thesis evaluates the fluid dynamic behavior of circulating fluidized bed (CFB) operating under conditions of dilute pneumatic conveying using chaos analysis of chaos and also further analysis in the time domain. The signals obtained were measured by an optical fiber probe which generated time series of fluctuating electrical signals representing solids concentration. The chaos analysis showed that the systems studied exhibit chaotic behavior, by having positive Kolmogorov entropy for all situations. The advantage of this type of analysis compared with the usual tools in the time domain and frequency domain (Fourier spectrum) is that it considers the nonlinear behavior that exists in this type of multiphase reactor. From their results, it was possible to describe in detail the fluid dynamics of the CFB, allowing correlating the parameters found with physical phenomena such as cluster formation and breakdown, the gas turbulence, particle-particle and particle-wall interactions and feed maldistribution. This analysis has led to the identification of three distinct regimes: diluted, resulted from a more complex flow due to turbulence of the gas phase; concentrated, where the presence of clusters decreases the average path length of particles and consequently reduces the complexity of the system; and a third regime not yet published in previous works, regarding the extremely dilute conditions, where the increased flow of solids caused the increase in complexity. In this condition, the gas phase and the predominant flow is more predictable when there is presence of a few particles. With this Ph.D. Thesis, it is intended to encourage the use of this method for at least as a complement to the technique usually used in signal analysis in this research area, that is, the Fourier power spectra / Doutorado / Engenharia de Processos / Doutor em Engenharia Química

Orientador: Marco Aurélio Cremasco / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Química / Made available in DSpace on 2018-08-26T02:42:06Z (GMT). No. of bitstreams: 1 Prieto_WesleyHeleno_M.pdf: 8369038 bytes, checksum: 55099f53f7bd5777f43bda2e728ffb67 (MD5) Previous issue date: 2014 / Resumo: A complexa dinâmica dos leitos fluidizados promove a necessidade de metodologias de análise de sinais que representem, com maior fidelidade, as características destes processos e também de técnicas de solução computacional de modelos matemáticos complexos para promover a implementação de novas ferramentas teóricas na caracterização de regimes fluidodinâmicos em sistemas particulados. Nas últimas décadas, a análise do caos se tornou grande aliada na investigação dos fenômenos cuja evolução temporal, aperiódica e sensível às condições iniciais, exiba determinismo. Neste sentido, o presente trabalho emprega a técnica de análise de caos para avaliar as grandezas entropia de Kolmogorov e dimensão de correlação associadas às flutuações de pressão em leito fluidizado (0,1 m de diâmetro) para partículas de FCC, painço e microesferas de vidro Geldart A, B e D. Esta Dissertação também se propõe a resolver um modelo matemático representativo da fluidodinâmica gás-partícula e dele abstrair séries temporais de perda de pressão para, posteriormente, serem submetidas à análise do caos determinístico e comparação com os resultados experimentais. Na etapa laboratorial, foram utilizados transdutores diferenciais de pressão a taxas de 1.000 Hz. O gás de fluidização foi ar ambiente a 25 °C. Para a solução do modelo foi utilizado o método clássico de Euler implementado no software MatLab R2012b. Dos resultados da primeira etapa, observou-se a presença de regiões típicas em todos os perfis de entropia de Kolmogorov e dimensão de correlação, sendo que para a condição de fluidização incipiente os valores dos invariantes foram máximos, logo em seguida evoluindo para uma condição de transição e estabilizando em uma situação menos caótica para o regime slugging. As curvas de fluidização obtidas pela resolução do modelo demonstraram superestimação da perda de pressão, porém, em termos de perfil, houve reprodutibilidade em relação às curvas experimentais. No que tange à análise caótica, os mesmos fenômenos foram notados para as séries temporais simuladas, constatando-se a presença das regiões de transição do leito fixo-incipiência-transição-slugging. De modo geral, torna-se evidente a relação entre parâmetros caóticos e as características físicas dos sistemas (experimentais e simulados), corroborando os invariantes do caos como auxiliares na classificação dos regimes de fluidização / Abstract: The complex dynamics of fluidized beds promotes the requirement of signals analysis methodologies that faithfully represent the characteristics of these processes and also techniques of computational solution of complex mathematical models to promote the implementation of new theoretical methods for characterizing fluid dynamic regimes in particulate systems. In recent decades, the analysis of chaos has become an important tool in the investigation of phenomena whose temporal evolution, aperiodic and sensitive to initial conditions, show determinism. In this regard, the present study employing the chaos analysis technique to evaluate the invariants Kolmogorov entropy and correlation dimension associated with the pressure fluctuations in the fluidized bed (0.1 m diameter) for particles of FCC, millet and glass microspheres (Geldart A, B and D). This work also proposes to solve a representative mathematical model of gas-particle fluid dynamics to obtain pressure time series to be submitted to the deterministic chaos analysis and compared with experimental results. In the experimental stage, differential pressure transducers at rates of 1,000 Hz were used. Fluidizing gas is ambient air at 25 °C. For the solution of the model the classical Euler method was used implemented in Matlab R2012b software. Through the results of the first step, the presence of typical regions were observed in all profiles of Kolmogorov entropy and correlation dimension, being for the condition of incipient fluidization the values of the chaotic invariants were maximum, shortly thereafter progressing to a transition condition and stabilizing in a less chaotic situation for the slugging regime. Fluidization curves obtained by solving of the mathematical model showed overestimation of pressure loss, however, in terms of profile, there was reproducibility as compared to the experimental curves. Referring to the chaotic analysis, the same phenomena were observed for the simulated time series, the presence of transition regions of fixed-bed-incipient-transition-slugging was observed. Generally, it is clear the relationship between chaotic parameters and physical characteristics of the systems (experimental and simulated), supporting the chaotic invariants as aids in classifying fluidization regimes / Mestrado / Engenharia de Processos / Mestre em Engenharia Química

Orientador: Alberto Vazquez Saa / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T15:42:31Z (GMT). No. of bitstreams: 1 Teles_RenatodeSa_D.pdf: 3942109 bytes, checksum: 7e41b541aa6eb7a186a4956d751a32c5 (MD5) Previous issue date: 2012 / Resumo: Fizemos um estudo sistemático dos aspectos clássicos e quânticos dos sistemas dinâmicos conhecidos como "bilhares". Introduzimos uma nova classe de bilhares classicamente caóticos cuja dinâmica quântica pode ser convenientemente descrita utilizando-se uma aproximação do tipo Galerkin, o que nos permitiu obter com boa precisão um grande numero de autovalores e autofunções e estudar algumas propriedades estatísticas do espectro de energia para esta nova classe de bilhares. Do ponto de vista da implementação numérica, estudamos também os efeitos de tamanho finito da matriz associada ao truncamento dos modos de Galerkin / Abstract: We consider classical and quantum aspects of the dynamical systems dubbed as "billiards". We introduce a new class of classically chaotic billiards for which the quantum dynamics can be conveniently described by a Galerkin type approximation, allowing us to obtain with good accuracy a large number of eigenvalues and eigenfunctions and to study some statistical properties of the energy spectrum of this new class of billiards. From the numerical implementation point of view, we consider also the finite size effects on the matrix corresponding to the truncation of the Galerkin modes / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

The thesis summarizes the current state of research of thermonuclear fusion with magnetic confinement and decribes the possible role of stochastization of magnetic field lines and magnetic perturbations in solving some of the problems that are encountered on the road to the exploitation of fusion. It presents a theoretical introduction to deterministic chaos and explains the connection of this theory to magnetic perturbations in tokamak. The results are presented mainly in the form of publications in journals and conference proceedings. Among them are: the comparison of chaotic diffusion of particles and field lines, where significant differences were found; the application of chaotic diffusion of particles to the problem of runaway electrons originating in disruptions, where our simulations contributed to explaining the experimental results from the JET tokamak; the calculation of spectra of perturbations for the COMPASS tokamak, done as a preparation for the upcoming experiments; and modelling of screening of perturbations by plasma, where the observations of divertor footprints show as a promising method to detect the screening.

The goal of this thesis is to contribute to the ambitious program of the foundation of developing statistical physics using chaos. We build a deterministic model of Brownian motion and provide a microscpoic derivation of the Fokker-Planck equation. Since the Brownian motion of a particle is the result of the competing processes of diffusion and dissipation, we create a model where both diffusion and dissipation originate from the same deterministic mechanism - the deterministic interaction of that particle with its environment. We show that standard diffusion which is the basis of the Fokker-Planck equation rests on the Central Limit Theorem, and, consequently, on the possibility of deriving it from a deterministic process with a quickly decaying correlation function. The sensitive dependence on initial conditions, one of the defining properties of chaos insures this rapid decay. We carefully address the problem of deriving dissipation from the interaction of a particle with a fully deterministic nonlinear bath, that we term the booster. We show that the solution of this problem essentially rests on the linear response of a booster to an external perturbation. This raises a long-standing problem concerned with Kubo's Linear Response Theory and the strong criticism against it by van Kampen. Kubo's theory is based on a perturbation treatment of the Liouville equation, which, in turn, is expected to be totally equivalent to a first-order perturbation treatment of single trajectories. Since the boosters are chaotic, and chaos is essential to generate diffusion, the single trajectories are highly unstable and do not respond linearly to weak external perturbation. We adopt chaotic maps as boosters of a Brownian particle, and therefore address the problem of the response of a chaotic booster to an external perturbation. We notice that a fully chaotic map is characterized by an invariant measure which is a continuous function of the control parameters of the map. Consequently if the external perturbation is made to act on a control parameter of the map, we show that the booster distribution undergoes slight modifications as an effect of the weak external perturbation, thereby leading to a linear response of the mean value of the perturbed variable of the booster. This approach to linear response completely bypasses the criticism of van Kampen. The joint use of these two phenomena, diffusion and friction stemming from the interaction of the Brownian particle with the same booster, makes the microscopic derivation of a Fokker-Planck equation and Brownian motion, possible.

La tribologie et l'analyse non-linéaire du signal est le sujet de mon travail de thèse. Dans la nature, les phénomènes linéaires sont l'exception ; rares sont les systèmes réels qui obéissent exclusivement à des lois linéaires. A l'opposée, les non-linéarités sont impliquées dans tous les processus naturels (réactions chimiques, mécanique, économie, etc.). Les systèmes frottant en sont un des exemples les plus courants, avec des applications très variées. Dans les systèmes de freinage, le frottement se trouve être à l'origine de nombreux problèmes d'instabilités. Les types d'instabilités auxquelles on a affaire dans ce cas sont celles des vibrations induites par le frottement. C'est justement sur ces instabilités que repose le principe Modalsens; un capteur- une lamelle- vient frotter sur un échantillon et ce frottement génère la vibration de celui-ci : le post-traitement par analyse de Fourier du signal vibratoire permet de distinguer des composantes liées au relief, au frottement et à la compressibilité des aspérités. Dans le cas de la méthode Modalsens, l'analyse de Fourier, qui est un outil linéaire, agit comme des lunettes aux travers desquelles est observé le signal et qui filtrerait toutes les composantes non-linéaires. Notre contribution s'inscrit dans cette optique: mettre en place une méthode performante d'analyse non-linéaire pour permettre de mieux appréhender l'analyse du comportement dynamique de Modalsens et de dégager de nouveaux estimateurs pour la caractérisation des surfaces textiles. Partant de là, les résultats obtenus nous serviront à proposer une modélisation du contact sur matériaux fibreux. / Tribology and nonlinear time series analysis are the main subject of my thesis. In nature, the Iinear events are the exception; few real systems follow linear laws exclusively. At the opposite, nonlinearities are involved in all natural processes (chemical reactions, mechanical engineering, economies, etc.). Systems involving dry friction are one of the most common examples, with a variety of applications. In braking systems, friction is found to cause many problems of instability. Types of instabilities addressed in this case are those of friction induced vibrations. The Modalsens method is precisely based on the exploitation of those instabilities: a sensor- a thin blade- rubs on a sample and friction induces its vibrations. Post-processing by Fourier analysis of the vibration signal can separate several components of the sample related to the relief, friction and compressibility of asperities. However, in the case of Modalsens method, Fourier analysis, which is a linear tool, acts like eyeglasses through which the signal is observed and that filters out all non-linear components. Our contribution is in this perspective: the establishment of an efficient method of nonlinear signal analysis to better understand the dynamic behavior of Modalsens and also generate new estimators for the characterization of textile surfaces. Hence, a model of contact on fibrous surface is proposed based on the obtained results.

A voz tem sido objeto de estudos em diferentes áreas da ciência. Nas últimas duas décadas os pesquisadores demonstraram a presença do caos na produção de voz. O objetivo deste trabalho é estabelecer padrões visuais de sinais de voz humana através da técnica não linear de reconstrução de espaço de fase e associá-los com suas correspondentes análises auditivo perceptiva e acústica. Foram analisados sinais de voz humana de sujeitos de ambos os gêneros, na faixa etária de 19 a 39 anos. Foram gravadas as vogais sustentadas /a/, /e/ e /i/ do português do Brasil, com uma taxa de amostragem de 22.050 Hz. Os sinais foram analisados a fim de obter medidas acústicas (Jitter, Shimmer e Coeficiente de Excesso). Foi utilizada a técnica de reconstrução de espaço de fase para descrever as características de dinâmica não linear dos sinais de voz, e para análise perceptivo auditiva foi utilizada a escala RASAT. Os resultados demonstram que métodos de dinâmica não linear como a reconstrução do espaço de fase, parece ser uma técnica apropriada para análise de sinais de voz, incorporando os componentes caótico e determinístico da voz humana. É sugerido que análise da dinâmica não linear não substitui as técnicas existentes, embora possa aperfeiçoar e complementar os métodos de análise disponíveis para os profissionais da saúde, como fonoaudiólogos e otorrinolaringólogos / Human voice has been the focus of study for different areas of science. Researches in the last two decades have demonstrated the existence of chaos in human voice production. The purpose of this work is to use nonlinear dynamics techniques in the analysis of normal voices from healthy subjects and correlate them to traditional acoustic parameters as well as perceptual analysis. Human voice signals from healthy subjects, both male and female, ranging in age from 19 to 39 years old were analyzed. Sustained vowel sounds /a/, /e/ and /i/, from brazilian Portuguese were recorded at a sampling rate of 22,050 Hz and analyzed in order to obtain acoustic measures (Jitter, Shimmer and coefficient of excess – EX). The phase space reconstruction technique was used to describe the nonlinear dynamic characteristics of voice signal samples. The results show, that non-linear dynamical method as phase space reconstruction seems to be a suitable technique for voice signals analysis, due to the chaotic component of the human voice. It is suggested, that non-linear dynamic analysis does not replace existing techniques instead, it may improve and complement the recent voice analysis methods available for health professionals, speech therapist and clinician

This dissertation focuses on predictability problems regarding the behaviour of the professional librarians in public-, school- and research libraries in specific crucial situations. The material was obtained by observations/participations (over 10 years) in the daily work in Swedish libraries by non-structured interviews and “free” discussions with librarians and library visitors. Over 200 interviews with 87 librarians and over 300 discussions with 261 library visitors are the fundament of the empirical basis of my study. These findings build up a theoretical basis (a heuristic model) grounded in ideas of deterministic chaos and complexity theory. Deterministic means, that the current state is the consequence of its preceding states, in my terms, the corporate memory in organizations. Chaotic means the sensitivity of initial condition. Deterministic chaos describes behaviour which satisfies the conditions of determinism but even shows the characteristics of chaos. The study shows that differences between the behaviour of the librarians and the predictions of the behaviour in crucial situations from the political leadership are essentially grounded in ·The history of Swedish libraries (deterministic rationality and self-rationality). ·The asymmetric information between librarians and politicians. ·Self-organization of librarians in the daily work. ·The “free” will of librarians in crucial situations grounded in the philosophy of Kant. The behaviour I could observe was studied in the following situations: ·The demand of a law, which secures the existence of public- and school libraries. ·The selection, development and installation of appropriate computer based information systems in public- school- and research libraries. ·The GÖK- and KUR-projects, which was based on the assumption that new ways to work with the daily patterns in libraries should open the library for more visitors, book loaners and information seekers. The issues discussed in this dissertation gave the following results: ·That the long time, in many cases even short time, unpredictability of librarian behaviour in for the library crucial situations is not only understandable – but also necessary for the development of the library. ·That the deterministic chaotic behaviour of the librarians is generated by self-rationality, asymmetric information, and self-organization. ·That the library is not a chaotic organization but a deterministic chaotic organization. Further I could see tendencies for the same behaviour in other professional, knowledge based Non Profit Organizations like schools, universities and hospitals.

Orientador: Marco Aurélio Cremasco / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Química / Made available in DSpace on 2018-08-23T18:40:20Z (GMT). No. of bitstreams: 1 Moura_HelderLimade_M.pdf: 13116282 bytes, checksum: b886f67e25c04de827b794c8f5a4c6ca (MD5) Previous issue date: 2013 / Resumo: Sinais caóticos são sinais cujo comportamento é aperiódico e sensível às condições iniciais ou às pequenas perturbações. Sob este aspecto, diversos campos do conhecimento, tais como engenharia, biologia e economia, podem fazer uso da análise de séries temporais para descrever situações características a seus estudos. Contudo, encontram-se dificuldades para classificar sistemas dinâmicos caóticos a partir de métodos tradicionais como, por exemplo, o espectro de potência de Fourier. Para uma nova abordagem, a reconstrução de atratores, a partir do método de Takens, vem sendo apontada como alternativa de análise para diferenciar o caos determinístico de um comportamento estocástico. A partir do caos determinístico, várias propriedades conhecidas como invariantes caóticas podem ser determinadas, como a dimensão de correlação e a entropia de Kolmogorov. No entanto, estudos recentes têm mostrado que ruídos limitam o desempenho de várias técnicas empregadas na identificação e previsão de sistemas determinísticos e, portanto, influenciando no cálculo dos invariantes caóticos. A extensão da influência do ruído na análise de dados experimentais é difícil de entender devido à falta de conhecimento sobre o nível e a natureza do ruído. Este trabalho, além de construir uma ferramenta para o cálculo dos invariantes caóticos, propõe uma abordagem sistemática para a redução de ruído em séries temporais de sinais de concentração de partículas de FCC, obtidos experimentalmente por uma sonda de fibra óptica em uma seção de riser de um leito fluidizado circulante (LFC). Para a determinação e a redução do nível de ruído foi utilizado o algoritmo de máxima verossimilhança (Schouten et al., 1994a) e o método de Schreiber (1993), respectivamente. Para tanto, adiciona-se o ruído no mapa de Hénon para, a seguir, ser aplicado sobre dados experimentais. Para avaliar a eficácia do método proposto, investiga-se a precisão da previsão para as séries caóticas a partir das redes neuronais artificiais e o valor da dimensão de correlação e entropia de Kolmogorov. Os resultados para identificação do nível de ruído e a sua redução mostram que a técnica proposta neste trabalho é promissora, pois conhecendo o nível de ruído, a redução deste é feita com maior precisão, em consequência disto, os resultados finais mantêm as características caóticas da dinâmica original. Sendo assim, é possível obter uma maior confiabilidade no grau de liberdade e previsibilidade na aplicação em sistemas experimentais / Abstract: Chaotic signals are signals whose behavior is aperiodic and sensitive to initial conditions or to small perturbations. In this regard, various fields of knowledge such as engineering, biology and economics, can make use of time series analysis to describe typical situations to its studies. However, it is difficult to classify chaotic dynamic systems from traditional methods such as Fourier power spectrum. Towards a new approach, reconstruction of attractors from the Takens's method has been suggested as an alternative analysis to differentiate the deterministic chaos of a stochastic behavior. Several properties known as chaotic invariants can be determined from the deterministic chaos such as the correlation dimension and Kolmogorov entropy. However, recent studies have shown that noise limits the performance of various techniques used in the identification and prediction of deterministic systems and influences the calculation of chaotic invariants. The extent of the noise influence in the analysis of experimental data is difficult to understand due to the lack of knowledge about the level and nature of the noise. This work elaborates a tool for the calculation of chaotic invariants and proposes a systematic approach to noise reduction in time series of particle concentration signals. The particle concentration signals were obtained experimentally by an optic fiber probe in a riser section of a circulating fluidized bed (CFB). To evaluate and reduce the noise levels the maximum likelihood algorithm (Schouten et al., 1994a) and the method of Schreiber (1993), were used, respectively. Therefore, the noise is added to the Hénon map to be applied on experimental data. To evaluate the effectiveness of the proposed method the accuracy of prediction by the artificial neural networks, the value of correlation dimension and Kolmogorov entropy from the chaotic time series are investigate. The results for the identification and reduction of noise show that the proposed technique is promising. The reduction is performed with higher accuracy knowing the noise level. Consequently, the final results maintain the original characteristics of chaotic dynamics. Therefore, it is possible to obtain a greater reliability in the degree of freedom and predictability in the application in experimental systems / Mestrado / Engenharia de Processos / Mestre em Engenharia Química

A voz tem sido objeto de estudos em diferentes áreas da ciência. Nas últimas duas décadas os pesquisadores demonstraram a presença do caos na produção de voz. O objetivo deste trabalho é estabelecer padrões visuais de sinais de voz humana através da técnica não linear de reconstrução de espaço de fase e associá-los com suas correspondentes análises auditivo perceptiva e acústica. Foram analisados sinais de voz humana de sujeitos de ambos os gêneros, na faixa etária de 19 a 39 anos. Foram gravadas as vogais sustentadas /a/, /e/ e /i/ do português do Brasil, com uma taxa de amostragem de 22.050 Hz. Os sinais foram analisados a fim de obter medidas acústicas (Jitter, Shimmer e Coeficiente de Excesso). Foi utilizada a técnica de reconstrução de espaço de fase para descrever as características de dinâmica não linear dos sinais de voz, e para análise perceptivo auditiva foi utilizada a escala RASAT. Os resultados demonstram que métodos de dinâmica não linear como a reconstrução do espaço de fase, parece ser uma técnica apropriada para análise de sinais de voz, incorporando os componentes caótico e determinístico da voz humana. É sugerido que análise da dinâmica não linear não substitui as técnicas existentes, embora possa aperfeiçoar e complementar os métodos de análise disponíveis para os profissionais da saúde, como fonoaudiólogos e otorrinolaringólogos / Human voice has been the focus of study for different areas of science. Researches in the last two decades have demonstrated the existence of chaos in human voice production. The purpose of this work is to use nonlinear dynamics techniques in the analysis of normal voices from healthy subjects and correlate them to traditional acoustic parameters as well as perceptual analysis. Human voice signals from healthy subjects, both male and female, ranging in age from 19 to 39 years old were analyzed. Sustained vowel sounds /a/, /e/ and /i/, from brazilian Portuguese were recorded at a sampling rate of 22,050 Hz and analyzed in order to obtain acoustic measures (Jitter, Shimmer and coefficient of excess – EX). The phase space reconstruction technique was used to describe the nonlinear dynamic characteristics of voice signal samples. The results show, that non-linear dynamical method as phase space reconstruction seems to be a suitable technique for voice signals analysis, due to the chaotic component of the human voice. It is suggested, that non-linear dynamic analysis does not replace existing techniques instead, it may improve and complement the recent voice analysis methods available for health professionals, speech therapist and clinician