Obstructive Sleep Apnea-Hypopnea Syndrome (OSAHS) is a serious sleep disordered affecting up to 24% of men and 9% of woman in the middle aged population. The current standard for the OSAHS diagnosis is Polysomnography (PSG), which refers to the continuous monitoring of multiple physiological variables over the course of a night. The main outcomes of the PSG test are the OSAHS severity measures, such as the Respiratory Disturbance Index (RDI), Arousal Index, Latencies and other information to determine the macro sleep architecture (MSA), which is defined by Wake, Rapid-eye-movement (REM) and non-REM states of sleep. The MSA results are essential for computing the diagnostic measures reported in a PSG. The existing methods of the MSA analysis require the recording of 5-7 electrophysiological signals, including the Electroencephalogram (EEG), Electroculogram (EOG), and the Electromyogram (EMG). Sleep clinicians have to depend on the manual scoring of the overnight data records using the criteria given by Rechtschaffen and Kales (R&K, 1968). The manual analysis of MSA is tedious, subjective and suffers from inter- and intra-scorer variability. Additionally, the RDI and the Apnea-Hypopnea Index (AHI) parameters although used as the primary measures of the OSAHS severity, suffers from subjectivity, low reproducibility and a poor correlation with the symptoms of OSAHS. Sleep is essentially a neuropsychological phenomenon, and the EEG remains the best technique for the functional imaging of the brain during sleep. The EEG is the direct result of the neuronal activity of the brain. However, despite the potential, the wealth of information available in the EEG signal remains virtually untapped in current OSAHS diagnosis. Although the EEG is extensively used in traditional sleep analysis, its usage is mainly limited to staging sleep, based on the four-decade old R&K criteria. This thesis addresses these issues plaguing the PSG. We develop a novel, fully-automated algorithm (Higher-order Estimated Sleep States, HESS-algorithm) for the MSA analysis, which requires only one channel of the EEG data. We also develop an objective MSA analysis technique that uses a single, one-dimensional slice of the Bispectrum of the EEG, representing a nonlinear transformation of a system function that can be considered as the EEG generator. The agreement between the human and the proposed technology was found to be in the range of 70%-87%, which are similar to those, possible between expert human scorers. The ability of the HESS algorithm to compute the MSA parameters reliably and objectively will make a dramatic impact on the diagnosis and treatment of OSAHS and other sleep diseases, such as insomnia. The proposed technology uses low-computation-load Bispectrum techniques independent of R&K Criteria (1968) making real-time automated analysis a reality. In the thesis we also propose a new index (the IHSI) to characterise the severity of sleep apnea. The new index is based on the hemispherical asymmetry of the brain and is computed from the EEG coherence analysis. We achieved a significant (p=0.0001) accuracy of up to 91% in classifying patients into apneic and non-apneic group. Our statistical analysis results show that the IHSI carries potential for providing us with a reproducible measure to assist in diagnosing of OSAHS. With the proposed methods in this thesis it may be possible to develop the technology that will not only attempt to screen the OSAHS patients but will be able to provide OSAHS diagnosis with detailed sleep architecture via home based test. These technologies will simplify the instrumentation dramatically and will make possible to extend EEG/MSA analysis to portable systems as well.

A aeroelasticidade estuda a interação mútua entre os efeitos aerodinâmicos e estruturais. É sabido que essa relação muitas vezes se comporta de maneira não linear, causando diversos problemas, tais como flutter, oscilações em ciclo limite, bifurcações e caos. Tais fenômenos são difíceis de serem diagnosticados, podendo causar problemas graves à estrutura das aeronaves e também inviabilizar as suas operações. Dentre as principais fontes de não linearidades em sistemas aeroelásticos, pode-se citar as de origem aerodinâmica e estrutural. As de origem estrutural, por sua vez, podem ter caráter distribuído ou concentrado. Sabe-se que os efeitos estruturais concentrados denominados enrijecimento e folga são os de maior impacto na aeroelasticidade não linear. Desse modo, o objetivo desse trabalho é estudar a interação não linear entre duas não linearidades estruturais, ou seja, o enrijecimento associado à rigidez em torção e a folga presente nas articulações das superfícies de controle de seções típicas aeroelásticas. Experimentos em túnel de vento são realizados utilizando um dispositivo que permite variar a intensidade do efeito de enrijecimento e do tamanho da folga na articulação da superfície de comando. O modelo numérico de seção típica aeroelástica também é utilizado e validado com dados experimentais. Análises por meio de diagramas de bifurcação de Hopf e técnicas baseadas em espectros de potência são utilizadas. Todas as respostas aeroelásticas foram caracterizadas através de ferramentas de análise nos domínios do tempo e da frequência, como técnica de reconstrução de espaço de estados e os espectros de alta ordem (HOS), os quais são importantes na identificação dos tipos de acoplamentos não lineares. Resultados indicam que a combinação dos efeitos de enrijecimento e folga são responsáveis pelo comportamento subcrítico das bifurcações de Hopf e que a intensidade do enrijecimento tem influência direta nas amplitudes de ciclo limite. / Aeroelasticity is the field of engineering that deals with the mutual interaction between the aerodynamic and structural dynamics effects. It is known that this relationship often shows nonlinear behavior, causing various problems such as flutter, limit cycle oscillations, bifurcations and chaos. Such phenomena are difficult to predict and can cause serious problems to the aircraft structure and also they can jeopardize their operations. The unsteady aerodynamic and structural dynamics provide the main sources of nonlinearities in aeroelastic systems. Structural nonlinearities can be treated as distributed or concentrated effects. It is know that the nonlinear concentrated structural effects referred as hardening and freeplay have a significant impact on nonlinear aeroelasticity. The objective of this work is to analyze an aeroelastic system under the influence of combined structural nonlinearities, i.e., the hardening nonlinearity in the pitch airfoil motion and the freeplay nonlinearity in the control surface hinge. Wind tunnel experiments are carried out using one device that allows to vary the intensity of the hardening effect and the size of the freeplay gap in the control surface hinge. The numerical model of the typical aeroelastic section is also used and validated with experimental data. All aeroelastic responses are characterized by analytical tools in time and frequency domains. It was used the state space reconstruction technique and the higher order spectral analysis (HOS) to identify types of nonlinear couplings. The results indicate that the combination of hardening and freeplay effects are responsible for inducing the subcritical behavior on the Hopf bifurcations and that the intensity of the stiffness has a direct influence on the limit cycle amplitudes.

A aeroelasticidade estuda a interação mútua entre os efeitos aerodinâmicos e estruturais. É sabido que essa relação muitas vezes se comporta de maneira não linear, causando diversos problemas, tais como flutter, oscilações em ciclo limite, bifurcações e caos. Tais fenômenos são difíceis de serem diagnosticados, podendo causar problemas graves à estrutura das aeronaves e também inviabilizar as suas operações. Dentre as principais fontes de não linearidades em sistemas aeroelásticos, pode-se citar as de origem aerodinâmica e estrutural. As de origem estrutural, por sua vez, podem ter caráter distribuído ou concentrado. Sabe-se que os efeitos estruturais concentrados denominados enrijecimento e folga são os de maior impacto na aeroelasticidade não linear. Desse modo, o objetivo desse trabalho é estudar a interação não linear entre duas não linearidades estruturais, ou seja, o enrijecimento associado à rigidez em torção e a folga presente nas articulações das superfícies de controle de seções típicas aeroelásticas. Experimentos em túnel de vento são realizados utilizando um dispositivo que permite variar a intensidade do efeito de enrijecimento e do tamanho da folga na articulação da superfície de comando. O modelo numérico de seção típica aeroelástica também é utilizado e validado com dados experimentais. Análises por meio de diagramas de bifurcação de Hopf e técnicas baseadas em espectros de potência são utilizadas. Todas as respostas aeroelásticas foram caracterizadas através de ferramentas de análise nos domínios do tempo e da frequência, como técnica de reconstrução de espaço de estados e os espectros de alta ordem (HOS), os quais são importantes na identificação dos tipos de acoplamentos não lineares. Resultados indicam que a combinação dos efeitos de enrijecimento e folga são responsáveis pelo comportamento subcrítico das bifurcações de Hopf e que a intensidade do enrijecimento tem influência direta nas amplitudes de ciclo limite. / Aeroelasticity is the field of engineering that deals with the mutual interaction between the aerodynamic and structural dynamics effects. It is known that this relationship often shows nonlinear behavior, causing various problems such as flutter, limit cycle oscillations, bifurcations and chaos. Such phenomena are difficult to predict and can cause serious problems to the aircraft structure and also they can jeopardize their operations. The unsteady aerodynamic and structural dynamics provide the main sources of nonlinearities in aeroelastic systems. Structural nonlinearities can be treated as distributed or concentrated effects. It is know that the nonlinear concentrated structural effects referred as hardening and freeplay have a significant impact on nonlinear aeroelasticity. The objective of this work is to analyze an aeroelastic system under the influence of combined structural nonlinearities, i.e., the hardening nonlinearity in the pitch airfoil motion and the freeplay nonlinearity in the control surface hinge. Wind tunnel experiments are carried out using one device that allows to vary the intensity of the hardening effect and the size of the freeplay gap in the control surface hinge. The numerical model of the typical aeroelastic section is also used and validated with experimental data. All aeroelastic responses are characterized by analytical tools in time and frequency domains. It was used the state space reconstruction technique and the higher order spectral analysis (HOS) to identify types of nonlinear couplings. The results indicate that the combination of hardening and freeplay effects are responsible for inducing the subcritical behavior on the Hopf bifurcations and that the intensity of the stiffness has a direct influence on the limit cycle amplitudes.

Higher-order spectral analysis of acoustical waveforms can provide phase information that is not retained in calculations of power spectral density. In the propagation of high intensity sound, nonlinearity can cause substantial changes in the waveform as frequency components interact with one another. The bispectrum, which is one order higher than power spectral density, may provide a useful measure of nonlinearity in propagation by highlighting spectral regions of interaction. This thesis provides a review of the bispectrum, places it in the context of nonlinear acoustic propagation, and presents spectra calculated as a function of distance for numerically propagated acoustic waveforms. The calculated spectra include power spectral density, quad-spectral density, bispectrum, spatial derivative of the bispectrum, bicoherence, and skewness function. / text