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We analyzed long-term temperature trends in Utah using a relatively new signal processing method called Empirical Mode Decomposition (EMD). We evaluated the available weather records in Utah and selected 52 stations, which had records longer than 60 years, for analysis. We analyzed daily temperature data, both minimum and maximums, using the EMD method that decomposes non-stationary data (data with a trend) into periodic components and the underlying trend. Most decomposition algorithms require stationary data (no trend) with constant periods and temperature data do not meet these constraints. In addition to identifying the long-term trend, we also identified other periodic processes in the data. While the immediate goal of this research is to characterize long-term temperature trends and identify periodic processes and anomalies, these techniques can be applied to any time series data to characterize trends and identify anomalies. For example, this approach could be used to evaluate flow data in a river to separate the effects of dams or other regulatory structures from natural flow or to look at other water quality data over time to characterize the underlying trends and identify anomalies, and also identify periodic fluctuations in the data. If these periodic fluctuations can be associated with physical processes, the causes or drivers might be discovered helping to better understand the system. We used EMD to separate and analyze long-term temperature trends. This provides awareness and support to better evaluate the extremities of climate change. Using these methods we will be able to define many new aspects of nonlinear and nonstationary data. This research was successful and identified several areas in which it could be extended including data reconstruction for time periods missing data. This analysis tool can be applied to various other time series records.

Este trabalho tem seu foco na monitoração dos processos de usinagem das máquinas ferramentas sem a utilização de sensores dedicados à medição direta das grandezas mecânicas envolvidas no processo de usinagem em si. Assim sendo, optou-se por um método de medição indireta utilizando um estimador de potência e torque baseado nas grandezas elétricas na entrada de energia do motor de indução da máquina ferramenta. O núcleo central do trabalho consiste na medição de processos de usinagem utilizando um dinamômetro de alta precisão próprio para máquina ferramenta para obter os valores médios e os modos de vibração do processo máquina ferramenta-usinagem e fazer a confrontação com os mesmos dados obtidos pelo estimador de torque. A pesquisa realizada utilizou ferramentas clássicas de processamento de sinais, como é o caso da FFT, assim como duas poderosas ferramentas atuais, a transformada de wavelet (WT) e a transformada de Hilbert-Huang (HHT). Em adição foi utilizado um processo de otimização para a determinação dos parâmetros do motor de indução on-line baseado em uma metaheurística denominada busca de harmonia (Harmony Search HS) / This work focuses on monitoring the machining processes in machine tools without the use of dedicated transducers to directly measure mechanicals quantities of the machining process. The approached method used the option of measuring the power and torque through a estimator based in the electrical quantities in the input of the induction motor used by machine tool. The core of the work consists in the measuring the mechanical processes of machining using a high precision dynamometer specified to machine tool to get the average values of mechanical quantities and the vibration modes of the set machine tool-machining process, the objective is to compare the same data group got from dynamometer and estimator. The research data was based on classical analysis tool such as Fourier transform (FFT) and on modern powerful tools such as wavelet transforms (WT) and Hilbert-Huang transform (HHT). To refine the measuring process of average values of torque and power using the induction motor a method to estimates the motor parameters was added based on an optimization method named harmony search (HS).

Este trabalho tem seu foco na monitoração dos processos de usinagem das máquinas ferramentas sem a utilização de sensores dedicados à medição direta das grandezas mecânicas envolvidas no processo de usinagem em si. Assim sendo, optou-se por um método de medição indireta utilizando um estimador de potência e torque baseado nas grandezas elétricas na entrada de energia do motor de indução da máquina ferramenta. O núcleo central do trabalho consiste na medição de processos de usinagem utilizando um dinamômetro de alta precisão próprio para máquina ferramenta para obter os valores médios e os modos de vibração do processo máquina ferramenta-usinagem e fazer a confrontação com os mesmos dados obtidos pelo estimador de torque. A pesquisa realizada utilizou ferramentas clássicas de processamento de sinais, como é o caso da FFT, assim como duas poderosas ferramentas atuais, a transformada de wavelet (WT) e a transformada de Hilbert-Huang (HHT). Em adição foi utilizado um processo de otimização para a determinação dos parâmetros do motor de indução on-line baseado em uma metaheurística denominada busca de harmonia (Harmony Search HS) / This work focuses on monitoring the machining processes in machine tools without the use of dedicated transducers to directly measure mechanicals quantities of the machining process. The approached method used the option of measuring the power and torque through a estimator based in the electrical quantities in the input of the induction motor used by machine tool. The core of the work consists in the measuring the mechanical processes of machining using a high precision dynamometer specified to machine tool to get the average values of mechanical quantities and the vibration modes of the set machine tool-machining process, the objective is to compare the same data group got from dynamometer and estimator. The research data was based on classical analysis tool such as Fourier transform (FFT) and on modern powerful tools such as wavelet transforms (WT) and Hilbert-Huang transform (HHT). To refine the measuring process of average values of torque and power using the induction motor a method to estimates the motor parameters was added based on an optimization method named harmony search (HS).

A exploração offshore tem crescido muito nos últimos anos e grandes estruturas e equipamentos têm sido projetados e construídos para remover o óleo que se encontra abaixo da superfície do mar. Para plataformas offshore fixas tipo jaqueta é necessário analisar os problemas decorrentes da exposição dessas instalações ao ambiente hostil do oceano. Estas perturbações induzem vibrações excessivas nas estruturas, afetando o conforto e a estabilidade da instalação, e para combater essas vibrações uma ferramenta matemática foi utilizada para monitorar o estado da integridade da estrutura, a Transformada de Hilbert-Huang (HHT). O HHT foi utilizada com sucesso para a identificação de parâmetros modais, como frequência fundamental e fator de amortecimento da plataforma. Finalmente, uma técnica de controle de vibração ativa baseada no Controle Linear Quadrático (LQ) é implementada com o objetivo de reduzir os efeitos de perturbações oscilatórias indesejáveis causados por ondas e correntes marinhas. / The offshore exploration has grown tremendously in recent years, and large structures and equipment has been designed and built to remove the oil that lies beneath the sea surface. For fixed jacket type offshore platforms is necessary to consider the problems arising from exposure of these facilities to the hostile ocean environment. These perturbations induce excessive vibrations in the structures affecting the comfort and stability of the facility, and for to combat these vibrations a mathematical tool was used to monitor the integrity health of the structure, namely the Hilbert-Huang Transform (HHT). The HHT was used for the successfully identification of modal parameters, as fundamental frequency and damping factor of the platform. Finally, an active vibration control technique based on the Control Linear Quadratic (LQ) is implemented aiming to reduce the effects of undesirable oscillatory perturbations caused by waves and marine current.

Signals recorded from the brain often show rhythmic patterns at different frequencies, which are tightly coupled to the external stimuli as well as the internal state of the subject. These signals also have transient structures related to spiking or sudden onset of a stimulus, which have a duration not exceeding tens of milliseconds. Further, brain signals are highly non-stationary because both behavioral state and external stimuli can change over a short time scale. It is therefore essential to study brain signals using techniques that can represent both rhythmic and transient components of the signal. In Chapter 2, we describe a multi-scale decomposition technique based on an over-complete dictionary called matching pursuit (MP), and show that it is able to capture both sharp stimulus-onset transient and sustained gamma rhythm in local field potential recorded from the primary visual cortex. Gamma rhythm (30 to 80 Hz), often associated with high-level cortical functions, has been proposed to provide a temporal reference frame (“clock”) for spiking activity, for which it should have least center frequency variation and consistent phase for extended durations. However, recent studies have proposed that gamma occurs in short bursts and it cannot act as a reference. In Chapter 3, we propose another gamma duration estimator based on matching pursuit (MP) algorithm, which is tested with synthetic brain signals and found to be estimating the gamma duration efficiently. Applying this algorithm to real data from awake monkeys, we show that the median gamma duration is more than 330 ms, which could be long enough to support some cortical computations.