Dissertations / Theses on the topic 'Multivariate filter'

This thesis includes two essays that are focused on developing multivariate filter approaches to be used for extracting common cyclical components where the common components can be used as an estimator of a business cycle. The first chapter aims to develop an optimal multivariate filter in order to extract common cyclical components of macroeconomic indicators. The filter allows macroeconomic series to be modeled as a phase shifted version of a coinciding business cycle (BC) while keeping other time series components such as the stochastic trend and idiosyncratic shocks intact (i.e. they are individually specified for each series). Earlier studies of Rünstler (2004), Valle e Azevedo et al. (2006) have applied phase shift in the form of a delay parameter when specifying lead-lag cycles. However, the lead-lag relationship is defined by rotating the baseline cycle which leads to loss of information. This deficiency is especially important if one considers working in continuous time. Therefore, this paper improves on the former technique by allowing a more flexible phase shift mechanism on the original BC. This in turn should lead to more realistic estimates and filters considering that the underlying data is generated through a continuous time framework. The study starts by presenting a structure for bi-variate time series system and then extends to model to incorporate a structure for three time series and beyond. Kalman filter and smoothing recursions are applied to compute the smoothed cycle estimates and to construct the likelihood function. Using simulated data, we test both model specifications by carrying out a grid search of the initial delay parameter to see the likelihood behavior as the parameter moves into fractional neighborhoods. Afterwards, applying the methodology to a set of EU countries and macroeconomic indicators; the study aims to shed light to the presence of cyclical heterogeneity at country level economic activity for major EU member states. A second empirical study provides analysis on how the model can be implemented for assigning a lead/lag ordering to three main economic indicators of a single country. The second chapter implements a multivariate non-parametric filtering approach; the Vertical Multivariate Singular Spectrum Analysis (V-MSSA) of Hassani and Mahmoudvand (2013) and Golyandina et al. (2013). to be applied for identifying a common economic cycle indicator. The methodology is a data-driven procedure that can decompose a time series into many sub components. By exploiting this ability of the SSA, the paper aims to first extract cyclical components based on frequency characteristics and then follow by choosing only common cyclical component pairs with-in the business cycle frequency spectrum. These components will then be aggregated for constructing an EU region wide Business cycle indicator. The chapter outlines each steps of the algorithm that will eventually identify the SSA filter to act as a band-pass filter. The study then proceeds with simulation based data where the common cycle can be controlled and extracted a priori as a benchmark to the SSA-based filter estimates. The study follows with an empirical analysis similar to the framework set in Valle e Azevedo et al. (2006) with the aim to identify a Euro region business cycle indicator. The SSA based filter estimate is compared with Euro region economic activity indicators; the EuroCoin and the quarterly GDP growth rate of the EU area. Our results presents evidence of a successful alternative for tracing the cyclical position of the EU economy from a much smaller data set. Moreover, the constructed indicator also could serve as an unobserved proxy for a monthly growth cycle. A further analysis is also conducted to reveal whether the SSA based approach can be considered as an alternative to parametric filtering methods by providing results of common cycle extraction using Unobserved component model alternatives.
This thesis includes two essays that are focused on developing multivariate filter approaches to be used for extracting common cyclical components where the common components can be used as an estimator of a business cycle. The first chapter aims to develop an optimal multivariate filter in order to extract common cyclical components of macroeconomic indicators. The filter allows macroeconomic series to be modeled as a phase shifted version of a coinciding business cycle (BC) while keeping other time series components such as the stochastic trend and idiosyncratic shocks intact (i.e. they are individually specified for each series). Earlier studies of Rünstler (2004), Valle e Azevedo et al. (2006) have applied phase shift in the form of a delay parameter when specifying lead-lag cycles. However, the lead-lag relationship is defined by rotating the baseline cycle which leads to loss of information. This deficiency is especially important if one considers working in continuous time. Therefore, this paper improves on the former technique by allowing a more flexible phase shift mechanism on the original BC. This in turn should lead to more realistic estimates and filters considering that the underlying data is generated through a continuous time framework. The study starts by presenting a structure for bi-variate time series system and then extends to model to incorporate a structure for three time series and beyond. Kalman filter and smoothing recursions are applied to compute the smoothed cycle estimates and to construct the likelihood function. Using simulated data, we test both model specifications by carrying out a grid search of the initial delay parameter to see the likelihood behavior as the parameter moves into fractional neighborhoods. Afterwards, applying the methodology to a set of EU countries and macroeconomic indicators; the study aims to shed light to the presence of cyclical heterogeneity at country level economic activity for major EU member states. A second empirical study provides analysis on how the model can be implemented for assigning a lead/lag ordering to three main economic indicators of a single country. The second chapter implements a multivariate non-parametric filtering approach; the Vertical Multivariate Singular Spectrum Analysis (V-MSSA) of Hassani and Mahmoudvand (2013) and Golyandina et al. (2013). to be applied for identifying a common economic cycle indicator. The methodology is a data-driven procedure that can decompose a time series into many sub components. By exploiting this ability of the SSA, the paper aims to first extract cyclical components based on frequency characteristics and then follow by choosing only common cyclical component pairs with-in the business cycle frequency spectrum. These components will then be aggregated for constructing an EU region wide Business cycle indicator. The chapter outlines each steps of the algorithm that will eventually identify the SSA filter to act as a band-pass filter. The study then proceeds with simulation based data where the common cycle can be controlled and extracted a priori as a benchmark to the SSA-based filter estimates. The study follows with an empirical analysis similar to the framework set in Valle e Azevedo et al. (2006) with the aim to identify a Euro region business cycle indicator. The SSA based filter estimate is compared with Euro region economic activity indicators; the EuroCoin and the quarterly GDP growth rate of the EU area. Our results presents evidence of a successful alternative for tracing the cyclical position of the EU economy from a much smaller data set. Moreover, the constructed indicator also could serve as an unobserved proxy for a monthly growth cycle. A further analysis is also conducted to reveal whether the SSA based approach can be considered as an alternative to parametric filtering methods by providing results of common cycle extraction using Unobserved component model alternatives.

Mestrado em Econometria Aplicada e Previsão
This study discusses four commonly used optimal approximations to the infinite order moving average filter that ideally extracts from a time series fluctuations within a specified range of periodicities. Based on our findings, we use two of those approximations in the estimation of two macroeconomic signals: business cycle fluctuations and medium to long run component of output growth rate. This study dis-tinguishes itself from related literature by showing how to successfully incorporate in the multivariate band-pass approximations factors estimated from a large panel of time series. As illustration, we apply these approximations to U.S. data. We evaluate the real-time performance of the indicators and provide forecasting comparisons. The results suggest that the multivariate indica¬tor outperforms the competing univariate indicator across all different settings considered. Moreover, multivariate methods that target smooth growth are useful to forecast quarterly GDP growth rate at short-term and to forecast yearly GDP growth.
Este estudo discute quatro aproximações óptimas ao filtro de medias moveis infinitas que idealmente isola de uma serie temporal flutuações compreendidas num determinado intervalo de periodicidades. De acordo com as nossas conclusões, utilizamos duas dessas aproximações na estimaçao de dois sinais macroeconómicos: flutuacoes de ciclo economico no produto e a componente de medio e longo prazo da taxa de crescimento do produto. Este estudo distingue-se da literatura corrente ao mostrar como integrar nas aproximacoes do filtro banda multivariado factores estimados a partir de um largo painel de sóeries temporais. Como ilustracao, aplicamos estas aproximacoes a dados dos E.U.A.. Avaliamos o desempenho dos in¬dicadores em tempo real e apresentamos comparacoes em termos de previsao. Os resultados sugerem que o indicador multivariado tem um desempenho claramente superior ao do indicador univariado em todos os cenóarios considerados. Adicionalmente, os móetodos multivariados que aproximam o crescimento alisado sao úteis na previsao da taxa de crescimento trimestral do PIB a curto prazo e para previsao do crescimento anual do PIB.

Identifying parameters for state-space models in high dimensioned cases requires a complex methodology. We offer an example of application for hedonic prices and the hyper-parameter estimation for dynamic supply chains. An algorithm is created based on the Kalman filter-smoother and Expectation-Maximization procerures. Stopping rules for the algorithm are analyzed and compared. We detected the best stopping rule for our environment. In this way, the hedonic prices estimated can be used for any decision process. The thesis point to an application in forecast analysis for product prices. Accurate forecasting of market price developments is essential in achieving superior market performance. Especially in oligopolistic markets for durable consumer products a robust understanding of selling prices is important, as it drives pricing behavior as well as procurement, inventory and production decisions. Moreover, a supply chain perspective is indispensable for pricing forecasts since companies not only compete for product sales but also for limited resources. The thesis explores the use of dynamic multivariate hedonics-based pricing models that explicitly model selling prices with the market valuation of constituting parts. The model is applied to TAC SCM, a supply-chain trading agent competition. To find unknown component prices series we apply the Kalman filter technique to smooth and forecast implicit prices using the EM algorithm. Finally, we present results of our analysis to establish the viability of this method.

The primate hand, a biomechanical structure with over twenty kinematic degrees of freedom, has an elaborate anatomical architecture. Although the hand requires complex, coordinated neural control, it endows its owner with an astonishing range of dexterous finger movements. Despite a century of research, however, the neural mechanisms that enable finger and grasping movements in primates are largely unknown. In this thesis, we investigate statistical models of finger movement that can provide insights into the mechanics of the hand, and that can have applications in neural-motor prostheses, enabling people with limb loss to regain natural function of the hands. There are many challenges associated with (1) the understanding and modeling of the kinematics of fingers, and (2) the mapping of intracortical neural recordings into motor commands that can be used to control a Brain-Machine Interface. These challenges include: potential nonlinearities; confounded sources of variation in experimental datasets; and dealing with high degrees of kinematic freedom. In this work we analyze kinematic and neural datasets from repeated-trial experiments of hand motion, with the following contributions: We identified static, nonlinear, low-dimensional representations of grasping finger motion, with accompanying evidence that these nonlinear representations are better than linear representations at predicting the type of object being grasped over the course of a reach-to-grasp movement. In addition, we show evidence of better encoding of these nonlinear (versus linear) representations in the firing of some neurons collected from the primary motor cortex of rhesus monkeys. A functional alignment of grasping trajectories, based on total kinetic energy, as a strategy to account for temporal variation and to exploit a repeated-trial experiment structure. An interpretable model for extracting dynamic synergies of finger motion, based on Gaussian Processes, that decomposes and reduces the dimensionality of variance in the dataset. We derive efficient algorithms for parameter estimation, show accurate reconstruction of grasping trajectories, and illustrate the interpretation of the model parameters. Sound evidence of single-neuron decoding of interpretable grasping events, plus insights about the amount of grasping information extractable from just a single neuron. The Laplace Gaussian Filter (LGF), a deterministic approximation to the posterior mean that is more accurate than Monte Carlo approximations for the same computational cost, and that in an off-line decoding task is more accurate than the standard Population Vector Algorithm.

Le traitement des images satellitaires est considéré comme l'un des domaines les plus intéressants dans les domaines de traitement d'images numériques. Les images satellitaires peuvent être dégradées pour plusieurs raisons, notamment les mouvements des satellites, les conditions météorologiques, la dispersion et d'autres facteurs. Plusieurs méthodes d'amélioration et de restauration des images satellitaires ont été étudiées et développées dans la littérature. Les travaux présentés dans cette thèse se concentrent sur la restauration des images satellitaires par des techniques de filtrage statistique non linéaire. Dans un premier temps, nous avons proposé une nouvelle méthode pour restaurer les images satellitaires en combinant les techniques de restauration aveugle et non aveugle. La raison de cette combinaison est d'exploiter les avantages de chaque technique utilisée. Dans un deuxième temps, de nouveaux algorithmes statistiques de restauration d'images basés sur les filtres non linéaires et l'estimation non paramétrique de densité multivariée ont été proposés. L'estimation non paramétrique de la densité à postériori est utilisée dans l'étape de ré-échantillonnage du filtre Bayésien bootstrap pour résoudre le problème de la perte de diversité dans le système de particules. Enfin, nous avons introduit une nouvelle méthode de la combinaison hybride pour la restauration des images basée sur la transformée en ondelettes discrète (TOD) et les algorithmes proposés à l'étape deux, et nos avons prouvé que les performances de la méthode combinée sont meilleures que les performances de l'approche TOD pour la réduction du bruit dans les images satellitaires dégradées
Satellite image processing is considered one of the more interesting areas in the fields of digital image processing. Satellite images are subject to be degraded due to several reasons, satellite movements, weather, scattering, and other factors. Several methods for satellite image enhancement and restoration have been studied and developed in the literature. The work presented in this thesis, is focused on satellite image restoration by nonlinear statistical filtering techniques. At the first step, we proposed a novel method to restore satellite images using a combination between blind and non-blind restoration techniques. The reason for this combination is to exploit the advantages of each technique used. In the second step, novel statistical image restoration algorithms based on nonlinear filters and the nonparametric multivariate density estimation have been proposed. The nonparametric multivariate density estimation of posterior density is used in the resampling step of the Bayesian bootstrap filter to resolve the problem of loss of diversity among the particles. Finally, we have introduced a new hybrid combination method for image restoration based on the discrete wavelet transform (DWT) and the proposed algorithms in step two, and, we have proved that the performance of the combined method is better than the performance of the DWT approach in the reduction of noise in degraded satellite images

In parametrized continuous state-space models, one can obtain estimates of the likelihood of the data for fixed parameters via the Sequential Monte Carlo methodology. Unfortunately, even if the likelihood is continuous in the parameters, the estimates produced by practical particle filters are not, even when common random numbers are used for each filter. This is because the same resampling step which drastically reduces the variance of the estimates also introduces discontinuities in the particles that are selected across filters when the parameters change. When the state variables are univariate, a method exists that gives an estimator of the log-likelihood that is continuous in the parameters. We present a non-trivial generalization of this method using tree-based o(N²) (and as low as O(N log N)) resampling schemes that induce significant correlation amongst the selected particles across filters. In turn, this reduces the variance of the difference between the likelihood evaluated for different values of the parameters and the resulting estimator is considerably smoother than naively running the filters with common random numbers. Importantly, in practice our methods require only a change to the resample operation in the SMC framework without the addition of any extra parameters and can therefore be used for any application in which particle filters are already used. In addition, excepting the optional use of interpolation in the schemes, there are no regularity conditions for their use although certain conditions make them more advantageous. In this thesis, we first introduce the relevant aspects of the SMC methodology to the task of likelihood estimation in continuous state-space models and present an overview of work related to the task of smooth likelihood estimation. Following this, we introduce theoretically correct resampling schemes that cannot be implemented and the practical tree-based resampling schemes that were developed instead. After presenting the performance of our schemes in various applications, we show that two of the schemes are asymptotically consistent with the theoretically correct but unimplementable methods introduced earlier. Finally, we conclude the thesis with a discussion.

The work done in this thesis aims to combine the knowledge of two research areas: the automatic control area and the power electronics area, in order to elaborate a methodology for controlling a three-phase shunt active filter system. Indeed, this subject has been widely handled by the specialists in the field of power electronics in order to eliminate voltage and current harmonics in electrical distribution networks. Most of existing control strategies of active filters have been formulated as a current reference tracking control design problem. The alternative approach that we propose is to formulate a three-phase shunt active filter as a linear perturbation rejection problem with zero references. The linearity of the mathematical model enables us to use the H∞ control paradigm in order to design a multivariable linear robust H∞ controller. Such a controller is able to reject harmonics generated by the nonlinear loads, and to maintain the stability and performance of the system against the variations in the physical parameters of the electric circuit. In order to validate the proposed approach, simulations are carried out in Matlab/Simulink environment, and the control laws are implemented on an experimental test bench
Le travail effectué dans cette thèse a pour objectif de combiner les connaissances de deux domaines de recherche : l’automatique et l’ électronique de puissance afin de dégager une méthodologie pour contrôler un filtre actif parallèle triphasé. En effet, ce sujet est largement traité par les spécialistes de l’électronique de puissance pour éliminer les harmoniques de tension et de courant sur un réseau de distribution électrique. La plupart des stratégies de commande sont basées sur la formulation du problème du filtrage actif comme un problème de suivi de consignes classiquement utilisé dans ce domaine. L’ approche que nous proposons est de considérer le problème comme un problème linéaire de rejet de perturbations. La modélisation linéaire du système permet la synthèse d’une loi de commande robuste multivariable en vue d’ une stabilisation robuste et d’ une performance H∞ robuste. Cette loi de commande devra permettre d’ éliminer les harmoniques qui apparaissent sur le réseau, et de maintenir la stabilité et la performance du système vis-à-vis les incertitudes sur les paramètres du modèle. La validité de l’ approche proposée est vérifiée en simulation à partir de l’ outil logiciel Matlab/Simulink, puis par la mise en œuvre sur un banc expérimental

O biodiesel tem sido amplamente utilizado como uma fonte de energia renovável, que contribui para a diminuição de demanda por diesel mineral. Portanto, existem várias propriedades que devem ser monitoradas, a fim de produzir e distribuir biodiesel com a qualidade exigida. Neste trabalho, as propriedades físicas do biodiesel, tais como massa específica, índice de refração e ponto de entupimento de filtro a frio foram medidas e associadas a espectrometria no infravermelho próximo (NIR) e espectrometria no infravermelho médio (Mid-IR) utilizando ferramentas quimiométricas. Os métodos de regressão por mínimos quadrados parciais (PLS), regressão de mínimos quadrados parciais por intervalos (iPLS), e regressão por máquinas de vetor de suporte (SVM) com seleção de variáveis por Algoritmo Genético (GA) foram utilizadas para modelar as propriedades mencionadas. As amostras de biodiesel foram sintetizadas a partir de diferentes fontes, tais como canola, girassol, milho e soja. Amostras adicionais de biodiesel foram adquiridas de um fornecedor da região sul do Brasil. Em primeiro lugar, o pré-processamento de correção de linha de base foi usado para normalizar os dados espectrais de NIR, seguidos de outros tipos de pré-processamentos que foram aplicados, tais como centralização dos dados na média, 1 derivada e variação de padrão normal. O melhor resultado para a previsão do ponto de entupimento de filtro a frio foi utilizando os espectros de Mid-IR e o método de regressão GA-SVM, com alto coeficiente de determinação da previsão, R2Pred=0,96 e baixo valor da Raiz Quadrada do Erro Médio Quadrático da previsão, RMSEP (C)= 0,6. Para o modelo de previsão da massa específica, o melhor resultado foi obtido utilizando os espectros de Mid-IR e regressão por PLS, com R2Pred=0,98 e RMSEP (g/cm3)= 0,0002. Quanto ao modelo de previsão para o índice de refração, o melhor resultado foi obtido utilizando os espectros de Mid-IR e regressão por PLS, com excelente R2Pred=0,98 e RMSEP= 0,0001. Para esses conjuntos de dados, o PLS e o SVM demonstraram sua robustez, apresentando-se como ferramentas úteis para a previsão das propriedades do biodiesel estudadas
Biodiesel has been widely used as a renewable energy source which contributes to the mineral diesel decrease demand. Therefore, there are several properties that must be monitored in order to produce and distribute biodiesel with the required quality. In this work, the biodiesel physical properties such as specific mass, refractive index and cold filter plugging point were measured and associated with near infrared spectroscopy (NIR) and mid-Infrared spectroscopy (mid-IR) spectra using chemometric tools. The Partial Least Squares Regression (PLS), Interval Partial Least Squares Regression (iPLS), and Support Vector Machines Regression (SVM) with variable selection by Genetic Algorithm (GA) methods were used to model the aforementioned properties. The biodiesel samples were synthesized from different sources such as canola, sunflower, corn, and soybean. Additional biodiesel samples were purchased from a Brazil South Region supplier. Firstly, the preprocessing baseline correction was used to normalize the NIR spectral data, following others preprocessing types were applied in such as the mean center, the first derivative and standard normal variate. The best result for predicting the cold filter plugging point was using Mid-IR spectra and GA-SVM regression method, with high coefficient determination of prediction, R2Pred = 0.94 and low value of the Root Mean Square Error of Prediction, RMSEP (C) = 0.7. For the specific mass prediction model, the best result was obtained using the Mid-IR spectrums and PLS regression, with the R2Pred = 0.98 and RMSEP (g/cm3) = 0.0002. As for a prediction model for the refractive index, the best result was obtained using the Mid-IR spectrums and PLS regression, with the R2Pred = 0.98 and RMSEP = 0.0001. For these datasets, the PLS and SVM models demonstrated theirs robustness, presenting themselves as useful tools for the biodiesel properties prediction studied

A retroalimentação de controladores preditivos que utilizam modelos em espaço de estado pode ser realizada de duas formas: (a) correção por bias, em que as saídas preditas são corrigidas adicionando-se um valor proporcional a discrepância encontrada entre o valor medido atual e sua respectiva predição e por (b) retroalimentação dos estados, onde se determinam as condições iniciais através da estimação dos estados, e a partir de uma melhor condição inicial se realizam as predições futuras usadas no cálculo das ações de controle. Nesta dissertação estas duas abordagens são comparadas utilizando a Planta Laboratorial de Seis Tanques Esféricos. As técnicas de Filtro de Kalman Estendido (EKF) e Filtro de Kalman Estendido com Restrições (CEKF) foram empregadas para estimar os estados não medidos. Inicialmente foram feitos testes off-line destes algoritmos de estimação. Para estes testes são utilizados uma série de dados da planta laboratorial do estudo de caso, na qual são estudadas as influências de diversos fatores de ajuste que determinam a qualidade final de estimação. Estes ajustes serviram de base para a aplicação destes algoritmos em tempo real, quando então, estimadores de estados estão associados ao sistema de controle do processo baseado em um algoritmo de controle preditivo. Após se ter certificado a qualidade das estimações de estado, partiu-se para sua utilização como uma alternativa de retroalimentação de controladores preditivos. Estes resultados foram comparados com os obtidos através da correção simples por bias. Os resultados experimentais apontam para uma marginal piora devido à retroalimentação por estimadores de estados frente à correção por bias, pelo menos para o caso do controlador preditivo linear utilizado na comparação. Entretanto, espera-se que resultados melhores sejam obtidos no caso de modelos preditivos não-lineares, uma vez que nestes casos o modelo é bem mais sensível à qualidade da condição inicial.
The feedback of controllers that use predictive models in state space can be accomplished in two ways: (a) bias correction, where the predicted outputs are corrected by adding a value proportional to the discrepancy found between the current measurement and its respective prediction; and by (b) state feedback, which establishes the initial conditions through the states estimation, and from a better initial condition are carried out the future predictions used in the calculation of control. In this thesis these two approaches are compared using a Laboratorial Plant of Six Spherical Tanks. The techniques of Extended Kalman Filter (EKF) and Constraint Extended Kalman Filter (CEKF) were used to estimate the unmeasured states. Initially, tests were carried out off-line for theses estimation algorithms. For such testing are used a dataset of the plant in case study, in which are studied the influences of several adjustment factors that they determine the final quality of estimation. These adjustments were used of base for the application of these algorithms in real time, when then state estimators are associated with the system of process control based on a predictive control algorithm. After having ascertained the quality of the state estimates, begins its use as an alternative for feedback of predictive controllers. These results were compared with those obtained by the simple correction of bias. The experimental results show a marginal worsening due to feedback from state estimated compared with bias correction, at least for the case of linear predictive controller used in the comparison. However, one expects that better results will be obtained in the case of non-linear predictive models, since in these cases the model is much more sensitive to the quality of the initial condition.

Cette thèse expose une application industrielle du filtre de Kalman étendu à grand gain pour l'estimation et le contrôle des compositions d'une colonne à distiller. Elle démontre l'intérêt pratique des observateurs pour le contrôle des procédés en exposant une méthodologie d'application et les résultats d'implantation obtenus sur site. Cette application industrielle a pour but d'améliorer le contrôle d'une unité de distillation en couplant un observateur avec un contrôleur multi-variable linéaire existant. Le contrôleur étant déterminé à l'avance, les travaux se sont essentiellement attachés à fournir des techniques numériques adaptées à la structure du modèle représentatif du procédé. Le développement d'un outil pour l'estimation des compositions d'une colonne à distiller multi-composant a ainsi été réalisé. Les solutions employées permettent une application de l'observateur en temps réel et garantissent sa robustesse vis-à-vis de certains problèmes numériques. Toutefois, les contraintes d'application nécessitent l'emploi du filtre de Kalman étendu itéré dans sa version continue-discrète. Dès lors, les résultats théoriques établis dans les travaux précédents qui garantissaient la convergence exponentielle de l'estimée vers la valeur n'existent plus. Enfin, les résultats de simulation et ceux obtenus sur site par couplage avec le contrôleur multi-variable sont validés.

O presente trabalho apresenta a descrição de um modelo matemático completo em seis graus de liberdade para um Veículo Submersível Autônomo (VSA) sub-atuado. Desenvolveram-se métodos de identificação de sistemas para identificar o modelo não linear do veículo. A fim de evitar problemas de divergência na estimação de parâmetros hidrodinâmicos do modelo, usou-se o método de transformação paramétrica. Usou-se o filtro estendido de Kalman como estratégia para o processo de estimação de parâmetros quando ruídos de natureza gaussiana estavam presentes no modelo e nas medidas. Com o objetivo de estimar um maior número de parâmetros de uma só vez, empregou-se o método de máxima verossimilhança. Os experimentos mostraram que o filtro de Kalman responde bem à estimação de parâmetros específicos, porém, divergiu facilmente à estimação de múltiplos parâmetros. Uma alternativa que apresentou melhor desempenho foi o método de máxima verossimilhança. Testaram-se manobras circulares e de zig-zags para a obtenção de dados do veículo. Para os ensaios experimentais, utilizou-se o VSA sub-atuado do Laboratório de Veículos Não Tripulados (LVNT) do Departamento de Engenharia Mecatrônica da Escola Politécnica da Universidade de São Paulo. Validou-se o modelo identificado mediante o simulador do veículo. Numa segunda etapa, desenvolveram-se controladores H¥ capazes de controlar a dinâmica do VSA em seus seis graus de liberdade. Projetaram-se controladores SISO (uma entrada e uma saída) e MIMO (múltiplas entradas e múltiplas saídas) com o fim de avaliar o acoplamento dinâmico do sistema. Projetaram-se controladores centralizados robustos para garantir as condições de operação num ambiente marinho e em condições de laboratório próximas às de uma aplicação real. As leis de controle são baseadas na técnica de sensibilidade mista H¥ que garantem condições de robustez do sistema de controle, tanto no desempenho quanto na estabilidade. Uma estrutura de controle de dois graus de liberdade (2GL) produziu melhores propriedades de desempenho comparada com a estrutura do controlador de um grau de liberdade. Compararam-se as respostas dos controladores descentralizados SISO e os controladores centralizados. O controlador 2GL garantiu as especificações do projeto, inclusive aquelas definidas no domínio do tempo. Um controlador central pode controlar o veículo na realização de manobras complexas em três dimensões que emulem a inspeção ou monitoramento de sistemas offshores ou outras tarefas comuns na exploração submarinha. O trabalho apresenta também a integração dos algoritmos de controle com o sistema de tempo real embarcado, os sensores inerciais de navegação, os motores elétricos para os atuadores lemes e o propulsor, o banco de baterias e o processador central ARM7 de 32 bits de ponto fixo. Traduziram-se os algoritmos de controle de ordem elevada para a aritmética de ponto fixo produzindo a execução rápida e, no possível, evitando a ocorrência de transbordamento de dados.
This work presents a full six degrees-of-freedom mathematical model description of a subactuated Autonomous Underwater Vehicle (AUV). The work developed methods of System Identification for identifying the nonlinear model of the vehicle. In order to avoid divergence problems in the process of hydrodynamic, it used the parametric transformation technique. It used the extended Kalman filter to estimate the model parameters subject to Gaussian noise, in the process and in the measurements. In order to tackle the problem of multiple parameter estimation at once, the work used the maximum likelihood approach. The experimental results showed that the Kalman filter approach is better when the aim is to estimate a specific parameter, however, it diverges easily when the aim is to estimate multiple parameters. The maximum likelihood technique showed better response to estimate multiple parameters of the model. Zig-zag and circular standard maneuvers were tested with the identification algorithms. For experimental tests, an AUV, namely Pirajuba and constructed by the Unmanned Vehicle Laboratory (LVNT), were used. Results were also assessed using an AUV six degrees of freedom simulator. In a second stage, the work developed H¥ controllers to manoeuvre the vehicle in six-degrees-of-freedom. Decoupled SISO (single input and single output variables) and MIMO (multiple input and multiple output variables) controllers were synthesized in order to validate the coupling dynamics of the AUV. Moreover, centralized robust controllers were developed to control the vehicle in the sea and in test tanks with extreme conditions close to the ocean environmental. The control techniques were based in the H¥ mixed sensitivity approach which guarantees robust performance and stability of the sub-actuated system. A structure of two-degrees-of-freedom (2GL) controller presented better performance compared with the classic single H¥ controller of one degree of freedom structure. A comparison between responses was used to validate the decoupling and centralized controllers. The 2GL controller has good performance specifications despite these defined in the time domain. A central controller can control the AUV in complex maritime task that require complex and three-dimensional manoeuvres. The work deals also with the implementation issues coding these advanced control algorithms into the real time embedded system including inertial sensors, electric motors for the propeller and actuator surfaces, battery banks, and the unit central process ARM7 of 32 bits of fixed point. The control algorithms were translated from floating point to fixed point arithmetic avoiding data overflow, seeking simplicity and fast task execution.

Electroencephalographic data recorded on the human scalp can be modeled as a linear mixture of underlying dipolar source generators. The characterization of such generators is the aim of several families of signal processing methods. In this HDR we consider in several details three of such families, namely 1) EEG distributed inverse solutions, 2) diagonalization methods, including spatial filtering and blind source separation and 3) Riemannian geometry. We highlight our contributions in each of this family, we describe algorithms reporting all necessary information to make purposeful use of these methods and we give numerous examples with real data pertaining to our published studies. Traditionally only the single-subject scenario is considered; here we consider in addition the extension of some methods to the simultaneous multi-subject recording scenario. This HDR can be seen as an handbook for EEG source analysis. It will be particularly useful to students and other colleagues approaching the field.

La technologie haut débit des puces à ADN permet de visualiser simultanément le niveau d'expression de plusieurs milliers de gènes ou groupe de gènes dans des conditions différentes Cette technologie haut débit génère une grande diversité de données qui implique un important travail d'analyse. Une de ces problématiques, concerne la recherche de règles d'associations qui consiste à extraire un ensemble de formules logiques conditionnelles permettant de déduire la valeur d'un attribut but à partir des valeurs d'autres attributs. La recherche de règles d'association peut être vue comme un problème d'optimisation puisque l'on recherche les règles optimisant un certain critère. La combinatoire associée au problème est très importante. Ceci ne permet pas d'utiliser pour des problèmes de grandes tailles (comme c'est le cas ici) des algorithmes exactes d'énumération. Il est donc nécessaire d'avoir recours à des heuristiques telles que par exemple les métaheuristiques. Le contexte de la thèse étant la résolution d'un problème d'optimisation combinatoire multi-objectif pour l'analyse de données obtenues à l'aide de la technologie des puces à ADN, nous nous focalisons sur la modélisation et la résolution multi-objectif du problème de recherche de règles d'association. Puis nous nous intéressons à l'apport des méthodes d'optimisation approchées, à savoir les algorithmes génétiques (AG) Nous avons proposé un algorithme génétique permettant de traiter des bases de données relatives à des expérimentations sur puces à ADN. Cet algorithme possède un codage et des opérateurs adaptés à la recherche de règles d'association et des mécanismes multi-objectif ont été implémentés. Nous avons mis en place un mécanisme adaptatif pour pouvoir appliquer plusieurs mutations selon l'évolution de l'algorithme et adapter leur taux d'application en fonction de l'amélioration apportée par chacun d'eux. Nous avons proposé une approche parallèle développée pour le problème de recherche de règles, dans laquelle différents algorithmes génétiques coopèrent. Plusieurs approches coopératives ont été proposées. Nous avons montré à la fois l'apport du parallélisme et l'apport de la coopération entre méthodes de différents types.

Cette thèse aborde le problème de diagnostic à base de modèles pour la classe des systèmes dynamiques modélisés sous forme LPV (Linéaires à Paramètres Variants). Nous présentons une nouvelle méthode de synthèse de filtres de détection et localisation robustes. Une condition suffisante est établie pour garantir les performances en terme de sensibilité du signal indicateur de défauts vis à vis de la classe de défauts considérés. La méthode proposée permet également de formuler des contraintes de robustesse vis-à-vis des paramètres variants dans le temps et des perturbations exogènes. L'approche permet de prendre en compte la loi de commande dans la synthèse du filtre de diagnostic. Le problème de synthèse est formulé comme un problème d'optimisation convexe sous contraintes et pouvant être résolu efficacement par les techniques LMI (Inégalités Linéaires Matricielles).
La méthodologie est appliquée à des exemples académiques et à un système industriel se prêtant particulièrement bien à une modélisation LPV, le circuit secondaire d'une centrale nucléaire. Les résultats obtenus montrent l'efficacité de la méthode.

碩士
國立高雄第一科技大學
環境與安全衛生工程研究所
103
Because of receiving lots of municipal, industrial and livestock wastewater, the An-Shun Drainage, a tributary of the Yan-Shoei Creek in southern Taiwan, is often severely polluted. For water pollution control, the riverwater of An-Shun Drainage is pumped and treated with contact filters before flowing into the Yan-Shoei Creek. The purposes of this study are to apply the multivariate statistical analysis to evaluate the significant parameters of contact filter for treating river water and to investigate treatability of this contact filter for various input loadings of pollutants in the river water. In this study, the parameters (pH, DO, SS, COD, BOD and temperature) with high factor loading were investigated by the factor analysis during the multivariate statistical analysis. Based on the results of multivariate statistical analysis, the primary significant parameters, called as organic pollution factors, were found to be pH, BOD and COD. Besides, SS and COD, called as climate factors, belonged to the secondary significant parameters. After the evaluation of significant parameters by multivariate analysis, the situations of low efficiency of contact filter were obtained from the further linear regression of influent and effluent parameters.

Exponential smoothing algorithms are very attractive for the practical world such as in industry. When considering bivariate exponential smoothing methods, in addition to the properties of univariate methods, additional properties give insight to relationships between the two components of a process, and also to the overall structure of the model. It is important to study these properties, but even with the merits the bivariate exponential smoothing algorithms have, exponential smoothing algorithms are nonstatistical/nonstochastic and to study the properties within exponential smoothing may be worthless. As an alternative approach, the (bivariate) ARIMA and the structural models which are classes of statistical models, are shown to generalize the exponential smoothing algorithms. We study these properties within these classes as they will have implications on exponential smoothing algorithms. Forecast properties are studied using the state space model and the Kalman filter. Comparison of ARIMA and structural model completes the study.
Mathematical Sciences
M. Sc. (Statistics)

Indiana University-Purdue University Indianapolis (IUPUI)
The aim of this study was to use multivariate statistical techniques to: (1) determine the reproducibility of fiber evidence analyzed by MSP, (2) determine whether XRF is an appropriate technique for forensic tape analysis, and (3) determine if DART/MS is an appropriate technique for forensic tape analysis. This was achieved by employing several multivariate statistical techniques including agglomerative hierarchical clustering, principal component analysis, discriminant analysis, and analysis of variance. First, twelve dyed textile fibers were analyzed by UV-Visible MSP. This analysis included an inter-laboratory study, external validations, differing preprocessing techniques, and color coordinates. The inter-laboratory study showed no statistically significant difference between the different instruments. The external validations had overall acceptable results. Using first derivatives as a preprocessing technique and color coordinates to define color did not result in any additional information. Next, the tape backings of thirty-three brands were analyzed by XRF. After chemometric analysis it was concluded that the 3M tapes with black adhesive can be classified by brand except for Super 33+ (Cold Weather) and Super 88. The colorless adhesive tapes were separated into two large groups which were correlated with the presence of aluminosilicate filler. Overall, no additional discrimination was seen by using XRF compared to the traditional instrumentation for tape analysis previously published. Lastly, the backings of eighty-nine brands of tape were analyzed by DART/MS. The analysis of the black adhesive tapes showed that again discrimination between brands is possible except for Super 33+ and Super 88. However, now Tartan and Temflex have become indistinguishable. The colorless adhesive tapes again were more or less indistinguishable from one another with the exception of Tuff Hand Tool, Qualpack, and a roll of 3M Tartan, which were found to be unique. It cannot be determined if additional discrimination was achieved with DART/MS because the multivariate statistical techniques have not been applied to the other instrumental techniques used during tape analysis.