This research develops a fault diagnosis method for complex systems in the presence of uncertainties and possibility of multiple solutions. Fault diagnosis is a challenging problem because data used in diagnosis contain random errors and often systematic errors as well. Furthermore, fault diagnosis is basically an inverse problem so that it inherits unfavorable characteristics of inverse problems: The existence and uniqueness of an inverse solution are not guaranteed and the solution may be unstable. The weighted least squares method and its variations are traditionally used for solving inverse problems. However, the existing algorithms often fail to identify multiple solutions if they are present. In addition, the existing algorithms are not capable of selecting variables systematically so that they generally use the full model in which may contain unnecessary variables as well as necessary variables. Ignoring this model uncertainty often gives rise to, so called, the smearing effect in solutions, because of which unnecessary variables are overestimated and necessary variables are underestimated. The proposed method solves the inverse problem using Bayesian inference. An engineering system can be parameterized using state variables. The probability of each state variable is inferred from observations made on the system. A bias in an observation is treated as a variable, and the probability of the bias variable is inferred as well. To take the uncertainty of model structure into account, multiple Bayesian models are created with various combinations of the state variables and the bias variables. The results from all models are averaged according to how likely each model is. Gibbs sampling is used for approximating updated probabilities. The method is demonstrated for two applications: the status matching of a turbojet engine and the fault diagnosis of an industrial gas turbine. In the status matching application only physical faults in the components of a turbojet engine are considered whereas in the fault diagnosis application sensor biases are considered as well as physical faults. The proposed method is tested in various faulty conditions using simulated measurements. Results show that the proposed method identifies physical faults and sensor biases simultaneously. It is also demonstrated that multiple solutions can be identified. Overall, there is a clear improvement in ability to identify correct solutions over the full model that contains all state and bias variables.

Growth release of trees following canopy disturbances is of interest to ecological scientists and forest managers. Using dendroecological techniques, I examined growth release of canopy and subcanopy trees following the formation of natural, fine-scale canopy gaps in old-growth, western red cedar-western hemlock forests of coastal British Columbia. I aimed to quantify detailed information on release of the three shade-tolerant tree species that constitute these stands: western red cedar (Thuja plicata), western hemlock (Tsuga heterophylla), and Pacific silver fir (Abies amabilis). As a first step, I calibrated the radial-growth averaging method to account for regional-scale variability and capture a more complete range of growth releases that may occur following the formation of fine-scale gaps in the study stands. A 25% threshold, 5-year moving average, and 10-year window emerged as appropriate parameters for detecting releases using radial-growth averaging. Basal area increment was also the most appropriate growth index for detecting releases. Establishing these empirically-based criteria was important for quantifying the magnitude and duration of releases. Tree diameter and growth rate prior to release were the most important predictors of the magnitude and duration of releases, but identity of the tree species and distance from the gap center were also important predictors. Western hemlock and Pacific silver fir were often growing slowly both in the canopy and subcanopy, giving them tremendous potential to release. For these species, releases were generally intensive and persistent. In contrast, western red cedar were often growing quickly both in the canopy and subcanopy, giving them less potential to release. Compared to western hemlock and Pacific silver fir, western red cedar releases were less intensive and persistent. Patterns related to distance from the gap center emerged for trees growing along the north-south axis of gaps. Regardless of species, increasing distance from the gap center resulted in decreasing magnitude and duration of releases. However, patterns for duration were complex, as the distance effect was greater for trees north of the gap center. Information on growth release of trees is useful for reconstructing the history of past canopy disturbances, elucidating mechanisms of tree species coexistence, and assessing and predicting stand changes due to forest management in coastal British Columbia.

Orientador: Claudio Aguinaldo Buzzi / Banca: Claudio Gomes Pessoa / Banca: Luis Fernando de Osório Mello / Resumo: Nosso objetivo neste trabalho é estudar o método do averaging através do grau topológico de Brouwer e utilizá-lo para investigar o número de ciclos limites que bifurcam de uma singularidade do tipo centro quando perturbamos um sistema de equações diferenciais através de um pequeno parâmetro ε. Começaremos apresentando o método do averaging que aaprece na literatura clássica e algumas aplicações deste. Depois faremos uma breve discussão sobre o grau topológico de Brouwer, seguido do teorema do averaging que faz menção a este conceito. Finalmente, exibiremos algumas aplicações inéditas do método. / Abstract: The aim of this is to study the averaging method using the Brouwer topological degree in order to investigative the number of limit cycles that can bifurcate from a center type singularity when a differential systemas is perturbed by a small parameter ε. To this respect, initially, we present "classical" averaging method and some of its applications. So we introduce the Brouwer topological degree, followed by the averaging theorem. Finally, we show some original applications of the averaging method. / Mestre

The impact of inequality on economic growth has become a topic of broad and current interest. Multiple researches investigated the issue but the disparity of opinions and empirical results is huge. The present thesis revises the pri- mary literature through a meta-analytical approach applying Bayesian Model Averaging (BMA) estimation technique. We examine 562 estimates collected from 58 studies published between 1991 and 2015. I find the evidence of the publication bias presence in the literature. The authors of primary studies tend to report preferentially negative and significant estimates. The BMA results suggest that the effect of inequality on growth is not straightforward and is likely not linear. A single pattern for inequality/growth relationship is not fea- sible since the results vary across used income inequality measures, estimation methods and data structure and quality. JEL Classification D31, O10, C11, C82 Keywords meta-analysis, inequality, economic growth, Bayesian model averaging, publication bias Author's e-mail 23376990@fsv.cuni.cz Supervisor's e-mail zuzana.havrankova@fsv.cuni.cz

Este trabalho descreve o projeto, a construção e a avaliação de um digitalizador de sinais controlado por microprocessador, desenvolvido para ser utilizado em Tomografia por Ressonância Magnética Nuclear, TORM. O digitalizador apresenta dois canais de entrada com digitalização simultânea em 256, 512 ou 1024 palavras por canal e com taxa de amostragem máxima de 22,7 Khz. A resolução é de 12 bits com conversão analógico/digital por aproximação sucessiva. Não há controles manuais o que exige um computador hospedeiro para o ajuste de parâmetros via interface de comunicação paralela destinada para este fim. Opcionalmente pode-se utilizar uma interface serial do tipo RS232C-EIA operando com velocidade máxima de 9600 bauds. O equipamento efetua o processamento local da média acumulativa do sinal, técnica empregada para melhorar a relação sinal/ruído no caso de ruído aleatório. Um circuito dedicado à monitoração permite que se visualize em monitor X-Y tanto o sinal como a sua média. No caso da média, por ela ser acumulativa, há um ajuste automático de escala / This work describes the design, construction and evaluation of a microprocessor controlled digitizer developed to be used in Magnetic Resonance Tomography or Imaging, MRI. The digitizer presents two input channels with simultaneous digitalization in 256, 512 or 1024 words per channel with a sample rate up to 22.7 Khz. A resolution of 12 bits is obtained with successive approximation A/D conversion. There are no manual controls. So a host computer is needed to adjust the parameters through a parallel communication interface available for this purpose. Optionally, a RS232-EIA type serial interface may be used, operating at speeds up to 9600 bauds. Signal average can be processed locally by the equipment. This technique is used to improve the signal to noise ratio in case of random noise. A dedicated circuit permits the visualization of the signal and or its average on an x-y monitor. To monitor cumulative averaged data an automatic scale adjustment is provided

Propõe-se um sistema para processamento em um mini computador, de sinais elétricos da cóclea gravados em fita magnética. As gravações são efetuadas nos hospitais, utilizando-se aparelhos de simples manuseio e de baixo custo. Obtém-se dados que auxiliarão no diagnóstico de patologias do órgão da audição. Os instrumentos existentes para a realização da eletrococleografia são da manipulação complexa além de terem alto custo. O sistema proposto simplifica muito a operação do equipamento empregado nos hospitais, obtendo-se uma redução do custo global do exame. No hospital, deve-se ter um circuito de controle, um gravador, um amplificador e um gerador de estímulos. No centro de computação deve-se ter um mini computador, outro gravador, filtros e uma interface de controle. Foram desenvolvidos no trabalho: o circuito de controle, os filtros, a interface de controle e todos os programas responsáveis pelo processamento. Atualmente, a eletrococleografia em todo o Brasil é realizada em apenas alguns centros hospitalares, devido aos fatores custo e complexidade de manuseio. Em vista dos bons resultados obtidos e do baixo custo do sistema proposto, conclui-se que, com o nosso método, poder-se-ia difundir a eletrococleografia para um grande número de centros hospitalares. / A system is proposed that uses a minicomputer for the processing of electrical potentials from the cochlea. These signals are previously recorded on magnetic tape at hospitals, using simple and inexpensive equipment. The results obtained by the processing provide valuable data for the diagnosis of hearing disorders. The available equipment for electrocochleography at the present time is rather complicated to use and very expensive. The proposed system eases the operation and has a low cost. At the hospital, one must have a control circuit, a tape recorder, an amplifier and a sound stimulator. At the computing center one needs a minicomputer, another tape recorder, filters and a control interface. In this work were developed: the control circuit, the filters, the control interface and all programs used in the processing of the data. Nowadays, the use of electrocochleography in Brazil is limited to a few medical centers, due to the cost and complexity of the equipment. It is hoped that the simpler system proposed here will contribute to a wider use of electrocochleography.

Orientador: Paulo Regis Caron Ruffino / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T22:03:50Z (GMT). No. of bitstreams: 1 GonzalesGargate_IvanItalo_D.pdf: 724522 bytes, checksum: bb313a00b360e7bea2a2411b759c7389 (MD5) Previous issue date: 2012 / Resumo: Nesta tese, estudamos um princípio de médias em equações diferenciais estocásticas sobre variedades folheadas com folhas compactas. Começaremos introduzindo o princípio de médias sobre equações diferenciais ordinárias reais. A título de comparação vamos rever conceitos básicos de variedade simplética com a finalidade de comparar/estender os resultados obtidos por Xue-Mei Li sobre um princípio de médias para um sistema Hamiltoniano estocástico completamente integrável. Nosso principal resultado é generalizar estas idéias para o caso de uma variedade M = (-a; a)n x N, onde N é uma variedade compacta sem bordo. Em particular mostraremos nossos resultados para o caso que a folheação é gerada por uma submersão de M sobre Rn. Finalmente apresentamos alguns exemplos / Abstract: In this thesis, we study the averaging principle for stochastic differential equations on foliated manifolds with compact leaves. We begin by introducing the averaging principle over real ordinary differential equations. For comparison we will review basic concepts of symplectic manifold in order to compare/extend the results obtained by Xue-Mei Li about a averaging principle for a completely integrable stochastic Hamiltonian system. Our main result is to generalize these ideas to the case of a manifold M = (-a; a)n x N, where N is a compact manifold without boundary. In particular our results show for the case that foliation is generated by an submersion of M over Rn. Finally we present some examples / Doutorado / Matematica / Doutor em Matemática

The main objective of our research was to develop a new bankruptcy prediction model for the Czech economy. For that purpose we used the logistic regression and 150,000 financial statements collected for the 2002-2016 period. We defined 41 explanatory variables (25 financial ratios and 16 dummy variables) and used Bayesian model averaging to select the best set of explanatory variables. The resulting model has been estimated for three prediction horizons: one, two, and three years before bankruptcy, so that we could assess the changes in the importance of explanatory variables and models' prediction accuracy. To deal with high skew in our dataset due to small number of bankrupt firms, we applied over- and under- sampling methods on the train sample (80% of data). These methods proved to enhance our classifier's accuracy for all specifications and periods. The accuracy of our models has been evaluated by Receiver operating characteristics curves, Sensitivity-Specificity curves, and Precision-Recall curves. In comparison with models examined on similar data, our model performed very well. In addition, we have selected the most powerful predictors for short- and long-term horizons, which is potentially of high relevance for practice. JEL Classification C11, C51, C53, G33, M21 Keywords Bankruptcy...

La technique de moyennation est un moyen efficace pour simplifier les transferts optimaux pour un satellite à faible poussée dans un problème à deux corps contrôlé. Cette thèse est une étude analytique et numérique du transferts orbital à poussée faible en temps optimal qui généralise l'application de la moyennation du problème à deux corps à des transferts dans le problème à deux corps perturbés et aux transfert d'une orbite proche de la Terre au point de Lagrange L1, dans le cadre du problème à quatre corps bi-circulaire où l’effet perturbatif de la Lune et du Soleil est modélisé. Dans le transfert à faible poussée à deux corps, nous comparons le cas du temps minimal et de l'énergie. Nous déterminons que le domaine elliptique pour les transferts orbitaux temps-minimal est géodésiquement convexe pour un transfert coplanaire et vers une orbite circulaire, contrairement au cas de l’énergie. Nous examinons ensuite l’effet la perturbation lunaire, nous montrons que dans ce cas le Hamiltonien moyenné se trouve être celui associé à un problème de navigation de Zermelo. Nous étudions numériquement à l’aide du code Hampath, les points conjugués pour caractériser l’optimalité globale des trajectoires. Enfin, nous construisons et réalisons numériquement un transfert d'une orbite terrestre au point de Lagrange L1, qui utilise la moyennation sur un arc (proche de la Terre) pour simplifier les calculs numériques. Dans ce dernier résultat nous voyons qu'un transfert concaténant une trajectoire moyennée avec une trajectoire temps minimal au voisinage du point de Lagrange est en effet proche d’un transfert de temps optimal calculé avec une méthode numérique de tir. / The technique of averaging is an effective way to simplify optimal low-thrust satellite transfers in a controlled two-body Kepler problem. This study takes the form of both an analytical and numerical investigation of low-thrust time-optimal transfers, extending the application of averaging from the two-body problem to transfers in the perturbed low-thrust two body problem and a low-thrust transfer from Earth orbit to the L1 Lagrange point in the bicircular four-body setting. In the low-thrust two-body transfer, we compare the time-minimal case with the energy-minimal case, and determine that the elliptic domain under time-minimal orbital transfers (reduced in some sense) is geodesically convex. We then consider the Lunar perturbation of an energy-minimal low-thrust satellite transfer, finding a representation of the optimal Hamiltonian that relates the problem to a Zermelo navigation problem and making a numerical study of the conjugate points. Finally, we construct and implement numerically a transfer from an Earth orbit to the L1 Lagrange point, using averaging on one (near-Earth) arc in order to simplify analytic and numerical computations. In this last result we see that such a `time-optimal' transfer is indeed comparable to a true time-optimal transfer (without averaging) in these coordinates.

Cette thèse présente des travaux originaux dans le domaine des méthodes de moyennisation d'ordre élevé. On s'intéresse notamment à des procédures de moyennisation dite stroboscopique ou quasi-stroboscopique dans des espaces de Banach ou de Hilbert. Ces procédures sont ensuite appliquées à des exemples concrets: des équations d'évolutions hautement oscillantes. Plus précisément, on montre dans un premier temps un résultat de moyennisation stroboscopique dans un espace de Banach où l'on obtient des estimations d'erreurs exponentielles. Ce théorème est ensuite appliqué sur deux équations des ondes semi-linéaire hautement oscillantes. On montre également que la Stroboscopic Averaging Method s'applique à une équation des ondes semi-linéaire avec conditions de Dirichlet. On trouve enfin numériquement, une dynamique intéressante de l'équation des ondes semi-linéaire mise en lumière par la procédure de moyennisation. Dans un second temps, on présente un théorème de moyennisation quasi-stroboscopique dans un espace de Hilbert quelconque avec des estimations d'erreurs exponentielles. Ce théorème est alors appliqué de façon indirecte à une équation de Schrödinger semi-linéaire oscillante. Cette équation est d'abord projeté dans un espace de dimension finie pour qu'on puisse lui appliquer le théorème de moyennisation quasi-stroboscopique. On écrit alors un résultat de moyennisation quasi-stroboscopique pour l'équation de Schrödinger semi-linéaire avec des estimations d'erreur polynomiales. / This thesis presents some original work in the field of high order averaging procedure. In particular, we are interested in stroboscopic and quasi-stroboscopic averaging procedure in abstract Banach or Hilbert spaces. This procedures is applied to concrete examples: some highly oscillatory evolution equations. More precisely, we first show a theorem of stroboscopic averaging in a Banach space where we obtain exponential error estimates. This theorem is then applied on two semi-linear and highly oscillatory wave equations. We also put in evidence that the {\it Stroboscopic Averaging Method} works fine with a semi-linear wave equation with Dirichlet conditions. Finally, the averaging procedure puts in evidence, numerically, an interesting dynamics regarding the semi-linear wave equation with Dirichlet conditions. In a second part, we present a quasi-stroboscopic averaging theorem in a Hilbert space with exponential error estimates. This theorem is applied on a semi-linear Schrödinger equation. This equation has first, to be project in a finite dimensional space in order to fit in the hypotheses of the theorem. We then write a quasi-stroboscopic averaging theorem for a semi-linear Schrödinger equation with polynomial error estimates.