<p>Diffusion is a phenomenon in which particles move from regions of higher density to regions of lower density. Many physical systems, in fields as diverse as plant biology and finance, are known to involve diffusion phenomena. Typically, diffusion systems are modeled by partial differential equations (PDEs), which include certain parameters. These parameters characterize a given diffusion system. Therefore, for both modeling and simulation of a diffusion system, one has to either know or determine these parameters. Moreover, as PDEs are infinite order dynamic systems, for computational purposes one has to approximate them by a finite order model. In this thesis, we investigate these two issues of model reduction and parameter estimation by considering certain specific cases of heat diffusion systems. </p><p>We first address model reduction by considering two specific cases of heat diffusion systems. The first case is a one-dimensional heat diffusion across a homogeneous wall, and the second case is a two-dimensional heat diffusion across a homogeneous rectangular plate. In the one-dimensional case we construct finite order approximations by using some well known PDE solvers and evaluate their effectiveness in approximating the true system. We also construct certain other alternative approximations for the one-dimensional diffusion system by exploiting the different modal structures inherently present in it. For the two-dimensional heat diffusion system, we construct finite order approximations first using the standard finite difference approximation (FD) scheme, and then refine the FD approximation by using its asymptotic limit.</p><p>As for parameter estimation, we consider the same one-dimensional heat diffusion system, as in model reduction. We estimate the parameters involved, first using the standard batch estimation technique. The convergence of the estimates are investigated both numerically and theoretically. We also estimate the parameters of the one-dimensional heat diffusion system recursively, initially by adopting the standard recursive prediction error method (RPEM), and later by using two different recursive algorithms devised in the frequency domain. The convergence of the frequency domain recursive estimates is also investigated. </p>

Made available in DSpace on 2015-03-03T15:08:47Z (GMT). No. of bitstreams: 1 FernandoCM_TESE.pdf: 4237848 bytes, checksum: 00e7cb467e7c1cded76198b12c9e6e82 (MD5) Previous issue date: 2013-08-23 / This work has as main objective to find mathematical models based on linear parametric estimation techniques applied to the problem of calculating the grow of gas in oil wells. In particular we focus on achieving grow models applied to the case of wells that produce by plunger-lift technique on oil rigs, in which case, there are high peaks in the grow values that hinder their direct measurement by instruments. For this, we have developed estimators based on recursive least squares and make an analysis of statistical measures such as autocorrelation, cross-correlation, variogram and the cumulative periodogram, which are calculated recursively as data are obtained in real time from the plant in operation; the values obtained for these measures tell us how accurate the used model is and how it can be changed to better fit the measured values. The models have been tested in a pilot plant which emulates the process gas production in oil wells / Este trabalho teve como objetivo principal encontrar modelos matem?ticos baseados em t?cnicas de estima??o param?trica lineares aplicado ao problema do c?lculo da vaz?o de g?s em po?os de petr?leo. Em particular se concentrou na obten??o de modelos de vaz?o aplicados ao caso de po?os que produzem pela t?cnica de plunger-lift em plataformas de petr?leo, pois nesse caso, ocorrem picos elevados nos valores da vaz?o que dificultam sua medi- ??o direta atrav?s de instrumentos. Para isso, desenvolveram-se estimadores baseados em m?nimos quadrados recursivos e fez-se uma an?lise das medidas estat?sticas tais como autocorrela??o, correla??o cruzada, variograma e o periodograma acumulado, que s?o calculadas recursivamente ? medida que dados s?o obtidos em tempo real da planta em opera??o; os valores obtidos para essas medidas indicaram o qu?o exato ? o modelo utilizado e de que forma ele pode ser alterado para melhor se adequar aos valores medidos. Os modelos obtidos foram testados em uma planta piloto que emula o processo de produ??o de g?s em po?os de petr?leo