2 resultados para Numerical Operator

em Universidade Federal do Rio Grande do Norte(UFRN)


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In a real process, all used resources, whether physical or developed in software, are subject to interruptions or operational commitments. However, in situations in which operate critical systems, any kind of problem may bring big consequences. Knowing this, this paper aims to develop a system capable to detect the presence and indicate the types of failures that may occur in a process. For implementing and testing the proposed methodology, a coupled tank system was used as a study model case. The system should be developed to generate a set of signals that notify the process operator and that may be post-processed, enabling changes in control strategy or control parameters. Due to the damage risks involved with sensors, actuators and amplifiers of the real plant, the data set of the faults will be computationally generated and the results collected from numerical simulations of the process model. The system will be composed by structures with Artificial Neural Networks, trained in offline mode using Matlab®

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In general, an inverse problem corresponds to find a value of an element x in a suitable vector space, given a vector y measuring it, in some sense. When we discretize the problem, it usually boils down to solve an equation system f(x) = y, where f : U Rm ! Rn represents the step function in any domain U of the appropriate Rm. As a general rule, we arrive to an ill-posed problem. The resolution of inverse problems has been widely researched along the last decades, because many problems in science and industry consist in determining unknowns that we try to know, by observing its effects under certain indirect measures. Our general subject of this dissertation is the choice of Tykhonov´s regulaziration parameter of a poorly conditioned linear problem, as we are going to discuss on chapter 1 of this dissertation, focusing on the three most popular methods in nowadays literature of the area. Our more specific focus in this dissertation consists in the simulations reported on chapter 2, aiming to compare the performance of the three methods in the recuperation of images measured with the Radon transform, perturbed by the addition of gaussian i.i.d. noise. We choosed a difference operator as regularizer of the problem. The contribution we try to make, in this dissertation, mainly consists on the discussion of numerical simulations we execute, as is exposed in Chapter 2. We understand that the meaning of this dissertation lays much more on the questions which it raises than on saying something definitive about the subject. Partly, for beeing based on numerical experiments with no new mathematical results associated to it, partly for being about numerical experiments made with a single operator. On the other hand, we got some observations which seemed to us interesting on the simulations performed, considered the literature of the area. In special, we highlight observations we resume, at the conclusion of this work, about the different vocations of methods like GCV and L-curve and, also, about the optimal parameters tendency observed in the L-curve method of grouping themselves in a small gap, strongly correlated with the behavior of the generalized singular value decomposition curve of the involved operators, under reasonably broad regularity conditions in the images to be recovered