Estimativa de fluxo de calor com variação espacial e temporal através do método de Monte Carlo com cadeias de Markov e transformadas integrais

• Autor(a) principal: Mescolin, Marques Fredman
• Data de Publicação: 2017
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/13711
• topic: Inverse problems; Boundary flux estimation; Bayesian inference; Integral transforms; Problemas inversos (Equações diferenciais); Estimativa de fluxo de calor; Inferência bayesiana; Transformadas integrais; Calor - Transmissão - Medição; Calor - Transmissão - Modelos matemáticos; Medidores de fluxo - Modelos matemáticos; CNPQ::ENGENHARIAS::ENGENHARIA MECANICA::FENOMENOS DE TRANSPORTE

This work addresses the inverse heat conduction problem to estimate a spatially and time varying heat flux imposed to a thermally thin plate within the Bayesian framework, employing the Markov Chain Monte Carlo method. In order to allow for the computer intensive task required by the inverse problem solution, the physical problem is modelled thorough a lumped formulation across the sample thickness, and the resulting differential equation is solved by means of the hybrid analytical-numerical methodology known as the Generalized Integral Tranform Technique. The inverse problem solution considers simulated transient measurements on the plate surface, as obtainable, for instance, through an infrared thermography system. Different Markov Random Fields priors are combined and analyzed for the estimation of the heat flux with variation in time and space: a total variation density and a Gaussian smoothness density. We also propose a combination of both, using a total variation prior for the space regularizations and a Gaussian smoothness variation for time regularization. The preliminary results obtained indicate the feasibility of the proposed approach, specially the combination of the total variation and Gaussian smoothness priors, which yielded the best results.