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Fabrizio Ruggeri

2012-12-07
12:30:00 - 14:30:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

A Bayesian approach is developed for estimating the thermal conductivity of a homogeneous material from the temperature evolution acquired in few internal points. Temperature evolution is described by the classical one- dimensional heat equation, in which the thermal conductivity is one of the coefficients. Noisy measurements lead to a partial differential equation with stochastic coefficients and, after discretisation in time and space, to a stochastic differential equation. Euler approximation at sampled points leads to a likelihood function, used in the Bayesian estimation of the thermal conductivity under different prior densities. An approach for generating latent observations over time in points where the temperature is not acquired is also included. Finally, the methodology is experimentally validated, considering a heated piece of polymethyl methacrylate (PMMA) with temperature measurements available in few points of the material and acquired at high frequency. (Joint work with Ettore Lanzarone and Sara Pasquali)