Inverse Problems in Heat Transfer
نویسنده
چکیده
17.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 17.2THE INVERSE HEAT-CONDUCTION PROBLEM A SPECTRAL STOCHASTIC APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 17.2.1Introduction: Representation of random variables . . . . . . . . . . . 9 17.2.2The stochastic inverse heat-conduction problem (SIHCP): Problem definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 17.2.3Adjoint problem and gradient calculations . . . . . . . . . . . . . . . . 15 17.2.4 Numerical Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 17 17.2.5Numerical results with the spectral approach . . . . . . . . . . . . . . 21 17.2.6Further developments on the use of spectral stochastic methods in inverse modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 17.3A BAYESIAN APPROACH TO THE INVERSE HEAT-CONDUCTION PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 17.3.1Revisiting the IHCP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 17.3.2Bayesian inverse formulation . . . . . . . . . . . . . . . . . . . . . . . . 29 17.3.3MCMC sampler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 17.3.4Numerical results with a Bayesian approach . . . . . . . . . . . . . . 34 17.3.5Further work on using Bayesian inference for inverse thermal problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
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