Bayesian Inference Approach to Estimate Robin Coefficient Using Metropolis Hastings Algorithm
A non-linear heat conduction problem is considered to identify the Robin coefficient using inverse analysis. The coefficient of heat transfer representing the corrosion damage, which is time dependent, is estimated for the surrogated data. The mathematical model is discretized using finite difference method and implicit scheme is incorporated for temperature time history. The Bayesian framework is applied to obtain the best estimates of unknown parameters and the standard deviation provides the useful information about uncertainty associated with the estimated parameter. The sampling space is explored using a powerful Metropolis-Hastings algorithm. The maximum a posterior, mean and standard deviation are obtained based on 10,000 samples. Results prove that Bayesian Inference approach does provide accurate parametric estimation to the inverse heat problem.
KeywordsBayesian inference Metropolis hastings Inverse heat conduction Parametric estimation Robin coefficient
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