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Inverse estimation of thermal properties using Bayesian inference and three different sampling techniques
S. Somasundharam,
Published in Taylor and Francis Ltd.
2017
Volume: 25
   
Issue: 1
Pages: 73 - 88
Abstract
In this article, three different thermal properties such as thermal conductivity, heat transfer coefficient and emissivity are retrieved simultaneously using Bayesian inverse framework. Metropolis–Hasting Markov Chain Monte-Carlo (MH-MCMC) sampling is more commonly used in the literature to sample through posterior probability distribution function (PPDF) to find the expectations such as mean, standard deviation. However, when the posterior is multi-model/correlated, sometimes MH-MCMC struck with one mode and fails to sample through other modes which have significant probability. Nevertheless, efficient sampling techniques are being developed during the last decade to overcome this problem. Therefore, in the present work two population-based sampling techniques such as Parallel Tempering (PT) and Evolutionary Monte-Carlo (EMC) are used along with MH-MCMC to sample through correlated PPDF to retrieve the above three thermal properties. The estimation is carried out at three levels of measurement errors. The experimental data are obtained by adding normally distributed random noise with mean at zero and standard deviation ‘σexp’ to the exact solution of the forward problem. The results show that when the measurement error is zero, i.e when σexp = 0.01 , all three techniques perform well and estimates the parameter reasonably good. However, at σexp = 0.01 and 0.5, MCMC estimates the parameter poorly, whereas both PT and EMC performs equally and estimates the parameter within a maximum of 9% deviation from the exact value. © 2016 Informa UK Limited, trading as Taylor & Francis Group.
About the journal
JournalData powered by TypesetInverse Problems in Science and Engineering
PublisherData powered by TypesetTaylor and Francis Ltd.
ISSN17415977
Open AccessNo
Concepts (21)
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    Bayesian networks
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    Chains
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    Distribution functions
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    Heat transfer
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    Inference engines
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    Inverse problems
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    Markov processes
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    Measurement errors
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    Monte carlo methods
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    Normal distribution
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    Statistics
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    Tempering
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    Thermal conductivity
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    Bayesian
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    CORRELATED POSTERIOR
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    EVOLUTIONARY MONTE CARLO
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    INVERSE HEAT TRANSFER
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    MARKOV CHAIN MONTE-CARLO
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    PARALLEL TEMPERING
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    Thermo-physical property
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    Parameter estimation