<p class="MsoNormal">Estimating the parameters that describe a thermal problem using Bayes statistics requires the specification of appropriate prior probabilities. That is p(P|D)=p(D|P)p(P)/p(D) where P = parameters. D=data and p(P) is the prior probability of the parameters. For thermal problems this means choosing prior probabilities that are reasonable. That is prior probabilities for density, specific heat, thermal conductivities, surface convective coefficients, radiative properties, emissivity and absorbtivity, and local heat release, Q are needed. It is common to choose Gaussian distributions for these priors. However, if the standard deviation is large, then this results in predictions that can be negative values—a result that is not possible for any parameter except for Q. Consequently, one must choose a prior that prevents this from occurring. Variational Bayes (VB) is an alternative to Monte Carlo simulation, particularly to Markov Chain Monte Carlo sampling, and assumes that complex distributions p(a,b) can be replaced by factorization, p(a,b)=p(a)p(b), the mean field theory of physics. Overall Variational Bayes yields a simpler but approximate posterior distribution of the parameters and is particularly important for posterior probabilities that have multiple maxima distributions. The paper describes the use of VB for a thermal protection system in which all of the parameters are restricted to positive values, but may have multiple local maxima. The posterior probabilities are also analyzed by generalized sensitivities to demonstrate the ideal data measurement times.</p>

Using Variational Bayes for Inverse Thermal Problems

Paper Proceedings: https://asmedigitalcollection.asme.org/HT/HT2021/volume/84874

ASME 2021 Heat Transfer Summer Conference (SHTC2021)

Supporting the need among researchers worldwide for additional online and multimedia content, ASME now offers the ASME Conference Video Collection. This platform will collect and provide long-term access to conference presentation videos, encompassing all technology areas within ASME's technical conference and events program. About 30,000-40,000 engineers across all mechanical engineering and related disciplines participate in ASME conferences each year. This includes authors of approximately 6,000 to 8,000 technical papers published by ASME, the majority of whom also submit video presentations for our virtual conferences. The video collection will be available as an add-on to existing product packages or as a separate subscription.