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首页> 外文期刊>International Journal of Heat and Mass Transfer >Using Bayesian statistics in the estimation of heat source in radiation
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Using Bayesian statistics in the estimation of heat source in radiation

机译：使用贝叶斯统计估计辐射中的热源

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摘要

An unknown transient heat source in a three-dimensional participating medium is reconstructed from temperature measurements using a Bayesian inference method. The heat source is modeled as a stochastic process. The joint posterior probability density function (PPDF) of heat source values at consecutive time points is computed using the Bayes' formula. The errors in thermocouple readings are modeled as independent identically distributed (i.i.d.) Gauss random variables. 'Maximum A Posteriori' (MAP) and posterior mean estimates of the heat source are then computed using a Markov chain Monte Carlo (MCMC) simulation method. The designed MCMC sampler is composed of a cycle of symmetric MCMC kernels. To increase the sampling speed, a model-reduction technique is used in the direct computation of temperatures at thermocouple locations given a guessed heat source, i.e. in the likelihood computation. Two typical heat source profiles are reconstructed using simulated data to demonstrate the presented methodologies. The results indicate that the Bayesian inference method can provide accurate point estimates as well as uncertainty quantification to the solution of the inverse radiation problem.
机译：使用贝叶斯推断方法从温度测量中重建三维参与介质中的未知瞬态热源。热源被建模为随机过程。使用贝叶斯公式计算连续时间点的热源值的联合后验概率密度函数（PPDF）。热电偶读数中的误差建模为独立的均匀分布（i.i.d.）高斯随机变量。然后使用马尔可夫链蒙特卡罗（MCMC）模拟方法计算出“最大后验”（MAP）和热源的后验均值。设计的MCMC采样器由一个对称的MCMC内核循环组成。为了提高采样速度，在给定推测的热源的情况下，即在似然计算中，在热电偶位置的温度的直接计算中使用了模型简化技术。使用模拟数据重建了两个典型的热源曲线，以演示所提出的方法。结果表明，贝叶斯推理方法可以为逆辐射问题的求解提供准确的点估计以及不确定性量化。

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