Estimation of parameters in multi-mode heat transfer problems using Bayesian inference : Effect of noise and a priori
Estimation of parameters in multi-mode heat transfer problems using Bayesian inference : Effect of noise and a priori
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DOI：
10.1016/j.ijheatmasstransfer.2007.08.031
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发表时间：
2008-05
影响因子：
5.2
通讯作者：
S. Parthasarathy;C. Balaji
中科院分区：
文献类型：
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作者：
S. Parthasarathy;C. Balaji
参数估计问题和热源/通量重建问题是最常见的一些逆传热问题。这些问题在科学和工程的许多领域都有应用。本文主要研究二维非定常热传导问题的传热参数估计问题，其中（a）对流边界条件，（B）对流和辐射边界条件。本文演示了在不同的噪声水平的测量数据的算法的性能的先验模型的效果。使用三种不同的先验模型，即正常的，日志正常和均匀的反问题。使用Metropolis-Hastings采样算法对后验PDF进行采样。单参数估计和多参数估计问题的解决和相应的先验模型的影响进行了研究。结果发现，平均值和最大后验估计的热导率和对流换热系数是不敏感的先验模型在所有考虑的噪声水平的单参数估计问题。在高噪声水平的两个参数估计问题，导热系数和对流系数的估计是敏感的先验模型。在单参数估计情况下，样本的标准差与估计误差相关。在三参数估计的情况下，由于对流系数和发射率之间的强相关性，相同的问题的替代解决方案被检索。然而，一个信息量更大的先验模型可以解决这个问题。
Parameter estimation problems and heat source/flux reconstruction problems are some of the most frequently encountered inverse heat transfer problems. These problems find their application in many areas of science and engineering. The primary focus of this paper is on the heat transfer parameter estimation for a two-dimensional unsteady heat conduction problem with (a) convection boundary condition and (b) convection and radiation boundary condition. The paper demonstrates the effect of a priori model on the performance of the algorithm at different noise levels in the measured data. The inverse problem is solved using three different a priori models namely normal, log normal and uniform. The posterior PDF is sampled using the Metropolis–Hastings sampling algorithm. Both single-parameter estimation and multi-parameter estimation problems are addressed and the effects of corresponding a priori models are studied. It was found that the mean and maximum a posteriori estimates for thermal conductivity and the convection heat transfer coefficient were insensitive to the a priori model at all the considered noise levels for the single-parameter estimation problem. At high noise levels in the two-parameter estimation problem, the estimates for thermal conductivity and convection coefficient were sensitive to the a priori model. It was also found that the standard deviation of the samples was correlated to the error in estimation in the single-parameter estimation case. In three parameter estimation case, alternate solutions to the same problem were retrieved due to a strong correlation between the convection coefficient and the emissivity. However, a more informative a priori model could address this issue.