A Bayesian inference approach to the ill‐posed Cauchy problem of steady‐state heat conduction
A Bayesian inference approach to the ill‐posed Cauchy problem of steady‐state heat conduction
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DOI：
10.1002/nme.2350
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发表时间：
2008-10
影响因子：
2.9
通讯作者：
Bangti Jin;J. Zou
中科院分区：
文献类型：
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作者：
Bangti Jin;J. Zou
本文研究了稳态热传导中Cauchy问题的贝叶斯推断方法，即概率校准边界温度。先验建模是通过马尔可夫随机场，其正则化性质进行了研究。采用分层贝叶斯模型自动选择正则化参数和检测噪声水平。后验状态空间探索使用马尔可夫链蒙特卡罗获得相关的统计。提出并分析了两种确定正则化参数和噪声水平的增广Tikhonov正则化方法。数值结果表明，贝叶斯推理方法能够给出解的精确估计，并量化了解的不确定性，而增广Tikhonov正则化方法具有精确性和灵活性.版权所有© 2008约翰威利父子有限公司.
This paper studies a Bayesian inference approach to the Cauchy problem in steady‐state heat conduction of probabilistically calibrating the boundary temperature. The prior modeling is achieved via the Markov random field, and its regularizing property is investigated. A hierarchical Bayesian model is adopted for selecting the regularization parameter and detecting the noise level automatically. The posterior state space is explored using the Markov chain Monte Carlo for obtaining relevant statistics. Two augmented Tikhonov regularization methods that could determine the regularization parameter and the noise level are proposed and analyzed. Numerical results indicate that the Bayesian inference approach could yield an accurate estimate of the solution with its uncertainties quantified, and the augmented Tikhonov regularization methods are accurate and flexible. Copyright © 2008 John Wiley & Sons, Ltd.