A markov random field model of contamination source identification in porous media flow
A markov random field model of contamination source identification in porous media flow
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DOI：
10.1016/j.ijheatmasstransfer.2005.09.016
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发表时间：
2006-03
影响因子：
5.2
通讯作者：
Jingbo Wang;N. Zabaras
中科院分区：
文献类型：
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作者：
Jingbo Wang;N. Zabaras
通过求解对流-弥散方程（ADE），采用分层贝叶斯计算方法，通过时间回溯求解定常多孔介质流中的污染源识别问题。污染物浓度被建模为成对马尔可夫随机场（MRF）和更新的分布，使用当前的浓度测量在有限的位置。使用分层贝叶斯分析来推导污染物浓度在过去时间点的后验分布。后验均值估计使用修改的单分量Gibbs算法计算。首先测试的方法是通过污染物识别的例子在一个均匀的多孔介质中使用扩散为主和对流为主的条件。一个非均质多孔介质流动的情况下，也检查。在所有的数值研究报告中，各向异性色散效应被认为是。验证了MRF模型能有效地模拟浓度场的空间相关性，所提出的方法能为不适定反问题提供精确解。
A contamination source identification problem in constant porous media flow is addressed by solving the advection–dispersion equation (ADE) with a hierarchical Bayesian computation method backward through time. The contaminant concentration is modeled as a pair-wise Markov random field (MRF) and the distribution is updated using current concentration measurements at finite locations. Hierarchical Bayesian analysis is used to derive the posterior distribution of the contaminant concentration at past time points. The posterior mean estimate is computed using a modified single-component Gibbs algorithm. The methodology is first tested via examples of contaminant identification in a homogeneous porous medium using both diffusion-dominated and convection-dominated conditions. A heterogeneous porous media flow case is also examined. In all the numerical studies reported, the anisotropic dispersion effect is considered. It is verified that the MRF model can effectively model the spatial correlation of the concentration field, and the presented approach can provide accurate solutions to the ill-posed inverse problem.