A constrained robust least squares approach for contaminant release history identification
A constrained robust least squares approach for contaminant release history identification
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DOI：
10.1029/2005wr004312
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发表时间：
2006-04
影响因子：
5.4
通讯作者：
A. Sun;S. Painter;G. Wittmeyer
中科院分区：
文献类型：
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作者：
A. Sun;S. Painter;G. Wittmeyer
污染源识别是地下水建模中重要的反问题类型，受到数据和模型不确定性的影响。以往的研究很少考虑模型的不确定性。在这项工作中，引入了一个解决污染物源恢复问题的强大框架。污染物源识别问题首先转化为求解不确定线性方程的问题，其中使用叠加技术构建响应矩阵。这里提出的公式是通用的，适用于任何多孔介质流动和传输求解器。鲁棒最小二乘（RLS）估计器起源于鲁棒识别领域，直接解释模型不确定性引起的误差，并已被证明可以显着降低最优解对模型和数据扰动的敏感性。在这项工作中，RLS 的一个新变体，即约束鲁棒最小二乘法 (CRLS)，被制定用于求解不确定的线性方程。 CRLS 允许施加额外的约束，例如非负性。 CRLS 的性能通过一维和二维测试问题得到证明。当系统病态且不确定时，我们发现 CRLS 的性能比其经典对应方法（非负最小二乘法）要好得多。因此，本工作中开发的源识别框架构成了在实际应用中恢复源发布历史的可靠工具。
Contaminant source identification is an important type of inverse problem in groundwater modeling and is subject to both data and model uncertainty. Model uncertainty was rarely considered in the previous studies. In this work, a robust framework for solving contaminant source recovery problems is introduced. The contaminant source identification problem is first cast into one of solving uncertain linear equations, where the response matrix is constructed using a superposition technique. The formulation presented here is general and is applicable to any porous media flow and transport solvers. The robust least squares (RLS) estimator, which originated in the field of robust identification, directly accounts for errors arising from model uncertainty and has been shown to significantly reduce the sensitivity of the optimal solution to perturbations in model and data. In this work, a new variant of RLS, the constrained robust least squares (CRLS), is formulated for solving uncertain linear equations. CRLS allows for additional constraints, such as nonnegativity, to be imposed. The performance of CRLS is demonstrated through one‐ and two‐dimensional test problems. When the system is ill‐conditioned and uncertain, it is found that CRLS gave much better performance than its classical counterpart, the nonnegative least squares. The source identification framework developed in this work thus constitutes a reliable tool for recovering source release histories in real applications.