Aquifer parameter identification with kriging and optimum parameterization
Aquifer parameter identification with kriging and optimum parameterization
复制标题
使用克里金法和最佳参数化识别含水层参数
DOI：
10.1029/wr019i001p00225
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发表时间：
1983
影响因子：
5.4
通讯作者：
Kil
中科院分区：
文献类型：
--
作者：
W. Yeh;Y. Yoon;Kil
为二维非稳态地下水流模型开发了一种新的参数识别方法。该方法是一种直接方法，因为它不需要迭代搜索参数。未知函数系数（参数）通过广义矩阵求逆方案最优确定。克里金法是一种无偏最小方差估计器，用作预采样滤波器来重建整个流域的水头分布。反问题的不适定性以不稳定和非唯一性为特征，可以通过利用有限元技术重新参数化来控制。开发了一组统计数据来明确量化系统建模误差和与参数不确定性相关的误差之间的权衡。这两种类型的误差被证明是参数维度的函数。估计参数的协方差矩阵的残差均方和迹可以作为确定最佳参数维数的良好指标。进行了一组数值实验来说明该方法。
A new parameter identification method is developed for a two-dimensional, unsteady state groundwater flow model. The method is a direct approach, as it requires no iterative searching of parameters. The unknown functional coefficients (parameters) are optimally determined by a generalized matrix inversion scheme. Kriging, an unbiased minimum variance estimator, is used as a presampling filter to reconstruct the head distribution for the entire flow domain. The ill-posedness of the inverse problem as characterized by instability and nonuniqueness is controlled by reparameterization utilizing the technique of finite elements. A set of statistics are developed to quantify explicitly the tradeoff between the system modeling error and the error associated with the parameter uncertainty. These two types of errors are shown to be a function of the parameter dimension. Residual mean square and trace of the covariance matrix of the estimated parameters serve as good indicators for the determination of the optimum parameter dimension. A set of numerical experiments are conducted to illustrate the methodology.