Using Resampling Residuals for Estimating Confidence Intervals of the Effective Viscosity and Forchheimer Coefficient
Using Resampling Residuals for Estimating Confidence Intervals of the Effective Viscosity and Forchheimer Coefficient
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DOI：
10.1007/s11242-017-0892-2
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发表时间：
2017-06
影响因子：
2.7
通讯作者：
I. Kuznetsov;Andrey V. Kuznetsov
中科院分区：
文献类型：
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作者：
I. Kuznetsov;Andrey V. Kuznetsov
确定多孔介质中流动的特征参数是一个复杂的反问题。确定这些参数的置信区间尤其困难。在本说明中，我们开发了一种方法的基础上利用自举，以找到模型参数的置信区间，这是通过最大限度地减少模型预测和公布的实验结果之间的差异。差异的特点是由目标函数定义为平方残差的总和，在实验测量的点。残差定义为实验测量值与该值的模型预测值之间的差值。我们利用自举法通过随机恢复残差生成替代实验数据，然后将其添加回模型预测。然后确定与大量替代数据最佳拟合的模型参数。通过分析最佳拟合参数值的直方图，我们能够找到这些参数的置信区间。我们利用开发的方法来确定有效粘度和Forchheimer系数的置信区间。
Determination of parameters characterizing flows in porous media is a complex inverse problem. It is especially difficult to determine confidence intervals of such parameters. In this note, we develop a method based on utilization of bootstrapping in order to find confidence intervals of model parameters, which are determined by minimizing the discrepancy between model predictions and published experimental results. The discrepancy is characterized by the objective function defined as the sum of squared residuals in the points where experimental measurements are taken. A residual is defined as the difference between the experimentally measured value and the model prediction of this value. We utilized bootstrapping to generate surrogate experimental data by randomly resampling residuals and then adding them back to model predictions. The model parameters that give the best fit with a large number of surrogate data were then determined. By analyzing the histograms of best-fit parameter values, we were able to find confidence intervals for these parameters. We utilized the developed method to determine confidence intervals for the effective viscosity and Forchheimer coefficient.