基于高斯过程回归的地下水模型结构不确定性分析与控制

Quantification and reduction of groundwater model structural uncertainty based on Gaussian process regression

目前针对模型结构不确定性的研究方法主要为贝叶斯模型平均方法,而该方法受到模型权重计算困难等影响,应用受限。基于数据驱动的模型结构误差统计学习方法最近得到关注。研究采用高斯过程回归方法对地下水模型结构误差进行统计模拟,并将DREAMzs算法与高斯过程回归相结合,对地下水模型和统计模型的参数同时进行识别。基于此方法,分别以理想岩溶裂隙海水入侵过程和溶质运移柱体实验为例,进行地下水数值模拟及预测结果的不确定性分析。相对于不考虑模型结构误差条件的不确定性分析,结果表明,考虑结构误差之后,能够明显减少参数识别过程中的参数补偿影响,且能显著提高模型的预测性能。因此,基于高斯过程回归的模型结构不确定性分析可以一定程度控制地下水数值模拟的不确定性,提高模型预测可靠性。

Nowadays, the main analysis method for groundwater model structural uncertainty is the Bayesian model averaging (BMA) method. But BMA suffers from the difficulty of model weight estimation, which makes its application infeasible. More attention is recently paid to the data-driven based model structural error analysis method. In this paper, the groundwater model structural error is statistically learnt based on Gaussian process regression, and then the parameters of the groundwater model and statistical model are identified simultaneously by combining the DREAMzs and Gaussian process regression algorithms. With this method, the uncertainty of groundwater model parameters and prediction results are analyzed. In addition, a synthetic numerical simulation of seawater intrusion in a karst fissure area and a solute transport column experiment are taken as case studies. In contrast with the uncertainty analysis without considering the model structural error, the impact of parameter compensation is significantly reduced by considering the model structural error. Moreover, the model prediction performance is also improved. Therefore, based on the model structural uncertainty analysis method proposed in this paper, the uncertainty of groundwater modeling can be reduced to some extent, as well the reliability of groundwater model prediction can be improved.