地下水污染监测井优化设计及污染源识别

Optimization Design of Groundwater Pollution Monitoring Wells and Identification of Contamination Source

在地下水污染源识别过程中,针对监测井监测值信息量不充分或监测值与模型参数关联性较弱的问题,提出一种基于贝叶斯公式与信息熵的监测井优化方法.构建二维地下水溶质运移模型,并运用GMS软件进行数值求解.为减少监测井优化设计及污染源识别过程中反复调用数值模型的计算负荷,采用克里金法建立数值模型的替代模型.以信息熵作为优化指标,筛选出不同监测类型的最优监测方案,并以监测成本和反演精度为参考因素,选定相应监测方案,最后运用差分进化自适应Metropolis算法进行污染源识别.算例研究表明:7口监测井的克里金替代模型的决定系数均大于0.98,可较好地替代原数值模型.基于监测成本最小的方案1(3号单井),其信息熵为12.772;兼顾监测成本和反演精度的方案2(井(2,3)组合),其信息熵为9.723;基于反演精度较高的方案3(3井(2,3,5)组合),其信息熵为9.377.方案1到方案3参数后验分布范围及标准差均逐渐减小,验证了信息熵是参数后验分布不确定性的有效量度.

In the process of identifying groundwater pollution sources,a monitoring well optimization method based on Bayesian formula and information entropy is proposed for the problem that the monitoring value of monitoring wells is insufficient or the correlation between monitoring values and model parameters is weak.The two-dimensional groundwater contaminant transport model was numerically solved by GMS software.To reduce the computational load of the numerical model repeatedly in the optimization design of the monitoring wells and the identification process of the pollution source,the Kriging method was used to establish the surrogate model of the numerical model.As an optimization index,the optimal monitoring schemes of different monitoring types were selected,and the monitoring cost and inversion accuracy were taken as reference factors for the corresponding monitoring schemes.Then,the differential evolution adaptive Metropolis algorithm was used to identify the pollution source.The case study results show that:The determination coefficient of the Kriging surrogate models of the 7 monitoring wells was greater than 0.98,which indicated that the Kriging surrogate models can well replace the original numerical model.The scheme 1(single well No.3)based on the lowest monitoring cost has an information entropy of 12.772;The scheme 2(the combination of well No.2 and No.3)taking the monitoring cost and inversion accuracy into account has an information entropy of 9.723;The scheme 3(the combination of well No.2,3 and 5)with higher inversion precision has an information entropy of 9.377.Both the posterior distribution ranges and the standard deviation of model parameters from scheme 1 to scheme 3 were gradually reduced,which verifies that the information entropy is an effective measure of the uncertainty of the posterior distribution of the parameters.