Optimization Design of Groundwater Pollution Monitoring Scheme and Inverse Identification of Pollution Source Parameters Using Bayes’ Theorem
Optimization Design of Groundwater Pollution Monitoring Scheme and Inverse Identification of Pollution Source Parameters Using Bayes’ Theorem
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地下水污染监测方案优化设计及利用贝叶斯定理反辨识污染源参数
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发表时间：
2020
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通讯作者：
Yanyan Li
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作者：
Shuangsheng Zhang;Jing Qiang;Hanhu Liu;Yanyan Li
在地下水污染源识别过程中，针对监测井监测数据不足或监测数据与模型参数相关性弱的问题，提出了一种基于贝叶斯公式和信息熵的监测井优选方法。建立了二维潜水溶质运移模型，并用GMS软件进行了求解。为减少监测方案优化设计和污染源识别过程中重复调用数值模型的计算量，采用克立格法建立数值模型的代理模型。在单井监测和监测频率确定的条件下，以监测点数D和监测时间间隔∆t最优为目标，分别对模型参数后验分布信息熵最小的单目标监测方案和信息熵最小、监测时间最短的多目标监测方案进行了优化。根据优化后的监测方案，采用延迟拒绝自适应Metropolis算法对污染源参数进行辨识。实例研究结果表明，在预先设定单井监测频率为10次的条件下，单目标最优监测方案为D = 37天，Δt = 20天。在该监测方案下，污染源参数α = (X S、 Y S、 T1、 T2、 Q S)的平均误差分别为0.09%、0.4%、4.72%、2.43%和9.29%。多目标优化监测方案为D = 37天，Δt = 2天。在该监测方案下，反演参数α = (X S、 Y S、 T1、 T2、 Q S)的平均误差分别为12.76%、3.77%、5.13%、1.36%和7.68%。与基于单目标优化的监测方案相比，尽管基于多目标优化的监测方案的5个参数的反演平均误差增加了2.75%，但监测时间从180天大幅减少到18天。
In the process of identifying groundwater pollution sources, in order to solve the problem that the monitoring data of monitoring wells was insufficient or the correlation between monitoring data and model parameters was weak, a monitoring well optimization method based on Bayesian formula and information entropy was proposed. Two-dimensional phreatic groundwater solute transport model was built and solved by using GMS software. To reduce the computational load of calling the numerical model repeatedly in the optimization design of the monitoring schemes and the identification process of the pollution sources, the Kriging method was used to establish the surrogate model of the numerical model. Under the condition of single well monitoring and determined monitoring frequency, with the target of optimization of monitoring position number D and monitoring time interval ∆ t , both the single-objective monitoring scheme with the minimum information entropy of the model parameter posterior distribution and the multi-objective monitoring scheme with the minimum information entropy and the shortest monitoring time were optimized respectively. According to the above-optimized monitoring schemes, the delayed rejection adaptive Metropolis algorithm was used to identify the pollution source parameters. The case study results showed that under the condition of pre-set single well monitoring with monitoring frequency of 10 times, the single-objective optimized monitoring scheme was D = 37 and Δt = 20 days. Under this monitoring scheme, the mean errors of inversion pollution source parameters α = ( X S , Y S , T 1 , T 2 , Q S ) were 0.09%, 0.4%, 4.72%, 2.43%, and 9.29%, respectively. The multi-objective optimized monitoring scheme was D = 37 and Δt = 2 days. Under this monitoring scheme, the mean errors of the inversion parameters α = ( X S , Y S , T 1 , T 2 , Q S ) were 12.76%, 3.77%, 5.13%, 1.36%, and 7.68%, respectively. Compared with the monitoring scheme based on the single-objective optimization, although the inversion mean error of the five parameters based on the multi-objective optimized monitoring scheme increased by 2.75%, the monitoring time significantly reduced from 180 to 18 days.