基于拉丁超立方抽样的改进型DRAM算法求解地下水污染反问题-《郑州大学学报(工学版)》

文章信息/Info

Title:: Improved MCMC method based on latin hypercube sampling for inverse problems of underground water pollution

作者:: 张双圣; 强静; 刘汉湖; 刘喜坤; 孙韶华; 1. 中国矿业大学环境与测绘学院;2. 徐州市城区水资源管理处; 3. 中国矿业大学数学学院;4. 山东省城市供排水水质监测中心

Author(s):: Zhang Shuangsheng1; 2; strong static 3; Liu Han Lake 1; Liu Xikun 2; Sun Shaohua 4; 1. School of Environment and Surveying, China University of Mining and Technology; 2. Xuzhou Urban Water Resources Management Office; 3. School of Mathematics, China University of Mining and Technology; 4. Shandong Provincial Water Supply and Drainage Water Quality Monitoring Center

Keywords:: 2D water quality model; Bayesian-Markov chain Monte Carlo method; Latin hypercube sampling; Delay rejection adaptive Metropolis algorithm; pollution source identification

摘要:: 针对运用贝叶斯统计方法求解地下水污染反问题时,经典MCMC算法求解结果受样本初始点影响的问题,提出了一种基于拉丁超立方抽样方法的改进型MCMC算法.将贝叶斯统计方法与二维水质对流-扩散方程相耦合,建立地下水污染源识别模型.构建一个污染物在地下水含水层中瞬时排放的算例,分别进行经典MCMC算法与改进型MCMC算法对污染源信息（污染源强度、排放位置（x,y）和排放时刻）的反求.算例研究表明,经典MCMC算法受样本初始点影响,容易出现反演结果局部最优,或者反演结果难以收敛的问题；改进型MCMC算法可实现反演结果的全局最优,而且反演结果不受样本初始点的影响,反演结果与真值基本一致,准确性与稳定性显著提高.

Abstract:: Aiming at the problem of the result affected by samples’ initial values with classical MCMC method, when the inverse problems of underground water pollution were solved by Bayesian statistical methods, an improved MCMC method based on latin hypercube sampling was presented. An underground water pollution source identification model was built by coupling Bayesian statistical methods to two-dimensional water quality convection-diffusion equation. An example of a pollutant in the underground aquifer discharged instantly was put forward, and the pollution source information including source’’s position, intensity and discharging time was solved by classical MCMC method and improved MCMC method separately. The example showed that the inversion results affected by initial values with classical MCMC method were locally optimal or difficult to convergence; on the contrary, the improved MCMC method could achieve a global optimization. The computed values solved by the improved MCMC method were basically the same as the truth values. The accuracy and stability were improved significantly.