基于拉丁超立方抽样的改进型多链DRAM算法求解地下水污染反问题

Improved Multi-chain DRAM Algorithm Based on Latin Hypercube Sampling for Inverse Problems of Underground Water Pollution

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(Metropolis算法)求解结果受样本初始点影响且计算效率低的问题,提出了一种基于拉丁超立方抽样方法的改进型多链延迟拒绝自适应Metropolis算法(DRAM)。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,分别运用Metropolis算法、多链Metropolis算法以及改进型多链DRAM算法对污染源信息(污染源强度、排放位置(x,y)和排放时长)进行反求。算例研究表明,Metropolis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;多链Metropolis算法虽然显著提高了反演结果的准确性,但是反演效率相对低下;改进型多链DRAM在保证反演准确性的条件下,可显著提高反演效率(相对于多链Metropolis算法提高68%),实现反演结果准确性与效率的双提高。

Aiming at the problem caused by samples’initial values with classical MCMC algorithm(Metropolis algorithm),when the inverse problems of underground water pollution were solved by Bayesian statistical methods,an improved multi-chain delayed rejection and adaptive Metropolis(DRAM)algorithm 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 Metropolis algorithm,multi-chain Metropolis algorithm and improved multi-chain DRAM algorithm respectively.The example showed that the inversion results affected by initial values with Metropolis algorithm were locally optimal or difficult to convergence,while the multi-chain Metropolis algorithm could significantly improve the accuracy of the inversion results,the inversion efficiency was relatively low.On the contrary,the improved multi-chain DRAM could significantly improved the inversion efficiency under the condition of accuracy(improved by 68%compared with the multi-chain Metropolis algorithm),realizing double improvement of inversion accuracy and efficiency.