Improved Sparse Grid Surrogate Model And Application In Uncertainty Analysis Of Groundwater Simulation

In order to improve the reliability of groundwater numerical simulation,model uncertainty analysis has become a research hotspot in the field of water resources and water environment.MCMC(Markov Chain Monte Carlo)method is the main quantitative analysis method of uncertainty at present,and it needs a large number of model executions to search the probability distribution space of model parameters.This leads to huge computational cost and time burden,which has become one of the obstacles in current uncertainty analysis.Surrogate model is an effective way to reduce the calculation time in groundwater simulation.By establishing a model that has the same or close accuracy as the original model to replace it,the purpose of improving computing efficiency is achieved.Hence,it is of great theoretical and practical significance to establish surrogate models of both high efficiency and high precision for the application of uncertainty analysis in groundwater resources management and protection practice.In this paper,the sparse grid(Sparse Grid,SG)surrogate model is taken as the research object.According to the node generation rules of SG,the accuracy and efficiency of SG surrogate model is improved by enhancing the adaptive generation efficiency of nodes and then SG surrogate model is applied to the uncertainty analysis of groundwater simulation.The main achievements include the following:(1)A dual adaptive sparse grid surrogate model(DA-LA-SG)coupled with local adaptive(LA)and dimensional adaptive(DA)is proposed.Based on the traditional sparse grid(SG)surrogate model,an improved surrogate model named DA-LA-SG is proposed.The performance of DA-LA-SG is tested by two analytical function examples and a numerical example of DNAPLs transport sandbox experiment.The results show that the performance of DA-LA-SG is better than that of LA-SG and DASG,that is,it can achieve higher surrogate accuracy with less cost.(2)The improved DA-LA-SG is successfully used to construct a surrogate model of likelihood function of DNAPLs multiphase flow migration model and parameter uncertainty is analyzed.A surrogate model of log-likelihood function for numerical simulation of DNAPLs migration is established by using DA-LA-SG method,and parameters uncertainty in DNAPLs migration is analyzed by MCMC.The results show that the surrogate model of PCE migration can be established efficiently and accurately by using DA-LA-SG,and the posterior distribution of model parameters is obtained by MCMC simulation,which reduces the uncertainty of model prediction.(3)An optimization-adaptive sparse grid(OA-SG)surrogate model is proposed,which couples dual adaptive sparse grid(DA-LA-SG)with repulsive particle swarm optimization(RPSO).Based on the DA-LA-SG,the algorithm RPSO is used to identify the extreme value area of surrogate object(likelihood function),and the generation efficiency of SG nodes is further improved by adjusting the node adaptive criteria value inside and outside the extreme value area.Two analytical function examples and a synthetic example of three-dimensional groundwater transport model are tested.The results show that the proposed OA-SG can realize the optimal allocation of SG nodes and further improve the establishment efficiency of surrogate models compared to DALA-SG.In addition,based on the OA-SG method,a surrogate model of log-likelihood function of groundwater transport model is established,which is successfully used to identify contamination sources.