A construction strategy of Kriging surrogate model based on Rosenblatt transformation of associated random variables and its application in groundwater remediation

Abstract

When using simulation-optimization models for optimizing the design of groundwater pumping-treatment plans for pollution, building a surrogate model for the numerical simulation model has become an effective means of overcoming the computational load of such models. However, previous studies often treated pumping time as a single optimization variable, leading to unnecessary excessive pumping. This paper considers the location, pumping rate, start time, and end time of each candidate pumping well as optimization variables, and proposes a Rosenblatt-transform-based optimal Latin hypercube sampling method for the associated random variables to ensure that the start time is less than or equal to the end time. This method is coupled with an adaptive sampling method based on batch local optimal solutions to construct a dynamic adaptive Kriging surrogate model for the numerical model, ensuring that the true value of the optimal remediation scheme is not lost. The results show that, at the final stage of remediation, the pollutant concentration in the 4 scenarios achieves comprehensive compliance. However, when considering the minimization of remediation costs as the evaluation criterion, the remediation scheme in scenario 1 (the pumping start and end times are independent optimization variables for all candidate pumping wells) is optimal. In the optimization design of groundwater pumping-treatment plans, the pumping wells should be arranged in the midstream and downstream regions of the contaminant plume and parallel to the regional flow direction. This paper provides a method reference for the construction and adaptive updating of surrogate models involving associated random variables, as well as guidance for the dynamic optimization of groundwater pumping and treatment at contaminated sites.