A construction strategy for conservative adaptive Kriging surrogate model with application in the optimal design of...

When the simulation-optimization model to optimize the groundwater extraction-treatment schemes is used, the construction of a surrogate model for the numerical simulation model has become an effective means to overcome the large calculation load of repeatedly calling the numerical model. However, there are still some problems in using the surrogate model, such as large training sample size, low accuracy, and poor optimization results. In this paper, a conservative adaptive Kriging surrogate model (CAKSM) was proposed by coupling the Kriging surrogate model, optimal solution adaptive sampling method (OSAS), and conservative prediction idea. Firstly, an initial Kriging surrogate model (IKSM) was built for the numerical simulation model of groundwater flow and solute transport. Then, the IKSM was coupled with the optimization model to construct the adaptive Kriging surrogate model (AKSM) by using OSAS. A safety margin was added to the AKSM to build the CAKSM. Finally, the simulation-optimization models based on IKSM, AKSM, and CAKSM were solved by the genetic algorithm, respectively. The results showed that the IKSM could well substitute for the simulation model. The AKSM significantly improved the approximation degree between the surrogate model and the simulation model at the optimal solution by supplementing a small number of new samples. CAKSM could effectively constrain the pollutant mass concentrations within the controlled value, improving the reliability of the optimization scheme. The optimal extraction wells based on different surrogate models were all well 5, well 6, and well 9. They were concentrated in the middle and lower reaches of the contaminated plume's central axis. The sequence for the remediation effects by different surrogate models from high to low was as follows: CAKSM, AKSM, and IKSM. The risk rate of the optimal remediation scheme from the hydraulic conductivity random fields was as high as 12.12%, and the risks were mainly located upstream of the pollution plume's central axis.