Optimal design of groundwater pollution monitoring network based on a back-propagation neural network surrogate model and grey wolf optimizer algorithm under uncertainty.

In the optimal design of groundwater pollution monitoring network (GPMN), the uncertainty of the simulation model always affects the reliability of the monitoring network design when applying simulation-optimization methods. To address this issue, in the present study, we focused on the uncertainty of the pollution source intensity and hydraulic conductivity. In particular, we utilized simulation-optimization and Monte Carlo methods to determine the optimal layout scheme for monitoring wells under these uncertainty conditions. However, there is often a substantial computational load incurred due to multiple calls to the simulation model. Hence, we employed a back-propagation neural network (BPNN) to develop a surrogate model, which could substantially reduce the computational load. We considered the dynamic pollution plume migration process in the optimal design of the GPMN. Consequently, we formulated a long-term GPMN optimization model under uncertainty conditions with the aim of maximizing the pollution monitoring accuracy for each yearly period. The spatial moment method was used to measure the approximation degree between the pollution plume interpolated for the monitoring network and the actual plume, which could effectively evaluate the superior monitoring accuracy. Traditional methods are easily trapped in local optima when solving the optimization model. To overcome this limitation, we used the grey wolf optimizer (GWO) algorithm. The GWO algorithm has been found to be effective in avoiding local optima and in exploring the search space more effectively, especially when dealing with complex optimization problems. A hypothetical example was designed for evaluating the effectiveness of our method. The results indicated that the BPNN surrogate model could effectively fit the input-output relationship from the simulation model, as well as significantly reduce the computational load. The GWO algorithm effectively solved the optimization model and improved the solution accuracy. The pollution plume distribution in each monitoring yearly period could be accurately characterized by the optimized monitoring network. Thus, combining the simulation-optimization method with the Monte Carlo method effectively addressed the optimal monitoring network design problem under uncertainty.

Simultaneous identification of groundwater pollution source and important hydrogeological parameters considering the noise uncertainty of observational data.

Groundwater pollution identification is an inverse problem. When solving the inverse problem using regular methods such as simulation-optimization or stochastic statistical approaches, requires repeatedly calling the simulation model for forward calculations, which is a time-consuming process. Currently, the problem is often solved by building a surrogate model for the simulation model. However, the surrogate model is only an intermediate step in regular methods, such as the simulation-optimization method that also require the creation and solution of an optimization model with the minimum objective function, which adds complexity and time to the inversion task and presents an obstacle to achieving fast inversion. In the present study, the extreme gradient boosting (XGBoost) method and the back propagation neural network (BPNN) method were used to directly establish the mapping relationships between the output and input of the simulation model, which could directly obtain the inversion results of the variables to be identified (pollution sources release histories and hydraulic conductivities) based on actual observational data for fast inversion. In addition, to consider the uncertainty of observation data noise, the inversion accuracy of the two machine learning methods was compared, and the method with higher precision was selected for the uncertainty analysis. The results indicated that both the BPNN and XGBoost methods could perform inversion tasks well, with a mean absolute percentage error (MAPE) of 4.15% and 1.39%, respectively. Using the BPNN, with better accuracy for uncertainty analysis, when the maximum probabilistic density value was selected as the inversion result, the MAPE was 2.13%. We obtained the inversion results under different confidence levels and decision makers of groundwater pollution prevention and control can choose different inversion results according to their needs.

Simultaneous identification of groundwater contaminant source and hydraulic parameters based on multilayer perceptron and flying foxes optimization.

Groundwater contaminant source identification (GCSI) has practical significance for groundwater remediation and liability. However, when applying the simulation-optimization method to precisely solve GCSI, the optimization model inevitably encounters the problems of high-dimensional unknown variables to identify, which might increase the nonlinearity. In particular, to solve such optimization models, the well-known heuristic optimization algorithms might fall into a local optimum, resulting in low accuracy of inverse results. For this reason, this paper proposes a novel optimization algorithm, namely, the flying foxes optimization (FFO) to solve the optimization model. We perform simultaneous identification of the release history of groundwater pollution sources and hydraulic conductivity and compare the results with those of the traditional genetic algorithm. In addition, to alleviate the massive computational load caused by the frequent invocation of the simulation model when solving the optimization model, we utilized the multilayer perception (MLP) to establish a surrogate model of the simulation model and compared it with the method of backpropagation algorithm (BP). The results show that the average relative error of the results of FFO is 2.12%, significantly outperforming the genetic algorithm (GA); the surrogate model of MLP can replace the simulation model for calculation with fitting accuracy of more than 0.999, which is better than the commonly used surrogate model of BP.