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.

Groundwater contamination source identification based on Sobol sequences-based sparrow search algorithm with a BiLSTM surrogate model.

In the traditional linked simulation-optimization method, solving the optimization model requires massive invoking of the groundwater numerical simulation model, which causes a huge computational load. In the present study, a surrogate model of the origin simulation model was developed using a bidirectional long and short-term memory neural network method (BiLSTM). Compared with the surrogate models built by shallow learning methods (BP neural network) and traditional LSTM methods, the surrogate model built by BiLSTM has higher accuracy and better generalization performance while reducing the computational load. The BiLSTM surrogate model had the highest R2 of the three with 0.9910 and the lowest RMSE with 3.7732 g/d. The BiLSTM surrogate model was linked to the optimization model and solved using the sparrow search algorithm based on Sobol sequences (SSAS). SSAS enhances the diversity of the initial population of sparrows by introducing Sobol sequences and introduces nonlinear inertia weights to control the search range and search efficiency. Compared with SSA, SSAS has stronger global search ability and faster search efficiency. And SSAS identifies the contamination source location and release intensity stably and reliably. The average relative error of SSAS for the identification of source location is 9.4%, and the average relative error for the identification of source intensity is 1.83%, which are both lower than that of SSA at 11.12% and 3.03%. This study also applied the Cholesky decomposition method to establish a Gaussian field for hydraulic conductivity to evaluate the feasibility of the simulation-optimization method.

Recognition of a linear source contamination based on a mixed-integer stacked chaos gate recurrent unit neural network-hybrid sparrow search algorithm.

Groundwater contamination source recognition involves the recovery of contamination source time series release histories from observation data. In the present study, a linear source contamination recognition task was addressed. When using a simulation-optimization inverse framework to solve the recognition task, high calculated expense and high dimensional search space always hinder the task efficiency. Moreover, traditional surrogate methods face obstacle of handling with time-sequence data. Therefore, a novel stacked chaos gate recurrent unit (SCGRU) neural network was proposed as a surrogate model to precisely emulate the sequence to sequence mapping relationship of a high computational running simulation model. To address the challenge of high dimensional search, a mixed-integer programming strategy was employed to reduce the dimension of unknown variables. Furthermore, a hybrid sparrow search algorithm (HSSA) was implemented to alleviate being trapped into local optimum. In particular, the proposed SCGRU-HSSA framework was utilized to determine the length and release intensities during the stress period of a linear source. Based on the results obtained, the following conclusions were derived: (1) SCGRU can replace the origin simulation model with high accuracy and fast running speed; (2) when using chaos sine mapping and a Cauchy mutation strategy, the SSA escaped from the local optimum, improving the search efficiency of the recognition task; and (3) SCGRU-HSSA methodology is stable and reliable in recognizing features of linear source contamination.

Identification of groundwater contamination sources and hydraulic parameters based on bayesian regularization deep neural network.

Simultaneous identification of various features of groundwater contamination sources and hydraulic parameters, such as hydraulic conductivities, can result in high-nonlinear inverse problem, which significantly hinders identification. A surrogate model was proposed to relieve computational burden caused by massive callings to simulation model in identification. However, shallow learning surrogate model may show limited fitting ability to high nonlinear problem. Thus, in this study, a simulation-optimization method based on Bayesian regularization deep neural network (BRDNN) surrogate model was proposed to efficiently solve high-nonlinear inverse problem. This method identified eight variables including locations and release intensities of two pollution sources and hydraulic conductivities of two partitions. Three hidden layers were employed in the BRDNN surrogate model, which profoundly improved the fitting capacity of nonlinear mapping relationship to the simulation model. Furthermore, Bayesian regularization was applied in the training process of neural network to solve overfitting problem. The results indicated that BRDNN was capable of establishing input-output interplay of high nonlinear inverse problem, which substantially reduced computational cost while ensuring a desirable level of accuracy. The utility of simulation-optimization on the basis of BRDNN surrogate model provided stable and reliable inversion results for groundwater contamination sources and hydraulic parameters.