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In this study, we designed a machine learning–based parallel global searching method using the Bayesian inversion framework for efficient identification of dense non-aqueous phase liquid (DNAPL) source characteristics and contaminant transport parameters in groundwater. Swarm intelligence organized hybrid-kernel extreme learning machine (SIO-HKELM) was proposed to approximate the forward and inverse input–output correlation with a high accuracy using the DNAPL transport numerical simulation model. An adaptive inverse-HKELM was established for preliminary estimation of the source characteristics and contaminant transport parameters to correct prior information and generate high-quality initial starting points of parallel searching. A local accurate forward-HKELM surrogate of the numerical model was embedded in the searching system for avoiding repetitive CPU-demanding likelihood evaluations. A sensitivity-based Metropolis criterion (MC), incorporating the dynamic particle swarm optimization (SD-PSO) algorithm, was developed for improving the search ergodicity and realizing precise inversion of all the unknown variables with drastic variations in sensitivity to the likelihood function. Results showed that the generalization capability and robustness of SIO-HKELM were superior to those of the traditional machine learning methods, including KELM and support vector regression (SVR), and it sufficiently approximated the forward and inverse input–output mapping of the numerical model with testing determination coefficients of 0.9944 and 0.6440, respectively. With high-quality prior information and initial starting points generated by the adaptive inverse-HKELM feed approach, the uncertainty in the inversion outputs was reduced, and the searching process rapidly converged to reasonable posterior distributions in around 60 iterations. Compared with the widely used multichain Markov chain Monte Carlo (MCMC) approach, the parallel searching lines generated by SD–PSO–MC adequately covered the searching space, and the "equifinality" effect was more effectively restrained by reducing the relative errors of all the point estimations to less than 8%. Therefore, the real source information reflected by the statistical characteristics of the SD–PSO–MC inversion outputs was more precise than that obtained using the multichain MCMC approach. [ABSTRACT FROM AUTHOR]

• Inverse modeling for simultaneous DNAPL-source characterization and contaminant transport parameter calibration. • A BHK-ELM is proposed for reliable surrogate modeling of the DNAPL-transport numerical simulation. • An SRD-SI algorithm is proposed to conduct enhanced identification for the sensitivity-varied variables. • A nonlinear homotopy-variational mechanism is construct for reasonably guiding the SRD-SI searching paths. Accurate source characterization and transport parameter estimation is important when seeking to predict the spatiotemporal distribution of dense non-aqueous phase liquid (DNAPL) contaminants in groundwater. However, this is a complex multimodal search problem prone to equifinality and premature convergence, which leads to considerable error. To address this, a sensitivity-relevant dynamic swarm intelligence (SRD-SI) algorithm embedded in a homotopy-variation mechanism is proposed in the present study to rationally balance the inversion processes of sensitivity-varied source characteristics and DNAPL transport parameters. In this approach, global optima are progressively approached in conjunction with the homotopy variation of the search space. Furthermore, to avoid computationally expensive numerical model repetition during the sensitivity analysis and inverse iterations, a Bayesian-based optimization framework that combines multiple kernel functions in a kernel extreme learning machine (KELM) model is designed considering the complex site conditions and statistical characteristics of the input variables, thus creating the Bayesian hybrid KELM (BHK-ELM) model for the reliable surrogate modeling of numerical DNAPL-transport simulations. The results show that the BHK-ELM model recognizes and effectively reconstructs the complex input − output mapping of the numerical model by increasing the determination coefficient R 2 to 0.9988 while improving the computational efficiency approximately 4500-fold. Because source characteristics and boundary conditions are far more sensitive than transport parameters to the contaminant distribution, conventional inverse modeling methods struggle to accurately identify these transport parameters. In contrast, the proposed inverse modeling system combining sensitivity analysis, swarm intelligence, and homotopy variation is more stable and provides significantly more accurate estimations for all unknown variables. Compared with the traditional SI algorithm, the homotopy-variation SRD-SI reduced the maximum inversion relative error from 46.22 % to 9.53 %, while the mean inversion relative error was reduced from 11.09 % to 3.90 %. [ABSTRACT FROM AUTHOR]

Groundwater contamination source identification (GCSI) is critical for taking effective measures to protect groundwater resources, assess risks, mitigate disasters, and design remediation strategies. Simulation–optimization techniques have been effective tools for GCSI. However, previous studies have applied individual surrogate models when replacing simulation models, rather than making efforts to combine various methods to improve the approximation accuracy of the surrogate model over the simulation model. In this study, the kernel extreme learning machine (KELM) model was proposed to enhance the surrogate model, and to approach GCSI problems, especially those of dense nonaqueous phase liquid-contaminated aquifers, more effectively. In addition, a kriging model and a support vector regression (SVR) model were built and compared with the KELM model, and various ensemble surrogate (ES) modeling techniques were applied to establish four ES models. Results showed that the KELM model was more accurate than the kriging and SVR models; however, the ES models performed much better than the three individual surrogate models. The most precise ES model increased the certainty coefficient (R2) to 0.9837, whereas limiting the maximum relative error to 13.14%. Finally, a mixed-integer nonlinear programming optimization model was established to identify the groundwater contamination source in terms of location and release history, and simultaneously assess aquifer parameters. The ES model developed in this article could reasonably predict the system response under given operation conditions. Replacement of the simulation model by the ES model considerably reduced the computation burden of the simulation–optimization process and simultaneously achieved high computation accuracy. [ABSTRACT FROM AUTHOR]

Groundwater pollution source identification (GPSI), which is critical for taking effective measures to protect groundwater resources, assess risks, and design remediation strategies, typically involves the solution of a nonlinear and ill-posed inverse problem. Regarding the inversion of dense non-aqueous phase liquid (DNAPL) sources, the special characteristics of pollutants render related research more complex. In the present study, homotopy-based optimization inverse theory and multi-kernel extreme learning machine (MK-ELM) were combined for efficiently solving GPSI problem while estimating aquifer parameters at a DNAPL-polluted site. The extreme learning machine incorporating multi kernels and whose parameters are obtained by means of a genetic algorithm (GA) was embedded in an optimization model for GPSI to replace the multiphase flow simulation model and to mitigate the considerable computational burdens of inversion iteration. The hybrid homotopy-particle swarm optimization (PSO) algorithm was constructed as a more efficient method for segmentally searching the global optimum in wide areas with low dependence on initial values. Results showed that the application of GA-based MK-ELM and hybrid homotopy-PSO effectively accomplish the simultaneous identification of source characteristics and aquifer parameters. The MK-ELM approximate the outputs of multiphase flow simulation model sufficiently with the certainty coefficient (R 2) increased to 0.9982, whereas the mean relative error was limited to 1.5168%. Compared to the widely used PSO algorithm, the hybrid homotopy-PSO algorithm significantly reduced the mean relative error of identification results from 6.77% to 2.89%. • A new approximation model and an improved global optimization method were proposed for efficiently solving GPSI problems. • A multi-kernel extreme learning machine is proposed to approximate the simulation model with higher robustness. • A hybrid homotopy-PSO algorithm is constructed as a more efficient tool for searching the global optimum in wide areas. [ABSTRACT FROM AUTHOR]

Surrogate-based simulation-optimization techniques are widely applied in developing optimal remediation strategies that increase the efficiency and reduce the cost of surfactant-enhanced aquifer remediation (SEAR) when clearing dense nonaqueous phase liquids (DNAPLs). In such processes, there are many uncertainty factors that may greatly affect the optimization outcome of a SEAR strategy selection. However, previous research on this subject rarely incorporates an uncertainty analysis. This paper presents an uncertainty analysis of both the simulation model and the ensemble surrogate model used to optimize SEAR strategies. Set pair analysis (SPA) and kriging methods were used to build the ensemble surrogate model. The probability distributions of the residuals of the outputs between the ensemble surrogate model and the simulation model, run on 100 testing samples, were analyzed to ascertain the uncertainty of the surrogate model, which was found to be less than 1.5%. The uncertainty of the simulation model was derived by combining a Monte Carlo random simulation with the Sobol' global sensitivity analysis. Finally, a stochastic nonlinear programming model was established to compute the optimal remediation strategies for the remediation target under different confidence levels. This research will allow decision makers to more confidently select the optimal remediation strategy for a given scenario by balancing the reliability of model prediction with the cost of the remediation strategy according to the demands of the project. [ABSTRACT FROM AUTHOR]

In this paper, a multi-algorithm genetically adaptive multi-objective (AMALGAM) method is proposed as a multi-objective optimization solver. It was implemented in the multi-objective optimization of a groundwater remediation design at sites contaminated by dense non-aqueous phase liquids. In this study, there were two objectives: minimization of the total remediation cost, and minimization of the remediation time. A non-dominated sorting genetic algorithm II (NSGA-II) was adopted to compare with the proposed method. For efficiency, the time-consuming surfactant-enhanced aquifer remediation simulation model was replaced by a surrogate model constructed by a multi-gene genetic programming (MGGP) technique. Similarly, two other surrogate modeling methods—support vector regression (SVR) and Kriging (KRG)—were employed to make comparisons with MGGP. In addition, the surrogate-modeling uncertainty was incorporated in the optimization model by chance-constrained programming (CCP). The results showed that, for the problem considered in this study, (1) the solutions obtained by AMALGAM incurred less remediation cost and required less time than those of NSGA-II, indicating that AMALGAM outperformed NSGA-II. It was additionally shown that (2) the MGGP surrogate model was more accurate than SVR and KRG; and (3) the remediation cost and time increased with the confidence level, which can enable decision makers to make a suitable choice by considering the given budget, remediation time, and reliability. [ABSTRACT FROM AUTHOR]