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An informed search strategy based on random statistical analysis was developed for synchronous recognition of groundwater pollution source information and aquifer parameters. An informed search iterative course (ISIC) was accordingly designed, and each iteration included the determination of attempt point and state transition. In this paper, two improvement techniques were first adopted for choosing attempt points and judging state transition in ISIC to improve search efficiency and precision. The first improvement was that the variable radius free search method was applied to choosing the attempt point, and the size of the search radius was constantly adjusted in ISIC, taking the search ergodicity and efficiency into account. The second improvement technique was a Tsallis formula used for state transition judgment, and the controlled factor in the Tsallis formula was regulated continuously so that the search could consider ergodicity and efficiency simultaneously. Furthermore, frequent calls to the groundwater pollution numerical simulator to calculate the likelihood have inflicted a huge computational burden during ISIC. An effective way is to construct a substitute for emulating the simulator with a low calculating load. However, the mapping relation between the import and export of the numerical simulator was complex and had many variables. The precision of the substitute based on shallow learning is low sometimes. Therefore, we adopted the deep learning method and built an improved deep confidence network (DCN) substitute to emulate the highly nonlinear simulator. Finally, the synchronous recognition results for groundwater pollution source information and aquifer parameters were gained when ISIC ceased. The above-mentioned methods were verified in a case involving groundwater pollution. The consequence indicated that the ISIC with an improved DCN substitute can synchronously recognize groundwater pollution source information and aquifer parameters with a high degree of precision and efficiency. [ABSTRACT FROM AUTHOR]

High-cost remediation of groundwater pollution makes it important to obtain exact information about the source. This is quite difficult to achieve in naturally ill-posed inverse problems of this kind. If the aquifer parameters are also unknown, the problem becomes even more challenging. To address this difficulty, we propose the alternating direction genetic algorithm (ADGA) approach, together with modification of the order of magnitude of the decision variables, to increase the accuracy of the results and computational efficiency. Seven scenarios were designed to test the accuracy of the proposed approach in aquifer with different properties, number of pollution sources, parameters and measurement errors. The results show that combining the ADGA approach with modification of the order of magnitude of the decision variables for identifying both groundwater pollution source and aquifer parameters significantly increases the accuracy of estimated results. The NE value for the estimated results decreased from 9.81% to 58.44% for different cases, and computation time is about half decreased. In addition, the approach is applicable in situations where concentrations of observational data with measurement error, and for multiple source locations and non-uniform media. [ABSTRACT FROM AUTHOR]

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This paper first proposed a parallel heuristic search strategy for simultaneous identification of groundwater contamination source and aquifer parameters. As identification results are influenced by many factors, such as noisy contamination concentration data, data denoising is necessary. The existing wavelet threshold denoising method has unavoidable shortcomings; therefore, this paper first proposed a new weighted–average wavelet variable–threshold denoising (WWVD) method to improve the denoising effect for concentration data, which further enhanced the subsequent identification accuracy. However, frequent calls to the simulation model could produce high computational cost during likelihood calculation. Hence, single surrogate model of the simulation model was developed to reduce cost; however, it presented limitation. Thus, this paper first developed a differential evolution–tabu search (DE-TS) hybrid algorithm to construct an optimal ensemble surrogate model, which assembled Gaussian process, kernel extreme learning machine, and support vector regression. The first proposed DE-TS algorithm also improved the approximation accuracy of surrogate model to simulation model. This paper first proposed and implemented a parallel heuristic search iterative process for simultaneous identification, and the identification results were obtained when the iteration process terminated. The accuracy and efficiency of these newly proposed approaches were tested through a hypothetical case. Results showed that the WWVD method not only improved the denoising effect for concentration data but also enhanced the subsequent identification accuracy. The OES model using DE-TS hybrid algorithm improved the approximation accuracy of surrogate model to simulation model, and the parallel heuristic search strategy is helpful for simultaneous identification of groundwater contamination source and aquifer parameters. [ABSTRACT FROM AUTHOR]

In this paper, a parallel heuristic search strategy based on Bayesian approach was first proposed for recognizing groundwater DNAPL contaminant source and aquifer parameters (unknown variables). Frequent calls to numerical simulation model effectuated large computational burden during likelihood calculation. Single surrogate system was established to reduce the burden, but it had unavoidable limitations. Thus, we first presented the particle swarm optimization-tabu search hybrid algorithm to construct an optimal combined surrogate system for the simulation model, which assembled Gaussian process, kernel extreme learning machine, support vector regression, and also improved the accuracy of the surrogate system to simulation model. Thereafter, a parallel heuristic search iterative process was first implemented for simultaneous recognition of unknown variables. Each round of iteration involved determination of candidate points and state transitions. The Monte Carlo approach was used widely for selecting candidate point, but it did not readily converge to posterior distribution when the probability density functions were complex. And the search ergodicity was weak. In order to improve the search ergodicity, a DE algorithm with variable mutation rate based on rand-to-best, 1, and bin strategy was first proposed in this paper to determine multiple candidate points. The recognition results were obtained when the iteration process terminated. The accuracy and efficiency of our approaches were demonstrated through a hypothetical case in DNAPLs-contaminated aquifer, and the recognizing accuracy was high. More importantly, the new simulation model based on the recognition results is helpful in calculating future contaminant plume in the aquifer, which can provide credible basis for groundwater contaminant remediation plan design and risk assessment. [ABSTRACT FROM AUTHOR]

Linked simulation-optimization (S/O) approaches have been extensively used as tools in coastal aquifer management. However, parameter uncertainties in seawater intrusion (SI) simulation models often undermine the reliability of the derived solutions. In this study, a stochastic S/O framework is presented and applied to a real-world case of the Longkou coastal aquifer in China. The three conflicting objectives of maximizing the total pumping rate, minimizing the total injection rate, and minimizing the solute mass increase are considered in the optimization model. The uncertain parameters are contained in both the constraints and the objective functions. A multiple realization approach is utilized to address the uncertainty in the model parameters, and a new multiobjective evolutionary algorithm (EN-NSGA2) is proposed to solve the optimization model. EN-NSGA2 overcomes some inherent limitations in the traditional nondominated sorting genetic algorithm-II (NSGA-II) by introducing information entropy theory. The comparison results indicate that EN-NSGA2 can effectively ameliorate the diversity in Pareto-optimal solutions. For the computational challenge in the stochastic S/O process, a surrogate model based on the multigene genetic programming (MGGP) method is developed to substitute for the numerical simulation model. The results show that the MGGP surrogate model can tremendously reduce the computational burden while ensuring an acceptable level of accuracy. [ABSTRACT FROM AUTHOR]

Hypothetical and real case studies were combined to explore the feasibility and effectiveness of a surrogate-based cyclic feedback updating approach for groundwater contamination source identification (GCSI) at dense non-aqueous-phase liquid (DNAPL)-contaminated sites. Support vector regression (SVR), kriging, and kernel extreme learning machine (KELM) models were integrated to build a surrogate model of the multiphase flow simulation model with a high computational efficiency. A mixed homotopy-differential evolution (DE) algorithm is presented to solve the optimization model, in which the integrated surrogate model was embedded, to obtain the identification results, and a cyclic feedback updating process was developed to gradually improve the results. Finally, GCSI uncertainty analysis was conducted using the Monte Carlo method. The results showed that the integrated surrogate model accurately approximates the simulation model, with a mean relative error of only 2.56%. The combination of the homotopy algorithm and DE algorithm provided an effective improvement over the traditional heuristic algorithm, and the mean relative error of the identified source characteristics was limited to 3.28%. GCSI accuracy was significantly improved after the application of the cyclic feedback updating method by reducing the mean relative error of the final identification results to 2.14%. In addition, the probability distribution characteristics of the identification results were obtained via uncertainty analysis to provide a comprehensive and reliable reference for decision makers. [ABSTRACT FROM AUTHOR]

In this study, we develop a parallel heuristic search strategy based on a Bayesian approach for simultaneously recognizing groundwater contaminant sources and aquifer parameters (unknown variables) at sites contaminated with dense non-aqueous phase liquids (DNAPLs). The parallel search strategy is time-consuming because thousands of simulation models must run in order to calculate the likelihood. Various stand-alone surrogate systems for the simulation models have been established, but they also have unavoidable limitations. Thus, we develop an optimal combined surrogate system by combining Gaussian process, kernel extreme learning machine, and support vector regression methods using a differential evolution algorithm with a variable mutation rate based on the rand-to-best/1/bin strategy, thereby improving the approximation accuracy of the surrogate system to the simulation model and significantly decreasing the high computational cost. Utilizing the optimal combined surrogate system reduced the CPU time by more than 400 times. In the iterative parallel heuristic search process, each round of iteration involves determining the candidate points and state transitions. The Monte Carlo approach is used widely for selecting candidate point, but this approach does not readily converge to the posterior distribution for unknown variables when the probability density function types are complex with weak search ergodicity. In order to improve the search ergodicity, we develop a particle swarm optimization algorithm with a non-linear decreasing inertia weight and Metropolis criterion, which is more suitable for unknown variables with complex probability density functions. The recognition results are obtained simultaneously when the iterative process terminates. We assess our proposed approaches based on a hypothetical case study at a three-dimensional site contaminated with DNAPLs. The results demonstrate that the parallel heuristic search strategy is helpful for the simultaneous recognition of DNAPL contaminant sources in groundwater and aquifer parameters. [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]

The purpose of this study was to identify an optimal surfactant-enhanced aquifer remediation (SEAR) strategy for aquifers contaminated by dense non-aqueous phase liquid (DNAPL) based on an ensemble of surrogates-based optimization technique. A saturated heterogeneous medium contaminated by nitrobenzene was selected as case study. A new kind of surrogate-based SEAR optimization employing an ensemble surrogate (ES) model together with a genetic algorithm (GA) is presented. Four methods, namely radial basis function artificial neural network (RBFANN), kriging (KRG), support vector regression (SVR), and kernel extreme learning machines (KELM), were used to create four individual surrogate models, which were then compared. The comparison enabled us to select the two most accurate models (KELM and KRG) to establish an ES model of the SEAR simulation model, and the developed ES model as well as these four stand-alone surrogate models was compared. The results showed that the average relative error of the average nitrobenzene removal rates between the ES model and the simulation model for 20 test samples was 0.8%, which is a high approximation accuracy, and which indicates that the ES model provides more accurate predictions than the stand-alone surrogate models. Then, a nonlinear optimization model was formulated for the minimum cost, and the developed ES model was embedded into this optimization model as a constrained condition. Besides, GA was used to solve the optimization model to provide the optimal SEAR strategy. The developed ensemble surrogate-optimization approach was effective in seeking a cost-effective SEAR strategy for heterogeneous DNAPL-contaminated sites. This research is expected to enrich and develop the theoretical and technical implications for the analysis of remediation strategy optimization of DNAPL-contaminated aquifers. [ABSTRACT FROM AUTHOR]

A mixed-integer non-linear programming (MINLP) with surrogate model was introduced to derive the optimal surfactant enhanced aquifer remediation (SEAR) process (remediation cost minimisation and removal rate maximisation) at a nitrobenzene-contaminated site. First, a 3D multi-phase flow simulation model was developed to simulate the SEAR process; using a radial basis function artificial neural network (RBFANN), the surrogate model was built which was an approximation of the simulation model; a MINLP was built to identify the optimal remediation strategies and genetic algorithm (GA) and penalty function were combined to solve the model; at last, the optimal remediation strategies were obtained. The approximation result of RBFANN was compared with that of back-propagation artificial neural network (BPANN), mean absolute error, mean relative error and coefficient of determination of the developed RBFANN model were 0.01, 2.27% and 0.85 respectively, which indicated much higher approximation accuracy than BPANN. The MINLP with surrogate model is a powerful tool for non-aqueous phase liquids (NAPLs) contaminated site remediation optimisation problem and it can greatly improve computational efficiency. [ABSTRACT FROM AUTHOR]

A surrogate model is introduced for identifying the optimal remediation strategy for Dense Non-Aqueous Phase Liquids (DNAPL)-contaminated aquifers. A Latin hypercube sampling (LHS) method was used to collect data in the feasible region for input variables. A surrogate model of the multi-phase flow simulation model was developed using a radial basis function artificial neural network (RBFANN). The developed model was applied to a perchloroethylene (PCE)-contaminated aquifer remediation optimization problem. The relative errors of the average PCE removal rates between the surrogate model and simulation model for 10 validation samples were lower than 5%, which is high approximation accuracy. A comparison of the surrogate-based simulation optimization model and a conventional simulation optimization model indicated that RBFANN surrogate model developed in this paper considerably reduced the computational burden of simulation optimization processes. [ABSTRACT FROM AUTHOR]

In this study, the S-shaped log-log drawdown-time curve typical of pumping tests in unconfined aquifers is reinvestigated via numerical experiments. Like previous investigations, this study attributes the departure of the S shape from the drawdown-time behavior of the confined aquifer to the presence of an 'additional' source of water. Unlike previous studies, this source of water is reinvestigated by examining the temporal and spatial evolution of the rate of change in storage in an unconfined aquifer during pumping. This evolution is then related to the transition of water release mechanisms from the expansion of water and compaction of the porous medium to the drainage of water from the unsaturated zone above the initial water table and initially saturated pores as the water table falls during the pumping of the aquifer. Afterward, the 1-D vertical drainage process in a soil column is simulated. Results of the simulation show that the transition of the water release mechanisms in the 1-D vertical flow without an initial unsaturated zone can also yield the S-shaped drawdown-time curve as in an unconfined aquifer. We therefore conclude that the transition of the water release mechanisms and vertical flow in the aquifer are the cause of the S-shaped drawdown-time curve observed during pumping in an unconfined aquifer. We also find that the moisture retention characteristics of the aquifer material have greater impact than its relative permeability characteristics on the drawdown-time curve. Furthermore, influences of the spatial variability of saturated hydraulic conductivity, specific storage, and saturated moisture content on the drawdown curve in the saturated zone are found to be more significant than those of other unsaturated properties. Finally, a cross-correlation analysis reveals that the drawdown at a location in a heterogeneous unconfined aquifer is mainly affected by local heterogeneity near the pumping and observation wells. Applications of a model assuming homogeneity to the estimation of aquifer parameters as such may require a large number of observation wells to obtain representative parameter values. In conclusion, we advocate that the governing equation for variably saturated flow through heterogeneous media is a more appropriate and realistic model that explains the S-shaped drawdown-time curves observed in the field. [ABSTRACT FROM AUTHOR]

Groundwater contamination source identification is critical for taking effective measures to design remediation strategies, assess contamination risks, and confirm contamination responsibilities. To resolve the "equifinality" problem resulting from simultaneous inversion of contamination source characteristics and aquifer parameters at dense non-aqueous phase liquid-contaminated sites, two reciprocal optimization frames for separately identifying the contamination sources and aquifer parameters were designed and connected. The two sets of identification results were corrected stepwise by means of a feedback correction iteration process, thereby sufficiently improving the identification accuracy. The ensemble learning machine (ESLM) incorporating Kriging, radical basis function neural network, support vector regression, and wavelet kernel extreme learning machine with swarm intelligence (SI) algorithm was embedded into the reciprocal inversion iterations to replace the multiphase flow simulation model for significantly improving the computational efficiency. To improve the optimization efficiency, a hyper-heuristic homotopy algorithm was constructed for segmentally searching the global optimum in wider areas with low dependence on initial values. Results showed that the combined application of SI-based ensemble learning machine (SI-ESLM) and hyper-heuristic homotopy algorithm effectively accomplished the simultaneous identification of contamination sources and aquifer parameters with high efficiency, while maintaining high accuracy. The SI-ESLM sufficiently approximated the outputs of the multiphase flow simulation model with increased certainty ( R 2 = 0.9977), while the mean relative error was limited to 1.5388%. Compared to traditional heuristic algorithms, this application of reciprocal inversion iterations and the hyper-heuristic homotopy algorithm significantly reduced the mean relative error of identification results from 6.51% to 1.03%. [Display omitted] • A reciprocal feedback inversion system is designed for contamination source identification. • Swarm intelligence-based ensemble learning machine is proposed for surrogate modeling. • Hyper-heuristic homotopy algorithm is constructed to form a progressive searching mechanism. [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]

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]