A multi-objective optimization method for remediation of DNAPL contaminated sites under uncertain conditions

Abstract

The present invention discloses a multi-objective optimization method for DNAPL contaminated site remediation under uncertain conditions. First, based on the dual uncertain conditions of aquifer heterogeneity and DNAPL pollution source area, a multi-objective optimization model is constructed, taking the injection volume of surfactant remediation wells as the decision variable, minimizing the total cost f1 of SEAR remediation and minimizing the distribution range #imgabs0# of NAPL phase after remediation as the optimization objectives, and taking the injection volume of remediation wells as the constraint conditions; secondly, to improve the computational efficiency of multi-phase flow multi-objective optimization, a deep convolutional neural network model is constructed to replace the computationally time-consuming SEAR remediation DNAPL multi-phase flow numerical model; finally, an optimization algorithm is used to call the surrogate model to solve the optimization model under uncertain conditions, and an optimal remediation plan under uncertain conditions is obtained. The present invention can efficiently obtain the optimal remediation plan for DNAPL contaminated sites under uncertain conditions.

Description

Technical Field

[0001] The present invention belongs to the intersection of pollution hydrogeology and deep learning, and specifically relates to a multi-objective optimization method for remediation of DNAPL contaminated sites under uncertain conditions. Background Art

[0002] Dense Non-Aqueous Phase Liquids (DNAPLs) pollution is difficult to remove due to its high density, low interfacial tension and low viscosity. A more effective remediation method is surfactant-enhanced aquifer remediation, which injects surfactants into injection wells and extracts them from extraction wells to carry out groundwater remediation. In order to achieve both economic and environmental benefits of groundwater remediation, multi-objective optimization is often used to obtain the optimal remediation plan. Whether the optimal plan is feasible depends on whether the numerical model used in the optimization accurately reflects the actual site characteristics, mainly the characteristics of the aquifer permeability and the DNAPL pollution source area. However, underground media often have strong heterogeneity, and sparse observation boreholes are often insufficient to accurately characterize the actual site aquifer permeability and the characteristics of the DNAPL pollution source area. Therefore, the optimization of remediation plans for groundwater contaminated sites needs to be carried out under the premise of considering the uncertainty of the underground medium field and the pollution source area. This type of problem usually evaluates the impact of uncertainty on the optimization results by considering multiple possible realizations of the underground medium field and the pollution source area.

[0003] Considering uncertainty in optimization will increase the number of simulation models that are repeatedly called by the optimization algorithm, that is, as the number of realizations of the underground medium field and pollution source area considered increases, this may bring an unbearable amount of calculation. In order to reduce the computational burden, alternative models are often used to replace the original time-consuming numerical models. However, under the condition of uncertainty in the characterization of the aquifer medium field and the DNAPL pollution source area, the alternative optimization algorithm calls SEAR to repair the DNAPL numerical model, which faces two major challenges.

[0004] First, the aquifer heterogeneity and the uncertain spatial parameters of the DNAPL pollution source area will lead to the "curse of dimensionality" problem, that is, the amount of calculation required to establish the surrogate model increases exponentially with the increase of the dimension of the uncertain parameters. Previous studies on groundwater remediation optimization often adopted homogenization or partitioning strategies to generalize the heterogeneous field using one or several parameters to reduce the dimensionality of the input parameters. However, considering that multiphase flow is very sensitive to permeability changes, the simplified permeability heterogeneity in the numerical model cannot reflect the migration of groundwater and DNAPL in the actual site, which may mislead the design of the surfactant enhanced aquifer remediation (SEAR) scheme. Therefore, innovative surrogate models are needed to cope with the challenges of high-dimensional input (high-dimensional spatial parameters that characterize the heterogeneous permeability field and DNAPL saturation field) in the SEAR remediation of DNAPL multiphase flow under uncertain conditions. Second, the saturation of the remediated NAPL phase obtained after SEAR remediation of DNAPL is a discontinuous spatial variable, which is difficult to be accurately predicted by existing surrogate models. In the past, it was often simplified to one or more local variables. However, NAPL after remediation may remain locally and become a long-term pollution source, posing a threat to groundwater quality. Only the overall average indicator cannot reflect the residual distribution of DNAPL after remediation. Therefore, innovative alternative models are needed to meet the challenge of replacing the spatially discontinuous distribution of NAPL saturation after remediation.

[0005] To address the two challenges of optimization under uncertain conditions, we established a deep convolutional neural network (CNN) as a surrogate model to replace the potential relationship between the high-dimensional uncertain inputs (i.e., heterogeneous permeability distribution, DNAPL source area structure, and SEAR remediation scheme) generated by different remediation schemes under uncertain contaminated sites and the DNAPL saturation field after remediation. Then, we established an optimization problem under uncertain conditions, and called the surrogate model CNN through the optimization algorithm non-dominated sorting genetic algorithm (NSGAII), forming a multi-objective optimization method CNN-NSGAII based on deep learning surrogate model under uncertain conditions, so as to achieve the purpose of efficiently searching for reliable optimal remediation schemes in contaminated sites with uncertain characterization. The feasibility of this multi-objective optimization method based on deep learning under uncertain conditions was analyzed and verified by a three-dimensional ideal example.

[0006] Alternative models for the SEAR remediation process of DNAPL source areas include artificial neural network, stepwise cluster analysis, polynomial response surface, polynomial chaos expansion, radial basis function, Kriging, support vector regression and Gaussian process.

[0007] The alternative model used in groundwater remediation optimization: 1. There is a dimensionality curse, which makes it impossible to replace the SEAR remediation process in a heterogeneous aquifer when there is uncertainty in the characterization of the contaminated site; 2. It is impossible to replace the spatial distribution of the global variable DNAPL saturation after remediation, resulting in an inability to fully evaluate the remediation effect. Summary of the invention

[0008] Purpose of the invention: In order to overcome the deficiencies in the prior art, the present invention proposes a multi-objective optimization method for the remediation of DNAPL contaminated sites under uncertain conditions, so as to achieve efficient acquisition of the optimal remediation solution for SEAR remediation of DNAPL in contaminated sites that are not finely characterized.

[0009] Technical solution: The multi-objective optimization method for remediation of DNAPL contaminated sites under uncertain conditions described in the present invention specifically includes the following steps:

[0010] (1) Establish a multi-objective optimization model under uncertain conditions: the decision variable is set as the flow rate of the SEAR treatment well; the optimization goal is to minimize the total cost of SEAR repair f 1 and minimize the distribution range of the NAPL phase after restoration The constraint condition is the flow limit of the treatment well; the uncertainty condition is the multiple realizations of the underground medium and the distribution of the pollution source area that meet the sparse observation data;

[0011] (2) Construct a deep convolutional neural network model to replace the time-consuming multiphase flow numerical model and achieve a high-dimensional replacement for the numerical model of SEAR repairing DNAPL;

[0012] (3) The optimization algorithm is used to call the trained alternative model to solve the optimization model under uncertain conditions and obtain the optimal repair solution under uncertain conditions.

[0013] Furthermore, the step (1) is implemented by the following formula:

[0014]

[0015] Among them, C 1 (m+n) represents the installation cost of m injection wells and n extraction wells (yuan); C 2 Represents the operating cost of the extraction well (yuan / m 3 );t represents the repair time; represents the flow rate of the jth extraction well; C 3 Represents the operating cost of the injection well (yuan / m 3 ); represents the flow rate of the i-th injection well;

[0016]

[0017] in, and Represents N r The distribution range of the restored NAPL phase f calculated by the realization 2 The mean and variance of λ represent the risk aversion coefficient. λ of 2 means that the confidence interval is 97.5%, that is, 97.5% represents the residual DNAPL saturation of the i-th grid; M(·) is an indicator function used to indicate whether a grid has a NAPL phase; N is the total number of grids;

[0018] Constraints:

[0019] Among them, Q max and Q min are the saturation thresholds, which are the maximum and minimum values ​​allowed for the injection well (In) and the extraction well (Ex), respectively.

[0020] Furthermore, the implementation process of step (2) is as follows:

[0021] The input and output fields of the numerical model are converted into three-dimensional images, and the local spatial correlation of the image data is fully extracted by convolution operation, so as to learn the potential mapping relationship between the input and output images. The SEAR repair well flow combination is converted into an image as follows:

[0022]

[0023] Where, ω=1,…,W; h=1,…,H; d=1,…,D; j=1,…N, N represents the number of wells; S rj >0 represents injection well; S rj <0 represents an extraction well. That is, the pixel value at the well position is the extraction / injection ratio, and the pixel value at other positions without a well is 0;

[0024] A convolutional layer is used to extract feature surfaces from the input image, and then the extracted feature surfaces are processed alternately through multiple residual dense blocks and downsampling layers. After each downsampling layer, the size of the feature surface will be halved. Finally, a series of feature surfaces containing high-level features are output. These feature surfaces are then processed alternately through RRDB and upsampling layers. After each upsampling layer, the size of the feature surface will double. Finally, the output image is reconstructed through a convolutional layer and the activation function Sigmoid activation.

[0025] Furthermore, the implementation process of step (3) is as follows:

[0026] The optimization algorithm continuously searches for new combinations of decision variables, and evaluates the decision variable combinations in the generated realization sets of underground media and pollution source areas by calling the trained alternative models, and finally obtains the optimal remediation plan under uncertain conditions.

[0027] Furthermore, the input field of the numerical model is a combination of a heterogeneous permeability field, a DNAPL saturation field, and a SEAR repair well flow rate, and the output field is a repaired DNAPL saturation field.

[0028] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention proposes a multi-objective optimization method that couples a deep convolutional neural network (CNN) and a multi-objective optimization algorithm (NSGA-II) under uncertain conditions; while considering the uncertainty in the characterization of the heterogeneous underground aquifer and the DNAPL pollution source area of ​​the actual contaminated site, the optimal remediation plan for SEAR remediation of DNAPL in the contaminated site is efficiently obtained; the present invention adopts CNN to replace the numerical model, overcomes the "curse of dimensionality", and realizes efficient prediction of global output variables under high-dimensional input, while greatly reducing the computational burden of optimization problems under uncertain conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a schematic diagram of the deep convolutional network structure;

[0030] Figure 2 It is a schematic diagram of the hydrogeological conceptual model of the study area;

[0031] Figure 3 is the reference field for permeability (ln k) and DNAPL saturation (S N0 ) reference field and ln k field and S N0 Schematic diagram of two implementations of field random selection;

[0032] Figure 4 This is a schematic diagram of the SSIM size obtained by evaluating CNN on the training and test data sets;

[0033] Figure 5Among the three random realizations, the numerical model UTCHEM (S N ) and alternative models Comparison of the predicted remaining DNAPL saturation distribution after SEAR remediation;

[0034] Figure 6 It is the Pareto optimal solution obtained by CNN alternative simulation-optimization method and all implementations (f 1 , f 2 )Solve the diagram;

[0035] Figure 7 is the target value DNAPL distribution area f predicted by the alternative model CNN and the numerical model UTCHEM 2 . DETAILED DESCRIPTION

[0036] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0037] The present invention proposes a multi-objective optimization method for remediation of DNAPL contaminated sites under uncertain conditions. First, a multi-objective optimization model under uncertain conditions is established; second, a substitute model is trained to replace the numerical model of SEAR remediation of DNAPL; finally, the substitute model is directly called by the multi-objective optimization algorithm to realize the substitute simulation-optimization framework. Specifically, the following steps are included:

[0038] For the optimization problem of SEAR repair of DNAPL, the decision variable is set as the flow rate of SEAR treatment wells (injection wells and extraction wells); the optimization goal is 1) to minimize the total cost of SEAR repair f 1 (the cost of arranging and operating the remediation wells) and 2) minimizing the distribution of the post-remediation NAPL phase The constraint condition is the flow limit of the treatment well. Considering the uncertainty of characterizing the contaminated site, there are many realizations of the underground medium and the pollution source area that meet the sparse observation data. Therefore, optimization is performed under such uncertain conditions. A strategy similar to uncertainty analysis is adopted to comprehensively consider all realizations and define the optimization goal under uncertain conditions. The established multi-objective optimization model under uncertain conditions is as follows:

[0039] Objective function 1: Among them, C 1 (m+n) represents the installation cost of m injection wells and n extraction wells (yuan); C 2 Represents the operating cost of the extraction well (yuan / m 3 );t represents the repair time; represents the flow rate of the jth extraction well; C 3 Represents the operating cost of the injection well (yuan / m 3); Represents the flow rate of the i-th injection well.

[0040] Objective function 2: in, and Represents N r The calculated f 2 The mean and variance of λ represent the risk aversion coefficient. λ of 2 means that the confidence interval is 97.5%, that is, 97.5% represents the residual DNAPL saturation of the ith grid; M(·) is an indicator function used to indicate whether a grid has a NAP1 phase; N is the total number of grids.

[0041] Constraints: Among them, Q max and Q min are the saturation thresholds, which are the maximum and minimum values ​​allowed for the injection well (In) and the extraction well (Ex), respectively.

[0042] The common non-dominated sorting genetic algorithm (NSGA-II) (Deb et al., 2002) is used to solve the above dual-objective optimization problem. The NSGA-II algorithm provides a set of solutions called Pareto optimal sets, which represent the trade-off solutions between conflicting objectives.

[0043] In order to realize the multiphase flow numerical model of SEAR repairing DNAPL called in the alternative optimization model, it is necessary to first run the multiphase flow numerical model to generate training samples. The input variables of the training samples are the heterogeneous permeability field, DNAPL saturation field and SEAR repair well flow combination, and the output variable is the repaired DNAPL saturation field. Then the training samples are used to train the alternative model.

[0044] The optimization algorithm is used to call the trained surrogate model to solve the optimization model under uncertain conditions. Specifically, the optimization algorithm continuously searches for new decision variable combinations, and evaluates the decision variable combinations in the generated realization sets of underground media and pollution source areas by calling the trained surrogate model, and finally obtains the optimal remediation solution under uncertain conditions.

[0045] The University of Texas Chemical Composition Simulator (UTCHEM) was used to simulate the multiphase flow migration process in the SEAR DNAPL source area to generate training samples for the alternative model. UTCHEM is a three-dimensional multiphase flow simulator that can simulate multi-component pollutant migration, complex geochemical reactions, and organic matter dissolution.

[0046] As a type of deep neural network, deep convolutional neural network (CNN) is suitable for processing image data. Therefore, when replacing the multiphase flow numerical model in the SEAR repair DNAPL process, it is necessary to convert the input field (heterogeneous permeability field, DNAPL saturation field, SEAR repair well flow combination) and output field (repaired DNAPL saturation field) of the numerical model into a three-dimensional image (i.e., a pixel matrix with a size of D×H×W), and use the convolution operation to fully extract the local spatial correlation of the image data, and then learn the potential mapping relationship between the input and output images. The way to convert the SEAR repair well flow combination into an image is as follows:

[0047]

[0048] Where, ω=1,…,W; h=1,…,H; d=1,…,D; j=1,…N, N represents the number of wells; S rj >0 represents injection well; S rj <0 represents an extraction well. That is, the pixel value at the well position is the extraction / injection ratio, and the pixel value at other positions without a well is 0.

[0049] The deep convolutional neural network (CNN) performs a coarsen-to-refine process on high-dimensional input images. In this process, the size of the feature surface extracted in the network undergoes a process of first shrinking and then recovering, so as to fully extract the multi-scale and hierarchical features implicit in the data, and then efficiently learn the input-output mapping relationship of the system. The basic network architecture to achieve this process is as follows: Figure 1 As shown. First, a convolutional layer (Conv) (Goodfellow, 2016) is used to extract feature faces from the input image. The extracted feature faces are then processed alternately through multiple residual-in-residualdense blocks (RRDB) (Wang et al., 2018) and downsampling layers (▽). After each downsampling layer, the feature face size is halved. Finally, a series of feature faces containing high-level features are output. These feature faces are then processed alternately through RRDB and upsampling layers (Δ). After each upsampling layer, the feature face size is doubled. Finally, the output image is reconstructed through a convolutional layer and activation function Sigmoid activation. The middle part of the network uses 2 consecutive RRDBs and applies an additional residual learning (output and input addition) to promote the conduction of information flow in this part (when the feature face size is the smallest).

[0050] Generate the underground medium permeability k field and the NAPL phase saturation S in the pollution source area that meet the observation data N0The absolute permeability k field uses the conditional sequential Gaussian simulation (SGSIM) in the Geostatistical Software Library (GSLIB) and takes the prior k value obtained from the borehole as the conditional input to generate a permeability realization that conforms to the prior information. In the aquifer corresponding to the permeability realization, the stochastic invasion percolation (SIP) algorithm is used to simulate DNAPL leakage and obtain the steady-state initial NAPL phase saturation (S N0 ) distribution. Then, according to the prior S obtained from drilling N0 The rejection sampling (RS) algorithm is used to select the DNAPL saturation realizations that meet the prior information from the initial DNAPL saturation realizations.

[0051] The feasibility of using deep convolutional neural networks to replace simulation-optimization methods is demonstrated through numerical experiments. The example is a 3D heterogeneous confined aquifer of 45m×25m×10m; Figure 2 As shown in the figure, the cylinder represents the hypothetical borehole, and the permeability and DNAPL saturation observations are obtained; the boreholes with up / down arrows are pumping / injection wells, respectively; the grayscale image and the isovoid represent the distribution of permeability and NAPL phase, respectively. The aquifer is evenly discretized into 45×25×10=11250 cells. The left and right boundaries of the aquifer are set as constant head boundaries, the hydraulic gradient is 0.001, and the other boundaries are zero flux boundaries. The parameter settings are detailed in Table 1.

[0052] Table 1 Parameter settings in numerical experiments

[0053]

[0054]

[0055] The permeability k-field realization was generated by conditional sequential Gaussian simulation (conditional SGSIM) in the Geostatistical Software Library (GSLIB). The parameters are detailed in Table 1. It is assumed that a total of 150 a priori k values ​​are sampled as conditional inputs. In the aquifer corresponding to each permeability realization, trichloroethylene (TCE) is leaked in the form of a point source at the top center of the aquifer, and the stochastic invasion percolation (SIP) algorithm is used to generate the initial DNAPL saturation (S N0 ), and then based on the 150 priors S obtained by assuming sampling N0 The rejection sampling algorithm is used to select the DNAPL saturation value that meets the prior information, such as Figure 3 As shown, Figure 3The first column is the permeability (ln k) reference field and DNAPL saturation (S N0 ) reference field, the two right columns show the ln k field and S N0 Two realizations of random selection of fields, both generated based on permeability and saturation observations obtained from 15 observation wells (vertical cylinders) as prior information.

[0056] SEAR repair sets up m = 6 injection wells and n = 3 extraction wells, such as Figure 2 As shown, the repair time is set to 30 days, and the installation cost coefficient of the well is C 1 Set to 5000 yuan, the operating cost coefficient of the pumping well is C 2 Set to 0.5 yuan / m 3 , the operating cost coefficient C of the injection well 3 Set to 201.5 yuan / m 3 , the flow ranges of the injection well and the extraction well are set to and Determine the number of realizations N for uncertain optimization by convergence analysis r is 500.

[0057] The surrogate model needs to replace the objective function f in the optimization problem. 2 , that is, from the input variables (permeability k field, DNAPL saturation field S N0 , SEAR well flow rate S) to output variable (DNAPL saturation field S after repair) N ). We chose to generate 5000 training samples to train CNN. The main hyperparameters of network training were set as follows: initial learning rate of 0.005 and batch size of 24. The trained model was obtained by training on NVIDIA Tesla V100 GPU for 200 epochs. The training accuracy was characterized by the structural similarity index (SSIM) (Wang et al., 2004). SSIM is an index that quantifies the structural similarity between two 2-D images. When calculating the SSIM of a 3-D image of size D×H×W, the 3D image needs to be converted into D H×W 2-D images. The closer the SSIM is to 1.0, the better the training effect.

[0058] The optimization algorithm NSGA-II uses the trained CNN model to solve the optimization model. The main parameters of the optimization algorithm are set as follows: population size is 100, optimization generation is 100, mutation probability is 0.11, and crossover probability is 0.70.

[0059] Figure 4The figure shows the substitution accuracy of CNN for the three-dimensional multiphase flow migration model. It can be seen that the median value of the substitution accuracy index SSIM of the CNN substitution model on 5000 training samples is 0.995, and the median value of SSIM obtained on 1000 test samples is 0.991, which shows that CNN can accurately predict the spatial distribution of DNAPL saturation after SEAR repair.

[0060] Figure 5 This further illustrates that CNN can accurately predict the saturation S of DNAPL after repair. N The figure compares the S of UTCHEM simulation on three random implementations in the test set. N Field, CNN prediction It can be seen that although the saturation field is complex and discontinuous in space, the prediction of CNN is very close to that of UTCHEM, and the prediction error in most areas is less than 0.05. Therefore, when solving the optimization model next, the optimization algorithm is used to directly call this alternative model CNN, which has a more accurate prediction but faster speed, to replace the time-consuming multiphase flow numerical model.

[0061] Analyze and optimize the optimal repair solution obtained in the last generation. Figure 6 It is the Pareto optimal solution obtained by CNN alternative simulation-optimization method (circle) and all realizations (f 1 , f 2 ) solution (squares), showing the obtained when considering 500 realizations The optimal Pareto frontier and solving the objective function The objective function f is calculated for 500 realizations 2 It can be seen that the Pareto front is nonlinear and shows a trend that the higher the repair cost, the less NAPL after repair, which is consistent with the actual situation. Therefore, the uncertainty optimization method can obtain the Pareto optimal solution with the correct trend.

[0062] In order to illustrate that the Pareto solution obtained by the CNN-based optimization algorithm is reliable, the objective function f predicted by the CNN replacement model is replaced by 2 The values ​​are compared with the simulation results of UTCHEM. Figure 7 As shown, the f obtained by CNN and UTCHEM 2 The scatter points of the values ​​are basically distributed on the 1:1 diagonal line, which means that the predicted values ​​of the alternative model CNN are very consistent with the simulation results of the UTCHEM numerical model; the absolute error between the two is mainly in (-40m 2 , 20m 2 ), relative to the total grid area (11250m 2) is very small. Therefore, the optimization algorithm NSGA-II can obtain a reliable Pareto optimal frontier by calling the alternative model CNN.

[0063] The fundamental purpose of using surrogate models to solve optimization problems is to reduce the computational burden, as shown in Table 2.

[0064] Table 2 Comparison of calculation efficiency

[0065]

[0066] In this optimization problem under uncertain conditions, without using a surrogate model (UTCHEM-NSGAII), at least 4,000,000 numerical simulations are required to reach convergence and obtain the optimal solution, that is, considering 500 realizations, 100 populations, and iterating at least 80 generations in the NSGA-II algorithm. A single simulation takes an average of about 12 minutes, and the total running time is about 800,000 hours. Using a surrogate model (CNN-NSGAII), it only takes about 129.5 hours to replace the 4,000,000 numerical models called in the optimization process. Previously, it took 1,240 hours to perform 6,000 numerical simulations, generate 6,000 training samples, and 5.5 hours to train the surrogate model. In general, the cost of CNN-NSGAII is only 1,375 hours, saving 99.8% of the time compared to the 800,000 hours of cost of UTCHEM-NSGAII.

Claims

1. A multi-objective optimization method for DNAPL contaminated site remediation under uncertain conditions. It is characterized in that The following steps are involved: (1) Establish a multi-objective optimization model under uncertain conditions: set the decision variable as the flow rate of the SEAR treatment well; The optimization goal is to minimize the total cost of SEAR repair f 1 and minimize the distribution range of the NAPL phase after restoration The constraints are the flow restrictions of the treatment wells; the uncertainties are the multiple realizations of the heterogeneous distribution of the aquifer medium and DNAPL pollution source areas that satisfy the sparse observation data; (2) Construct a deep convolutional neural network model to replace the time-consuming multiphase flow numerical model and achieve a high-dimensional replacement for the numerical model of SEAR repairing DNAPL; (3) Using the optimization algorithm to call the trained alternative model to solve the optimization model under uncertain conditions, and obtain the optimal repair solution under uncertain conditions; The implementation process of step (2) is as follows: The input and output fields of the numerical model are converted into three-dimensional images, and the local spatial correlation of the image data is fully extracted by convolution operation, so as to learn the potential complex mapping relationship between the input and output images. The way to convert the SEAR repair well flow combination into an image is as follows: Where, ω=1,…,W; h=1,…,H; d=1,…,D; j=1,…N, N represents the number of wells; S rj >0 represents injection well; S rj <0 represents an extraction well, that is, the pixel value at the well position is the extraction / injection ratio, and the pixel value at other positions without a well is 0; A convolutional layer is used to extract feature surfaces from the input image, and then the extracted feature surfaces are processed alternately through multiple residual dense blocks and downsampling layers. After each downsampling layer, the size of the feature surface will be halved. Finally, a series of feature surfaces containing high-level features are output. These feature surfaces are then processed alternately through RRDB and upsampling layers. After each upsampling layer, the size of the feature surface will double. Finally, the output image is reconstructed through a convolutional layer and the activation function Sigmoid activation.

2. The multi-objective optimization method for remediation of DNAPL contaminated sites under uncertain conditions according to claim 1, It is characterized in that The step (1) is implemented by the following formula: Among them, C 1 (m+n) represents the installation cost of m injection wells and n extraction wells; C 2 represents the operating cost of the pumping well; t represents the repair time; represents the flow rate of the jth extraction well; C 3 represents the operating cost of the injection well; represents the flow rate of the i-th injection well; in, and Represents N r The distribution range of the restored NAPL phase f calculated by the realization 2 The mean and variance of λ represent the risk aversion coefficient. λ of 2 means that the confidence interval is 97.5%, that is, 97.5% represents the residual DNAPL saturation of the i-th grid; M(·) is an indicator function used to indicate whether a grid has a NAPL phase; N is the total number of grids; Constraints: Among them, Q max and Q min are the saturation thresholds, which are the maximum and minimum values ​​allowed for the injection well In and the extraction well Ex respectively.

3. The multi-objective optimization method for remediation of DNAPL contaminated sites under uncertain conditions according to claim 1, It is characterized in that The implementation process of step (3) is as follows: The optimization algorithm continuously searches for new combinations of decision variables, and evaluates the decision variable combinations in the generated realization sets of underground media and pollution source areas by calling the trained alternative models, and finally obtains the optimal remediation plan under uncertain conditions.

4. The multi-objective optimization method for remediation of DNAPL contaminated sites under uncertain conditions according to claim 1, It is characterized in that The input field of the numerical model is a combination of a strongly heterogeneous permeability field, a DNAPL saturation field, and a SEAR repair well flow rate; and the output is a repaired DNAPL saturation field.

Images