CN114386329A - Multi-objective optimization method for DNAPL (deoxyribonucleic acid-Polypropylene) polluted site remediation under uncertain conditions - Google Patents

Multi-objective optimization method for DNAPL (deoxyribonucleic acid-Polypropylene) polluted site remediation under uncertain conditions Download PDF

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CN114386329A
CN114386329A CN202210025261.3A CN202210025261A CN114386329A CN 114386329 A CN114386329 A CN 114386329A CN 202210025261 A CN202210025261 A CN 202210025261A CN 114386329 A CN114386329 A CN 114386329A
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施小清
莫绍星
杜建雯
康学远
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Nanjing University
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Abstract

The invention discloses a multi-objective optimization method for DNAPL (sodium alginate and potassium alginate) polluted site remediation under an uncertain condition1And minimizing the extent of distribution of NAPL phases after remediation
Figure DDA0003464194960000011
Taking the injection amount of the repair well as a constraint condition for optimizing the target; secondly, in order to improve the computational efficiency of multi-target optimization of the multiphase flow, a deep convolutional neural network model is constructed to replace an SEAR (search algorithm) restoration DNAPL (fast online phase and linear programming language) multiphase flow numerical model with time-consuming calculated amount; and finally, calling the substitution model by adopting an optimization algorithm to solve the optimization model under the uncertain condition to obtain the optimal model under the uncertain conditionAnd (4) an excellent repair scheme. The invention can realize the high-efficiency acquisition of the DNAPL polluted site optimal repair scheme under uncertain conditions.

Description

Multi-objective optimization method for DNAPL (deoxyribonucleic acid-Polypropylene) polluted site remediation under uncertain conditions
Technical Field
The invention belongs to the crossing field of polluted hydrogeology and deep learning, and particularly relates to a multi-objective optimization method for repairing a DNAPL (deoxyribonucleic acid-PL) polluted site under an uncertain condition.
Background
Heavy Non-Aqueous Phase Liquids (DNAPLS) contamination is difficult to remove due to their high density, low interfacial tension and low viscosity characteristics. The effective repairing method is surfactant reinforced aquifer repairing, which is implemented by injecting surfactant into an injection well and extracting the surfactant from the extraction well. In order to achieve economic and environmental benefits of groundwater remediation simultaneously, multi-objective optimization is often employed to obtain an optimal remediation scheme. Whether the optimal scheme is feasible or not depends on whether the numerical model called in optimization accurately reflects the actual site characteristics, mainly the characteristics of aquifer permeability and DNAPL polluted source regions. However, the underground medium tends to be strongly heterogeneous, and sparse observation boreholes tend to be insufficient to accurately characterize actual site aquifer permeability and DNAPL contaminated source zones. Therefore, the optimization of the remediation scheme for the underground water polluted site needs to be developed on the premise of considering uncertainty of the carved underground medium field and the polluted source area. Such problems are typically addressed by considering multiple possible realizations of the subsurface media field and the contaminated source region to assess the impact of uncertainty on the optimization results.
Considering uncertainty in the optimization increases the number of times the optimization algorithm repeatedly calls the simulation model, i.e. as the number of realizations of the subsurface medium field and the contaminated source region under consideration increases, this may result in burdensome computational effort. To reduce the computational burden, surrogate models are often used to replace the otherwise time-consuming numerical models. However, under the condition that the aqueous medium field and the DNAPL pollution source region are not defined, the substitute optimization algorithm calls the sea to repair the DNAPL numerical model with two challenges.
First, uncertainty spatial parameters of aquifer heterogeneity and DNAPL polluted source regions can lead to the problem of "disaster of dimension" (i.e., the amount of computation required to build a surrogate model increases exponentially and sharply with increasing uncertainty parameter dimensions. In the prior art, a homogenization or partitioning strategy is usually adopted for groundwater remediation optimization research, and a heterogeneous field is generalized by one or more parameters, so that the dimension of input parameters is reduced. However, considering that multiphase flow is very sensitive to permeability variation, heterogeneity of simplified permeability in the numerical model cannot reflect migration of groundwater and DNAPL of the actual site, and further may mislead design of Surfactant Enhanced Aquifer Remediation (sea) scheme. Therefore, innovative surrogate models are needed to address the challenge of SEAR to repair the high dimensional inputs (high dimensional spatial parameters characterizing heterogeneous permeability fields and DNAPL saturation fields) present in DNAPL multiphase flow processes under uncertain conditions. Secondly, the saturation of the repaired NAPL phase obtained after the DNAPL is repaired by the SEAR is a discontinuous space variable, and the existing substitution model is difficult to predict more accurately. To reduce to one or more local variables as usual. However, the repaired NAPL may be partially remained and become a long-term pollution source, which threatens the quality of groundwater, and the residual distribution of the repaired DNAPL cannot be reflected only by the overall average index. Therefore, innovative surrogate models are needed to address the challenge of replacing spatially discontinuously distributed NAPL saturations after remediation.
In order to solve two challenges brought by optimization under uncertain conditions, a deep Convolutional Neural Network (CNN) is established as a substitution model, and substitution of potential relations between high-dimensional uncertain input (namely heterogeneous permeability distribution, DNAPL source region structure and SEAR repair scheme) generated by different repair schemes and a repaired DNAPL saturation field in the underground of an uncertain depicted polluted field is realized. And then establishing an optimization problem under an uncertain condition, calling a substitution model CNN through an optimization algorithm non-dominated sorting genetic algorithm (NSGAII), and forming a multi-objective optimization method CNN-NSGAII based on a deep learning substitution model under the uncertain condition so as to achieve the purpose of efficiently searching a reliable optimal repair scheme in a depicted uncertain polluted site. The feasibility of the multi-objective optimization method based on deep learning under the uncertain condition is analyzed and verified through a three-dimensional ideal example.
The existing substitution models for replacing the SEAR repair process of the DNAPL polluted source region include an artificial neural network (artificial neural network), distributed cluster analysis (stepwise cluster analysis), a polynomial response surface (polynomial response surface), chaotic polynomial expansion (polynomial cross expansion), radial basis function (radial basis function), Kriging (Kriging), support vector regression (support vector regression), Gaussian process (Gaussian process), and the like.
The substitute model adopted in the groundwater remediation optimization is as follows: 1. the method has the advantages that the dimension disaster can not realize the substitution of the SEAR repair process in the heterogeneous aquifer when the uncertainty of the polluted site description is considered; 2. the spatial distribution of the global variable DNAPL saturation after repair cannot be replaced, so that the repair effect cannot be comprehensively evaluated.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides a multi-objective optimization method for repairing a DNAPL (deoxyribonucleic acid PL) polluted site under an uncertain condition, and the optimal repair scheme for repairing the DNAPL by using SEAR (laser induced fluorescence spectroscopy) in the polluted site which is not precisely depicted is efficiently obtained.
The technical scheme is as follows: the invention relates to a multi-objective optimization method for repairing a DNAPL (deoxyribonucleic acid-Polypropylene) polluted site under an uncertain condition, which specifically comprises the following steps of:
(1) establishing a multi-objective optimization model under an uncertain condition: setting a decision variable as the flow of the SEAR treatment well; the optimization objective is to minimize the total cost f of SEAR repairs1And minimizing the extent of distribution of NAPL phases after remediation
Figure BDA00034641949400000310
The constraint condition is the flow limit of the treatment well; the uncertain condition is a plurality of realizations of distribution of underground media and pollution source regions meeting sparse observation data;
(2) constructing a deep convolutional neural network model to replace a time-consuming multiphase flow numerical model, and realizing high-dimensional replacement of the numerical model of the SEAR repaired DNAPL;
(3) and calling the trained substitution model by adopting an optimization algorithm to solve the optimization model under the uncertain condition, so as to obtain the optimal repair scheme under the uncertain condition.
Further, the step (1) is realized by the following formula:
Figure BDA0003464194940000031
wherein, C1(m + n) represents installation costs (dollars) for m injection wells and n extraction wells; c2Representing the operating costs of the extraction well (yuan/m)3) (ii) a t represents the repair time;
Figure BDA0003464194940000032
representing the flow rate of the jth pumping well; c3Representing operating costs of injection wells (dollars/m)3)；
Figure BDA0003464194940000033
Representing the flow rate of the ith injection well;
Figure BDA0003464194940000034
wherein,
Figure BDA0003464194940000035
and
Figure BDA0003464194940000036
each represents NrThe distribution range f of the repaired NAPL phase obtained by the calculation2Mean and variance of; λ represents the risk aversion coefficient, with λ taking 2 meaning a confidence interval of 97.5%, i.e. 97.5%
Figure BDA00034641949400000311
Representing the residual DNAPL saturation of the ith grid; m (-) is an indication function for indicating whether a trellis has NAPL phases; n is the total number of grids;
constraint conditions are as follows:
Figure BDA0003464194940000039
wherein Q ismaxAnd QminIs a saturation threshold, and is an injection well (In)) And the maximum and minimum values allowed for the extraction well (Ex).
Further, the step (2) is realized as follows:
converting an input field and an output field of the numerical model into three-dimensional pictures, and fully extracting the local spatial correlation of picture data by utilizing convolution operation so as to learn the potential mapping relation between input pictures and output pictures; the mode of converting the SEAR repair well flow combination into the picture is as follows:
Figure BDA0003464194940000041
wherein ω is 1, …, W; h1, …, H; d is 1, …, D; j is 1, … N, N represents the well number; srj>0 represents an injection well; srj<0 represents the extraction well. That is, the pixel value at the well position is the extraction/injection rate, and the pixel values at other positions without a well are 0;
extracting a feature plane from an input image by using a convolution layer, then processing the extracted feature plane by a multi-residual error dense block and a down-sampling layer alternately, reducing the size of the feature plane by half every time of passing through the down-sampling layer, finally outputting a series of feature planes containing high-level features, then processing the feature planes alternately by an RRDB and an up-sampling layer, doubling the size of the feature plane every time of passing through the up-sampling layer, and finally reconstructing an output image by a convolution layer and activation of an activation function Sigmoid.
Further, the step (3) is realized as follows:
and continuously searching new decision variable combinations by the optimization algorithm, and evaluating the decision variable combinations in the generated realization set of the underground medium and the pollution source area by calling the trained substitution model to finally obtain the optimal repair scheme under the uncertain condition.
Further, an input field of the numerical model is a combination of the heterogeneous permeability coefficient field, the DNAPL saturation field and the SEAR restoration well flow rate, and an output field of the numerical model is the restored DNAPL saturation field.
Has the advantages that: compared with the prior art, the invention has the beneficial effects that: the invention provides a multi-objective optimization method for coupling a deep Convolutional Neural Network (CNN) and a multi-objective optimization algorithm NSGA-II under an uncertain condition; under the condition that uncertainty exists in the depiction of a heterogeneous underground aquifer and a DNAPL polluted source region of an actual polluted site, the optimal repair scheme for repairing the DNAPL by the SEAR in the polluted site is efficiently obtained; the invention adopts CNN to replace a numerical model, overcomes dimension cursing, realizes high-efficiency prediction of global output variables under high-dimensional input, and greatly reduces the calculation burden of optimization problems under uncertain conditions.
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FIG. 1 is a schematic diagram of a deep convolutional network structure;
FIG. 2 is a schematic view of a hydrogeological conceptual model of a research area;
FIG. 3 is a reference field for permeability (ln k) and DNAPL saturation (S)N0) Reference field and ln k field and SN0Two implementation diagrams for field random selection;
FIG. 4 is a schematic diagram of the SSIM size obtained by evaluation of the CNN in the training and testing data set;
FIG. 5 is a numerical model UTCHEM (S) in three random implementationsN) And a substitution model
Figure BDA0003464194940000051
A comparison plot of predicted residual DNAPL saturation distributions after sea repair;
FIG. 6 is a pareto optimal solution obtained by the CNN substitution simulation-optimization method
Figure BDA0003464194940000052
And (f) in all implementations1，f2) The figure is solved;
FIG. 7 is a target DNAPL distribution area f predicted by surrogate model CNN and numerical model UTCHEM2A comparative graph of (a).
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides a multi-objective optimization method for repairing a DNAPL (deoxyribonucleic acid-Polypropylene) polluted site under an uncertain condition, which comprises the following steps of firstly, establishing a multi-objective optimization model under the uncertain condition; secondly, training a substitution model to realize substitution of the numerical model of the SEAR repaired DNAPL; and finally, directly calling the substitution model through a multi-objective optimization algorithm to realize a substitution simulation-optimization framework. The method specifically comprises the following steps:
setting decision variables as flow rates of SEAR governing wells (an injection well and an extraction well) aiming at the optimization problem of SEAR repairing DNAPL; optimization objectives are 1) minimizing the total cost f of SEAR repairs1(cost of deployment and operation of remedial wells) and 2) minimizing the extent of distribution of NAPL phases after remediation
Figure BDA0003464194940000053
The constraint is the flow limit of the remedial well. Considering that the carved polluted site has uncertainty, the underground medium and the polluted source region which meet the sparse observation data have a plurality of realizations, therefore, the optimization is carried out under the uncertain condition, the strategy similar to uncertainty analysis is adopted, all realizations are comprehensively considered, and the optimization target under the uncertain condition is defined
Figure BDA0003464194940000054
The established multi-objective optimization model under the uncertain condition is as follows:
objective function 1:
Figure BDA0003464194940000055
wherein, C1(m + n) represents installation costs (dollars) for m injection wells and n extraction wells; c2Representing the operating costs of the extraction well (yuan/m)3) (ii) a t represents the repair time;
Figure BDA0003464194940000056
representing the flow rate of the jth pumping well; c3Representing operating costs of injection wells (dollars/m)3)；
Figure BDA0003464194940000057
Representing the flow rate of the ith injection well.
The objective function 2:
Figure BDA0003464194940000061
wherein,
Figure BDA0003464194940000062
and
Figure BDA0003464194940000063
each represents NrImplementing the calculated f2Mean and variance of; λ represents the risk aversion coefficient, with λ taking 2 meaning a confidence interval of 97.5%, i.e. 97.5%
Figure BDA0003464194940000064
Representing the residual DNAPL saturation of the ith grid; m (-) is an indication function for indicating whether a trellis has NAPL phases; n is the total number of grids.
Constraint conditions are as follows:
Figure BDA0003464194940000066
wherein Q ismaxAnd QminIs a threshold for saturation, which is the maximum and minimum values allowed for the injection (In) and extraction (Ex) wells, respectively.
The above dual target optimization problem is solved using a common Non-dominant ordering Genetic Algorithm (Non-dominant sequencing Algorithm-II, NSGA-II) (Deb et al, 2002). The NSGA-II algorithm provides a set of solutions called the pareto optimal set, which represents trade-off solutions between conflicting objectives.
In order to realize the multi-phase flow numerical model of the SEAR repairing DNAPL called in the substitution optimization model, firstly, the multi-phase flow numerical model is operated to generate a training sample, the input variable of the training sample is the heterogeneous permeability coefficient field, the DNAPL saturation field and the SEAR repairing well flow combination, and the output variable is the repaired DNAPL saturation field. The surrogate model is then trained using the training samples.
And calling the trained substitution model by adopting an optimization algorithm to solve the optimization model under the uncertain condition. Specifically, the optimization algorithm continuously searches for new decision variable combinations, and evaluates the decision variable combinations in the generated realization set of the underground medium and the pollution source area by calling a trained substitution model, so as to finally obtain the optimal restoration scheme under the uncertain condition.
A university of texas chemical composition simulator (UTCHEM) was used to simulate the multiphase flow migration process of sea governing DNAPL contaminated source zones for generating training samples for surrogate models. UTCHEM is a three-dimensional multiphase flow simulator that can simulate multi-component contaminant transport, complex geochemical reactions, and organic matter dissolution.
The deep convolutional neural network CNN is one of deep neural networks, and is suitable for processing image data. Therefore, when a multiphase flow numerical model in the course of repairing the DNAPL by replacing the sea needs to be converted into a three-dimensional picture (i.e., a pixel matrix with a size of D × H × W) by an input field (heterogeneous permeability coefficient field, DNAPL saturation field, sea repair well flow rate combination) and an output field (repaired DNAPL saturation field) of the numerical model, and the local spatial correlation of picture data is fully extracted by using convolution operation, so as to learn a potential mapping relationship between input and output pictures. The mode of converting the SEAR repair well flow combination into the picture is as follows:
Figure BDA0003464194940000071
wherein ω is 1, …, W; h1, …, H; d is 1, …, D; j is 1, … N, N represents the well number; srj>0 represents an injection well; srj<0 represents the extraction well. That is, the pixel value at the well position is the extraction/injection rate, and the pixel value at the other positions without a well is 0.
The deep convolutional neural network CNN performs coarsening to refinement (coarse-to-fine) processing on the high-dimensional input picture. In the process, the size of the feature plane extracted in the network is reduced and then recovered, so that the multi-scale and hierarchical features implicit in the data are fully extracted, and the input-output mapping relation of the system is efficiently learned. The basic network architecture for implementing this process is shown in fig. 1. Firstly, a convolutional layer (Conv) (Goodfellow, 2016) is used to extract the feature plane from the input image, then the extracted feature plane is processed alternately by a multi-residual dense block (RRDB) (Wang et al, 2018) and a down-sampling layer (v), the feature plane size is halved after each down-sampling layer, finally, a series of feature planes containing high-level features are output, the feature planes are processed alternately by the RRDB and the up-sampling layer (delta), the feature plane size is doubled after each up-sampling layer, and finally, the output image is reconstructed after a convolutional layer and activation function Sigmoid activation. The middle part of the network takes 2 consecutive RRDBs and applies an extra residual learning (sum of output and input) to facilitate the conduction of this part (when the feature plane size is minimal) of the information flow.
Generating underground medium permeability k field and pollution source region NAPL phase saturation S meeting observation dataN0And the field realization sets are respectively used for generating training samples and solving the optimization model. The absolute permeability k field adopts conditional sequential Gaussian simulation (conditional SGSIM) in a geological statistics software library (GSLIB), and a priori k value obtained by drilling is taken as a condition input to generate permeability which accords with priori information to realize the permeability. Simulating DNAPL leakage by using a random invasion infiltration (SIP) algorithm in an aquifer corresponding to permeability realization to obtain steady-state initial NAPL phase saturation (S)N0) And (4) distribution. Then a priori S obtained from the boreholeN0And (4) screening DNAPL saturation implementation meeting the prior information from the initial DNAPL saturation implementation by using a Rejection Sampling (RS) algorithm.
The feasibility of the deep convolutional neural network to replace a simulation-optimization method is demonstrated through numerical experiments. The calculation example is a 3-dimensional heterogeneous confined aquifer 45m multiplied by 25m multiplied by 10 m; as shown in fig. 2, the cylinder represents a hypothetical borehole, and observations of permeability and DNAPL saturation were obtained; the drill holes with up/down arrows are respectively pumping/water injection wells; the grayscale map and the iso-volume represent the permeability and NAPL phase distribution, respectively. The aqueous layer was uniformly dispersed into 45 × 25 × 10 ═ 11250 unit cells. The left and right boundaries of the aquifer are set as constant water head boundaries, the hydraulic gradient is 0.001, and the rest boundaries are zero flux boundaries. The parameters are set up in table 1.
Table 1 parameter settings in numerical experiments
Figure BDA0003464194940000081
Figure BDA0003464194940000091
The permeability k-field implementation is generated by conditional sequential gaussian simulation (conditional SGSIM) in a Geostatistical Software Library (GSLIB), the parameters are detailed in table 1, and it is assumed that sampling results in a total of 150 prior k values as conditional inputs. In each aquifer where permeability is achieved, Trichloroethylene (TCE) leaks out at the top center of the aquifer in a point source manner, and a random invasion infiltration (SIP) algorithm is adopted to generate initial DNAPL saturation (S)N0) Then a total of 150 priors S based on hypothetical samplesN0Value, using a reject sampling algorithm to screen out DNAPL saturations that meet the prior information, as shown in FIG. 3, where FIG. 3 is the first column of permeability (ln k) reference field and DNAPL saturations (S)N0) With reference to the reference field, the right two columns show the ln k fields and SN0Two implementations of field random selection, both fields generated as a priori information from permeability and saturation observations obtained from 15 observation wells (vertical cylinders).
The SEAR remediation is provided with m-6 injection wells and n-3 extraction wells, as shown in FIG. 2, the remediation time is set to 30 days, and the installation cost coefficient C of the wells is1Set as 5000 yuan, the running cost coefficient C of the extraction well2Set to 0.5 yuan/m3Injection well operating cost factor C3Set to 201.5 yuan/m3The flow ranges of the injection well and the extraction well are respectively set
Figure BDA0003464194940000092
And
Figure BDA0003464194940000093
Figure BDA0003464194940000094
determining the number of realizations N for uncertain optimization by convergence analysisrIs 500.
What the surrogate model needs to replace is the objective function f in the optimization problem2I.e. from the input variables (permeability k-field, DNAPL saturation field SN0SEAR well flow S) to output variable (repaired DNAPL saturation field S)N) Alternative(s) to (3). We chose to generate 5000 training samples to train the CNN. The main hyper-parameters of the network training are set as follows: the initial learning rate (learning rate) was 0.005 and the batch size (batch size) was 24. 200 epochs are trained on the NVIDIATesla V100 GPU to obtain a trained model. The training accuracy is characterized by the Structural Similarity Index (SSIM) (Wang et al, 2004). SSIM is an index for quantifying structural similarity between two 2-D pictures, and when the SSIM of a 3-D picture with the size of D multiplied by H multiplied by W is calculated, a three-dimensional picture needs to be converted into D pieces of H multiplied by W2-D pictures. Closer to 1.0 SSIM indicates better training.
And the optimization algorithm NSGA-II calls the trained CNN model to solve the optimization model. The main parameters of the optimization algorithm are set as follows: the population number is 100, the optimized generation number is 100, the mutation probability is 0.11, and the cross probability is 0.70.
Fig. 4 shows the substitution accuracy of the CNN substituted three-dimensional multiphase flow migration model. It can be seen that the median of the substitution accuracy index SSIM of the CNN substitution model on 5000 training samples is 0.995, and the median of the SSIM obtained on 1000 test samples is 0.991, which indicates that the CNN can accurately predict the spatial distribution of DNAPL saturation after sea repair.
FIG. 5 further illustrates that CNN can predict DNAPL saturation S after repair more accuratelyNA field. The graphs compare the S of three random realizations of the UTCHEM simulation in the test setNField, CNN prediction
Figure BDA0003464194940000105
The field and the difference between the two. It can be seen that although the saturation field is spatially complex and discontinuous, the prediction of CNN is very close to UTCHEM and the prediction error is in most regionsAre all less than 0.05. Therefore, when the optimization model is solved next, the optimization algorithm is used to directly call the substitute model CNN with more accurate prediction but faster prediction to substitute the time-consuming multiphase flow numerical model.
And analyzing and optimizing to obtain the optimal repair scheme of the last generation. FIG. 6 is a pareto optimal solution obtained by the CNN substitution simulation-optimization method
Figure BDA0003464194940000101
(circles) and (f) on all realizations1，f2) Solution (Block), showing results obtained when 500 implementations are considered
Figure BDA0003464194940000102
And solving the objective function
Figure BDA0003464194940000103
Figure BDA0003464194940000103
500 implemented objective functions f of a time-wise computation2The value is obtained. It can be seen that the pareto frontier is non-linear and presents a tendency for the higher the cost of repair, the less NAPL after repair, which is consistent with the practical situation. Thus, the uncertainty optimization method can obtain pareto optimal solutions for the correct trends.
To illustrate that the pareto solution obtained by the optimization algorithm based on CNN is reliable, the CNN is used for replacing the objective function f predicted by the model2The values were compared to the simulation results for UTCHEM. As shown in FIG. 7, f from CNN and UTCHEM2The scatter of the values is substantially distributed on the 1:1 diagonal, which means that the predicted value of the surrogate model CNN is very consistent with the simulation result of the UTCHEM numerical model; the absolute error of the two is mainly (-40 m)2，20m2) Relative to the total area of the grid (11250 m)2) Is very small. Therefore, the optimization algorithm NSGA-II can obtain a reliable pareto optimal leading edge by calling the surrogate model CNN.
The fundamental goal of using surrogate models to solve the optimization problem is to reduce the computational burden, as shown in table 2.
TABLE 2 comparison of computational efficiencies
Figure BDA0003464194940000104
In this optimization problem under uncertain conditions, instead of using the surrogate model (UTCHEM-NSGAII), it takes at least 4000000 numerical simulations to reach convergence and obtain the optimal solution, i.e. 100 populations, considering 500 realizations, and iterate through the NSGA-II algorithm for at least 80 generations. The single simulation took on average about 12 minutes and the total run time was about 800000 hours. With the surrogate model (CNN-NSGAII), the 4000000 numerical model called in the surrogate optimization process only took about 129.5 hours. Previously, it took 1240 hours to perform 6000 numerical simulations, to generate 6000 training samples, and 5.5 hours to train the surrogate model. Overall, the cost of CNN-NSGAII is only 1375 hours, which is a 99.8% time savings over the 800000 hours cost of UTCHEM-NSGAII.

Claims (5)

1. A multi-objective optimization method for DNAPL contaminated site remediation under uncertain conditions is characterized by comprising the following steps:
(1) establishing a multi-objective optimization model under an uncertain condition: setting a decision variable as the flow of the SEAR treatment well; the optimization objective is to minimize the total cost f of SEAR repairs1And minimizing the extent of distribution of NAPL phases after remediation
Figure FDA00034641949300000110
The constraint condition is the flow limit of the treatment well; the uncertain condition is multiple realizations of heterogeneous distribution of aquifer media and DNAPL (deoxyribonucleic acid PL) polluted source regions meeting sparse observation data;
(2) constructing a deep convolutional neural network model to replace a time-consuming multiphase flow numerical model, and realizing high-dimensional replacement of the numerical model of the SEAR repaired DNAPL;
(3) and calling the trained substitution model by adopting an optimization algorithm to solve the optimization model under the uncertain condition, so as to obtain the optimal repair scheme under the uncertain condition.
2. The multi-objective optimization method for repairing a DNAPL contaminated site under the uncertain conditions as claimed in claim 1, wherein the step (1) is realized by the following formula:
Figure FDA0003464194930000011
wherein, C1(m + n) represents installation costs (dollars) for m injection wells and n extraction wells; c2Representing the operating costs of the extraction well (yuan/m)3) (ii) a t represents the repair time;
Figure FDA0003464194930000012
representing the flow rate of the jth pumping well; c3Representing operating costs of injection wells (dollars/m)3)；
Figure FDA0003464194930000013
Representing the flow rate of the ith injection well;
Figure FDA0003464194930000014
wherein,
Figure FDA0003464194930000015
and
Figure FDA0003464194930000016
each represents NrThe distribution range f of the repaired NAPL phase obtained by the calculation2Mean and variance of; λ represents the risk aversion coefficient, with λ taking 2 meaning a confidence interval of 97.5%, i.e. 97.5%
Figure FDA0003464194930000017
Figure FDA0003464194930000018
Representing the residue of the ith trellisDNAPL saturation; m (-) is an indication function for indicating whether a trellis has NAPL phases; n is the total number of grids;
constraint conditions are as follows:
Figure FDA0003464194930000019
wherein Q ismaxAnd QminIs a threshold for saturation, which is the maximum and minimum values allowed for the injection (In) and extraction (Ex) wells, respectively.
3. The multi-objective optimization method for repairing a DNAPL contaminated site under the uncertain conditions as claimed in claim 1, wherein the step (2) is implemented as follows:
converting an input field and an output field of the numerical model into three-dimensional pictures, and fully extracting the local spatial correlation of picture data by utilizing convolution operation so as to learn a potential complex mapping relation between input and output pictures; the mode of converting the SEAR repair well flow combination into the picture is as follows:
Figure FDA0003464194930000021
wherein ω is 1, …, W; h1, …, H; d is 1, …, D; j is 1, … N, N represents the well number; srj>0 represents an injection well; srj<0 represents the extraction well. That is, the pixel value at the well position is the extraction/injection rate, and the pixel values at other positions without a well are 0;
extracting a feature plane from an input image by using a convolution layer, then processing the extracted feature plane by a multi-residual error dense block and a down-sampling layer alternately, reducing the size of the feature plane by half every time of passing through the down-sampling layer, finally outputting a series of feature planes containing high-level features, then processing the feature planes alternately by an RRDB and an up-sampling layer, doubling the size of the feature plane every time of passing through the up-sampling layer, and finally reconstructing an output image by a convolution layer and activation of an activation function Sigmoid.
4. The multi-objective optimization method for repairing a DNAPL contaminated site under the uncertain conditions as claimed in claim 1, wherein the step (3) is implemented as follows:
and continuously searching new decision variable combinations by the optimization algorithm, and evaluating the decision variable combinations in the generated realization set of the underground medium and the pollution source area by calling the trained substitution model to finally obtain the optimal repair scheme under the uncertain condition.
5. The multi-objective optimization method for DNAPL contaminated site remediation under the uncertain conditions of claim 3, wherein the input field of the numerical model is a combination of a strong heterogeneous permeability coefficient field, a DNAPL saturation field, and a SEAR remediation well flow rate; the output is the repaired DNAPL saturation field.
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