Large-scale sea water pollution traceability monitoring station optimization layout method coupling efficient optimization and fine simulation
By constructing a three-dimensional hydrodynamic-water quality coupling model and a radial basis function surrogate model, and combining Sobol sensitivity analysis and Latin hypercube experimental design, the layout of large-scale marine water pollution source tracing monitoring stations was optimized, solving the problem of insufficient accuracy in monitoring station layout and achieving efficient and accurate water pollution source tracing.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- DALIAN MARITIME UNIVERSITY
- Filing Date
- 2025-12-30
- Publication Date
- 2026-05-08
AI Technical Summary
In large-scale marine water pollution source tracing, existing technologies lack precision in the deployment of monitoring stations, leading to strong subjectivity and high degree of blindness in the tracing process, making it difficult to meet the needs of accurate source tracing. Furthermore, existing methods are computationally expensive and inefficient.
A three-dimensional hydrodynamic-water quality coupled model was constructed using numerical simulation software. Key decision variables were determined through Sobol sensitivity analysis. By combining radial basis function surrogate model and Latin hypercube experimental design, the layout of monitoring stations was optimized to achieve efficient water pollution source tracing.
It significantly improved the optimization efficiency and accuracy of monitoring station deployment, reduced computational consumption, and achieved efficient and precise monitoring station deployment, meeting the accuracy requirements for tracing water pollution sources in large-scale marine areas.
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Figure CN121997807A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of water pollution source identification technology, and in particular to a method for optimizing the deployment of large-scale marine water pollution source tracing monitoring stations that couples efficient optimization and fine simulation. Background Technology
[0002] In recent years, with the continuous development of the economy and people's living standards, water pollution incidents have occurred frequently, including transportation accidents, sewage pipe bursts, illegal sewage treatment plant discharges, terrorist attacks, and extreme natural disasters (such as earthquakes). These incidents have caused serious damage to the environment, economy, and sustainable social development. Therefore, how to quickly and accurately identify water pollution sources based on existing technologies to reduce their negative impacts has become an urgent problem to be solved. Pollution source identification is generally regarded as an ill-posed inverse problem, involving complex physical, chemical, and biological reactions and closely related to hydrodynamic conditions. This problem has been studied in various water systems, such as canal irrigation systems, groundwater systems, water supply networks, and water systems. To solve this problem, various methods have been proposed, including classical regularization methods, optimization algorithms, and Bayesian inference methods.
[0003] In early research, the Tikhonov regularization method, as one of the classic regularization methods, was widely used. However, due to its reliance on simple physical models, it was difficult to address the problem of pollution source identification in complex water systems. With the development of computer technology, optimization algorithms (such as genetic algorithms, heuristic harmony search algorithms, and particle swarm optimization) combined with water quality simulation models have been used for pollution source identification, mainly by adjusting decision variables to reduce the error between simulated and observed values. However, these methods are computationally expensive and require a large number of simulations. Bayesian inference methods can provide the distribution range of pollution sources, but they also face the problem of low computational efficiency. To reduce computational costs, surrogate models (such as multinomial regression and kriging) have been introduced, but they are prone to getting trapped in local optima in high-dimensional nonlinear problems and lack dynamic exploration capabilities. In addition, although parallelization techniques can shorten computation time, existing research rarely combines them with surrogate-optimization methods for pollution source identification.
[0004] Although progress has been made in large-scale marine water pollution source tracing technology, its identification accuracy heavily depends on the number and spatial distribution of monitoring stations. Precise source tracing requires optimized monitoring deployment. Traditional monitoring deployments are often based on expert experience, historical data statistics, or simple spatial uniformity principles, failing to deeply couple "source tracing" with "deployment." This results in strong subjectivity and high degree of blindness, making it difficult to meet the needs of precise source tracing. Therefore, an innovative technical solution is urgently needed to closely integrate refined water environment-hydrodynamic models, efficient optimization algorithms, and optimized monitoring station deployment to construct a closed-loop, adaptive large-scale marine water quality monitoring and management system. Summary of the Invention
[0005] In view of this, the present invention provides a method for optimizing the deployment of large-scale marine water pollution source tracing monitoring stations by coupling efficient optimization and fine simulation. By approximating the water pollution transport model through a radial basis function surrogate model, the Latin hypercube experimental design is applied to the pollution source identification problem to achieve efficient water pollution source tracing. Furthermore, the optimization scheme of monitoring stations is optimized by comprehensively considering cost and monitoring accuracy.
[0006] Therefore, the present invention provides the following technical solution: A method for optimizing the deployment of large-scale marine water pollution source tracing monitoring stations by coupling efficient optimization and refined simulation includes: A three-dimensional hydrodynamic-water quality coupled model was constructed using numerical simulation software; The key decision variables of the three-dimensional hydrodynamic-water quality coupling model were determined through Sobol sensitivity analysis. Initialize the radial basis function surrogate model; The time-series concentrations of pollutants are obtained by iteratively solving the radial basis function surrogate model. Based on the time-series concentrations of the pollutants, a monitoring station deployment scheme is obtained with the goal of maximizing source tracing accuracy and minimizing deployment costs.
[0007] Furthermore, the three-dimensional hydrodynamic-water quality coupling model includes:
[0008] In the formula, Q represents the source or sink flow per unit area; , These are transformation coefficients between orthogonal curvilinear coordinate systems and Cartesian coordinate systems. They typically appear in curvilinear coordinate systems and are used to correct for the effects of coordinate changes. U represents the horizontal coordinate in the curvilinear coordinate system; The velocity component, V is η velocity components; This indicates the change in water level relative to a reference water level, i.e., the free water surface elevation. Indicates the still water depth relative to a reference water level; Momentum equation: level Direction:
[0009] level Direction:
[0010] In the formula, The hydrostatic pressure gradient in the direction of , In order to be in hydrostatic pressure gradient in the direction; express The imbalance of Reynolds stress in the direction of the Reynolds stress. express The imbalance of Reynolds stress in the direction; The vertical eddy viscosity coefficient; The density of the water body; and This represents the momentum change caused by external factors, including the momentum effects of drainage, receding water, wind stress, and bottom shear stress; f is the Coriolis force coefficient, used to describe the Coriolis force caused by the Earth's rotation; u, v, Represented respectively in orthogonal curvilinear coordinate systems , , The velocity changes in three directions; t represents time; It is defined in motion The vertical velocity in space, The following continuity equation is obtained in the coordinate system:
[0011] in, For inflow items, This is an outflow term.
[0012] Furthermore, the key decision variables for determining the three-dimensional hydrodynamic-water quality coupling model through Sobol sensitivity analysis include: Source tracing decision variables include: the location of the pollution source and the time-series emission concentration of each pollutant; Calculate the sensitivity index of each traceability decision variable, and the traceability decision variable with a sensitivity index greater than a preset threshold is designated as the key decision variable.
[0013] Furthermore, the initialization of the radial basis function surrogate model includes: A set of initial sample points is generated in the parameter space based on Latin hypercube experimental design. The objective function values of the initial sample points were calculated using a three-dimensional hydrodynamic-water quality coupling model. An initial radial basis function surrogate model is constructed based on the objective function values of the initial sample points.
[0014] Furthermore, the objective function includes:
[0015] in, , These are the weight vector and the polynomial coefficients, respectively. Let be a linear polynomial with d variables.
[0016] Furthermore, the radial basis function surrogate model is iteratively solved to achieve water pollution source tracing, including: Candidate points are generated on the radial basis function surrogate model using an optimization algorithm; Predict the objective function value of candidate points using a radial basis function surrogate model; Calculate the minimum Euclidean distance between the candidate point and all evaluated points; The minimum Euclidean distance and the objective function value are weighted and summed to obtain the comprehensive score of the candidate points; Candidate points whose comprehensive score is greater than a preset threshold are used as evaluation points for the next round of iteration of the radial basis function surrogate model; The optimal solution is output once the maximum number of evaluations or the convergence condition is reached.
[0017] Furthermore, based on the time-series concentrations of the pollutants, a monitoring station deployment scheme is obtained with the goal of maximizing source tracing accuracy and minimizing deployment costs, including: Generate several monitoring point deployment plans based on existing monitoring points in the target sea area; A comprehensive evaluation index is constructed based on traceability accuracy and deployment cost. Calculate the total evaluation index for each scheme, and the scheme with the highest total evaluation index is the final monitoring station deployment scheme.
[0018] Furthermore, the deployment of the monitoring stations satisfies physical constraints, including: The water depth in the area where the monitoring point is located is greater than the minimum operating depth; The monitoring point is located in an area outside the sovereign waterway; The monitoring point is located in an area with poor power and communication infrastructure.
[0019] Furthermore, the deployment cost: The product of the number of monitoring stations and the cost of a single monitoring station; The accuracy of the source tracing is:
[0020] in, This is the sum of the absolute errors between the time-series pollutant concentration values output by the model and the actual observed values. This represents the standard deviation between the actual observed values.
[0021] Furthermore, based on the time-series concentrations of the pollutants, a monitoring station deployment scheme is obtained with the goal of maximizing source tracing accuracy and minimizing deployment costs, including: Calculate the traceability accuracy index:
[0022] Calculate the economic cost index:
[0023]
[0024] The decision variable M can be represented as: M=Mj= (1) j ) Deployable within the region The total number; Normalize the traceability accuracy indicators and economic cost indicators:
[0025]
[0026] in, This represents the minimum value for the traceability accuracy index. This represents the maximum value of the traceability accuracy index. To maximize the economic cost, This represents the minimum economic cost. The normalized results are weighted and fused to form the overall evaluation index:
[0027] in, , These are the weighting coefficients.
[0028] Advantages and positive effects of the present invention: This method uses Sobol sensitivity analysis to efficiently screen out highly sensitive decision variables, reducing the identification dimensionality and thus significantly improving the optimization efficiency and accuracy of complex aquatic environment models.
[0029] This method, through Latin hypercube experimental design, can more efficiently cover the entire space of sensitive decision variables.
[0030] This method simplifies the three-dimensional hydrodynamic-water quality coupling model by using a radial basis function surrogate model, resulting in lower computational cost and effective optimization of high-dimensional problems.
[0031] This method obtains the time-series concentration of pollutants through a radial basis function surrogate model and combines it with actual detection values to determine the source tracing accuracy. The goal is to obtain a monitoring station deployment scheme with the aim of maximizing source tracing accuracy and minimizing deployment costs. Attached Figure Description
[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0033] Figure 1 This is a schematic diagram of the structure of a three-dimensional hydrodynamic-water quality coupling model.
[0034] Figure 2 This is a schematic diagram of a framework for rapid identification of water pollutants that couples the PODS high-performance optimization algorithm with a high-precision hydrodynamic-water pollutant propagation model.
[0035] Figure 3 This is a schematic diagram of the Delft3d water quality-hydrodynamic model of the monitoring area.
[0036] Figure 4 This is a comparison chart of the correction progress of our method and traditional methods.
[0037] Figure 5 This is a comparison chart of the simulated concentrations of the optimal solution for tracing the source of water pollution in a large-scale marine area at different monitoring stations.
[0038] Figure 6 This is an example of the deployment of a combination of monitoring stations in the case of three known pollution sources.
[0039] Figure 7 This is the flowchart of this method. Detailed Implementation
[0040] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.
[0041] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.
[0042] This invention provides a method for optimizing the deployment of large-scale marine water pollution source tracing monitoring stations that couples efficient optimization with refined simulation, including: S1. A three-dimensional hydrodynamic-water quality coupled model was constructed using numerical simulation software; S2. Key decision variables for the three-dimensional hydrodynamic-water quality coupling model were determined through Sobol sensitivity analysis. S3. Generate initial parameter sample points based on Latin hypercube experimental design, run the water pollution transport model in parallel, and obtain initial simulation data; S4. Construct a radial basis function surrogate model based on the initial sample set to approximate the error objective function; S5. A dynamic coordinate search strategy is adopted, and candidate points are generated by combining a truncated normal distribution, and the number of coordinates to be disturbed is dynamically adjusted. S6. Select multiple evaluation points based on the agent-distance metric, allocate them to multi-processor parallel computing, and update the agent model; S7. Repeat S4-S6 until the maximum number of evaluations or the convergence condition is reached, and output the optimal solution.
[0043] Combination Figure 2 and Figure 7 As shown, a method for optimizing the deployment of large-scale marine water pollution source tracing monitoring stations by coupling efficient optimization and fine simulation includes the following steps: S1. A three-dimensional hydrodynamic-water quality coupled model was constructed using numerical simulation software. Figure 1 As shown: The edges of the area to be detected were obtained using satellite maps and ArcGIS software, and vector boundary files were generated by manually drawing lines. Orthogonal rectangular grids were used for grid division, and a three-dimensional hydrodynamic-water quality model was constructed using Delft3D, combined with DEM data, hydrogeological parameters, and pollution source survey data. The key decision variables of the model were then calibrated.
[0044] The specific governing equations of the three-dimensional hydrodynamic-water quality model include: 1) Continuity equation:
[0045] In the formula, Represents the source or sink flow per unit area; , These are the transformation coefficients between orthogonal curvilinear coordinate systems and Cartesian coordinate systems. They typically appear in curvilinear coordinate systems and are used to correct for the effects of coordinate transformations; U and V are respectively... And the velocity components of η.
[0046] 2) Momentum equation: level Direction:
[0047] level Direction:
[0048] In the formula, The hydrostatic pressure gradient in the direction of , In order to be in The hydrostatic pressure gradient in the direction of the direction; express The imbalance of Reynolds stress in the direction of the Reynolds stress. express The imbalance of Reynolds stress in the direction; The vertical eddy viscosity coefficient; Density of water; and This represents the momentum change caused by external factors, including the momentum effects of drainage, receding water, wind stress, and bottom shear stress; f is the Coriolis force coefficient, used to describe the Coriolis force caused by the Earth's rotation; u, v, Represented respectively in orthogonal curvilinear coordinate systems , , The velocity changes in three directions; t represents time; It is defined in motion The vertical velocity in space, The following continuity equation is obtained in the coordinate system:
[0049] in, For inflow items, This is an outflow term.
[0050] Based on historical monitoring data of pollutants in the area to be studied, the parameters of the three-dimensional hydrodynamic-water quality model of the area to be studied were calibrated, including the diffusion coefficient and degradation rate. The topographic data of the area to be studied were also corrected in combination with the actual situation.
[0051] The simulation model includes six sub-models: hydrological model, emission model, 1D hydrodynamic model, 1D transport model, 3D hydrodynamic model and 3D water quality model. However, in the pollutant identification problem, the changes in substances have no effect on the hydrodynamic changes of the system. Therefore, it is only necessary to simulate the 1D or 3D hydrodynamic model to generate the hydrodynamic conditions for the water quality model.
[0052] S2. Based on the sensitivity of the source-tracing decision variables, determine the key decision variables of the three-dimensional hydrodynamic-water quality coupling model through Sobol sensitivity analysis: 1) Source tracing decision variables include: pollution source location and time-series emission concentration of each pollutant.
[0053] 2) Sobol sensitivity analysis determines sensitivity indices by quantifying the first-order and higher-order effects of source decision variables on the output outcome: The first-order effect is the sum of the absolute deviations between the observed and simulated values, and the formula is:
[0054] Higher-order effects are the interactions between observed and simulated values, and the formula is:
[0055] in, , For tracing back to the source decision variables, The number of decision variables for tracing back to the source; For tracing decision variables The first-order sensitivity indicates the direct impact; For tracing decision variables The overall sensitivity represents the direct impact and interaction effects. The total variance of the output result Y; For only by The resulting variance; For the reason The variance caused by its interaction with other parameters. This is a sensitivity indicator.
[0056] 3) Source tracing decision variables whose sensitivity indicators exceed a preset threshold are considered key decision variables, expressed as follows: , This indicates the number of key traceability decision variables. < .
[0057] When selecting parameters, the first step is to list all possible source tracing decision variables according to the model requirements, such as pollution source location, pollutant concentration, and emission time, and define the reasonable range of values for each parameter. Then, use the SOBOL sequence to generate N. (2d+2) sample points (d is the parameter dimension), in fact N must satisfy N= (k) 10) or N=512 d. The generated sample points are input into the three-dimensional hydrodynamic-water quality model, and the output results corresponding to each parameter combination are calculated in parallel. Finally, the high-sensitivity parameters are screened based on the core formula of the SOBOL method.
[0058] S3. Initial parameter sample points are generated based on Latin hypercube experimental design, and the water pollution transport model is run in parallel to obtain initial simulation data.
[0059] Latin hypercube experimental design is used to generate sample points across multiple variables, ensuring that the distribution of each variable is uniformly covered while reducing correlation between samples. 1) Determine the key source-tracing decision variables and physical constraint range of the three-dimensional hydrodynamic-water quality coupling model.
[0060] 2) Sample selection based on key traceability decision variables: d key traceability decision variables, generate m sample points, m≥2d; the range of each key decision variable is divided into m equal probability intervals, and a value is randomly selected in each interval, and the sample points of each parameter dimension are evenly distributed and non-repeated through permutation and combination.
[0061] 3) Divide the m sample points into k processors, with each processor processing m / k samples. Simulate using a three-dimensional hydrodynamic-water quality coupling model, outputting time-series simulation results and corresponding evaluation indicators. Use the standardized relative average error (RSA), i.e., the sum of the absolute deviations between observed and simulated values, as the objective function to evaluate the error between the two. The formula is:
[0062] in, Vector of key decision variables That is, each sample contains d parameters that need to be optimized; for Next The monthly average of the simulated values of the s-th substance at each location; This represents the monthly average of the corresponding observations; s yes The standard deviation of can be used for normalization. index of position ; t is the month index, ;s is the pollutant index, .
[0063] S4. Construct a radial basis function surrogate model based on the initial sample set and the corresponding objective function set: A radial basis function surrogate model is used to approximate the relationship between key decision variables and evaluation indicators, replacing the three-dimensional hydrodynamic-water quality coupling model.
[0064] Constructing a radial basis function surrogate model includes: 1) Calculate the basis function values for all sample point pairs and construct N. N matrix , ; Represents sample points and The Euclidean distance between them.
[0065] 2) Proxy model expression:
[0066] in, , These are the weight vector and the polynomial coefficients, respectively. Let be a linear polynomial with d variables.
[0067] 3) Obtain by solving the following system of linear equations. and ,make .
[0068] =
[0069] The radial basis function surrogate model needs to generate new candidate points and select evaluation points to call the real model in each iteration of optimization. This is used to update and rebuild.
[0070] S5. Employ a dynamic coordinate search strategy, combined with a truncated normal distribution to generate candidate points, and dynamically adjust the number of coordinates to be disturbed: In the early stages of optimization, perturbation variables are used to explore the global solution space. When the solution set is improved to a certain extent, dynamic coordinate search is needed to dynamically reduce the number of perturbation variables and perform local fine-tuning search to avoid destroying the searched feasible and high-quality solutions.
[0071] 1) Coordinates of the subset of optimal solutions found so far with perturbation .
[0072] The number of coordinates is determined by the probability variable. To control this, its value decreases as the number of evaluations n increases, and the calculation formula is as follows:
[0073] in, , The total number of decision variables; , The initial number of points, This represents the maximum number of evaluations.
[0074] 2) Obtain a cut-off normal distribution (mean 0, standard deviation ) through random perturbation. Several candidate points are generated in the process, and it must be ensured that the candidate points are located within the feasible region.
[0075] 3) Based on the history of successful or failed iterations, dynamically adjust the perturbation radius. If there are consecutive successes (a better solution is found), increase the perturbation radius. To expand the search scope, and vice versa. But when If the value is too small or there is no improvement over a long period, restart the search to avoid getting trapped in a local optimum.
[0076] S6. Select multiple evaluation points based on the agent-distance metric, allocate them to multi-processor parallel computing, and update the agent model: The surrogate-distance metric consists of surrogate model predictions and a distance metric, dynamically balancing global exploration and local exploitation by combining the two. A radial basis function surrogate model is used to predict the objective function values of candidate points. The smaller the value, the better the potential quality of the candidate point. The distance metric calculates the minimum Euclidean distance between the candidate point and all evaluated points, encouraging the selection of candidate points far away from the evaluated areas and avoiding duplicate sampling.
[0077] The overall score of the candidate points is calculated using a weighted cyclic strategy, where Ws represents the weighted score of the proxy criteria, where 0 1, and the weighted score of the distance from the standard. A high Ws indicates a greater reliance on surrogate model predictions (biased towards local development), while a low Ws indicates a greater reliance on distance metrics (biased towards global exploration).
[0078] Agent-distance metric is generated based on dynamic coordinate search. Candidate points For each candidate point Calculate its proxy value and minimum distance P candidate points are selected from these as the next batch of evaluation points.
[0079] A weighted cyclical strategy is used to alternate between global and local searches, balancing the surrogate model's predicted values and the spatial distance between candidate points. The weight score Ws for each evaluation point is sequentially ranked from the following... Select from, among which The final judgment criteria As shown below:
[0080] in, The minimum distance.
[0081] S7. Repeat steps 4-6 until the maximum number of evaluations or the convergence condition is reached, and output the optimal solution.
[0082] S8. Based on the time-series concentration of pollutants, obtain a monitoring station deployment plan with the goal of maximizing source tracing accuracy and minimizing deployment costs.
[0083] Generate several monitoring point deployment plans based on existing monitoring points in the target sea area; An overall evaluation index is constructed based on the accuracy of source tracing and the deployment cost; the overall evaluation index of each scheme is calculated, and the deployment scheme with the highest overall evaluation index is the final monitoring station deployment scheme.
[0084] The deployment of monitoring stations meets physical constraints, including: The water depth in the area where the monitoring point is located is greater than the minimum operating depth; The monitoring point is located in an area outside the sovereign waterway; The monitoring point is located in an area with poor power and communication infrastructure.
[0085] The deployment cost is the product of the number of monitoring stations and the cost of a single monitoring station; The accuracy of traceability is:
[0086] in, This is the sum of the absolute errors between the time-series pollutant concentration values output by the model and the actual observed values. This represents the standard deviation between the actual observed values.
[0087] Based on the time-series concentration of pollutants, a monitoring station deployment scheme is obtained with the goal of maximizing source tracing accuracy and minimizing deployment costs, including: Calculate the traceability accuracy index:
[0088] Calculate the economic cost index:
[0089]
[0090] The decision variable M can be represented as: M=Mj= (1) j ) Deployable within the region The total number; Normalize the traceability accuracy indicators and economic cost indicators:
[0091]
[0092] in, This represents the minimum value for the traceability accuracy index. This represents the maximum value of the traceability accuracy index. To maximize economic cost, To minimize economic cost; The normalized results are weighted and fused to form the overall evaluation index:
[0093] in, , These are the weighting coefficients.
[0094] The monitoring station deployment scheme is obtained through optimization algorithm with the goal of maximizing the overall evaluation index.
[0095] A large-scale marine water pollution source tracing and monitoring station optimization system that couples efficient optimization with refined simulation includes: Pollution transport simulation module: A three-dimensional hydrodynamic-water quality coupling model is constructed using numerical simulation software; key decision variables of the three-dimensional hydrodynamic-water quality coupling model are determined through Sobol sensitivity analysis; Proxy model building module: Initializes the radial basis function surrogate model; Dynamic candidate generation module: Iteratively solves the radial basis function surrogate model to obtain the time-series concentration of pollutants; Optimization Decision Module: Based on the time-series concentration of pollutants, a monitoring station deployment plan is obtained with the goal of maximizing source tracing accuracy and minimizing deployment costs.
[0096] Example Taking a certain bay as an example, this semi-enclosed sea area is an important aquaculture area, waterway, and oil extraction area. Its coastal area is densely industrialized and has busy port traffic, facing a high risk of sudden water pollution. Furthermore, its water exchange capacity is weak, making it prone to pollutant accumulation and facing the dual risks of land-based and ship-borne pollution. Therefore, the timeliness of monitoring and early warning, as well as the accuracy of source tracing, are extremely important. Utilizing the research sea area such as... Figure 3 Two monitoring stations (21,70) and (29,62) are shown to observe the concentrations of three pollutants (total nitrogen, total phosphorus, and chlorophyll A). This method is then used to trace the source of water pollution and select the optimal monitoring station deployment scheme.
[0097] 1. Construct a three-dimensional hydrodynamic-water quality coupled model using Delft3D: This embodiment is based on Delft3D, and under the conditions of obeying the Boussinesq approximation, hydrostatic pressure assumption, and quasi-3D assumption, combined with Based on the turbulence closure model and convection-diffusion equations, the three-dimensional hydrodynamic-water quality model is constructed, and the specific governing equations include: Continuity equation:
[0098] In the formula, Q represents the source or sink flow per unit area; , These are transformation coefficients between orthogonal curvilinear coordinate systems and Cartesian coordinate systems. They typically appear in curvilinear coordinate systems and are used to correct for the effects of coordinate changes. U represents the horizontal coordinate in the curvilinear coordinate system; U is The velocity component, V is η velocity components; This indicates the change in water level relative to a reference water level, i.e., the free water surface elevation. This indicates the still water depth relative to a reference water level.
[0099] Momentum equation: level Direction:
[0100] level Direction:
[0101] In the formula, The hydrostatic pressure gradient in the direction of , In order to be in The hydrostatic pressure gradient in the direction of the direction; express The imbalance of Reynolds stress in the direction of the Reynolds stress. express The imbalance of Reynolds stress in the direction; The vertical eddy viscosity coefficient; Density of water; and This represents the momentum change caused by external factors, including the momentum effects of drainage, receding water, wind stress, and bottom shear stress; f is the Coriolis force coefficient, used to describe the Coriolis force caused by the Earth's rotation; u, v, Represented respectively in orthogonal curvilinear coordinate systems , , The velocity changes in three directions; t represents time; It is defined in motion The vertical velocity in space, The following continuity equation is obtained in the coordinate system:
[0102] in, For inflow items, This is an outflow term.
[0103] The 3D hydrodynamic-water quality model uses orthogonal curvilinear coordinates in the horizontal direction and uses [other coordinates] in the vertical direction. Coordinate transformation can better fit fixed shoreline boundaries and bottom topography. Delft3D uses staggered meshes and solves the problem based on the finite difference method, dividing each time step into two half-steps. Internal or The two-dimensional problem is then solved separately in each direction, thus transforming it into two one-dimensional problems that are solved separately.
[0104] After the model is built, the parameters of the three-dimensional hydrodynamic-water quality model of the study area are calibrated by using historical monitoring data of pollutants in the study area. The parameters include diffusion coefficient and degradation rate. The model is also corrected by combining the actual topographic data of the study area to make the simulation process consistent with the actual situation.
[0105] The structural diagram of the simulation model is as follows Figure 1 As shown.
[0106] 2. Key decision variables for the three-dimensional hydrodynamic-water quality coupling model were determined through Sobol sensitivity analysis: Source tracing decision variables include: pollution location, pollutant concentration, and emission time; In reality, the location of the contamination can be directly determined. In this case, for example... Figure 3 As shown, (19, 66) is the pollution location, so the main focus is on identifying the pollution concentration and emission time at (19, 66).
[0107] Two observation stations (21, 70) and (29, 62) observed concentrations of three pollutants (total nitrogen, total phosphorus, and chlorophyll A). These concentrations are influenced by 11 substances (NH4, NO3, PON1, PON2, PON3, DON, POP1, POP2, POP3, PO4, DOP) at location (19, 66). Therefore, the decision variable is the concentration of these 11 substances at a given time at the pollution location (19, 66). However, if each substance is divided into 12 months, the decision variable becomes 12*11*1, resulting in too high a dimensionality for further algorithm optimization. Therefore, SOBOL sensitivity analysis was used to screen the source tracing parameters, ultimately determining the decision variable to be 12.
[0108] 3. Based on the Latin hypercube experimental design, initial parameter sample points are generated to run the water pollution transport model in parallel to calculate the true objective function values of the samples, and a radial basis function surrogate model is constructed: 1) To generate Latin hypercube sample points, the range of each parameter needs to be divided into several equally probable intervals. In each interval, a value is randomly selected. Through permutation and combination, the sample points of each parameter dimension are evenly distributed and do not repeat. Then, the model is parallelized and the sample points are split into k processors.
[0109] 2) Select a finite number of sample points , ,..., And calculate the true objective function value for each sample point. The error between observed and simulated values can be described by the following equation:
[0110] in, For the decision variable vector, That is, each sample contains d real-valued parameters that need to be optimized; The monthly average value of the simulated value of the s-th substance at the l-th position under parameter x; This represents the monthly average of the corresponding observations; s yes The standard deviation of can be used for normalization. Number of positions t represents the number of months. ; s represents the amount of pollutants .
[0111] 3) The mathematical expression for the radial basis function surrogate model is:
[0112] Choose basis functions To capture local nonlinear features and enhance global trend fitting by adding polynomial terms, the weight vector is fitted by solving the following system of linear equations. and polynomial coefficients ,make = .
[0113] =
[0114] 4) Coordinates of a subset of the optimal solutions found so far A dynamic coordinate search strategy is used to generate around the optimal solution. Candidate points And combine the agent-distance metric for each candidate point Calculate its proxy value and minimum distance P candidate points are selected from these points as the next batch of evaluation points to update the radial basis function surrogate model.
[0115] Repeat steps 1)-4) above until the maximum number of evaluations or convergence condition is reached, output the optimal solution, and compare the progress of source identification using PODS and GA expansion with water quality model calibration under the manual solution framework, such as... Figure 4 As shown.
[0116] Figure 5 The study illustrates the impact of monitoring stations at different distances (far and near) from the pollution source on the source tracing results of large-scale marine water pollution in the case of a single pollution source—the source tracing accuracy of the near-point monitoring station is significantly higher than that of the far-point station.
[0117] Figure 6 This embodiment describes the deployment of a combination of monitoring stations in the case of three known pollution sources.
[0118] For each group of monitoring stations, a high-precision hydrodynamic-water quality model is run, and its data is regarded as "measured data" for that group of monitoring stations. Then, the pollution source tracing steps are performed to output the optimal pollution source parameters to obtain the simulated observation values for that group of monitoring stations. Finally, the CF value between the simulated observation values and the "measured data" is calculated to quantify the accuracy of the source tracing.
[0119] Number of monitoring stations:
[0120] Decision variable: Optimization of water quality monitoring station deployment involves optimizing the location of monitoring stations. The decision variable M can be represented as: M=Mj= (1) j ) Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for optimizing the deployment of large-scale marine water pollution source tracing monitoring stations by coupling efficient optimization and refined simulation, characterized in that, include: A three-dimensional hydrodynamic-water quality coupled model was constructed using numerical simulation software; The key decision variables of the three-dimensional hydrodynamic-water quality coupling model were determined through Sobol sensitivity analysis. Initialize the radial basis function surrogate model; The time-series concentrations of pollutants are obtained by iteratively solving the radial basis function surrogate model. Based on the time-series concentrations of the pollutants, a monitoring station deployment scheme is obtained with the goal of maximizing source tracing accuracy and minimizing deployment costs.
2. The method according to claim 1, characterized in that, The three-dimensional hydrodynamic-water quality coupling model includes: In the formula, Q represents the source or sink flow per unit area; , These are transformation coefficients between orthogonal curvilinear coordinate systems and Cartesian coordinate systems. They typically appear in curvilinear coordinate systems and are used to correct for the effects of coordinate changes. U represents the horizontal coordinate in the curvilinear coordinate system; The velocity component, V is η velocity components; This indicates the change in water level relative to a reference water level, i.e., the free water surface elevation. Indicates the still water depth relative to a reference water level; Momentum equation: level Direction: level Direction: In the formula, The hydrostatic pressure gradient in the direction of , In order to be in The hydrostatic pressure gradient in the direction of the direction; express The imbalance of Reynolds stress in the direction of the Reynolds stress. express The imbalance of Reynolds stress in the direction; The vertical eddy viscosity coefficient; Density of water; and This represents the momentum change caused by external factors, including the momentum effects of drainage, receding water, wind stress, and bottom shear stress; f is the Coriolis force coefficient, used to describe the deflection force caused by the Earth's rotation; u, v, Represented respectively in orthogonal curvilinear coordinate systems , , The velocity changes in three directions; t represents time; It is defined in motion The vertical velocity in space, The following continuity equation is obtained in the coordinate system: in, For inflow items, This is an outflow term.
3. The method according to claim 1, characterized in that, The key decision variables for the three-dimensional hydrodynamic-water quality coupling model, determined through Sobol sensitivity analysis, include: Source tracing decision variables include: the location of the pollution source and the time-series emission concentration of each pollutant; Calculate the sensitivity index of each traceability decision variable, and the traceability decision variable with a sensitivity index greater than a preset threshold is designated as the key decision variable.
4. The method according to claim 1, characterized in that, The initialization of the radial basis function surrogate model includes: A set of initial sample points is generated in the parameter space based on Latin hypercube experimental design. The objective function values for the initial sample points were calculated using a three-dimensional hydrodynamic-water quality coupling model. An initial radial basis function surrogate model is constructed based on the objective function values of the initial sample points.
5. The method according to claim 4, characterized in that, The objective function includes: in, , These are the weight vector and the polynomial coefficients, respectively. Let be a linear polynomial with d variables.
6. The method according to claim 4, characterized in that, Iteratively solving the radial basis function surrogate model to achieve water pollution source tracing includes: Candidate points are generated on the radial basis function surrogate model using an optimization algorithm; Predict the objective function value of candidate points using a radial basis function surrogate model; Calculate the minimum Euclidean distance between the candidate point and all evaluated points; The minimum Euclidean distance and the objective function value are weighted and summed to obtain the comprehensive score of the candidate points; Candidate points whose comprehensive score is greater than a preset threshold are used as evaluation points for the next round of iteration of the radial basis function surrogate model; The optimal solution is output once the maximum number of evaluations or the convergence condition is reached.
7. The method according to claim 1, characterized in that, Based on the time-series concentrations of the pollutants, a monitoring station deployment scheme is obtained with the goal of maximizing source tracing accuracy and minimizing deployment costs, including: Generate several monitoring point deployment plans based on existing monitoring points in the target sea area; A comprehensive evaluation index is constructed based on traceability accuracy and deployment cost. Calculate the total evaluation index for each scheme, and the scheme with the highest total evaluation index is the final monitoring station deployment scheme.
8. The method according to claim 1, characterized in that, The deployment of the monitoring stations meets physical constraints, including: The water depth in the area where the monitoring point is located is greater than the minimum operating depth; The monitoring point is located in an area outside the sovereign waterway; The monitoring point is located in an area with poor power and communication infrastructure.
9. The method according to claim 1, characterized in that, The deployment cost: The product of the number of monitoring stations and the cost of a single monitoring station; The accuracy of the source tracing is: in, This is the sum of the absolute errors between the time-series pollutant concentration values output by the model and the actual observed values. This represents the standard deviation between the actual observed values.
10. The method according to claim 1, characterized in that, Based on the time-series concentrations of the pollutants, a monitoring station deployment scheme is obtained with the goal of maximizing source tracing accuracy and minimizing deployment costs, including: Calculate the traceability accuracy index: Calculate the economic cost index: The decision variable M can be represented as: M=Mj= (1 j ) Deployable within the region The total number; Normalize the traceability accuracy indicators and economic cost indicators: in, This represents the minimum value for the traceability accuracy index. This represents the maximum value of the traceability accuracy index. To maximize the economic cost, This represents the minimum economic cost. The normalized results are weighted and fused to form the overall evaluation index: in, , These are the weighting coefficients.