Pond multi-objective optimization management method for agricultural drainage basin non-point source pollution regulation and control

Abstract

The invention discloses a pond multi-objective optimization management method oriented to agricultural watershed non-point source pollution regulation and control, and relates to the technical field of agricultural watershed non-point source pollution abatement. Multi-dimensional attributes such as pond application types, morphological characteristics and sediment nutrient states are integrated into a unified quantitative framework for the first time, and a generalized additive model is constructed to obtain a multi-objective optimization model; nonlinearity and interaction of pond attributes on river water quality influence can be accurately captured, and the accuracy of river nitrogen and phosphorus concentration prediction is improved. According to the method, pond management measures are quantified into controllable decision variables, a multi-target dynamic optimization model for balancing environmental benefits and economic benefits is established, a Pareto optimal solution is used for replacing a traditional experience decision, a scientific, efficient and quantitatively-implemented pond management scheme is provided, the one-sidedness of a single target is avoided, and the method is suitable for large-scale popularization and application. The cost minimization is realized while the non-point source pollution reduction is maximized, and the accurate configuration and scientific quantitative decision of pond management resources are realized.

Description

Technical Field

[0001] This invention relates to the field of agricultural watershed non-point source pollution control technology, and more specifically to a multi-objective optimization management method for ponds for the regulation of agricultural watershed non-point source pollution. Background Technology

[0002] Currently, agricultural non-point source pollution is one of the main causes of water environment problems such as excessive nitrogen and phosphorus concentrations and eutrophication in water bodies. Ponds, as small water bodies widely distributed within watersheds, play a dual and dynamic role in regulating this type of pollution. Ponds are both "sinks" of pollutants, reducing nitrogen and phosphorus loads through processes such as interception, sedimentation, plant uptake, and microbial activity; and potential "sources" of pollutants, especially when pond sediments are nutrient-saturated and environmental disturbances (such as heavy rainfall, temperature increases, and hypoxia) may trigger the release of endogenous nitrogen and phosphorus, exacerbating the pollution risk of downstream water bodies. This dual nature of source-sink function makes the impact of ponds on downstream water quality complex and difficult to predict. Current research suggests that the source-sink function transformation of ponds is comprehensively affected by the multidimensional attributes of ponds, including their use type, morphological characteristics, and sediment nutrient status. Therefore, when utilizing pond management to improve pollution reduction, it is necessary to clarify the impact mechanism of pond attributes on river water quality and to develop efficient pond management schemes for the treatment of agricultural non-point source pollution through the modification and optimization of pond attributes.

[0003] However, existing pond management methods have the following shortcomings and deficiencies. First, current technologies are still insufficient in quantifying the response of river water quality to ponds. Traditional methods are mostly based on linear assumptions or empirical judgments, usually focusing only on the relationship between single indicators such as pond area or quantity and river water quality, failing to systematically consider the interaction between multiple dimensions of pond use, morphology, and sediment nutrient status, and their nonlinear impact on river water quality. Therefore, it is difficult to accurately reveal the complex mechanisms of ponds in nitrogen and phosphorus pollution control, leading to deviations between predicted results and actual control effects, thus restricting the scientific nature of management decisions. Second, existing pond management schemes often focus on the local implementation of single measures (such as dredging or ecological bank protection). Although such measures may improve local water quality, their emission reduction effects in other areas are highly uncertain due to insufficient consideration of spatial heterogeneity factors such as land use, landscape patterns, and pollution loads, limiting the systematic control effect of such homogeneous management technologies at the watershed scale. In addition, comprehensive pond management should not only aim to promote non-point source pollution reduction but also take into account implementation costs. However, existing technologies often focus on the single objective of improving water quality or controlling costs, lacking a dynamic decision-making model that integrates water quality response mechanisms, engineering cost constraints, and multi-objective optimization. This makes it difficult for management solutions to achieve a balance between environmental and economic benefits in practice, thus limiting the efficient use of resource allocation.

[0004] Therefore, how to propose the optimal solution for pond management under the multiple optimization objectives of maximizing water quality improvement and minimizing costs is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention provides a multi-objective optimization management method for ponds for the control of non-point source pollution in agricultural watersheds, in order to solve the problems existing in the background art.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A multi-objective optimization management method for ponds aimed at controlling non-point source pollution in agricultural watersheds includes: Step 1: Select several typical river sections within the watershed, collect surface water samples, and determine their total nitrogen and total phosphorus concentrations; select several typical ponds within the watershed, clarify the ponds' uses and types, collect pond sediment samples, and determine their total nitrogen and total phosphorus concentrations. Step 2: For the selected river cross section, divide it into circular buffer zones with the sampling point as the center; count the number of ponds in the circular buffer zone; estimate the total nitrogen and total phosphorus concentrations of sediments in each pond based on the type of use of the ponds; and calculate the total nitrogen and total phosphorus status of sediments in the ponds within the buffer zone. Step 3: Calculate the morphological indicators of the pond within the circular buffer zone, including the pond shape complexity, pond area, and distance between the pond and the river. Step 4: Using the total nitrogen and total phosphorus concentrations of the river cross-section as response variables, and the total nitrogen and total phosphorus concentrations of pond sediments obtained in Step 2 and the pond morphology indicators obtained in Step 3 as explanatory variables, a generalized additive model for river nitrogen and phosphorus regulation is constructed. Based on the deviation between the measured values ​​and the model prediction values ​​of each river cross-section, a baseline correction value specific to the river cross-section is constructed. In the prediction simulation, this value is superimposed on the results of the nonlinear interaction effect evaluation model to establish the prediction equations for the response of river total nitrogen and total phosphorus concentrations to changes in pond attributes. Step 5: Define the decision variables for the pond management project and construct the state transition equations for the decision variables of the pond management project; Step 6: Based on the prediction equations of the response of total nitrogen and total phosphorus concentrations in rivers to changes in pond attributes and the state transition equations of decision variables for pond management projects, establish a multi-objective dynamic optimization model for pond management with the goal of maximizing non-point source nitrogen and phosphorus pollution reduction and minimizing project implementation costs. Step 7: Use an evolutionary algorithm to solve the constructed multi-objective dynamic optimization model for pond management to obtain the Pareto non-dominated solution set; Step 8: Based on the multi-objective decision-making method, screen and rank the Pareto non-dominated solutions to determine the optimal management scheme for the pond.

[0007] Optionally, step 2 specifically includes: based on the measured total nitrogen and total phosphorus concentrations of the pond sediments, calculating the average total nitrogen and total phosphorus concentrations of the sediments for each type of pond according to different pond uses, and assigning them to the same type of ponds within the buffer zone; summing the total nitrogen concentrations (tns) of the sediments in individual ponds within the buffer zone to obtain the total nitrogen status (TNS) of the buffer zone pond sediments; and summing the total phosphorus concentrations (tps) of the sediments in individual ponds within the buffer zone to obtain the total phosphorus status (TPS) of the buffer zone pond sediments.

[0008] Optionally, step 3 specifically includes: Step 3.1: The pond shape complexity is characterized by the pond landscape pattern index at the class scale, and the index with the highest correlation with the total nitrogen concentration and total phosphorus concentration of the river section is selected by Spearman rank correlation test as the pond shape complexity index PS. Step 3.2: The area pa of a single pond is calculated based on the pond water area vector file. The total pond area PA is obtained by summing the areas of all individual ponds within the buffer zone. Step 3.3: The distance pd between a single pond and a river cross-section sampling point is calculated by the nearest neighbor analysis tool. The connection distance PD between the pond and the river is obtained by summing the distances between all ponds and river cross-section sampling points within the buffer zone.

[0009] Optionally, step 4 specifically includes: Step 4.1: Using the total nitrogen concentration (TN) and total phosphorus concentration (TP) at the river cross-section as response variables, and the pond shape complexity index (PS), total pond area (PA), pond-river connectivity distance (PD), total nitrogen state (TNS) of sediments in the buffer pond, and total phosphorus state (TPS) of sediments in the buffer pond as explanatory variables, a generalized additive model for river nitrogen and phosphorus regulation is constructed. The formula is as follows: ; In the formula, the subscript Represents the river section number. For link functions, cross-section TN or TP, For the intercept term, Represents residual, Represents a nonparametric smoothing function. The tensor product smoothing function is a function that integrates the interaction of three indicators, PA, PD, and TNS / TPS, based on the three-dimensional source-sink regulation concept of area-distance-sediment. Step 4.2: Based on the deviation between the measured values ​​and the model predictions for each cross-section, calculate the baseline correction amount that takes into account the specificity of the cross-section. The formula is as follows: ; In the formula, Let be the baseline correction amount for section s. To measure the total nitrogen or total phosphorus concentration at river cross-sections, These are simulated values ​​of total nitrogen or total phosphorus concentrations at river cross sections under baseline conditions. Step 4.3: During the prediction simulation, updating the values ​​of the explanatory variables yields the predicted value of section s, as shown in the formula: ; In the formula, The values ​​at section s are simulated values ​​obtained using a generalized additive model of river nitrogen and phosphorus regulation. , , , and The model input values ​​that represent the changes; Step 4.4: For each cross section, the baseline correction is superimposed on the model prediction, and the prediction result is obtained through the inverse transform of the link function, as shown in the formula: ; In the formula, This represents the final predicted result of the total nitrogen or total phosphorus concentration in the river at the cross-section. Representative link function The inverse transform of .

[0010] Optionally, step 5 specifically includes: Step 5.1 defines the pond-river water system connectivity project as a continuous decision variable. The degree of modification to the water flow path between the pond and the river directly affects the PD value; the pond area modification project is defined as a continuous decision variable. The value represents the degree of modification to the pond area; a positive value represents an increase in the area (PA value), while a negative value represents a decrease in the area (PA value). The decision-making definition for the pond dredging project is a binary decision variable. 1 represents dredging, and 0 represents no dredging. Dredging directly reduces the TNS and TPS values ​​of the pond. The pond shoreline renovation project is defined as a continuous decision variable. Shoreline modification will increase the PS value; the subscripts in the above variables Represents a river cross-section, subscript Representing the The first cross-section corresponds to the buffer zone within the first... A pond, and These represent the upper and lower limits of the proportion of the renovation project to connect the pond and the river system. and These represent the upper and lower limits of the area renovation ratio, respectively. This represents the upper limit of the increase in shoreline complexity. Step 5.2, the state transition equations for the changes in PD, PS, PA, TNS, and TPS values ​​as the pond management project is implemented are set as follows: ; ; ; ; ; In the formula, , , , The first s The first cross-section corresponds to the buffer zone within the first... i The sampling points were located at the distance between the pond and the river cross-section, and the pond area, total nitrogen content, and total phosphorus content of the pond sediments were recorded. For the first The number of ponds in the buffer zone corresponds to each cross section.

[0011] Optionally, step 6 specifically includes: Step 6.1, the objective function for maximizing the reduction of non-point source nitrogen and phosphorus pollution is defined as: ; ; In the formula, This refers to the current river section number, which belongs to a set. , The number of river cross sections, and These are the total nitrogen and total phosphorus concentrations at the river cross-section after the decision-making change; Step 6.2, the objective function for minimizing the cost of the pond management project is defined as:

[0012] In the formula, The unit price for the construction cost of the pond-river water system connection project. The unit price for the construction cost of the pond dredging project. The unit price for the construction cost of the pond area renovation project. This refers to the unit price for the construction cost of the pond shoreline renovation project.

[0013] Optionally, step 7 specifically includes: using a non-dominated sorting genetic algorithm with an elitist strategy to solve the Pareto non-dominated solution set of the multi-objective dynamic optimization model for pond management, setting optimization parameters including: objective dimension, initial population size, number of generations, crossover probability and mutation probability, and performing iterative calculations; when the number of calculations reaches the number of generations, the Pareto non-dominated solution set for pond optimization management is obtained.

[0014] Optionally, step 8 specifically includes: Step 8.1: The superior-inferior solution distance method is used as a multi-objective decision-making method to screen pond optimization schemes; a decision matrix is ​​constructed based on the Pareto non-dominated solution set for pond optimization management. ,in It is a solution in the Pareto non-dominated solution set. This is the index of the solution in the solution set. The spatial dimension index of the solution. Let be the total number of solutions in the non-dominated solution set. The total number of spatial dimensions of the non-dominated solution set; Step 8.2: Determine the weights of the three optimization objectives for pond management. ,in Calculate the weighted normalization matrix : ; Step 8.3: Based on each optimization objective attribute, determine the optimal value in the weighted normalization matrix as the positive ideal solution. The worst value is taken as the negative ideal solution. The distance between each candidate solution and the positive ideal solution is calculated using Euclidean distance. and the distance to the negative ideal solution Leave: ; ; Step 8.4: Calculate the proximity coefficient of each candidate pond optimization scheme. : ; in The closer the value is to 1, the better the solution; select The scheme corresponding to the maximum value is taken as the optimal scheme for pond management.

[0015] Optionally, it also includes using a vector normalization method to... Standardization is performed to obtain the standardized matrix. The formula is: .

[0016] As can be seen from the above technical solution, compared with the prior art, this invention discloses a multi-objective optimization management method for ponds in agricultural watershed non-point source pollution control. It overcomes the limitations of traditional methods, such as neglecting multi-factor interaction effects, relying on linear assumptions, and lacking systematic optimization. This provides a scientific, efficient, and quantitatively implementable pond management solution for agricultural watershed non-point source pollution control. This invention, for the first time, integrates multi-dimensional attributes such as pond usage type, morphological characteristics (area, shape, and distance from river), and sediment nutrient status into a unified quantitative framework. By constructing a generalized additive model, it can accurately capture the nonlinear and interactive effects of pond attributes on river water quality, improving the accuracy of river nitrogen and phosphorus concentration prediction. Furthermore, this invention quantifies pond management measures into controllable decision variables, establishing a multi-objective dynamic optimization model that balances environmental and economic benefits. It replaces traditional empirical decision-making with Pareto optimal solutions, avoiding the one-sidedness of a single objective. It maximizes non-point source pollution reduction while minimizing costs, achieving precise allocation and scientific quantitative decision-making for pond management resources. Attached Figure Description

[0017] 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 only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of the method flow provided by the present invention.

[0019] Figure 2 This is a diagram of Pareto non-dominated solutions and optimal dispersal points for an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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 are within the scope of protection of the present invention.

[0021] This invention discloses a multi-objective optimization management method for ponds aimed at controlling non-point source pollution in agricultural watersheds, such as... Figure 1 As shown, it includes: Step 1: Select several typical river sections within the watershed, collect surface water samples, and determine their total nitrogen and total phosphorus concentrations; select several typical ponds within the watershed, clarify the ponds' uses and types, collect pond sediment samples, and determine their total nitrogen and total phosphorus concentrations. Step 2: For the selected river cross section, divide it into circular buffer zones with the sampling point as the center; count the number of ponds in the circular buffer zone; estimate the total nitrogen and total phosphorus concentrations of sediments in each pond based on the type of use of the ponds; and calculate the total nitrogen and total phosphorus status of sediments in the ponds within the buffer zone. Step 3: Calculate the morphological indicators of the pond within the circular buffer zone, including the pond shape complexity, pond area, and distance between the pond and the river. Step 4: Using the total nitrogen and total phosphorus concentrations of the river cross-section as response variables, and the total nitrogen and total phosphorus concentrations of pond sediments obtained in Step 2 and the pond morphology indicators obtained in Step 3 as explanatory variables, a generalized additive model for river nitrogen and phosphorus regulation is constructed. Based on the deviation between the measured values ​​and the model prediction values ​​of each river cross-section, a baseline correction value specific to the river cross-section is constructed. In the prediction simulation, this value is superimposed on the results of the nonlinear interaction effect evaluation model to establish the prediction equations for the response of river total nitrogen and total phosphorus concentrations to changes in pond attributes. Step 5: Define the decision variables for the pond management project and construct the state transition equations for the decision variables of the pond management project; Step 6: Based on the prediction equations of the response of total nitrogen and total phosphorus concentrations in rivers to changes in pond attributes and the state transition equations of decision variables for pond management projects, establish a multi-objective dynamic optimization model for pond management with the goal of maximizing non-point source nitrogen and phosphorus pollution reduction and minimizing project implementation costs. Step 7: Use an evolutionary algorithm to solve the constructed multi-objective dynamic optimization model for pond management to obtain the Pareto non-dominated solution set; Step 8: Based on the multi-objective decision-making method, screen and rank the Pareto non-dominated solutions to determine the optimal management scheme for the pond.

[0022] In one specific embodiment, step 1 specifically includes: Step 1.1, the principles for selecting river cross-sections include: focusing on key control locations such as the upstream and downstream of the main stream and major tributaries, and reflecting the impact of pollution from different land use types.

[0023] Step 1.2: Determine the intended use of the pond through on-site investigation. Typical uses of ponds include, but are not limited to: irrigation ponds, aquaculture ponds, rural domestic ponds, and wastewater treatment ponds. The selection of ponds should cover all typical use types.

[0024] In one specific embodiment, step 2 specifically includes: estimating the total nitrogen and total phosphorus concentrations of sediments in each pond within the buffer zone based on the pond's usage type; that is, based on the typical pond sediment total nitrogen and total phosphorus concentrations measured in step 1, calculating the average total nitrogen and total phosphorus concentrations of sediments for each type of pond according to different pond usage types, and assigning these values ​​to the ponds of the same type within the buffer zone. The total nitrogen concentration (tns) of sediments in individual ponds within the buffer zone is summarized to obtain the total nitrogen state (TNS) of the buffer zone pond sediments; the total phosphorus concentration (tps) of sediments in individual ponds within the buffer zone is summarized to obtain the total phosphorus state (TPS) of the buffer zone pond sediments.

[0025] In one specific embodiment, step 3 specifically includes: Step 3.1: The pond shape complexity is characterized by the pond landscape pattern indices at the class scale (SHAPE_MN, LSI, FRAC_MN, and PARA_MN). These landscape pattern indices are calculated using pond spatial location raster data and FRAGSTATS 4.2 software. Using the Spearman rank correlation test, the indices with the highest correlation to total nitrogen (TN) and total phosphorus (TP) concentrations at the river cross-section are selected as the pond shape complexity (PS) index.

[0026] Step 3.2: The area of ​​a single pond (pa) is calculated by ArcMap 10.7 software based on the pond water area vector file. The total area of ​​all individual ponds in the buffer is then summed to obtain the pond area (PA).

[0027] Step 3.3: The distance (pd) between a single pond and a river cross-section sampling point is calculated using the nearest neighbor analysis tool in ArcMap 10.7 software. The distances between all ponds and river cross-section sampling points within the buffer zone are summarized to obtain the pond-river connectivity distance (PD).

[0028] In one specific embodiment, step 4 specifically includes: Step 4.1: Using the total nitrogen concentration (TN) and total phosphorus concentration (TP) at the river cross-section as response variables, and the pond shape complexity index (PS), total pond area (PA), pond-river connectivity distance (PD), total nitrogen state (TNS) of sediments in the buffer pond, and total phosphorus state (TPS) of sediments in the buffer pond as explanatory variables, a generalized additive model for river nitrogen and phosphorus regulation is constructed. The formula is as follows: ; In the formula, the subscript Represents the river section number. For link functions, cross-section TN or TP, For the intercept term, Represents residual, Represents a nonparametric smoothing function. The tensor product smoothing function is a function that integrates the interaction of three indicators, PA, PD, and TNS / TPS, based on the three-dimensional source-sink regulation concept of area-distance-sediment. Step 4.2: Based on the deviation between the measured values ​​and the model predictions for each cross-section, calculate the baseline correction amount that takes into account the specificity of the cross-section. The formula is as follows: ; In the formula, Let be the baseline correction amount for section s. To measure the total nitrogen or total phosphorus concentration at river cross-sections, These are simulated values ​​of total nitrogen or total phosphorus concentrations at river cross sections under baseline conditions. Step 4.3: During the prediction simulation, updating the values ​​of the explanatory variables yields the predicted value of section s, as shown in the formula: ; In the formula, The values ​​at section s are simulated values ​​obtained using a generalized additive model of river nitrogen and phosphorus regulation. , , , and The model input values ​​that represent the changes; Step 4.4: For each cross section, the baseline correction is superimposed on the model prediction, and the prediction result is obtained through the inverse transform of the link function, as shown in the formula: ; In the formula, This represents the final predicted result of the total nitrogen or total phosphorus concentration in the river at the cross-section. Representative link function The inverse transform of .

[0029] In one specific embodiment, step 5 specifically includes: Step 5.1 defines the pond-river water system connectivity project as a continuous decision variable. The degree of modification to the water flow path between the pond and the river directly affects the PD value; the pond area modification project is defined as a continuous decision variable. The value represents the degree of modification to the pond area; a positive value represents an increase in the area (PA value), while a negative value represents a decrease in the area (PA value). The decision-making definition for the pond dredging project is a binary decision variable. 1 represents dredging, and 0 represents no dredging. Dredging directly reduces the TNS and TPS values ​​of the pond. The pond shoreline renovation project is defined as a continuous decision variable. Shoreline modification will increase the PS value; the subscripts in the above variables Represents a river cross-section, subscript Representing the The first cross-section corresponds to the buffer zone within the first... A pond, and These represent the upper and lower limits of the proportion of the renovation project to connect the pond and the river system. and These represent the upper and lower limits of the area renovation ratio, respectively. This represents the upper limit of the increase in shoreline complexity. Step 5.2, the state transition equations for the changes in PD, PS, PA, TNS, and TPS values ​​as the pond management project is implemented are set as follows: ; ; ; ; ; In the formula, , , , The first s The first cross-section corresponds to the buffer zone within the first... i The sampling points were located at the distance between the pond and the river cross-section, and the pond area, total nitrogen content, and total phosphorus content of the pond sediments were recorded. For the first The number of ponds in the buffer zone corresponds to each cross section.

[0030] In one specific embodiment, step 6 specifically includes: Step 6.1, the objective function for maximizing the reduction of non-point source nitrogen and phosphorus pollution is defined as: ; ; In the formula, This refers to the current river section number, which belongs to a set. , The number of river cross sections, and These are the total nitrogen and total phosphorus concentrations at the river cross-section after the decision-making change; Step 6.2, the objective function for minimizing the cost of the pond management project is defined as: ; In the formula, The unit price for the construction cost of the pond-river water system connection project. The unit price for the construction cost of the pond dredging project. The unit price for the construction cost of the pond area renovation project. This refers to the unit price for the construction cost of the pond shoreline renovation project.

[0031] In a specific embodiment, step 7 specifically includes: using a non-dominated sorting genetic algorithm with an elitist strategy to solve the Pareto non-dominated solution set of the multi-objective dynamic optimization model for pond management, setting optimization parameters including: objective dimension, initial population size, number of generations, crossover probability and mutation probability, and performing iterative calculations; when the number of calculations reaches the number of generations, the Pareto non-dominated solution set for pond optimization management is obtained.

[0032] In one specific embodiment, step 8 specifically includes: Step 8.1: The superior-inferior solution distance method is used as a multi-objective decision-making method to screen pond optimization schemes; a decision matrix is ​​constructed based on the Pareto non-dominated solution set for pond optimization management. ,in It is a solution in the Pareto non-dominated solution set. This is the index of the solution in the solution set. The spatial dimension index of the solution. Let be the total number of solutions in the non-dominated solution set. The total number of spatial dimensions of the non-dominated solution set; Using vector normalization method to Standardization is performed to obtain the standardized matrix. The formula is: .

[0033] Step 8.2: Determine the weights of the three optimization objectives for pond management. ,in Calculate the weighted normalization matrix : ; Step 8.3: Based on each optimization objective attribute, determine the optimal value in the weighted normalization matrix as the positive ideal solution. The worst value is taken as the negative ideal solution. The distance between each candidate solution and the positive ideal solution is calculated using Euclidean distance. and the distance to the negative ideal solution : ; ; Step 8.4: Calculate the proximity coefficient of each candidate pond optimization scheme. : ; in The closer the value is to 1, the better the solution; select The scheme corresponding to the maximum value is taken as the optimal scheme for pond management.

[0034] The following specific embodiment is introduced to further illustrate the method of the present invention; The study area is an agricultural watershed in Anhui Province, with a watershed area of ​​approximately 90 km². 2 It is located on the north bank of the Chaohu Lake basin. For example... Figure 1 As shown, the multi-objective optimization management method for ponds aimed at controlling non-point source pollution in agricultural watersheds is carried out in the following steps: Step 1: Select 43 typical river monitoring sections within the basin, namely... The cross-sections cover two main streams and important tributaries within the basin, and the surrounding land use types encompass the main land use types in the basin, such as farmland, woodland, and residential areas. The total nitrogen concentration (0.522–4.75 mg / L) and total phosphorus concentration (0.002–0.384 mg / L) of surface water were measured at all river cross-sections. Twenty-six typical ponds within the basin were selected, and their uses were clarified based on field surveys, including four main categories: irrigation ponds, aquaculture ponds, rural domestic ponds, and tailwater treatment ponds. The total nitrogen concentration (1.32–45.9 mg / g) and total phosphorus concentration (0.469–16.5 mg / g) of sediments in these 26 ponds were measured.

[0035] Step 2: For the selected 43 typical river monitoring sections, a circular buffer zone with a diameter of 400 m was drawn, centered on the sampling point of each section. A total of 308 ponds were identified within each buffer zone, with a minimum of 1 and a maximum of 27 ponds. Based on the total nitrogen and total phosphorus concentrations of sediments from 26 ponds of different uses measured in Step 1, the average total nitrogen and total phosphorus concentrations of sediments for each type of pond were calculated (Table 1). The average concentrations from Table 1 were assigned to the corresponding ponds within the buffer zone to obtain TNS and TPS. The TNS and TPS of all ponds within each buffer zone were then summed to obtain TNS and TPS.

[0036] Table 1. Average concentrations of total nitrogen and total phosphorus in sediments from ponds of different uses

[0037] Step 3: Using FRAGSTATS 4.2 software, calculate the pond landscape pattern indices at the scale for each buffer zone, including SHAPE_MN, LSI, FRAC_MN, and PARA_MN. SHAPE_MN is selected as the index with the highest correlation to total nitrogen concentration at the river cross-section, and LSI is selected as the index with the highest correlation to total phosphorus concentration. Using ArcMap 10.7 software, calculate the area pa of a single pond, and sum all pa values ​​within the 43 buffer zones to obtain the total pond area PA of the buffer zones. Using ArcMap 10.7 software, calculate the distance (pd) between a single pond and the river cross-section sampling point, and sum all pd values ​​within the 43 buffer zones to obtain the connectivity distance PD between the ponds and the river within the buffer zones.

[0038] Step 4: Use a generalized additive model to establish quantitative relationships between variables in the data. The formula is as follows: ; ; In this model, TN and TP are the response variables. Among the explanatory variables, SHAPE_MN and LSI are set as nonlinear smoothing terms, and the model is fitted using a smoothing curve. PA, PD, and TNS are set as tensor product smoothing terms to capture the complex interactions among these three variables, allowing the model to simultaneously consider their joint effects on the response variable. For model parameter settings, a gamma distribution family and a log link function were chosen to accommodate the positive and skewed distribution of the response variable. The restricted maximum likelihood method was used for model fitting. Results for the nonlinear model of TN show that the adjusted R0... 2 The R² value reached 0.642, with a bias explained by 55.7%, indicating that the model has a good fit. Results for the nonlinear model of TP show that the adjusted R² value... 2 The p-value was 0.192, and the bias explained was 52.7%, indicating that the model has a good fit. The p-values ​​of the smoothing terms SHAPE_MN and LSI, as well as the tensor product smoothing term, were all less than 0.05. This method can effectively utilize the generalized additive model to accurately capture the nonlinear relationship and interaction between river water quality concentration and pond attributes, providing a reliable foundation for subsequent prediction and simulation. Based on the deviation between the measured values ​​and the model predictions at each cross-section, the baseline correction amount considering the cross-section specificity was calculated. and This baseline correction is then superimposed onto the model predictions, and the inverse transformation of the link function is used to obtain the prediction function for the total nitrogen and total phosphorus concentration response of the pond attributes for each river section.

[0039] Step 5: Consider pond-river system connectivity, pond area modification, pond dredging, and pond shoreline modification as pond management engineering measures for the study area. The upper and lower boundaries of the value are set to -0.2 and 0.2 respectively. The upper and lower boundaries of the value are set to -0.2 and 0.2 respectively. The upper limit for the value is set to 0.1. The implementation cost (in ten thousand yuan) for each pond management project is as follows: , , , .

[0040] Step 6: Define three objective equations for pond management optimization, including minimizing the average total nitrogen concentration at the river cross-section. Minimize the average total phosphorus concentration in river sections and minimize pond management costs The formulas are as follows: ; ;

[0041] Step 7: The NSGA-II algorithm parameters are set as shown in Table 2. The algorithm will stop iterating after reaching the maximum number of iterations.

[0042] Table 2 NSGA-II Algorithm Parameter Settings

[0043] After 400 iterations, a Pareto solution set containing 200 non-dominated solutions was obtained. The Pareto non-dominated solution scatter plot is shown below. Figure 2 As shown, the optimized average total nitrogen concentration at river sections ranged from 1.25 to 1.53 mg / L (mean 1.35 mg / L), and the optimized average total phosphorus concentration ranged from 0.0469 to 0.102 mg / L (mean 0.0595 mg / L). The total implementation cost ranged from 2.33 million to 3.17 million yuan (mean 2.71 million yuan). Compared to the unoptimized average total nitrogen concentration (1.44 mg / L) and average total phosphorus concentration (0.0729 mg / L) at the river sections, the 200 pond management schemes obtained by this invention reduced non-point source nitrogen and phosphorus pollution and improved river water quality.

[0044] Step 8: Construct the decision matrix based on the Pareto non-dominated solution set. Standardize it to obtain Okay. Setting the weights of the three objective functions to 1 / 3 each, we obtain the weighted normalization matrix. Given that all three objective functions aim to be minimized, we set... The minimum value of each target dimension is The maximum value is Calculate the scores of each candidate scheme. , and ,according to The sorting shows that the 65th non-dominated solution is the optimal solution in the solution set. Figure 2 This refers to the optimal management scheme for the ponds. This scheme can reduce the average total nitrogen concentration at 43 river sections to 1.35 mg / L and the average total phosphorus concentration to 0.0536 mg / L, with a total implementation cost of 2.48 million yuan. Selecting a specific river section, we reviewed the pond management engineering data included in the optimal scheme. For example, there are three ponds in the buffer zone corresponding to river section No. 2. The optimal scheme indicates that none of the three ponds need dredging, but the area of ​​each pond needs to be reduced (by 9.02%-18.0%), and the connectivity between each pond and the river section needs to be strengthened (reducing the connection distance between the pond and the river by 9.02%-18.1%). The pond shape complexity needs to be increased by 4.31% through pond shoreline modification engineering. Through the implementation of the above pond management engineering, the total nitrogen concentration at river section No. 2 can be reduced from 1.45 mg / L to 1.41 mg / L, and the total phosphorus concentration can be reduced from 0.277 mg / L to 0.220 mg / L.

[0045] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0046] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-objective optimization management method for ponds for the control of non-point source pollution in agricultural watersheds, characterized in that, include: Step 1: Select several typical river sections within the watershed, collect surface water samples, and determine their total nitrogen and total phosphorus concentrations; Several typical ponds within the watershed were selected to clarify their intended use and type. Sediments from the ponds were collected and their total nitrogen and total phosphorus concentrations were measured. Step 2: For the selected river cross section, divide it into circular buffer zones with the sampling point as the center; count the number of ponds in the circular buffer zone; estimate the total nitrogen and total phosphorus concentrations of sediments in each pond based on the type of use of the ponds; and calculate the total nitrogen and total phosphorus status of sediments in the ponds within the buffer zone. Step 3: Calculate the morphological indicators of the pond within the circular buffer zone, including the pond shape complexity, pond area, and distance between the pond and the river. Step 4: Using the total nitrogen and total phosphorus concentrations of the river cross-section as response variables, and the total nitrogen and total phosphorus concentrations of pond sediments obtained in Step 2 and the pond morphology indicators obtained in Step 3 as explanatory variables, a generalized additive model for river nitrogen and phosphorus regulation is constructed. Based on the deviation between the measured values ​​and the model prediction values ​​of each river cross-section, a baseline correction value specific to the river cross-section is constructed. In the prediction simulation, this value is superimposed on the results of the nonlinear interaction effect evaluation model to establish the prediction equations for the response of river total nitrogen and total phosphorus concentrations to changes in pond attributes. Step 5: Define the decision variables for the pond management project and construct the state transition equations for the decision variables of the pond management project; Step 6: Based on the prediction equations of the response of total nitrogen and total phosphorus concentrations in rivers to changes in pond attributes and the state transition equations of decision variables for pond management projects, establish a multi-objective dynamic optimization model for pond management with the goal of maximizing non-point source nitrogen and phosphorus pollution reduction and minimizing project implementation costs. Step 7: Use an evolutionary algorithm to solve the constructed multi-objective dynamic optimization model for pond management to obtain the Pareto non-dominated solution set; Step 8: Based on the multi-objective decision-making method, screen and rank the Pareto non-dominated solutions to determine the optimal management scheme for the pond.

2. The multi-objective optimization management method for ponds for the control of non-point source pollution in agricultural watersheds according to claim 1, characterized in that, Step 2 specifically includes: based on the measured total nitrogen and total phosphorus concentrations of the pond sediments, calculating the average total nitrogen and total phosphorus concentrations of the sediments for each type of pond according to different pond uses, and assigning these values ​​to the same type of ponds within the buffer zone; summing the total nitrogen concentrations (tns) of the sediments in individual ponds within the buffer zone to obtain the total nitrogen status (TNS) of the buffer zone pond sediments; and summing the total phosphorus concentrations (tps) of the sediments in individual ponds within the buffer zone to obtain the total phosphorus status (TPS) of the buffer zone pond sediments.

3. The multi-objective optimization management method for ponds for the control of non-point source pollution in agricultural watersheds according to claim 1, characterized in that, Step 3 specifically includes: Step 3.1: The pond shape complexity is characterized by the pond landscape pattern index at the class scale, and the index with the highest correlation with the total nitrogen concentration and total phosphorus concentration of the river section is selected by Spearman rank correlation test as the pond shape complexity index PS. Step 3.2: The area pa of a single pond is calculated based on the pond water area vector file. The total pond area PA is obtained by summing the areas of all individual ponds within the buffer zone. Step 3.3: The distance pd between a single pond and a river cross-section sampling point is calculated by the nearest neighbor analysis tool. The connection distance PD between the pond and the river is obtained by summing the distances between all ponds and river cross-section sampling points within the buffer zone.

4. The multi-objective optimization management method for ponds for the control of non-point source pollution in agricultural watersheds according to claim 1, characterized in that, Step 4 specifically includes: Step 4.1: Using the total nitrogen concentration (TN) and total phosphorus concentration (TP) at the river cross-section as response variables, and the pond shape complexity index (PS), total pond area (PA), pond-river connectivity distance (PD), total nitrogen state (TNS) of sediments in the buffer pond, and total phosphorus state (TPS) of sediments in the buffer pond as explanatory variables, a generalized additive model for river nitrogen and phosphorus regulation is constructed. The formula is as follows: ； In the formula, the subscript Represents the river section number. For link functions, cross-section TN or TP, For the intercept term, Represents residual, Represents a nonparametric smoothing function. The tensor product smoothing function is a function that integrates the interaction of three indicators, PA, PD, and TNS / TPS, based on the three-dimensional source-sink regulation concept of area-distance-sediment. Step 4.2: Based on the deviation between the measured values ​​and the model predictions for each cross-section, calculate the baseline correction amount that takes into account the specificity of the cross-section. The formula is as follows: ； In the formula, Let be the baseline correction amount for section s. To measure the total nitrogen or total phosphorus concentration at river cross-sections, These are simulated values ​​of total nitrogen or total phosphorus concentrations at river cross sections under baseline conditions. Step 4.3: During the prediction simulation, updating the values ​​of the explanatory variables yields the predicted value of section s, as shown in the formula: ； In the formula, The values ​​at section s are simulated values ​​obtained using a generalized additive model of river nitrogen and phosphorus regulation. , , , and The model input values ​​that represent the changes; Step 4.4: For each cross section, the baseline correction is superimposed on the model prediction, and the prediction result is obtained through the inverse transform of the link function, as shown in the formula: ； In the formula, This represents the final predicted result of the total nitrogen or total phosphorus concentration in the river at the cross-section. Representative link function The inverse transform of .

5. A multi-objective optimization management method for ponds for the control of non-point source pollution in agricultural watersheds according to claim 4, characterized in that, Step 5 specifically includes: Step 5.1 defines the pond-river water system connectivity project as a continuous decision variable. The degree of modification to the water flow path between the pond and the river directly affects the PD value; the pond area modification project is defined as a continuous decision variable. The value represents the degree of modification to the pond area; a positive value represents an increase in the area (PA value), while a negative value represents a decrease in the area (PA value). The decision-making definition for the pond dredging project is a binary decision variable. 1 represents dredging, and 0 represents no dredging. Dredging directly reduces the TNS and TPS values ​​of the pond. The pond shoreline renovation project is defined as a continuous decision variable. Shoreline modification will increase the PS value; the subscripts in the above variables Represents a river cross-section, subscript Representing the The first cross-section corresponds to the buffer zone within the first... A pond, and These represent the upper and lower limits of the proportion of the renovation project to connect the pond and the river system. and These represent the upper and lower limits of the area renovation ratio, respectively. This represents the upper limit of the increase in shoreline complexity. Step 5.2, the state transition equations for the changes in PD, PS, PA, TNS, and TPS values ​​as the pond management project is implemented are set as follows: ； ； ； ； ； In the formula, , , , The first s The first cross-section corresponds to the buffer zone within the first... i The sampling points were located at the distance between the pond and the river cross-section, and the pond area, total nitrogen content, and total phosphorus content of the pond sediments were recorded. For the first The number of ponds in the buffer zone corresponds to each cross section.

6. The multi-objective optimization management method for ponds for the control of non-point source pollution in agricultural watersheds according to claim 1, characterized in that, Step 6 specifically includes: Step 6.1, the objective function for maximizing the reduction of non-point source nitrogen and phosphorus pollution is defined as: ； ； In the formula, This refers to the current river section number, which belongs to a set. , The number of river cross sections, and These are the total nitrogen and total phosphorus concentrations at the river cross-section after the decision-making change; Step 6.2, the objective function for minimizing the cost of the pond management project is defined as: In the formula, The unit price for the construction cost of the pond-river water system connection project. The unit price for the construction cost of the pond dredging project. The unit price for the construction cost of the pond area renovation project. This refers to the unit price for the construction cost of the pond shoreline renovation project.

7. A multi-objective optimization management method for ponds for the control of non-point source pollution in agricultural watersheds according to claim 1, characterized in that, Step 7 specifically includes: using a non-dominated sorting genetic algorithm with an elitist strategy to solve the Pareto non-dominated solution set of the multi-objective dynamic optimization model for pond management, setting optimization parameters including: objective dimension, initial population size, number of generations, crossover probability and mutation probability, and performing iterative calculations; when the number of calculations reaches the number of generations, the Pareto non-dominated solution set for pond optimization management is obtained.

8. A multi-objective optimization management method for ponds for the control of non-point source pollution in agricultural watersheds according to claim 1, characterized in that, Step 8 specifically includes: Step 8.1: The superior-inferior solution distance method is used as a multi-objective decision-making method to screen pond optimization schemes; a decision matrix is ​​constructed based on the Pareto non-dominated solution set for pond optimization management. ,in It is a solution in the Pareto non-dominated solution set. This is the index of the solution in the solution set. The spatial dimension index of the solution. Let be the total number of solutions in the non-dominated solution set. The total number of spatial dimensions of the non-dominated solution set; Step 8.2: Determine the weights of the three optimization objectives for pond management. ,in Calculate the weighted normalization matrix : ； Step 8.3: Based on each optimization objective attribute, determine the optimal value in the weighted normalization matrix as the positive ideal solution. The worst value is taken as the negative ideal solution. The distance between each candidate solution and the positive ideal solution is calculated using Euclidean distance. and the distance to the negative ideal solution : ； ； Step 8.4: Calculate the proximity coefficient of each candidate pond optimization scheme. : ； in The closer the value is to 1, the better the solution; select The scheme corresponding to the maximum value is taken as the optimal scheme for pond management.

9. A multi-objective optimization management method for ponds for the control of non-point source pollution in agricultural watersheds according to claim 8, characterized in that, This also includes using vector normalization methods to... Standardization is performed to obtain the standardized matrix. The formula is: 。

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