A pond multi-objective optimization management method for agricultural watershed non-point source pollution regulation

Abstract

The application discloses a kind of pond multi-objective optimization management methods for agricultural watershed non-point source pollution regulation, it is related to agricultural watershed non-point source pollution control technical field, for the first time, the multi-dimensional attributes such as pond use type, form feature and sediment nutrient state are integrated into unified quantification framework, by constructing generalized additive model, the nonlinearity and interaction of the influence of pond attribute on river water quality can be accurately captured, the accuracy of river nitrogen and phosphorus concentration prediction is improved. Pond management measures are quantified as controllable decision variables, a multi-objective dynamic optimization model is established to balance environmental benefits and economic benefits, the traditional experience decision is replaced by Pareto optimal solution, a scientific and efficient pond management scheme is proposed, which can be quantitatively implemented, avoiding the one-sidedness of single target, maximizing non-point source pollution reduction while minimizing cost, achieving precise allocation and scientific and quantitative decision of pond management resources.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of agricultural watershed non-point source pollution control, more particularly to a water pond multi-objective optimization management method for agricultural watershed non-point source pollution regulation. BACKGROUND

[0002] At present, agricultural watershed non-point source pollution is one of the main causes of water body nitrogen and phosphorus concentration exceeding standard and eutrophication and other water environmental problems. As a widely distributed small and micro water body in the watershed, the water pond plays a dual and dynamic role in regulating such pollution. The water pond is not only a "sink" of pollutants, which reduces nitrogen and phosphorus load through interception, sedimentation, plant absorption and microbial activity, but also a potential source of pollutants, which may trigger the release of internal source nitrogen and phosphorus and exacerbate the pollution risk of downstream water body especially when the sediment nutrients of the water pond are saturated and the environment is disturbed (such as rainstorm events, temperature rise, oxygen deficiency, etc.). The dual nature of the source-sink function makes the influence of the water pond on the downstream water quality complex and difficult to predict. Current research believes that the conversion of the source-sink function of the water pond is comprehensively affected by the multi-dimensional attributes of the water pond, including the type of water pond use, morphological characteristics and sediment nutrient status. Therefore, when using water pond management to improve pollution reduction, the influence mechanism of the water pond attributes on the river water quality should be clarified, and the water pond management scheme for efficient control of agricultural non-point source pollution should be developed through the transformation and optimization of the water pond attributes.

[0003] However, the existing water pond management method has the following defects and deficiencies. First, the existing technology is still insufficient in quantifying the response relationship of river water quality to the water pond. The traditional method is mostly based on linear assumption or empirical judgment, usually only focusing on the relationship between a single indicator such as the area or number of the water pond and the river water quality, without systematically considering the interaction between the multi-dimensional attributes such as the water pond use, morphology and sediment nutrient status and their nonlinear influence on the river water quality. Therefore, it is difficult to accurately reveal the complex mechanism of the water pond in the regulation of nitrogen and phosphorus pollution, resulting in deviation between the prediction results and the actual regulation effect, which restricts the scientificity of the management decision. Second, the existing water pond management scheme mostly focuses on the local implementation of a single measure (such as dredging or ecological revetment). Although such measures may improve the water quality of local water body, due to the lack of consideration of spatial heterogeneity factors such as land use, landscape pattern and pollution load, the reduction effect of the measures in other areas is uncertain, which limits the systematic regulation effect of the homogeneous management technology at the watershed scale. In addition, the comprehensive management of the water pond should not only aim at promoting non-point source pollution reduction, but also consider the implementation cost. However, the existing technology often focuses on a single target of water quality improvement or cost control, lacks a dynamic decision-making model integrating the water quality response mechanism, engineering cost constraint and multi-objective optimization, which makes it difficult for the management scheme to achieve the balance between environmental and economic benefits in practice, thereby limiting the efficient use of resources.

[0004] Therefore, how to propose an optimal scheme for pond management under the multi-optimization objectives of maximizing water quality improvement and minimizing cost is a problem to be solved by those skilled in the art. SUMMARY

[0005] Therefore, the present application provides a water pond multi-objective optimization management method for agricultural watershed non-point source pollution regulation to solve the problems in the background art.

[0006] To achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0007] A water pond multi-objective optimization management method for agricultural watershed non-point source pollution regulation, comprising:

[0008] Step 1, selecting multiple typical river sections in the watershed, collecting surface water samples and measuring the total nitrogen concentration and total phosphorus concentration; selecting multiple typical ponds in the watershed, determining the purpose type of the ponds, collecting pond sediment samples and measuring the total nitrogen concentration and total phosphorus concentration;

[0009] Step 2, for the selected river section, taking the sampling point as the center, dividing a circular buffer zone; counting the number of ponds in the circular buffer zone, estimating the total nitrogen concentration and total phosphorus concentration of the sediment of each pond based on the purpose type of the pond, and calculating the total nitrogen and total phosphorus status of the sediment of the pond in the buffer zone;

[0010] Step 3, calculating the shape index of the pond in the circular buffer zone, including the complexity of the shape of the pond, the area of the pond and the distance between the pond and the river;

[0011] Step 4, taking the total nitrogen and total phosphorus concentrations of the river section as response variables, taking the total nitrogen concentration and total phosphorus concentration of the pond sediment obtained in step 2 and the shape index of the pond obtained in step 3 as explanatory variables, constructing a generalized additive model for river nitrogen and phosphorus regulation; based on the deviation between the measured values and the predicted values of each river section, constructing a baseline correction quantity specific to the river section, and adding it to the results of the nonlinear interaction effect evaluation model in the prediction simulation, to establish a prediction equation for the response of the total nitrogen and total phosphorus concentrations of the river to the changes in the properties of the pond;

[0012] Step 5, defining the state transition equation of the pond management engineering decision variable;

[0013] Step 6, based on the prediction equation for the response of the total nitrogen and total phosphorus concentrations of the river to the changes in the properties of the pond and the state transition equation of the pond management engineering decision variable, establishing a multi-objective dynamic optimization model for pond management aiming at maximizing the reduction of non-point source nitrogen and phosphorus pollution and minimizing the engineering implementation cost;

[0014] Step 7, using an evolutionary algorithm to solve the constructed multi-objective dynamic optimization model for pond management, and obtaining a Pareto non-inferior solution set.

[0015] 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.

[0016] 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.

[0017] Optionally, step 3 specifically includes:

[0018] 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.

[0019] 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.

[0020] 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.

[0021] Optionally, step 4 specifically includes:

[0022] 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:

[0023] ;

[0024] In the formula, the subscript Represents the river section number. For link functions, cross-section TN or TP, For the intercept term, Represents residuals, Represents a nonparametric smoothing function. The representative tensor product smoothing function is based on the area-distance-sediment three-dimensional source-sink regulation idea to integrate the interaction of PA, PD and TNS / TPS three indexes.

[0025] Step 4.2, based on the deviation between the measured value of each section and the predicted value of the model, the baseline correction amount considering the specificity of the section is calculated, the formula is:

[0026] ;

[0027] In the formula, is the baseline correction amount of section s, is the measured concentration of total nitrogen or total phosphorus of the river section, is the simulation value of the total nitrogen or total phosphorus concentration of the river section under the baseline condition;

[0028] Step 4.3, in the prediction simulation, the value of the explanatory variable is updated to obtain the predicted value of section s, the formula is

[0029] ;

[0030] In the formula, is the simulation value obtained by using the river nitrogen and phosphorus regulation generalized additive model at section s, , , , and represent the changed model input value;

[0031] Step 4.4, for each section, the baseline correction amount is added to the model predicted value, and the prediction result is obtained through the inverse transformation of the linking function, the formula is:

[0032] ;

[0033] In the formula, is the final prediction result of the total nitrogen or total phosphorus concentration of the river section, represents the inverse transformation of the linking function .

[0034] Optionally, the step 5 specifically includes:

[0035] Step 5.1, the water pond-river system connection project is defined as a continuous decision variable , which represents the degree of water flow path reconstruction between the water pond and the river, directly affecting the PD value; the water pond area reconstruction project is defined as a continuous decision variable , which represents the degree of water pond area reconstruction, a positive value represents expanding the area, that is, increasing the PA value, and a negative value represents reducing the area, that is, reducing the PA value; the water pond dredging project decision is defined as a binary decision variable , 1 represents dredging, 0 represents no dredging, and dredging will directly reduce the TNS and TPS values of the pond; the pond shoreline reconstruction project is defined as a continuous decision variable , and shoreline reconstruction will increase the PS value; the subscript in the above variables represents the river section, and the subscript represents the th section corresponding to the th pond in the buffer zone, and respectively represent the upper and lower limits of the pond-river system connection distance reconstruction ratio, and respectively represent the upper and lower limits of the area reconstruction ratio, represents the upper limit of the shoreline complexity increase ratio;

[0036] Step 5.2, the state transition equation of PD, PS, PA, TNS and TPS values with the implementation of the pond management project is set as:

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] ;

[0042] In the formula, , , , are the pond-river section sampling point distance, pond area, pond sediment total nitrogen status and pond sediment total phosphorus status of the s th pond in the buffer zone corresponding to the i th section, is the number of ponds in the buffer zone corresponding to the th section.

[0043] Optionally, the step 6 specifically comprises:

[0044] Step 6.1, the maximum reduction target function of non-point source nitrogen and phosphorus pollution is defined as:

[0045] ;

[0046] ;

[0047] In the formula, is the current river section number, belonging to the set , is the number of river sections, and is the total nitrogen and total phosphorus concentration of the river section after the decision change;

[0048] Step 6.2, the water pond management engineering cost minimization objective function is defined as:

[0049]

[0050] In the formula, is the water pond-river system connection engineering construction cost unit price, is the water pond desilting engineering construction cost unit price, is the water pond area reconstruction engineering construction cost unit price, is the water pond shoreline reconstruction engineering construction cost unit price.

[0051] Optionally, the step 7 specifically comprises: using a non-dominated sorting genetic algorithm with elitism to solve the Pareto non-inferior solution set of the water pond management multi-objective dynamic optimization model, setting optimization parameters including: target dimension, initial population size, evolution algebra, crossover probability and mutation probability, and performing iterative operation; and when the operation times reach the evolution algebra, the Pareto non-inferior solution set of the water pond optimization management is obtained.

[0052] Optionally, the step 8 specifically comprises:

[0053] Step 8.1, using the superior-inferior solution distance method as a multi-objective decision method to screen the water pond optimization scheme; and constructing a decision matrix based on the Pareto non-inferior solution set of the water pond optimization management , wherein is one solution in the Pareto non-inferior solution set, is the serial number of the solution in the solution set, is the serial number of the space dimension of the solution, is the total number of solutions in the non-inferior solution set, is the total number of space dimensions of the non-inferior solution set;

[0054] Step 8.2, determining the weight of the three optimization objectives of the water pond management , wherein , the weighted standardized matrix is calculated :

[0055] ;

[0056] Step 8.3, according to the properties of each optimization objective, determining the optimal value in the weighted standardized matrix as the positive ideal solution and the worst value as the negative ideal solution ; and using the Euclidean distance to calculate the distance between each candidate scheme and the positive ideal solution and the distance between the positive ideal solution and the negative ideal solution :

[0057] ;

[0058] ;

[0059] Step 8.4, calculating the closeness coefficient of each candidate water pond optimization scheme :

[0060] ;

[0061] wherein , the value closer to 1 indicates that the scheme is better; selecting the scheme corresponding to the maximum value as the optimal water pond management scheme.

[0062] Optionally, the vector normalization method is used to standardize to obtain a standardized matrix , and the formula is:

[0063] .

[0064] According to the technical scheme, compared with the prior art, the application discloses a water pond multi-objective optimization management method for agricultural watershed non-point source pollution regulation and control, overcomes the limitations of traditional methods, such as ignoring multi-factor interaction effect, relying on linear assumption, and lacking systematic optimization, and provides a scientific and efficient water pond management scheme for non-point source pollution treatment in an agricultural watershed, which can be quantitatively implemented. The application first integrates multi-dimensional attributes such as water pond use type, morphological characteristics (area, shape, and distance from river), and sediment nutrient state into a unified quantitative framework, accurately captures the nonlinearity and interaction of the influence of water pond attributes on river water quality by constructing a generalized additive model, and improves the accuracy of river nitrogen and phosphorus concentration prediction. The application further quantizes water pond management measures as controllable decision variables, establishes a multi-objective dynamic optimization model for balancing environmental benefits and economic benefits, replaces the traditional experience decision with a Pareto optimal solution, avoids one-sidedness of a single target, maximizes non-point source pollution reduction while minimizing cost, and realizes precise allocation and scientific and quantitative decision of water pond management resources. BRIEF DESCRIPTION OF DRAWINGS

[0065] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only embodiments of the present application, and those skilled in the art can obtain other drawings according to the provided drawings without creative labor.

[0066] Figure 1 The method flowchart provided by the present application is shown.

[0067] Figure 2 The Pareto non-inferior solution and optimal solution scatter diagram for the embodiments provided by the present application is shown. DETAILED DESCRIPTION

[0068] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0069] The embodiment of the present application discloses a water pond multi-objective optimization management method for agricultural watershed non-point source pollution regulation, as shown in Figure 1 The embodiment of the present application discloses a water pond multi-objective optimization management method for agricultural watershed non-point source pollution regulation, as shown in

[0070] Step 1, a plurality of typical river sections in the watershed are selected, surface water samples are collected and total nitrogen concentration and total phosphorus concentration are measured; a plurality of typical water ponds in the watershed are selected, the use types of the water ponds are determined, sediment samples of the water ponds are collected and total nitrogen concentration and total phosphorus concentration are measured;

[0071] Step 2, for the selected river sections, the sampling points thereof are taken as the centers to divide circular buffer zones; the number of water ponds in the circular buffer zones is counted, the total nitrogen concentration and total phosphorus concentration of the sediment of each water pond are estimated based on the use types of the water ponds, and the total nitrogen and total phosphorus states of the sediment of the water ponds in the buffer zones are calculated;

[0072] Step 3, the morphological indexes of the water ponds in the circular buffer zones are calculated, including the water pond shape complexity, the water pond area and the water pond and river connection distance;

[0073] Step 4, the total nitrogen and total phosphorus concentrations of the river sections are taken as response variables, the total nitrogen concentration and total phosphorus concentration of the sediment of the water ponds obtained in step 2 and the morphological indexes of the water ponds obtained in step 3 are taken as explanation variables, and a river nitrogen and phosphorus regulation generalized additive model is constructed; based on the deviation between the measured values and the model predicted values of each river section, a baseline correction amount specific to the river section is constructed, which is superimposed to the nonlinear interaction effect evaluation model result in the prediction simulation, and a prediction equation of the river total nitrogen and total phosphorus concentration responding to the water pond attribute change is established;

[0074] Step 5, the water pond management engineering decision variable is defined, and a state transition equation of the water pond management engineering decision variable is constructed;

[0075] Step 6, based on the prediction equation of the total nitrogen and total phosphorus concentration of the river responding to the change of the pond attribute and the state transition equation of the decision variable of the pond management engineering, a multi-objective dynamic optimization model of pond management is established to maximize the reduction of non-point source nitrogen and phosphorus pollution and minimize the implementation cost of the engineering;

[0076] Step 7, the evolutionary algorithm is used to solve the constructed multi-objective dynamic optimization model of pond management, and the Pareto non-inferior solution set is obtained;

[0077] Step 8, the Pareto non-inferior solution is screened and sorted based on the multi-objective decision method, and the optimal management scheme of the pond is determined.

[0078] In a specific embodiment, step 1 specifically comprises:

[0079] Step 1.1, the selection principle of the river section includes: focusing on covering key control positions such as upstream and downstream of the main stream, main tributaries, etc., and reflecting the influence of pollution of different land use types.

[0080] Step 1.2, the purpose type of the pond is determined through field investigation, and the typical purpose type of the pond includes but is not limited to: irrigation pond, aquaculture pond, rural domestic pond and tail water treatment pond. The selection of the pond should cover all typical purpose types.

[0081] In a specific embodiment, step 2 specifically comprises: the total nitrogen concentration and total phosphorus concentration of the sediment of each pond in the buffer zone are estimated based on the purpose type of the pond, that is, based on the typical pond sediment total nitrogen concentration and total phosphorus concentration determined in step 1, the average sediment total nitrogen concentration and total phosphorus concentration of each type of pond is calculated according to different pond purpose types, and is assigned to the same type of pond in the buffer zone. The total nitrogen concentration (tns) of the sediment of a single pond in the buffer zone is summarized to obtain the total nitrogen state (TNS) of the sediment of the pond in the buffer zone, and the total phosphorus concentration (tps) of the sediment of a single pond in the buffer zone is summarized to obtain the total phosphorus state (TPS) of the sediment of the pond in the buffer zone.

[0082] In a specific embodiment, step 3 specifically comprises:

[0083] Step 3.1, the shape complexity of the pond is represented by the class-scale pond landscape pattern index (SHAPE_MN, LSI, FRAC_MN and PARA_MN), which is calculated by the spatial position grid data of the pond and the FRAGSTATS 4.2 software. The four indexes are selected by Spearman rank correlation test, and the highest correlation indexes of the total nitrogen concentration (TN) and the total phosphorus concentration (TP) of the river section are selected as the shape complexity (PS) index.

[0084] 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).

[0085] 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).

[0086] In one specific embodiment, step 4 specifically includes:

[0087] 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:

[0088] ;

[0089] In the formula, the subscript Represents the river section number. For link functions, cross-section TN or TP, For the intercept term, Represents residuals, 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.

[0090] 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:

[0091] ;

[0092] In the formula, 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;

[0093] 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:

[0094] ;

[0095] wherein, is the simulated value of the generalized additive model using river nitrogen and phosphorus regulation at the section s, , , , and represent the changed model input values;

[0096] Step 4.4, for each section, the baseline correction amount is added to the model prediction value, and the prediction result is obtained by inverse transformation of the linking function, the formula is:

[0097] ;

[0098] wherein, is the final prediction result of the total nitrogen or total phosphorus concentration of the river at the section, represents the inverse transformation of the linking function .

[0099] In a specific embodiment, step 5 specifically comprises:

[0100] Step 5.1, the water pond-river system connection project is defined as a continuous decision variable , which represents the degree of modification of the water flow path between the water pond and the river, directly affecting the PD value; the water pond area modification project is defined as a continuous decision variable , which represents the degree of modification of the water pond area, a positive value represents an enlarged area, i.e. an increased PA value, and a negative value represents a reduced area, i.e. a reduced PA value; the water pond dredging project decision is defined as a binary decision variable , 1 represents dredging, and 0 represents no dredging, dredging will directly reduce the TNS and TPS values of the water pond; the water pond shoreline modification project is defined as a continuous decision variable , shoreline modification will increase the PS value; in the above variables, the subscript represents the river section, and the subscript represents the th section corresponding to the th water pond in the buffer zone, and represent the upper and lower limits of the water pond-river system connection distance modification ratio, and represent the upper and lower limits of the area modification ratio, represents the upper limit of the shoreline complexity increase ratio;

[0101] Step 5.2, the state transition equation of PD, PS, PA, TNS and TPS values changing with the implementation of the water pond management project is set as:

[0102] ;

[0103] ;

[0104] ;

[0105] ;

[0106] ;

[0107] 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.

[0108] In one specific embodiment, step 6 specifically includes:

[0109] Step 6.1, the objective function for maximizing the reduction of non-point source nitrogen and phosphorus pollution is defined as:

[0110] ;

[0111] ;

[0112] 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;

[0113] Step 6.2, the objective function for minimizing the cost of the pond management project is defined as:

[0114] ;

[0115] 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.

[0116] In one specific embodiment, step 7 specifically comprises: solving the Pareto non-inferior solution set of the pond management multi-objective dynamic optimization model by using the non-dominated sorting genetic algorithm with elitist strategy, setting the optimization parameters including: target dimension, initial population size, evolution number, crossover probability and mutation probability, and performing iterative operation; and obtaining the Pareto non-inferior solution set of the pond optimization management when the operation number reaches the evolution number.

[0117] In one specific embodiment, step 8 specifically comprises:

[0118] Step 8.1, using the superior and inferior solution distance method as a multi-objective decision-making method to screen the pond optimization scheme; and constructing a decision matrix based on the Pareto non-inferior solution set of the pond optimization management , wherein is a solution in the Pareto non-inferior solution set, is the serial number of the solution in the solution set, is the spatial dimension serial number of the solution, is the total number of solutions in the non-inferior solution set, is the total number of spatial dimensions of the non-inferior solution set;

[0119] The vector normalization method is used to standardize to obtain the standardized matrix , and the formula is:

[0120] .

[0121] Step 8.2, determining the weight of the three optimization objectives of the pond management , wherein , the weighted standardized matrix is calculated:

[0122] ;

[0123] Step 8.3, according to the properties of each optimization objective, determining the optimal value in the weighted normalized matrix as the positive ideal solution , and the worst value as the negative ideal solution ; using the Euclidean distance to calculate the distance between each candidate scheme and the positive ideal solution and the distance between each candidate scheme and the negative ideal solution :

[0124] ;

[0125] ;

[0126] Step 8.4, calculating the closeness coefficient of each candidate pond optimization scheme :

[0127] ;

[0128] wherein , the value closer to 1 indicates the scheme is better; select the scheme corresponding to the maximum value as the optimal scheme for the water pond management.

[0129] A specific embodiment is introduced below to further illustrate the method of the present application;

[0130] The study area is an agricultural watershed in Anhui Province, with a watershed area of about 90 km 2 , located on the north bank of Chaohu Lake. As Figure 1 shown, the multi-objective optimization management method for water pond control of agricultural watershed non-point source pollution proceeds in the following steps:

[0131] Step 1, select 43 typical river monitoring sections in the watershed, i.e. The sections cover two main streams and important tributaries in the watershed, and the land use types around the sections cover the main land use types in the watershed, such as farmland, forest land and residential area. The total nitrogen concentration (0.522-4.75 mg / L) and total phosphorus concentration (0.002-0.384 mg / L) of surface water at all river sections were measured. A total of 26 typical water ponds were selected in the watershed, and the purpose of the water ponds was determined according to field investigation, including irrigation ponds, breeding ponds, rural domestic ponds and tail water treatment ponds. The total nitrogen concentration (1.32-45.9 mg / g) and total phosphorus concentration (0.469-16.5 mg / g) of the sediments of the 26 water ponds were determined.

[0132] Step 2, for the 43 selected typical river monitoring sections, divide a circular buffer zone with a diameter of 400 m with the sampling point of each section as the center, and count a total of 308 water ponds contained in the buffer zone, with the minimum number of water ponds in the buffer zone being 1 and the maximum number being 27. Based on the total nitrogen concentration and total phosphorus concentration of the sediments of the 26 water ponds of different use types determined in step 1, calculate the average total nitrogen concentration and total phosphorus concentration of each type of water pond (Table 1). Assign the average concentration in Table 1 to the same type of water pond in the buffer zone, i.e. obtain tns and tps. Summing up the tns and tps of all water ponds in each buffer zone can obtain TNS and TPS.

[0133] Table 1 Average total nitrogen and total phosphorus concentrations of sediments of water ponds of different use types

[0134]

[0135] Step 3, the class-scale pond landscape pattern indices of each buffer zone were calculated by FRAGSTATS 4.2 software, including SHAPE_MN, LSI, FRAC_MN and PARA_MN. The index with the highest correlation with the total nitrogen concentration of the river section was SHAPE_MN, and the index with the highest correlation with the total phosphorus concentration was LSI. The area of a single pond pa was calculated by ArcMap 10.7 software, and the total pond area PA of all pa values in 43 buffer zones was obtained. The distance (pd) between a single pond and the sampling point of the river section was calculated by ArcMap 10.7 software, and the distance PD between the pond and the river in the buffer zone was obtained by summing up all pd values in 43 buffer zones.

[0136] Step 4, the quantitative relationship between variables was established by using generalized additive model, and the formula was:

[0137] ;

[0138] ;

[0139] where TN and TP were response variables, SHAPE_MN and LSI in the explanatory variables were set as nonlinear smooth terms, and the model was fitted by a smooth curve; PA, PD and TNS were set as tensor product smooth terms, which were used to capture the complex interaction between the three variables and allowed the model to consider their joint effects on the response variables. In terms of model parameter settings, the gamma distribution family and the log link function were selected to adapt to the characteristics of the response variables being positive and having skew distribution, and the restricted maximum likelihood method was used for model fitting. The results of the nonlinear model for TN showed that the adjusted R 2 squared of the model reached 0.642, and the deviance explained was 55.7%, indicating that the model had good goodness of fit; the results of the nonlinear model for TP showed that the adjusted R 2 squared of the model was 0.192, and the deviance explained was 52.7%, indicating that the model had good goodness of fit. The p values of the smooth terms SHAPE_MN and LSI and the tensor product smooth terms were all less than 0.05. This method can effectively use generalized additive model to accurately capture the nonlinear relationship and interaction between river water quality concentration and pond properties, providing a reliable basis for subsequent prediction and simulation. Based on the deviation between the measured values and the predicted values of each section, the baseline correction amount and was calculated considering the specificity of the section, and the baseline correction amount was added to the model predicted value, and the prediction function of the total nitrogen and total phosphorus concentration response to the pond properties for each river section was obtained through the inverse transformation of the link function.

[0140] Step 5, considering the pond-river system connection, pond area reconstruction, pond dredging and pond shoreline reconstruction as the pond management engineering measures of the study area. The upper and lower boundaries of the value are-0.2 and 0.2, respectively, The upper and lower boundaries of the value are-0.2 and 0.2, respectively, The upper limit of the value is 0.1. The implementation cost of each pond management engineering (ten thousand yuan) is: , , , .

[0141] Step 6, three pond management optimization target equations are set, including minimizing the average concentration of total nitrogen in river section , minimizing the average concentration of total phosphorus in river section and minimizing the cost of pond management , the formulas are respectively:

[0142] ;

[0143] ;

[0144]

[0145] Step 7, the NSGA-II algorithm parameter setting is shown in Table 2. The iteration stops when the algorithm runs to the maximum iteration number.

[0146] Table 2 NSGA-II algorithm parameter setting

[0147]

[0148] After 400 iterations of operation, a set of 200 non-inferior solutions containing Pareto solution set is obtained, and the Pareto non-inferior solution scatter diagram is shown in Figure 2 , wherein the optimization result of the average concentration of total nitrogen in river section is between 1.25 and 1.53 mg / L (the average is 1.35 mg / L), the optimization result of the average concentration of total phosphorus in river section is between 0.0469 and 0.102 mg / L (the average is 0.0595 mg / L), and the total implementation cost is between 233 and 317 thousand yuan (the average is 271 thousand yuan). Compared with the average concentration of total nitrogen (1.44 mg / L) and the average concentration of total phosphorus (0.0729 mg / L) in river section before optimization, the 200 pond management schemes obtained by the present application reduce the non-point source nitrogen and phosphorus pollution and improve the river water quality.

[0149] Step 8, based on the Pareto non-inferior solution set, a decision matrix is constructed, and after standardization 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 solution. , 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.

[0150] 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.

[0151] 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 plan for the pond. 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 residuals, 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 inverse transform; Step 5 specifically includes: Step 5.1 defines the pond-river water system connectivity project as a continuous decision variable. The PD value represents the degree of modification to the water flow path between the pond and the river, directly affecting 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 section, the pond area, the total nitrogen content of the pond sediments, and the total phosphorus content of the pond sediments. For the first The number of ponds in the buffer zone corresponds to each cross section.

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 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.

5. 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.

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 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.

7. A multi-objective optimization management method for ponds for the control of non-point source pollution in agricultural watersheds according to claim 6, 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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