A Multi-objective Segmented Optimization Method for Grey-Green-Blue Measures Coupling SWMM with Wild Dog Optimization Algorithm

Abstract

The present invention provides a multi-objective segmented optimization method for gray-green-blue measures coupling the wild dog optimization algorithm and SWMM, which relates to the technical field of urban waterlogging control. By analyzing the waterlogging distribution, the present invention determines the measure type, scale and cost, and constructs an optimization model with the objectives of minimizing the total investment cost and maximizing the runoff reduction rate. The decision variables include the drainage flow of the pumping station, etc. The flow is analyzed by the hourly water storage method, and the variable relationship is established through multiple regression. In the first round, the wild dog algorithm is used to generate the Pareto solution set, and then it is optimized in combination with the SWMM model to obtain the Pareto front solution set applicable to areas lacking data. The present invention can enhance urban resilience.

Description

Technical Field

[0001] The present invention relates to the technical field of urban waterlogging control, and particularly to a multi-objective segmented optimization method for grey-green-blue measures coupling the wild dog optimization algorithm and SWMM. Background Art

[0002] In recent years, climate change has led to changes in the global precipitation pattern. The rapid development of urbanization has changed the runoff infiltration process. Under the superposition of problems such as mismatched drainage system design, urban waterlogging has become a challenge that needs to be jointly addressed globally. Grey-green-blue measures are particularly important for urban waterlogging control. However, due to the complexity of the operation mechanism and the uncertainty of the synergy effect, grey measures, especially pumping stations, are not used as decision variables in traditional multi-objective optimization models. At present, the research on urban drainage planning at the basin scale lacks systematicness, and the synergy effects of pumping station drainage flow, regional water surface ratio, and green measure layout ratio on the runoff generation and concentration process are not fully considered. How to achieve the organic combination of grey-green-blue measures and quantify the synergy effect remains an urgent problem to be solved.

[0003] The grey-green-blue hybrid infrastructure framework involves multiple factors. Under the complex multi-dimensional coupling relationship, the effective allocation of resources is crucial. Reasonably arranging the location and scale of green measures and regulating pumping stations to ensure the maximization of water management benefits. Therefore, how to determine the optimal ratio of grey-green-blue measures depends on the balance among multiple objectives. Integrating hydrological models and optimization algorithms to analyze the synergy mechanism of grey-green-blue measures can find the optimal spatial combination plan. However, it is also challenging to obtain and process various types of high-precision basic data required for the rainstorm flood model. Summary of the Invention

[0004] In order to overcome the deficiencies of the prior art, the purpose of the present invention is to provide a multi-objective segmented optimization method for grey-green-blue measures coupling the wild dog optimization algorithm and SWMM, which is applicable to both data-deficient areas and regions with modeling conditions. The present invention narrows the constraint range of decision variables through a segmented optimization strategy and seeks the optimal spatial layout plan. It provides a new idea for drainage optimization in data-deficient areas and, at the same time, provides better technical support for enhancing urban resilience.

[0005] To achieve the above purpose, the present invention provides the following solution:

[0006] A multi-objective segmented optimization method for grey-green-blue measures coupling the wild dog optimization algorithm and SWMM, comprising:

[0007] Determine the current situation of waterlogging distribution and simulation results based on the basic data of the study area collected and sorted out, and determine the types, scales, parameters, and unit investment costs of grey-green-blue measures;

[0008] Optimize the types and layouts of the grey-green-blue measures based on the current situation of waterlogging distribution;

[0009] Construct a multi-objective optimization model, with the minimum total investment cost and the maximum reduction rate of the total runoff volume as the objective functions, and the drainage flow rate of the pumping station, the water surface ratio, the depression green space ratio, and the permeable pavement ratio as the decision variables. Combine the area constraints, effectiveness constraints, and the fitting relationship between the decision variables to set the constraint conditions;

[0010] Based on the above-mentioned grey-green-blue measures and the multi-objective optimization model, use the hourly water storage calculation method to analyze the drainage flow rate of the pumping station under different working conditions, and establish a mathematical relationship expression between the decision variables through multiple regression analysis as the equality constraint;

[0011] Use the wild dog optimization algorithm to perform the first iterative optimization on the multi-objective optimization model, and generate the Pareto solution set and the decision variable range;

[0012] Construct a SWMM model based on the above-mentioned basic data, and use historical rainfall data for calibration and verification to ensure the accuracy of the SWMM model;

[0013] Couple the SWMM model with the wild dog optimization algorithm, update the objective function and constraint conditions based on the decision variable range of the first optimization, and perform the second optimization to generate the Pareto front solution set of the spatial layout of the grey-green-blue measures.

[0014] Preferably, the above-mentioned basic data includes: rainfall data, land use type, drainage network information, pumping station parameters, elevation data, and river water level data.

[0015] Preferably, optimize the type and layout of the grey-green-blue measures based on the current situation of waterlogging distribution, including:

[0016] Layout storage pumping stations near the river and in waterlogging-prone areas as grey measures;

[0017] According to the suitability of land use types, layout depression green spaces in ordinary green areas, and reconstruct permeable pavements in residential areas, commercial areas, and road areas as green measures;

[0018] Expand the water surface ratio of the original river and lake in the study area as blue measures.

[0019] Preferably, the decision variables of the multi-objective optimization model are: ; where X represents the vector of decision variables; q represents the flow rate of the drainage pumping station in the study area; p i represents the i water surface ratio of the x j represents the j area ratio of the mRepresents the number of water body types, n Represents the number of green measures;

[0020] The calculation formula of the objective function is: ; where, f 1 Represents the total investment cost, A Is the sum of the present value of investment and the present value of operation and management per unit flow of the drainage pump station; B i Is the cost of excavating the i th type of water body per cubic meter; h i Is the i th water depth of the water body; F Is the area of the study area; P 0,i Is the i th current water surface rate; C j Is the j th total construction cost and maintenance and operation cost of LID measures; f 2 Represents the total runoff reduction rate; α A Is the runoff coefficient before implementing any measures; α Is the runoff coefficient after implementing blue-green measures, △t Is the drainage time of the pump station;

[0021] The expression of the constraint condition is: ; where, P i * Is the i th minimum water surface rate of the water body; x i * Is the i th minimum layout area rate of green measures; P Is the rainfall, β Is the percentage of the external drainage flow of the pump station; T Is the designed drainage duration.

[0022] Preferably, the formula of the step-by-step water volume regulation calculation method is:

[0023]

[0024] Where, V 1 、 V 2 Are the water storage volumes of the river at the beginning and end of the time period respectively; Q 1 、 Q2 The influent water volumes at the beginning and end of the time period, respectively; P 1 and P 2 The rainfall amounts for each time period, respectively, φ is the rainfall runoff coefficient of the permeable pavement; Δt is the time interval between the beginning and end of the time period, F green and F harden are the area of the green space in the study area and the area of the hardened ground in the study area, respectively.

[0025] Preferably, the wild dog optimization algorithm includes:

[0026] Initializing the population and generating random solutions;

[0027] Evaluating the fitness through non-dominated sorting and selecting the optimal solutions;

[0028] Simulating the hunting behavior of wild dogs, including the rules of siege, pursuit, scavenging, and survival, and updating the positions of the solutions;

[0029] Iterating until the termination condition is met and outputting the Pareto solution set.

[0030] Preferably, based on the basic data, an SWMM model is constructed and calibrated and verified using historical rainfall data to ensure the accuracy of the SWMM model, including:

[0031] Using ArcGIS to convert the CAD files of different land use types in the study area into SHP files by layers. Considering the elevation changes, land use types, street distributions, and stormwater wells in the study area, the study area is divided into several sub-catchments, and the roads are divided separately;

[0032] Using ArcGIS to split and merge the drainage pipelines in the study area, dividing the drainage areas according to the north-south direction of the main drainage pipelines, exporting the SHP files, and converting the SHP files into inp files recognizable by SWMM through the inpPINS plugin;

[0033] The parameters in the SWMM model are divided into deterministic parameters and calibration parameters; the deterministic parameters include the characteristic width, area, slope, permeability rate of the sub-catchments, the pipe diameters, burial depths, and stormwater well depths of the pipe networks; among them, the area of each sub-catchment is statistically calculated through the "Calculate Geometry" function in ArcGIS, and the area proportion of different land use types is calculated; the elevation data is converted and the average slope is calculated through the 3DAnalyst and Spatial Analyst functions; the calibration parameters are taken according to the SWMM model manual and the parameter value ranges in the study area;

[0034] The model parameters of the SWMM model are initially adjusted using the comprehensive runoff coefficient, and the parameter values in different regions within the empirical range are used, and the accuracy of the SWMM model is improved through multiple adjustments;

[0035] Two sets of measured data of historical rainfall ponding are used for calibration and verification respectively. The maximum overflow volume of the simulated flood-prone points is evenly distributed on the road area, and the simulated value of the maximum surface ponding depth is obtained through calculation. The relative error between the simulated value and the measured ponding depth is calculated to verify the accuracy of the SWMM model; the formula for the relative error is as follows: ; where H 1 is the measured value of ponding at the monitoring point; H 2 is the simulated value of ponding at the monitoring point.

[0036] Preferably, the SWMM model is coupled with the wild dog optimization algorithm. Based on the decision variable range of the first optimization, the objective function and constraints are updated, and the second optimization is carried out to generate the Pareto front solution set of the spatial layout of the green-gray-blue measures, including:

[0037] Based on the range of decision variables corresponding to the Pareto front of the first optimization, the multi-objective optimization function is updated with the average pumping station drainage flow and average water surface rate of all schemes as known variables, and the constraints are updated with the extreme values of the low-lying green space rate and permeable pavement rate;

[0038] An optimization model of the updated multi-objective function is constructed through Python, and iteration is realized with the wild dog optimization algorithm;

[0039] The automatic establishment of the SWMM model is realized through Python, and the wild dog optimization algorithm is coupled to realize the automatic optimization of the layout areas of low-lying green spaces and permeable pavements;

[0040] Based on the obtained optimization model of the multi-objective function, the wild dog optimization algorithm is used for iteration to obtain the Pareto front of the second optimization, and the solution set of the spatial layout scheme under the green measures is determined.

[0041] A multi-objective segmented optimization system for green-gray-blue measures with wild dog optimization algorithm coupled with SWMM, including:

[0042] A data collection unit for determining the current situation of ponding distribution and simulation results based on the basic data of the study area collected and sorted out, and determining the types, scales, parameters and unit investment costs of green-gray-blue measures;

[0043] A measure optimization unit for optimizing the types and layouts of the green-gray-blue measures based on the current situation of ponding distribution;

[0044] The target construction unit is used to construct a multi-objective optimization model, with the minimum total investment cost and the maximum runoff volume reduction rate as the objective functions, the pumping station drainage flow rate, water surface ratio, sunken green space ratio, and permeable pavement ratio as decision variables, and the constraint conditions are set in combination with area constraints, effectiveness constraints, and the fitting relationship between decision variables;

[0045] The multi-objective optimization unit is used to analyze the pumping station drainage flow rate under different working conditions based on the gray-green-blue measures and the multi-objective optimization model by using the hourly water volume regulation calculation method, and establish a mathematical relationship expression between decision variables through multiple regression analysis as an equality constraint;

[0046] The first optimization unit is used to perform the first iterative optimization of the multi-objective optimization model by using the wild dog optimization algorithm to generate a Pareto solution set and the decision variable range;

[0047] The model construction unit is used to construct a SWMM model based on the basic data and perform calibration and verification by using historical rainfall data to ensure the accuracy of the SWMM model;

[0048] The second optimization unit is used to couple the SWMM model and the wild dog optimization algorithm, update the objective function and constraint conditions based on the decision variable range of the first optimization, and perform the second optimization to generate a Pareto front solution set for the spatial layout of gray-green-blue measures.

[0049] According to the specific embodiments provided by the present invention, the following technical effects are disclosed by the present invention:

[0050] The present invention fully considers the synergistic effect of gray-green-blue measures, especially the runoff reduction effect of pumping stations. Traditional models usually focus on a single flood prevention measure, or take gray measures and water surface ratio as known conditions instead of decision variables of the model. The present invention creatively proposes a multi-objective segmented optimization model for urban waterlogging prevention considering pumping station drainage flow rate, water surface area, and LID measures. This segmented optimization strategy creatively solves the bottleneck of data acquisition and processing in hydrological models, is applicable to data-deficient areas and regions with modeling conditions, expands the application scope of the optimization model, provides a new idea for solving the drainage optimization in data-lacking areas, and also provides better technical support for enhancing urban resilience. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required to be used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0052] Figure 1The flowchart of steps provided by the embodiments of the present invention;

[0053] Figure 2 The schematic diagram of the technical route provided by the embodiments of the present invention;

[0054] Figure 3 The schematic diagram of the generalization of the SWMM model in the main urban area of a certain city provided by the embodiments of the present invention;

[0055] Figure 4 The error between the simulated waterlogging value and the measured waterlogging value of the SWMM model in the research area provided by the embodiments of the present invention;

[0056] Figure 5 The Pareto front set obtained by secondary optimization in the main urban area of a certain city provided by the embodiments of the present invention. Detailed implementation manners

[0057] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0058] The purpose of the present invention is to provide a multi-objective segmented optimization method for grey-green-blue measures coupling the wild dog optimization algorithm and SWMM, considering the runoff reduction effect of pumping stations, applicable to areas lacking data, and enhancing urban resilience.

[0059] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0060] Figure 1 The flowchart of steps provided by the embodiments of the present invention, as Figure 1 shown, the present invention provides a multi-objective segmented optimization method for grey-green-blue measures coupling the wild dog optimization algorithm and SWMM, including:

[0061] Step 100: Determine the current situation of waterlogging distribution and simulation results based on the basic data of the research area collected and sorted, and determine the types, scales, parameters, and unit investment costs of grey-green-blue measures;

[0062] Step 200: Optimize the types and layouts of grey-green-blue measures based on the current situation of waterlogging distribution and simulation results;

[0063] Step 300: Build a multi-objective optimization model with the minimization of the total investment cost and the maximization of the runoff volume reduction rate as the objective functions, and the drainage flow rate of the pumping station, the water surface ratio, the depression green space ratio, and the pervious pavement ratio as the decision variables. Combine the area constraints, effectiveness constraints, and the fitting relationships between the decision variables to set the constraints;

[0064] Step 400: Based on the gray-green-blue measures and the multi-objective optimization model, use the hourly water volume regulation calculation method to analyze the drainage flow rate of the pumping station under different working conditions, and establish a mathematical relationship expression between the decision variables through multiple regression analysis as the equality constraint;

[0065] Step 500: Use the wild dog optimization algorithm to perform the first iterative optimization on the multi-objective optimization model to generate the Pareto solution set and the decision variable range;

[0066] Step 600: Build a SWMM model based on the basic data, and use the historical rainfall data for calibration and verification to ensure the accuracy of the SWMM model;

[0067] Step 700: Couple the SWMM model with the wild dog optimization algorithm, update the objective function and constraints based on the decision variable range of the first optimization, and perform the second optimization to generate the Pareto front solution set of the spatial layout of the gray-green-blue measures.

[0068] Specifically, as Figure 2 shown, a multi-objective segmented optimization method for gray-green-blue measures coupling the wild dog optimization algorithm and SWMM in this embodiment includes:

[0069] Step 1: Collection and collation of basic data and information in the study area; mainly including basic data such as rainfall, waterlogging distribution, elevation, drainage pipe network, land use, river water level, and existing pumping station drainage flow rate required for building the SWMM model; carry out real-time monitoring of regional rainfall and waterlogging to obtain the current situation of waterlogging distribution. And determine the scale, parameters, and unit investment cost of various gray-green-blue measures in combination with local actual conditions and planning and design. Specifically: go to the intersection of the main urban area of the study area to carry out waterlogging monitoring, and record the waterlogging process and the maximum waterlogging depth.

[0070] Step 2: Selection of gray-green-blue measures; based on the current situation of regional waterlogging distribution in Step 1, determine the specific types, design parameters, and layouts of gray-green-blue measures.

[0071] Step 2.1: Select appropriate gray-green-blue measures based on the planning and design of the study area. Select the pumping station as the gray measure to achieve rapid drainage, and the location and quantity of the pumping station are expanded and newly built according to the current situation of the study area. Select to build a regulating pumping station near the river and near the waterlogging-prone areas with serious waterlogging.

[0072] Step 2.2, the green measures include sunken green spaces and permeable pavements. The layout areas, locations, and design parameters of various green measures are determined according to the planning and design of the study area. Considering the differences in the suitability of different green measures for different land use types and the difficult construction in old urban areas, sunken green spaces are arranged on ordinary green lands, and permeable pavements are rebuilt on residential areas, commercial areas, and road lands.

[0073] Step 2.3, the water surface ratio in the study area is used to represent the blue measures, and the original rivers and lakes in the study area are excavated and expanded.

[0074] Step 3, establishment of a multi-objective optimization model; based on the grey-green-blue measures selected in Step 3, determine the objective function for the study area with the lowest total investment cost and the largest reduction rate of total runoff volume, use the drainage pump flow rate, lake water surface ratio, river water surface ratio, sunken green space rate, and permeable pavement rate as decision variables, and use the regional area constraint, effectiveness constraint, and fitting relationship between decision variables as constraint conditions to construct a regional multi-objective optimization model.

[0075] Step 3.1, based on the grey-green-blue measures selected in Step 2, determine the decision variables as follows:

[0076]

[0077] In the formula, X represents the vector of decision variables; q represents the flow rate of the drainage pump in the study area (m 3 / s); p i represents the i th water body type (lake, river) water surface ratio; x j represents the j th green measure (sunken green space, permeable pavement) area ratio.

[0078] Step 3.2, optimize the grey-green-blue measures with the minimum total investment cost and the largest reduction rate of total runoff volume as the objective function to seek a balance between economic and environmental benefits. The specific calculation formula is as follows:

[0079]

[0080] In the formula, f 1 represents the total investment cost. A is the sum of the present value of investment and the present value of operation and management per unit flow rate of the drainage pump (10,000 yuan); B i is the cost (10,000 yuan) for excavating each cubic meter of the i th water body (river, lake); h i is thei The water depth (m) of a water body (river, lake); F is the area of the study area; P 0,i is the i species of current water surface ratio; C j is the j total construction cost and maintenance and operation cost of the f 2 represents the total runoff reduction rate; α A is the runoff coefficient before implementing any measures; α is the runoff coefficient after implementing blue-green measures, △t is the drainage time of the pumping station. The remaining symbols are the same as those appearing before.

[0081] Step 3.3, the constraint range of parameters mainly considers area constraints and effectiveness constraints. The maximum value of blue-green measures is determined according to the planning and design of the study area and land use restrictions; the minimum drainage flow of the pumping station is determined according to the target of the external drainage flow of the region. In addition, the water storage and infiltration effects of blue-green measures will affect the runoff generation and concentration process. It is also necessary to take the fitting relationship between the drainage pumping station, the water surface ratio, and the green measure rate as a constraint condition. The formula is as follows:

[0082]

[0083] In the formula, P i * is the i minimum water surface ratio of the x i * is the i minimum layout area ratio of the P species of green measures; β is the rainfall (mm), T is the percentage of the external drainage flow of the pumping station. Considering that a part of the rainfall is consumed and stored by other facilities, 80% of the rainfall is used to calculate the runoff;

[0084] Step 4, fitting of decision variable relationships; based on the gray-green-blue measures selected in Step 3 and the multi-objective optimization model established in Step 4, the drainage flow of the pumping station corresponding to different water surface ratios and depression green space ratios is calculated using the hourly water storage and regulation calculation method, and the mathematical relationship expression between decision variables is fitted using the multiple regression analysis method as an equality constraint condition.

[0085] Step 4.1, When calculating the regulation and storage of waterlogging drainage volume in the planning area, the regulation and storage effects between various measures need to be considered. The regulation and storage calculation is carried out for each time period according to the normal water level, starting drainage water level, lowest control water level and highest control water level of the river. The formula is as follows:

[0086]

[0087] In the formula, V 1 and V 2 are the water storage volumes of the river at the beginning and end of the time period (m 3 ); Q 1 and Q 2 are the inflow water volumes at the beginning and end of the time period (m 3 ); P 1 and P 2 are the rainfall amounts for each time period. Considering that a part of the rainwater is lost, 80% of the rainfall amount is taken to calculate the design rainfall amount (mm). φ is the rainfall runoff coefficient of the permeable pavement, generally 0.08 - 0.45, and is taken as 0.2; Δt is the time interval between the beginning and end of the time period (h); the meanings of the other symbols are the same as above.

[0088] Step 5, The first optimization for areas lacking data; Based on the regional multi-objective optimization model obtained in Steps 4 and 5, the wild dog optimization algorithm is used for iterative calculation to obtain the Pareto front of the first optimization and the range of decision variables.

[0089] Step 5.1, Use Python to write the wild dog optimization algorithm, define the multi-objective function based on Steps 3 and 4, and initialize the population to generate a set of random solutions.

[0090] Step 5.2, Evaluate the fitness of each solution, perform non-dominated sorting according to the values of the objective functions, and select the optimal solution.

[0091]

[0092] In the formula, and are the values of the th searcher in the current iteration substituted into the objective functions and .

[0093] Step 5.3, Regard the problem space as a predation space, simulate the processes of siege, pursuit, scavenging and survival when wild dogs hunt large prey, and iteratively improve the solutions through the update rules. The formula is as follows:

[0094] ① Siege: Multiple searchers approach the location of the prey, that is, move towards the optimized location of our target. Search and obtain a new location:

[0095]

[0096] Where, is the new location of the th searcher; is an integer randomly generated within the interval ; is the initial population size; is a randomly generated wild dog subgroup; is the current location of the searcher; is the globally optimal individual in the previous iteration; : is a random scaling factor within

[0097] to change the size and direction of the movement trajectory; ② Pursuit: Hunt small prey, that is, search near the globally optimal location individual

[0098]

[0099] in the current iteration and obtain a new location: is a random number within;

[0100] ③ Scavenging: The behavior of finding and eating carrion during random walking, that is, select a new location between the current location and any searcher:

[0101]

[0102] Where, , are two randomly selected searchers, ;

[0103] ④ Survival, calculate the survival probability of each dog. When the survival probability is less than a certain value, it is necessary to move to near the globally optimal individual and update the "leader", that is, the globally optimal individual location according to the new fitness function value;

[0104]

[0105]

[0106] Where, is a binary number of 0 or 1;

[0107] Step 5.4, repeat Step 5.3 until the iteration stop condition is met; through multiple iterations, obtain the first optimized Pareto front and the range of decision variables.

[0108] Step 6, construction and verification of the SWMM model; construct the SWMM model based on the data in Step 1, and perform calibration and verification using two historical rainfall data sets.

[0109] Step 6.1, use ArcGIS to convert CAD files of different land use types in the study area into SHP files layer by layer. Considering the actual situations such as elevation changes, land use types, street distributions, and stormwater wells in the study area, divide the study area into several sub-catchments, and divide the roads separately.

[0110] Step 6.2, use ArcGIS to reasonably split and merge the drainage pipelines in the study area, divide the drainage areas according to the north-south orientation of the main drainage pipelines, and export the SHP files. Convert the SHP files into inp files recognizable by SWMM through the inpPINS plugin.

[0111] Step 6.3, the parameters in the model are divided into deterministic parameters and calibrated parameters. The deterministic parameters include the characteristic width, area, slope, and permeability of the sub-catchments, as well as the pipe diameter, buried depth, and stormwater well depth of the pipe network. Among them, the area of each sub-catchment can be statistically calculated through the "Calculate Geometry" function in ArcGIS, and the area proportion of different land use types can be calculated. The average slope can be converted and calculated from the elevation data through the 3DAnalyst and Spatial Analyst functions, and other parameters are obtained according to the regional planning and design data. The calibrated parameters such as the Manning coefficient, infiltration rate, and depression storage volume of the catchment need to be empirically determined with reference to the SWMM model manual and the parameter value range of the study area.

[0112] Step 6.4, initially adjust the model parameters using the comprehensive runoff coefficient, and adjust the parameters multiple times according to the parameter values in different regions within the empirical range to improve the model accuracy. Then, use the measured data of two historical rainfall waterlogging events to perform calibration and verification respectively. The maximum overflow volume of the simulated waterlogging points is evenly distributed on the road area to calculate the simulated value of the maximum surface waterlogging depth, and calculate the relative error between the simulated value and the measured waterlogging depth to verify the accuracy of the model. The formula is as follows:

[0113]

[0114] where H 1 is the measured waterlogging value at the monitoring point, in cm; H 2 is the simulated waterlogging value at the monitoring point, in cm.

[0115] Step 7, coupling of the wild dog optimization algorithm and the SWMM model; Based on the Pareto frontiers of the first optimization and the ranges of decision variables obtained in Step 5, the average values of the pumping station drainage flow rate and the water surface ratio are taken as known variables, and the extreme values of the sunken green space rate and the permeable pavement rate are used to update the objective function and the ranges of decision variables. Through Python programming, the automatic establishment, operation, and analysis of the SWMM model are realized, and the wild dog optimization algorithm is coupled to automatically optimize the layout areas of sunken green spaces and permeable pavements, obtaining the Pareto frontiers of the second optimization as the solution set of the spatial layout plans for the gray-green-blue measures.

[0116] Step 7.1, based on the ranges of decision variables corresponding to the solutions of the Pareto frontiers of the first optimization obtained in Steps 4 and 5, update the multi-objective optimization function with the average pumping station drainage flow rate and the average water surface ratio of all solutions as known variables, and update the constraint conditions with the extreme values of the sunken green space rate and the permeable pavement rate.

[0117] Step 7.2, construct an updated multi-objective function optimization model through Python and implement iteration with the wild dog optimization algorithm.

[0118] Step 7.3, realize the automatic establishment of the SWMM model through Python and couple the wild dog optimization algorithm to automatically optimize the layout areas of sunken green spaces and permeable pavements. At this time, the surface runoff calculated by the model is used to obtain the total runoff reduction rate compared with the surface runoff before implementing any measures.

[0119] Step 7.4, based on the multi-objective optimization models constructed in Steps 7.2 and 7.3, adopt the wild dog optimization algorithm for iteration to obtain the Pareto frontiers of the second optimization and obtain the solution set of the spatial layout plans under the green measures.

[0120] Example:

[0121] Apply the optimization method described in the present invention to the main urban area of Handan City, Hebei Province. The technical process includes:

[0122] Collection and collation of basic data and information of the study area, selection of gray-green-blue measures, establishment of a multi-objective optimization model, fitting of decision variable relationships, first optimization of data-deficient areas, construction and verification of the SWMM model, coupling of the wild dog optimization algorithm and the SWMM model. The specific process is as follows:

[0123] (1) Collect and collate relevant basic data of the study area. Include land use, 20-year return period design rainfall, unit cost of gray-green-blue measures, unit price of green measures, etc. Among them, the land use data includes the area of the study area and the area proportion of each land use type. The area of the study area is about 24.204 km 2, there is currently 2.2% of the river water surface and 0.3% of the lake water surface, and the average water depth of the main rivers is about 3.16 m. The land use types include 12.63% roads, 40.14% residential areas, 18.82% green spaces, 22.66% commercial areas, and 3.26% industrial land.

[0124] (2) The drainage areas in the study area are relatively independent, and the ends of the drainage pipe networks are all connected to the Qin River and the Fuyang River. Most of the existing outlets of the gravity rainwater pipes are close to the river bottom, resulting in slow flow velocity in the pipes and prone to river water backflow during the flood season. Therefore, in this embodiment, 5 strong drainage pump stations are considered to be newly built and rebuilt along the river as gray measures, and the river and lake water surfaces are widened as blue measures. Considering the differences in the suitability of different green measures according to land use types and the large construction difficulty in the old urban areas, sunken green spaces are selected to be arranged on ordinary green lands, and permeable pavements are rebuilt in residential areas, commercial areas, and road lands.

[0125] (3) Taking the lowest total investment cost and the largest reduction rate of the total runoff volume as the objective function of the study area, the balance between economic and environmental benefits is sought. The total investment cost mainly includes the annual infrastructure cost and management and maintenance cost. The unit cost of each measure obtained by referring to relevant literature and the construction plan of Handan City and other materials is shown in Table 1. The annual reduction rate of the total runoff volume is the ratio of the sum of the discharge of the drainage pump station outside the study area and the reduction amount under the action of blue-green measures to the surface runoff volume before no measures are implemented. The formula for the multi-objective function is sorted out as follows:

[0126]

[0127] In the formula, f 1 represents the total investment cost, f 2 represents the reduction rate of the total runoff volume. q represents the flow rate of the drainage pump station in the study area (m 3 / s); p 1 and p 2 respectively represent the water surface ratios of lakes and rivers; x 1 and x 2 represent the area ratios of sunken green spaces (calculated as a percentage of the green space area in the study area) and permeable pavements.

[0128] Table 1 Basic costs and operation and management expenses corresponding to different measures

[0129]

[0130] Referring to the planning and design of the reference research area, the minimum pumping station drainage flow is calculated with the goal of discharging 40% of the flood volume within 24 hours for the runoff generated by rainfall. The water surface ratio and green measures are mainly restricted by the area. To ensure that the research area has a significant runoff reduction effect, the minimum water surface ratio is set to the existing water surface ratio; referring to the relevant indicators of other sponge city pilot projects, the proportion of sunken green space area is set to be no less than 30% (calculated as % of the green space area in the planning area), and the pervious pavement rate is no less than 10% (calculated as % of the hardened area in the planning area). The maximum values of each parameter are restricted by the area of the research area. After sorting, the constraint condition formulas for decision variables are as follows:

[0131]

[0132] (4) The water volume regulation for each time period is adopted to calculate the external drainage flow of the pumping station corresponding to different water surface ratios, sunken green spaces and pervious pavement rates. The initial set pre-drainage water level of the river channel in this implementation area is 3.4 m, and the highest water surface line of the middle and lower reaches of the river network area is controlled within 5.1 m. It is considered that the drainage flow of the pumping station obtained at this time is relatively reasonable. After rainfall, the internal river water level is controlled between the highest control water level and the lowest control water level by starting the pumping and discharging. To ensure timely emptying of the storage capacity in the polder for regulating floods and preventing the next rainstorm and flood, the flood volume stored in the river ponds needs to be completely discharged on the same day, and the river channel returns to the normal water level before the rain. Based on this, the minimum drainage flow is calculated. According to the basic data of the main urban area of Handan and the constraint conditions in the mathematical model, the approximate working condition ranges of the water surface ratio, sunken green space ratio and pervious pavement rate are determined. The calculation results of the drainage flow under different water surface ratios (2.5% - 5%), sunken green space ratios (30% - 70%) and pervious pavement rates (10% - 26.4%) are shown in Table 2. The fitting relationship formula between the parameters is obtained by using the multiple regression analysis method as follows:

[0133]

[0134] Table 2 Pumping station drainage flow corresponding to different water surface ratios, sunken green space ratios and pervious pavements

[0135]

[0136] (5) The wild dog optimization algorithm is used to iterate the multi-objective function optimization model to obtain the first optimized Pareto solution set and the corresponding decision variable range. It can be seen from the Pareto solution set that the cost is between 293.72 million yuan and 431.74 million yuan, but the reduction rate is between 34% and 44.2%. From the distribution of decision variables, the range of the drainage flow of the pumping station is from 18.18 to 28.08 m 3 / s, the variation ranges of the lake rate and water surface rate are 2.63% - 2.79% and 4.5% - 4.7% respectively, the range of the sunken green space rate is 31.6% - 69% (calculated based on the green area), and the variation range of the permeable pavement rate is 10% - 12.4%. Considering the uniform distribution of the drainage pump station flow rate, the concentrated water surface rate, and the relatively complex control in the SWMM model during the second optimization, the average values of 23%, 2.7%, and 4.65% are selected as fixed values respectively.

[0137] (6) For the data required for a high-precision hydrological model, the SWMM model can be further coupled to optimize the spatial layout of green measures for the second time. The high-precision data required to build the hydrological model include elevation information, land use type area, drainage pipe network, historical rainfall data, waterlogging monitoring data, etc. Based on the above data, the study area is divided into 5 drainage sub-areas, 1,519 sub-catchments, 282 nodes, 282 pipelines, and 24 drainage outlets, see Figure 3 .

[0138] There are two types of parameters in the model: deterministic parameters and empirical parameters. Deterministic parameters can be obtained by calculation or direct extraction, while empirical parameters need to refer to relevant literature and standards to determine the empirical values. In this embodiment, the comprehensive runoff coefficient method is used to initially determine the value range of empirical parameters, and then the absolute errors between the simulated water depths and the measured water depths of the waterlogging points during two rainfall events on June 26, 2022, and July 5, 2022 are used for calibration and verification respectively. The errors are all within 20%, see Figure 4 , indicating that the simulation effect of the model is good. The final values of the calibrated parameters are shown in Table 3.

[0139] Table 3 Values of the calibrated parameters of the SWMM model

[0140]

[0141] (7) Update the objective function and constraints according to the results of the first optimization to obtain the following formula:

[0142]

[0143] In the formula, f 3 represents the total investment cost updated based on the first optimization. f 4 represents the runoff volume reduction rate updated based on the first optimization; S is the surface runoff volume (m 3 ) obtained from the second optimization, S A is the surface runoff volume (m 3 ) without setting any measures.

[0144] The LID parameters need to be set in the inp file, and the specific values are determined according to the experience in the study area. By calling the PySWMM library, the automatic establishment, operation, and analysis of the SWMM model are realized through Python programming. The DOA optimization algorithm is coupled to automatically optimize the layout areas of different LID measures, and the solution set of the optimal spatial layout of green measures after the second optimization in the study area is obtained. As the cost increases from 308 million yuan to 345 million yuan in the second-stage optimization process, the reduction rate increases from 44.5% to 45.1%, as shown in Figure 5 .

[0145] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. The same or similar parts among the various embodiments can be referred to each other.

[0146] Specific examples are used in this article to elaborate on the principles and implementation methods of the present invention. The descriptions of the above embodiments are only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, based on the idea of the present invention, there will be changes in the specific implementation methods and application scopes. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A multi-objective segmented optimization method for grey-green-blue measures coupling the wild dog optimization algorithm and SWMM, characterized in that Including: Determine the current situation of waterlogging distribution based on the basic data collected and sorted in the study area, and determine the types, scales, parameters and unit investment costs of gray-green-blue measures; Optimize the types and layouts of the gray-green-blue measures based on the current situation of waterlogging distribution; Construct a multi-objective optimization model, with the minimum total investment cost and the maximum reduction rate of total runoff as the objective functions, and the drainage flow of the pumping station, water surface ratio, depression green space ratio and permeable pavement ratio as decision variables. Set the constraint conditions in combination with area constraints, effectiveness constraints and the fitting relationship between decision variables; Based on the gray-green-blue measures and the multi-objective optimization model, use the hourly water volume regulation calculation method to analyze the drainage flow of the pumping station under different working conditions, and establish a mathematical relationship expression between decision variables through multiple regression analysis as an equality constraint; Use the wild dog optimization algorithm to perform the first iterative optimization on the multi-objective optimization model to generate the Pareto solution set and the decision variable range; Construct a SWMM model based on the basic data, and use historical rainfall data for calibration and verification to ensure the accuracy of the SWMM model; Couple the SWMM model with the wild dog optimization algorithm, update the objective function and constraint conditions based on the decision variable range of the first optimization, and perform the second optimization to generate the Pareto front solution set of the spatial layout of gray-green-blue measures; Couple the SWMM model with the wild dog optimization algorithm, update the objective function and constraint conditions based on the decision variable range of the first optimization, and perform the second optimization to generate the Pareto front solution set of the spatial layout of gray-green-blue measures, including: Based on the range of decision variables corresponding to the Pareto front of the first optimization, update the multi-objective optimization function with the average drainage flow of the pumping station and the average water surface ratio of all schemes as known variables, and update the constraint conditions with the extreme values of the depression green space ratio and the permeable pavement ratio; Construct an optimization model of the updated multi-objective function through Python, and implement iteration with the wild dog optimization algorithm; Automatically establish the SWMM model through Python, and couple the wild dog optimization algorithm to automatically optimize the layout areas of depression green spaces and permeable pavements; Based on the obtained optimization model of the multi-objective function, use the wild dog optimization algorithm for iteration to obtain the Pareto front of the second optimization, and determine the solution set of the spatial layout under green measures.

2. The multi-objective segmented optimization method of green, gray, and blue measures by coupling the wild dog optimization algorithm with SWMM according to claim 1, characterized in that, The basic data includes: rainfall data, land use type, drainage network information, pumping station parameters, elevation data and river water level data.

3. The multi-objective segmented optimization method for green, blue and gray measures coupling SWMM with the wild dog optimization algorithm according to claim 1, wherein Optimizing the types and layouts of the gray-green-blue measures based on the current situation of waterlogging distribution includes: Install storage pumping stations near rivers and in flood-prone areas as gray measures; According to the suitability of land use types, install depression green spaces in ordinary green areas, and reconstruct permeable pavements in residential areas, commercial areas and road areas as green measures; Expand the water surface ratio of the original rivers and lakes in the study area as blue measures.

4. The multi-objective segmented optimization method for green, gray, and blue measures by coupling the wild dog optimization algorithm with SWMM according to claim 1, wherein, The decision variables of the multi-objective optimization model are as follows: ; Among them, X a vector representing decision variables; q the flow rate of the drainage pumping station in the study area; p i represents the i water surface ratio of the x j represents the j area ratio of the m n number of water body types,represents the number of green measures; The calculation formula of the objective function is as follows: ; where f 1 represents the total investment cost, A is the sum of the present value of investment and the present value of operation and management per unit flow of the drainage pump station; B i is the cost of excavating per cubic meter of the i th type of water body; h i is the water depth of the i th type of water body; F is the area of the study area; P 0,i is the i th type of current water surface ratio; C j is the total construction cost and maintenance and operation cost of the j th type of LID measure; f 2 represents the total runoff reduction rate; α A is the runoff coefficient before implementing any measures; α is the runoff coefficient after implementing blue-green measures, △t is the drainage time of the pump station. The expression of the constraint condition is: ; where P i * is the minimum water surface ratio of the i th type of water body; x i * is the minimum layout area ratio of the i th type of green measure; P is the rainfall, β is the percentage of the external drainage flow of the pump station; T is the designed waterlogging drainage duration.

5. The multi-objective segmented optimization method for green, blue and gray measures by coupling the wild dog optimization algorithm with SWMM according to claim 4, wherein The formula of the hourly water volume regulation calculation method is: Among them, V 1 and V 2 are the river storage volumes at the beginning and end of the time period respectively; Q 1 and Q 2 are the inflow water volumes at the beginning and end of the time period respectively; P 1 and P 2 are the rainfall amounts for each time period, φ is the rainfall runoff coefficient of the permeable pavement; F green and F harden are the area of the green space in the study area and the area of the hardened ground in the study area respectively.

6. The multi-objective segmented optimization method for grey-green-blue measures by coupling the wild dog optimization algorithm with SWMM according to claim 1, wherein The wild dog optimization algorithm includes: Initialize the population and generate random solutions; Evaluate the fitness through non-dominated sorting and select the optimal solution; Simulate the hunting behavior of wild dogs, including siege, pursuit, scavenging and survival rules, and update the position of the solution; Iterate until the termination condition is met, and output the Pareto solution set.

7. The multi-objective segmented optimization method for green, gray, and blue measures by coupling the wild dog optimization algorithm with SWMM according to claim 1, characterized in that, Construct an SWMM model based on the basic data, and use historical rainfall data for calibration and verification to ensure the accuracy of the SWMM model, including: Use ArcGIS to convert CAD files of different land use types in the study area into SHP files layer by layer. Considering the elevation changes, land use types, street distributions, and stormwater wells in the study area, divide the study area into several sub-catchments, and divide the roads separately; Use ArcGIS to split and merge the drainage pipelines in the study area, divide the drainage sub-areas according to the north-south direction of the main drainage pipelines, export the SHP files, and convert the SHP files into inp files recognizable by SWMM through the inpPINS plug-in; Divide the parameters in the SWMM model into deterministic parameters and calibrated parameters; the deterministic parameters include the characteristic width, area, slope, permeability rate of the sub-catchments, pipe diameters, burial depths, and stormwater well depths of the pipe network; among them, the area of each sub-catchment is statistically calculated through the "Calculate Geometry" function in ArcGIS, and the area proportion of different land use types is calculated; the elevation data is converted and the average slope is calculated through the 3D Analyst and Spatial Analyst functions; the calibrated parameters are taken according to the SWMM model manual and the parameter value ranges in the study area; Use the comprehensive runoff coefficient to preliminarily adjust the model parameters of the SWMM model, and take the parameter values of different regions within the empirical range, and improve the accuracy of the SWMM model through multiple adjustments; Calibration and verification are respectively carried out using the measured data of accumulated water from two historical rainfall events. The maximum overflow volume of the flood-prone points simulated is evenly distributed over the road area, and the simulated value of the maximum surface water depth is obtained through calculation. The relative error between the simulated value and the measured water depth is calculated to verify the accuracy of the SWMM model; the formula for the relative error is as follows: ; where H 1 is the measured value of water accumulation at the monitoring point; H 2 is the simulated value of water accumulation at the monitoring point.

8. A multi-objective segmented optimization system for grey-green-blue measures coupling the wild dog optimization algorithm with SWMM, characterized in that, Including: A data collection unit for determining the current situation of waterlogging distribution and simulation results based on the basic data of the study area collected and sorted out, and determining the types, scales, parameters, and unit investment costs of the gray-green-blue measures; A measure optimization unit for optimizing the types and layouts of the gray-green-blue measures based on the current situation of waterlogging distribution; A target construction unit for constructing a multi-objective optimization model, with the minimum total investment cost and the maximum reduction rate of total runoff as the objective functions, and the pump station drainage flow, water surface rate, depression green space rate, and permeable pavement rate as decision variables, and setting constraint conditions in combination with area constraints, effectiveness constraints, and fitting relationships between decision variables; A multi-objective optimization unit for analyzing the pump station drainage flow under different working conditions by using the hourly water storage calculation method based on the gray-green-blue measures and the multi-objective optimization model, and establishing a mathematical relationship expression between decision variables through multiple regression analysis as an equality constraint; A first optimization unit for using the wild dog optimization algorithm to perform the first iterative optimization on the multi-objective optimization model, generating a Pareto solution set and the decision variable range; A model construction unit for constructing an SWMM model based on the basic data, and using historical rainfall data for calibration and verification to ensure the accuracy of the SWMM model; A second optimization unit for coupling the SWMM model with the wild dog optimization algorithm, updating the objective function and constraint conditions based on the decision variable range of the first optimization, performing the second optimization, and generating a Pareto front solution set for the spatial layout of the gray-green-blue measures; The implementation steps of the second optimization unit include: Based on the range of decision variables corresponding to the first optimized Pareto front, update the multi-objective optimization function with the average pumping station drainage flow and average water surface rate of all schemes as known variables, and update the constraint conditions with the extreme values of the depression green space rate and permeable pavement rate; Construct an optimization model of the updated multi-objective function through Python and implement iteration with the wild dog optimization algorithm; Automatically establish the SWMM model through Python and couple the wild dog optimization algorithm to automatically optimize the layout areas of depression green spaces and permeable pavements; Based on the obtained optimization model of the multi-objective function, adopt the wild dog optimization algorithm for iteration to obtain the Pareto front of the second optimization and determine the solution set of the spatial layout plan under green measures.

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