A structure and spatial layout optimization design method for coupling Hydrus-1D and SWMM model

Abstract

This invention provides a structural and spatial layout optimization design method coupling Hydros-1D and SWMM models, relating to the fields of sponge city construction and urban stormwater management. The method includes the following steps: S1: Collecting and acquiring drainage system data and design storm and measured rainfall data for urban catchment areas; S2: Establishing the initial structure of the Hydros-1D and SWMM models; S3: Coupling the Hydros-1D model with a genetic algorithm to construct a vertical structural design optimization framework, obtaining optimization results, and calculating carbon emissions and costs per unit area; S4: Inputting the structural optimization results as input parameters into the SWMM model, and establishing a spatial layout optimization framework in conjunction with NSGA-II, using the sub-catchment area as the decision variable; S5: Calling the Hydros-1D and SWMM models based on a Python environment; S6: Obtaining the optimal bioretention facility design scheme through an integrated structural and layout optimization method; significantly reducing carbon emissions and costs while ensuring runoff reduction effects.

Description

Technical Field

[0001] This invention relates to the field of sponge city construction and urban stormwater management technology, and in particular to a structural and spatial layout optimization design method that couples the Hydrus-1D and SWMM models. Background Technology

[0002] With the acceleration of urbanization, the large number of impermeable underlying surfaces has led to increasingly prominent urban stormwater problems. Bioretention facilities, as the core green infrastructure for sponge city construction, are widely used because they combine interception, storage, infiltration and pollution reduction functions.

[0003] However, existing design methods have the following limitations: First, traditional methods often focus on spatial layout optimization based on hydrological models such as SWMM, improving runoff control solely by adjusting the area and location of facilities, while neglecting the influence of differences in the internal vertical structure of bioretention facilities, such as the thickness of the filler layer and the permeability coefficient. This results in optimization results that fail to truly reflect the linkage between the facility's microstructure and the region's macro-runoff control. Second, while the Hydrus-1D model can accurately depict the vertical water transport and infiltration processes of individual facilities, it is limited to microscale simulation; the SWMM model focuses on regional hydrological and hydrodynamic analysis. The two lack effective coupling, parameter transfer relies on empirical assumptions, and there is no dynamic feedback mechanism, making it difficult to connect the optimization needs of vertical structure and spatial layout. Third, existing optimizations often take runoff control as the sole objective, lacking quantitative consideration of carbon emissions throughout the facility's construction lifecycle, such as the carbon footprint of material production and construction, and economic costs, such as material and construction costs. This leads to an imbalance between environmental benefits and economic efficiency in the design scheme, failing to meet the "low-consumption, high-efficiency, and low-carbon" construction requirements of green infrastructure. Summary of the Invention

[0004] The main objective of this invention is to provide a structural and spatial layout optimization design method that couples the Hydrus-1D and SWMM models, thereby solving the problems of single optimization dimension, lack of collaborative design, fragmented model application, inefficient parameter transfer, one-sided target system, and insufficient evaluation dimensions.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for optimizing the structure and spatial layout of coupled Hydrus-1D and SWMM models, comprising the following steps: S1: Collect and obtain drainage system data and design storm and measured rainfall data for urban catchment areas; S2: Establish the initialization structure for the Hydrus-1D model and the SWMM model; S3: Couple the Hydrus-1D model with the genetic algorithm to construct a vertical structure design optimization framework to obtain optimization results such as the thickness of the filler medium layer, permeability coefficient, and porosity, and calculate carbon emissions and costs per unit area. S4: Input the structural optimization results into the SWMM model as input parameters, and combine NSGA-II to establish a spatial layout optimization framework with the sub-catchment area as the decision variable. S5: Using the Python environment to call the Hydrus-1D and SWMM models, realize dynamic modification of model parameters and optimization iterative calculation; S6: Obtain the optimal design scheme for bioretention facilities through an integrated optimization method of structure and layout.

[0006] In the preferred embodiment, the data collected in step S1 includes: Data on the drainage system network structure, underlying land use, regional design storm data, and measured rainfall data for urban catchment areas.

[0007] In the preferred embodiment, the initialization structure for establishing the Hydrus-1D model and the SWMM model includes: A vertical one-dimensional water transport model of a bioretention facility was established on the Hydrus-1D platform. The facility profile was generalized as a one-dimensional soil column with a total depth set as the initial value H, and divided into a cover layer, a planting soil layer, a filler medium layer, and an infiltration layer. The thicknesses of the planting soil layer and the filler medium layer were used as decision variables for vertical structure optimization, with initial values ​​set as follows: The formula is:

[0008] In the formula, H represents the total depth of the bioretention facility as a soil column in the Hydrus-1D model, and H1 and H2 represent the thickness of the planting soil layer and the thickness of the fill medium layer of the bioretention facility, respectively. , The initial parameter values ​​represent H1 and H2; For each layer, soil hydraulic parameters are input, and the Van Genuchten model is used to characterize the soil moisture characteristic curve. The upper boundary is set as an atmospheric boundary condition and the rainfall process is input. The lower boundary is set as a free drainage condition. The initial condition is set as the stratified gradient distribution of profile water content. The model outputs indicators such as the change of water content in each stratum and the infiltration flux.

[0009] In the preferred scheme, step S2, the process of establishing the SWMM model initialization structure, is as follows: First, sub-catchments are divided according to the catchment boundaries of the study area. The impermeability, area and topographic slope of each sub-catchment are determined, and surface runoff and runoff paths are set. Then, deploy the bioretention facility units, connect them to the corresponding sub-catchment areas, and input the facility design parameters at the same time; The model establishes a node and pipe network structure by setting up either a design rainstorm or a measured rainfall process as the rainfall input, and defines hydraulic parameters such as node elevation and pipe length. The model outputs surface runoff and node water level indicators.

[0010] In the preferred embodiment, step S3 includes: The thickness of the planting soil layer H1 and the thickness of the filler medium layer H2 are used as decision variables, and their value ranges are set. Construct a multi-objective function with runoff reduction effect, carbon emissions per unit area, and construction cost as the multiple objective functions. The formula is as follows:

[0011] In the formula, f 1 represents the objective function, which is to maximize the runoff reduction effect, and n represents the number of rainfall events. Let be the outflow reduction rate under the i-th rainfall event. Let be the peak flow reduction rate under the i-th rainfall event; f 2 represents objective function 2, which aims to minimize the carbon emissions from facility construction, where Let H1 be the amount of the j-th material used in the construction of the bioretention facility, and H2 be the decision variables. Let J be the carbon emission factor of the j-th material; f 3 represents objective function 3, which is to minimize the construction cost of the facility. w0 is the basic cost of constructing the bioretention facility per unit area, and c1 and c2 are the unit layer thickness costs of the planting soil layer and the filler medium layer; where: The runoff reduction effect was calculated using infiltration flow simulated by the Hydrus-1D model. Carbon emissions were converted from material usage and carbon emission factors calculated for each layer thickness. Construction costs were calculated based on material usage and unit cost calculated for each layer thickness. The formulas for calculating the runoff reduction rate and peak reduction rate are as follows:

[0012] In the formula, V in V represents the inflow rate. out Q represents the outflow rate. in Q represents the peak value of the inflow process. out This represents the peak value of the outflow process. The decision variables are encoded as binary chromosome individuals. The population is iterated through selection, crossover and mutation operations of genetic algorithm. The parameters of each generation are input into the Hydrus-1D model to calculate the flow process and evaluate fitness. After iterative convergence, the optimal configuration of the planting soil layer and the filler medium layer is output, the corresponding carbon emissions and costs per unit area are calculated, and the average porosity and permeability coefficient of the facility medium layer are obtained by weighting.

[0013] The preferred scheme includes: after converting the binary encoding of individuals in each generation of the population into parameters, reconstructing the thickness of each layer of the Hydrus-1D model based on the converted parameters, mapping the operation of soil hydraulic parameters, simulating design rainstorms and measured rainfall processes with different return periods, extracting infiltration flow, and determining the runoff reduction effect.

[0014] In the preferred scheme, the optimization results of step S3 can be converged through Pareto front solution classification to obtain three facility structure design schemes that are biased towards runoff reduction, carbon emission reduction and cost economy.

[0015] In the preferred embodiment, step S4 specifically includes the following: The optimal parameters of the vertical structure are input into the LID module of the SWMM model, and this optimized vertical structure is uniformly adopted in all sub-catchments. The expression is:

[0016] In the formula, , ks1 and ks2 are the saturated water content of the planting soil layer and the filler medium layer, respectively; H1 and H2 are the thicknesses of the planting soil layer and the filler medium layer, respectively. The ratio of the actual deployment area to the maximum allowable deployment area of ​​bioretention facilities in each sub-catchment area is used as the decision variable. The feasible deployment area is then converted into the actual deployment area using the following formula:

[0017] In the formula, 'a' represents the decision variable matrix for spatial layout optimization, 'K' represents the number of K sub-catchments in the study area where spatial layout optimization is to be carried out, and 'A' represents the number of sub-catchments. k RA represents the actual area of ​​bioretention facilities deployed in the k-th sub-catchment. k The maximum operational deployment area of ​​the bioretention facility representing the kth sub-catchment area; Construct a multi-objective function with runoff reduction effect, carbon emissions, and construction cost as objectives, as shown in the formula:

[0018] In the formula: f 1 represents the objective function for maximizing runoff reduction, and n represents the number of rainfall input events used to evaluate the runoff reduction effect at the system's outlets. Let be the reduction rate of the total outflow from the system outlet under the i-th rainfall event. Let be the peak discharge reduction rate of the system outlet under the i-th rainfall event;f 2. The objective function for minimizing the total carbon emissions from the construction of bioretention facilities in the region is EF. bio To optimize carbon emissions per unit area of ​​bioretention facilities; f 3 is the objective function for minimizing the total construction cost of the overall bioretention facility in the region. bio To optimize the construction cost per unit area of ​​bioretention facilities; The runoff reduction effect is calculated by comparing the total outflow and peak flow before and after facility installation, using the following formula:

[0019] In the formula, The total outflow during the system discharge process before the bioretention facility is deployed. This refers to the total outflow from the system outlet after the bioretention facility is installed. The peak flow rate of the system outlet before the bioretention facility is deployed. The peak flow rate of the system outlet after the bioretention facility is installed; The area vectors of the sub-catchment areas are encoded as chromosome individuals. Through non-dominated sorting, crowding calculation, and selection, crossover, and mutation operations of the NSGA-II algorithm, a Pareto front solution set is formed, resulting in an optimized spatial layout scheme.

[0020] In the preferred embodiment, step S5 specifically includes the following: The unified operating environment and data structure are initialized, and common variables are constructed to store rainfall process data, hydraulic parameters of soil and filler media, maximum deployable area of ​​sub-catchment areas, and outfall monitoring nodes. The vertical structural thickness combination and layered hydraulic parameters of the facility are transcribed into a Hydrus-1D model. The profile mesh and material mapping are reconstructed, boundary conditions are set, calculations are performed, flow sequences are extracted, and relevant indicators, carbon emissions, and costs are calculated. The SWMM model file is dynamically rewritten according to the decision variables of the sub-catchment area. In the SUBCATCHMENTS section, the equivalent impermeability is reduced based on the original impermeability and area. In the LID_USAGE section, the bioretention facility item is inserted, while keeping other hydraulic structure sections unchanged. The optimization process involves parallel processing of each generation of the population, and process pool scheduling is used to ensure computational efficiency and repeatability. After convergence, the Pareto front solution set and related indicators are output. Output representative solutions and form a comparison table. Verify the constraints such as the layout area of ​​individual sub-catchment areas. Add penalty functions or eliminate candidate solutions that do not meet the constraints.

[0021] In the preferred scheme, the optimal bioretention facility design scheme obtained in step S6 includes the optimal set of vertical structural parameters h. * =[H * 1,H * 2], Optimal spatial layout parameter set a * =[a * 1,a * 2,…,a * K [ ], and the corresponding outflow process and objective function value of the discharge outlet under each rainfall process.

[0022] This embodiment acquires relevant data and couples the Hydrous-1D and SWMM models to construct a vertical structure design optimization framework. The structural optimization results are input into the SWMM model as input parameters. Combined with NSGA-II, a spatial layout optimization framework is established. The Hydrous-1D and SWMM models are called to realize dynamic modification and optimization iteration calculation of model parameters, achieve a comprehensive trade-off between runoff control, carbon emissions, and costs, realize multi-dimensional collaborative optimization, and simultaneously meet the needs of micro-facility performance and macro-regional runoff control. This improves the accuracy of layout design, enhances hydrological, environmental, and economic benefits, improves the dynamic control capability of parameters, and increases the applicability of application scenarios. Attached Figure Description

[0023] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart of the design method of the present invention; Figure 2 This is a schematic diagram of the coupling framework for optimization calculations using the Hydrus-1D and SWMM models of this invention. Detailed Implementation

[0024] Example 1 like Figure 1-2 As shown, a structural and spatial layout optimization design method coupling Hydrus-1D and SWMM models includes the following steps: S1: Collect and obtain drainage system data and design storm and measured rainfall data for urban catchment areas; S2: Establish the initialization structure for the Hydrus-1D model and the SWMM model; S3: Couple the Hydrus-1D model with the genetic algorithm to construct a vertical structure design optimization framework, obtain optimization results such as the thickness of the filler medium layer, permeability coefficient, and porosity, and calculate carbon emissions and costs per unit area; S4: The structural optimization results are used as input parameters to the SWMM model, and a spatial layout optimization framework is established in conjunction with NSGA-II, with the sub-catchment area as the decision variable. S5: Using the Python environment to call the Hydrus-1D and SWMM models, realize dynamic modification of model parameters and optimization iterative calculation; S6: Obtain the optimal design scheme for bioretention facilities through an integrated optimization method of structure and layout.

[0025] This embodiment acquires relevant data and couples the Hydrous-1D and SWMM models to construct a vertical structure design optimization framework. The structural optimization results are input into the SWMM model as input parameters. Combined with NSGA-II, a spatial layout optimization framework is established. The Hydrous-1D and SWMM models are called to realize dynamic modification and optimization iteration calculation of model parameters, achieve a comprehensive trade-off between runoff control, carbon emissions, and costs, realize multi-dimensional collaborative optimization, and simultaneously meet the needs of micro-facility performance and macro-regional runoff control. This improves the accuracy of layout design, enhances hydrological, environmental, and economic benefits, improves the dynamic control capability of parameters, and increases the applicability of application scenarios.

[0026] This embodiment combines vertical structural design parameters (such as soil layer thickness, permeability coefficient, and porosity) with spatial layout parameters (such as the area of ​​sub-catchment areas) to construct a multi-objective optimization problem with runoff reduction rate, carbon emissions, and cost as objectives. By combining it with the NSGA-II optimization framework, the design parameters of the bioretention facility are optimized, thereby maximizing environmental benefits and effectively controlling construction costs while ensuring runoff reduction effects.

[0027] In the preferred embodiment, the data collected in step S1 includes: Collect and acquire drainage system data and design storm and measured rainfall data for urban catchment areas. Collect and organize drainage system network structure data, underlying land use data, etc., for urban catchment areas, and obtain regional design storm and measured rainfall data.

[0028] In the preferred embodiment, step S2: establishing the initialization structure of the Hydrus-1D model and the SWMM model, including: Step S2.1: Establish a vertical one-dimensional water transport model for the bioretention facility in the Hydrus-1D platform. The facility profile is generalized as a one-dimensional soil column, with the total depth set as the initial value H. It is then divided into layers according to actual function, including a cover layer, a planting soil layer, a filler medium layer, and an infiltration layer. The thicknesses of the planting soil layer and the filler medium layer are used as decision variables for vertical structure optimization, with initial values ​​set to [values ​​to be filled in]. .

[0029]

[0030] In the formula, H represents the total depth of the bioretention facility as a soil column in the Hydrus-1D model, and H1 and H2 represent the thickness of the planting soil layer and the thickness of the fill medium layer of the bioretention facility, respectively. , The initial parameter values ​​for H1 and H2 can be set to 1 / 2 of the total depth.

[0031] For each layer, including porosity, saturated hydraulic conductivity, residual water content, and field capacity, the VanGenuchten (VG) model was used to characterize the soil moisture characteristic curves, ensuring that the permeability of different layers could be accurately described. Parameter values ​​were selected using recommended values ​​for different soil media provided by the Hydrus-1D platform, with specific values ​​determined based on the soil texture of the study area to be optimized, as shown in Table 1.

[0032] Table 1. Hydrus-1D Typical Parameter Database Based on Soil Texture

[0033] in, Represents the residual volumetric water content, characterizing the properties of bound water in porous media; The saturated volumetric water content represents the volume ratio of water when the pores are filled with water, characterizing the porosity and water storage capacity of the medium. Representing the reciprocal of the intake suction, it reflects the influence of the magnitude of the medium's pore suction on the curve shape in the description of soil moisture characteristic curves, and characterizes the medium's moisture retention capacity. This represents the pore size distribution parameter, which characterizes the uniformity of the pore size distribution in the medium. A larger value indicates a wide range of pore size distribution, while a smaller value indicates a concentrated pore size distribution. It represents the permeability coefficient, which characterizes the seepage characteristics of water in pores.

[0034] Regarding the boundary conditions: the upper boundary is set as an atmospheric boundary condition, and the rainfall process is input; the lower boundary is set as a free drainage condition according to design requirements to simulate bottom leakage or discharge processes; the initial conditions are set as a stratified gradient distribution of profile water content. The model output includes water content changes, infiltration flux, surface runoff, and evapotranspiration in each layer, thus comprehensively characterizing the water transport process of the facility's vertical structure. Through the above settings, the Hydrus-1D initialization model is completed. The model outputs indicators such as water content changes and infiltration flux in each layer, laying a simulation foundation for subsequent vertical structure optimization.

[0035] Step S2.2: Establish a hydrological and hydrodynamic initialization SWMM model for the area to be spatially optimized in the EPA-SWMM5 platform.

[0036] In this embodiment, a vertical one-dimensional water transport model was constructed on the Hydrus-1D platform and a regional hydrological and hydrodynamic model was constructed on the EPA-SWMM5 platform. The hierarchical structure, parameter values ​​and boundary conditions were clarified to accurately characterize the vertical water transport process of the facility and the regional runoff collection and discharge patterns.

[0037] In the preferred scheme, firstly, the catchment area is divided into sub-catchments based on the catchment boundaries of the study area. The impermeability, area, and topographic slope of each sub-catchment are determined, and surface runoff generation and runoff paths are established. Then, deploy the bioretention facility units and connect them to the corresponding sub-catchment areas. At the same time, input the design parameters of the facilities, including area, vertical structural layers, and media characteristics. The initial values ​​can be the recommended values ​​in the "SWMM Stormwater Management Model User Manual".

[0038] Set the design storm or measured rainfall process as the rainfall input, establish the network structure of nodes and pipes based on the drainage system data of the area to be optimized, and clarify the hydraulic parameters such as node elevation, pipe length, slope and roughness to ensure the correct simulation of runoff collection and discharge process.

[0039] Establish the node and pipeline network structure, clarify the hydraulic parameters such as node elevation and pipeline length, and output the surface runoff and node water level indicators of the model.

[0040] With this initialization setting, the SWMM model can output various indicators, including surface runoff, node water level, pipe flow, and outlet flow, providing a regional-scale model for subsequent parameter coupling and spatial layout optimization with Hydrus-1D.

[0041] Step S3: Couple the Hydrus-1D model with the genetic algorithm to construct a vertical structure design optimization framework.

[0042] In the preferred embodiment, step S3 includes: Step S3.1: Determine decision variables: Based on the Hydrus-1D model, the thickness H1 of the planting soil layer and the thickness H2 of the filler medium layer in the vertical structure of the bioretention facility are used as decision variables. The range of values ​​for the variables is set according to engineering standards, planning documents or literature data, which serves as the optimization search space in the genetic algorithm, as shown in Table 2.

[0043] Table 2 Decision variables for the vertical structure of bioretention facilities

[0044] Step S3.2: Construct a multi-objective function, with runoff reduction effect, carbon emissions per unit area, and construction cost as the multi-objective functions. The formula is as follows:

[0045] The runoff reduction effect was calculated by the infiltration flow rate simulated by the Hydrus-1D model under different return periods of design rainstorms and typical measured rainfall processes; carbon emissions were obtained by converting the material usage and carbon emission factor calculated for each layer thickness; and construction costs were calculated based on the material usage and unit cost calculated for each layer thickness.

[0046] In the formula, f 1 represents objective function 1, which is to maximize runoff reduction effect, and n represents the number of rainfall input events used to evaluate the runoff reduction effect. Let be the outflow reduction rate under the i-th rainfall event. Let be the peak flow reduction rate under the i-th rainfall event. The average of the two is used as the evaluation index of runoff reduction effect under a single rainfall event. The average of the runoff reduction effect index under multiple rainfall events is used as the objective function. f 2 represents objective function 2, which aims to minimize the carbon emissions from facility construction, where The amount of the j-th material used in the construction of the bioretention facility can be calculated using decision variables H1 and H2, yielding the volume or weight of the applied material. Let J be the carbon emission factor of the j-th material; f 3 represents objective function 3, which is to minimize the construction cost of the facility. w0 is the basic cost of building the bioretention facility per unit area. c1 and c2 are the unit layer thickness costs of the planting soil layer and the filler medium layer. We can take w0 = 223 yuan, c1 = 0.141 yuan / mm, and c2 = 0.206 yuan / mm.

[0047] The formulas for calculating runoff reduction rate and peak runoff reduction rate are as follows:

[0048] In the formula, V in V represents the inflow rate. out Q represents the outflow rate. in Q represents the peak value of the inflow process. out This represents the peak value of the outflow process.

[0049] The carbon emission factors of the construction materials used in the construction of bioretention facilities are shown in the table below. Sandy soil and medium-coarse sand were used for structural design optimization, while the carbon emission factors of the remaining materials were used for carbon emission calculations in spatial layout optimization. Table 3 Carbon emission factors of typical construction materials used in bioretention facilities

[0050] Step S3.3: Constructing the Genetic Algorithm Solution Framework: A Genetic Algorithm (GA) is used as the optimization tool. The decision variables H1 and H2 are encoded as chromosome individuals, composed of binary codes. Selection, crossover, and mutation operations are used to form an iterative population. Each generation of individuals, after being converted from binary codes into parameters, is input into the Hydrus-1D model to change the thickness of the corresponding layer, obtaining the corresponding outflow process. The fitness of the individuals is then evaluated using the objective function. Through iterative updates, the genetic algorithm gradually converges to the optimal vertical structure scheme that satisfies runoff reduction, carbon emission, and cost constraints, calculating the outflow process and evaluating fitness. The preferred scheme includes: after converting the binary encoding of individuals in each generation of the population into parameters, reconstructing the thickness of each layer of the Hydrus-1D model based on the converted parameters, mapping the operation of soil hydraulic parameters, simulating design rainstorms and measured rainfall processes with different return periods, extracting infiltration flow, and determining the runoff reduction effect.

[0051] In the preferred scheme, the optimization results of step S3 can be converged through Pareto front solution classification to obtain three facility structure design schemes that are biased towards runoff reduction, carbon emission reduction and cost economy.

[0052] Step S3.4: Output Optimization Results: After iterative convergence, the optimal configuration of the planting soil layer and the filler medium layer is output. Simultaneously, the corresponding carbon emissions per unit area and construction costs are calculated. The average porosity and permeability of the entire facility's medium layer are calculated by weighting the thickness of the two medium layers with corresponding parameters such as porosity and permeability coefficient, and then input into the SWMM model. The optimization results of the vertical structure here can be classified and converged based on the obtained Pareto front solutions according to three objective functions, resulting in three facility structure design schemes: one biased towards runoff reduction, one biased towards carbon emission reduction, and one biased towards cost economy, providing decision-makers with a more comprehensive design solution.

[0053] In the preferred embodiment, step S4 specifically includes the following: Step S4.1: Input the optimal parameters of the vertical structure (including the thickness of each layer, permeability coefficient, porosity, and carbon emissions and costs per unit area) into the LID module of the SWMM model. All sub-catchment areas adopt the optimized vertical structure to ensure that the spatial layout optimization is based on the performance of the individual facilities obtained from the optimization, as shown in Table 4.

[0054] Table 4. Parameter correspondence of LID module when vertical structure optimization results are input into the SWMM model.

[0055] The calculation process of converting variable values ​​from Hydrus-1D to the SWMM model is shown in equations (4)-(6):

[0056] In the formula, , ks1 and ks2 are the saturated water content of the planting soil layer and the filler medium layer, respectively, and the permeability coefficients of the planting soil layer and the filler medium layer, respectively.

[0057] Step S4.2: Determine the layout optimization decision variables. Set the ratio of the actual deployment area to the maximum allowable deployment area of ​​bioretention facilities in each sub-catchment as the optimization decision variable. Convert the deployable area of ​​the sub-catchment into the actual deployment area, as shown in formulas (7)-(8):

[0058] In the formula, a represents the decision variable matrix for spatial layout optimization, a k (k=1,2,…,K) represents the ratio of the actual area of ​​the bioretention facility in the k-th sub-catchment to the maximum allowable area of ​​that sub-catchment, with values ​​ranging from 0 to 1. K represents the total number of K sub-catchments in the study area where spatial layout optimization is to be performed. A k RA represents the actual area of ​​bioretention facilities deployed in the k-th sub-catchment. k The maximum operational area of ​​the bioretention facility in the k-th sub-catchment zone.

[0059] Step S4.3: Construct a multi-objective function with runoff reduction effect, carbon emissions, and construction cost as objectives. The runoff reduction effect is calculated by comparing the total outflow and peak flow before and after facility deployment, using the following formula:

[0060] In the formula: f 1 represents objective function 1, which is to maximize the runoff reduction effect, and n represents the number of rainfall input events used to evaluate the runoff reduction effect of the system's outlets. Let be the reduction rate of the total outflow from the system outlet under the i-th rainfall event. Let be the peak flow reduction rate of the system outlet under the i-th rainfall event. The average of the two is used as the evaluation index of runoff reduction effect under a single rainfall event. The average of the runoff reduction effect index under multiple rainfall events is used as the objective function. f 2 represents objective function 2, which aims to minimize the total carbon emissions from the construction of bioretention facilities in the region, where A k EF represents the actual area of ​​bioretention facilities deployed in the k-th sub-catchment. bio The optimal carbon emissions per unit area of ​​the bioretention facility obtained in step 3.4 represent the carbon emissions per unit area of ​​the facility. f 3 represents objective function 3, which is to minimize the total construction cost of the overall bioretention facility in the region.bio This represents the construction cost per unit area of ​​the optimized bioretention facility obtained in step 3.4.

[0061] The runoff reduction effect was assessed by comparing the total outflow and peak flow of the drainage system outlets in the catchment area before and after facility deployment, obtained from SWMM simulations. The reduction rate was calculated as the runoff reduction performance index. The formulas for calculating the runoff reduction rate and peak reduction rate at the outlets are shown in Equation (10):

[0062] In the formula, The total outflow during the system discharge process before the bioretention facility is deployed. This refers to the total outflow from the system outlet after the bioretention facility is installed. The peak flow rate of the system outlet before the bioretention facility is deployed. The peak flow rate at the system outlet after the bioretention facility is installed.

[0063] Step S4.4: Establish a spatial layout optimization framework for bioretention facilities that couples the SWMM model and the NSGA-II algorithm. The NSGA-II algorithm is used to solve the above spatial layout optimization problem. First, the area vector a=[a1,a2,…,aK] of the sub-catchment is encoded as chromosome individuals, and an initial population is randomly generated. Then, in each generation d iteration, the actual values ​​of the binary encoding parameters of the chromosome individuals are input into the SWMM model to calculate runoff reduction, carbon emissions, and economic costs, and then evaluated through a multi-objective fitness function. Next, the selection, crossover, and mutation operations of individuals are realized through non-dominated sorting and crowding calculation, and the Pareto front solution set is formed generation by generation. Finally, a multi-objective trade-off spatial layout scheme for bioretention facilities is obtained, providing a planning basis for regional scale.

[0064] In the preferred embodiment, step S5, as follows: Figure 2 As shown, the model uses the Python environment to call the Hydrus-1D and SWMM models to achieve dynamic modification of model parameters and iterative optimization calculations.

[0065] Step S5.1: Unified Operating Environment and Data Structure Initialization. Complete the programming calls and coupled calculations of Hydros-1D and SWMM within the same computing environment, setting up a unified time period control, random seed, and result output directory structure; construct common variables to store basic information such as rainfall process data (multiple current-period design rainstorm sequences), hydraulic parameters of soil and filler media, maximum deployable area of ​​sub-catchment areas, and outfall monitoring nodes. This step ensures that parameters across different modules can be uniformly read and written back, ensuring variable consistency.

[0066] Step S5.2: Parameterization and Dynamic Writing of the Vertical Structure of the Hydrous-1D Model. The thickness combinations of the facility's vertical structure (thickness of the planting soil layer and the filler medium layer) and layered hydraulic parameters (such as the van Genuchten model parameter set, porosity, permeability coefficient, etc.) are transcribed into the input profile and material library fields of the Hydrous-1D model, and dynamically updated according to the values ​​of the optimization variables. The variable update process and calculation are as follows: The profile mesh and material mapping are reconstructed layer by layer to ensure a one-to-one correspondence between layer thickness and material parameters; the rainfall process is used as the upper boundary atmospheric condition sequence input, and free drainage is used for the bottom boundary, with the initial condition set as water content distribution, completing the boundary condition settings for model solution; the model calculation is executed and the bottom outflow sequence is extracted to calculate the total outflow reduction rate and peak flow reduction rate; based on the final optimization results, the carbon emissions and construction cost per unit area of ​​the bioretention facility are calculated as input variables for subsequent spatial layout optimization.

[0067] Step S5.3: Dynamic modification of the SWMM model input file. Without changing the baseline network topology, the SWMM model file is dynamically rewritten according to the decision variables of the sub-catchment (the layout area ratio vector a=[a1,a2,…,aK]): In the [SUBCATCHMENTS] section of the .inp file, the equivalent impermeability is reduced according to the layout area based on the original impermeability and area of ​​each sub-catchment; in the [LID_USAGE] section, bioretention facility entries are inserted, and geometric parameters such as representative width are derived and written according to the area; other hydraulic structure sections (nodes, pipes, boundaries) are kept unchanged, and only layout-related sections are quickly replaced to reduce I / O and running time.

[0068] Step S5.4: Multi-objective optimization iteration and parallel solution of the SWMM model. Parallel computation is performed on each generation of the population during the optimization process, and evolution is based on non-dominated sorting and crowding distance. To ensure computational efficiency and repeatability, a process pool scheduling, baseline result caching, and result management method that aligns filenames with individual IDs are adopted. After convergence, the Pareto front solution set, corresponding index values, and the area matrix of each sub-catchment are output.

[0069] Step S5.5: Result Output and Reasonableness Verification. Output representative solutions from the converged solution set, including the total area of ​​the region, total cost, total carbon emissions, runoff reduction benefits (total outflow / peak reduction rate), and the allocated area of ​​each sub-catchment, forming a comparison table to aid decision-making; simultaneously, retain the corresponding SWMM model file for backup and verification. Verify the reasonableness of the constraints, such as ensuring that a single sub-catchment does not exceed the maximum available area, that emission nodes do not exceed water levels exceeding limits, and that the facility area does not exceed the area of ​​green facilities that can be deployed in the sub-catchment. Add penalty functions or eliminate candidate solutions that do not meet the constraints.

[0070] This project successfully achieved a triple objective of "runoff reduction, low-carbon emission reduction, and cost control." By optimizing the vertical structure (such as the thickness of the planting soil layer and the filler medium layer) through genetic algorithms, it reduced carbon emissions and construction costs per unit area. Combined with the NSGA-II algorithm to optimize the spatial layout, it balanced the reduction rate of total outflow from regional outlets and the reduction rate of peak flow under typical rainfall recurrence periods, thereby maximizing the synergistic benefits of hydrology, environment, and economy.

[0071] In the preferred embodiment, step S6 utilizes the integrated structural and layout optimization method to achieve a comprehensive trade-off between runoff control, carbon emissions, and cost, thereby obtaining the optimal bioretention facility design scheme. The final design scheme includes the optimal set of vertical structural parameters h for the bioretention facility. * =[H * 1,H * 2], Optimal spatial layout parameter set a * =[a * 1,a * 2,…,a * K [ ], and the corresponding outflow process and objective function value of the discharge outlet under each rainfall process.

[0072] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for optimizing the structure and spatial layout of a coupled Hydrus-1D and SWMM model, characterized in that, Includes the following steps: S1: Collect and obtain drainage system data and design storm and measured rainfall data for urban catchment areas; S2: Establish the initialization structure for the Hydrus-1D model and the SWMM model; S3: Couple the Hydrus-1D model with the genetic algorithm to construct a vertical structure design optimization framework to obtain optimization results such as the thickness of the filler medium layer, permeability coefficient, and porosity, and calculate carbon emissions and costs per unit area. S4: Input the structural optimization results into the SWMM model as input parameters, and combine NSGA-II to establish a spatial layout optimization framework with the sub-catchment area as the decision variable. S5: Using the Python environment to call the Hydrus-1D and SWMM models, realize dynamic modification of model parameters and optimization iterative calculation; S6: Obtain the optimal design scheme for bioretention facilities through an integrated optimization method of structure and layout.

2. The structural and spatial layout optimization design method for coupling the Hydrus-1D and SWMM models according to claim 1, characterized in that, The data collected in step S1 includes: Data on the drainage system network structure, underlying land use, regional design storm data, and measured rainfall data for urban catchment areas.

3. The structural and spatial layout optimization design method for coupling the Hydrus-1D and SWMM models according to claim 1, characterized in that, The initialization structure for establishing the Hydrus-1D model and the SWMM model includes: A vertical one-dimensional water transport model of a bioretention facility was established on the Hydrus-1D platform. The facility profile was generalized as a one-dimensional soil column with a total depth set as the initial value H, and divided into a cover layer, a planting soil layer, a filler medium layer, and an infiltration layer. The thicknesses of the planting soil layer and the filler medium layer were used as decision variables for vertical structure optimization, with initial values ​​set as follows: The formula is: In the formula, H represents the total depth of the bioretention facility as a soil column in the Hydrus-1D model, and H1 and H2 represent the thickness of the planting soil layer and the thickness of the fill medium layer of the bioretention facility, respectively. , The initial parameter values ​​represent H1 and H2; For each layer, soil hydraulic parameters are input, and the Van Genuchten model is used to characterize the soil moisture characteristic curve. The upper boundary is set as an atmospheric boundary condition and the rainfall process is input. The lower boundary is set as a free drainage condition. The initial condition is set as the stratified gradient distribution of profile water content. The model outputs indicators such as the change of water content in each stratum and the infiltration flux.

4. The structural and spatial layout optimization design method for coupling the Hydrus-1D and SWMM models according to claim 1, characterized in that, In step S2, the process of establishing the SWMM model initialization structure is as follows: First, sub-catchments are divided according to the catchment boundaries of the study area. The impermeability, area and topographic slope of each sub-catchment are determined, and surface runoff and runoff paths are set. Then, deploy the bioretention facility units, connect them to the corresponding sub-catchment areas, and input the facility design parameters at the same time; The model establishes a node and pipe network structure by setting up either a design rainstorm or a measured rainfall process as the rainfall input, and defines hydraulic parameters such as node elevation and pipe length. The model outputs surface runoff and node water level indicators.

5. The structural and spatial layout optimization design method for coupling the Hydrus-1D and SWMM models according to claim 4, characterized in that, Step S3 includes: The thickness of the planting soil layer H1 and the thickness of the filler medium layer H2 are used as decision variables, and their value ranges are set. Construct a multi-objective function with runoff reduction effect, carbon emissions per unit area, and construction cost as the multiple objective functions. The formula is as follows: In the formula, f 1 represents the objective function, which is to maximize the runoff reduction effect, and n represents the number of rainfall events. Let be the outflow reduction rate under the i-th rainfall event. Let be the peak flow reduction rate under the i-th rainfall event; f 2 represents objective function 2, which aims to minimize the carbon emissions from facility construction, where Let H1 be the amount of the j-th material used in the construction of the bioretention facility, and H2 be the decision variables. Let J be the carbon emission factor of the j-th material; f 3 represents objective function 3, which is to minimize the construction cost of the facility. w0 is the basic cost of constructing the bioretention facility per unit area, and c1 and c2 are the unit layer thickness costs of the planting soil layer and the filler medium layer; where: The runoff reduction effect was calculated using infiltration flow simulated by the Hydrus-1D model. Carbon emissions were converted from material usage and carbon emission factors calculated for each layer thickness. Construction costs were calculated based on material usage and unit cost calculated for each layer thickness. The formulas for calculating the runoff reduction rate and peak reduction rate are as follows: In the formula, V in V represents the inflow rate. out Q represents the outflow rate. in Q represents the peak value of the inflow process. out This represents the peak value of the outflow process. The decision variables are encoded as binary chromosome individuals. The population is iterated through selection, crossover and mutation operations of genetic algorithm. The parameters of each generation are input into the Hydrus-1D model to calculate the flow process and evaluate fitness. After iterative convergence, the optimal configuration of the planting soil layer and the filler medium layer is output, the corresponding carbon emissions and costs per unit area are calculated, and the average porosity and permeability coefficient of the facility medium layer are obtained by weighting.

6. The structural and spatial layout optimization design method for coupling the Hydrus-1D and SWMM models according to claim 5, characterized in that, include: After converting the binary encoding of each individual in each generation of the population into parameters, the thickness of each layer of the Hydrus-1D model is reconstructed based on the converted parameters. The soil hydraulic parameters are then mapped to simulate design rainstorms and measured rainfall processes with different return periods. Infiltration flow is extracted to determine the runoff reduction effect.

7. The structural and spatial layout optimization design method for coupling the Hydrus-1D and SWMM models according to claim 5, characterized in that, The optimization results of step S3 can be converged through Pareto front solution classification to obtain three facility structure design schemes that are biased towards runoff reduction, carbon emission reduction, and cost economy.

8. The structural and spatial layout optimization design method for coupling the Hydrus-1D and SWMM models according to claim 1, characterized in that, Step S4 specifically includes the following: The optimal parameters of the vertical structure are input into the LID module of the SWMM model, and this optimized vertical structure is uniformly adopted in all sub-catchments. The expression is: In the formula, , ks1 and ks2 are the saturated water content of the planting soil layer and the filler medium layer, respectively; H1 and H2 are the thicknesses of the planting soil layer and the filler medium layer, respectively. The ratio of the actual deployment area to the maximum allowable deployment area of ​​bioretention facilities in each sub-catchment area is used as the decision variable. The deployment area is converted into the actual deployment area using the following formula: In the formula, 'a' represents the decision variable matrix for spatial layout optimization, 'K' represents the number of K sub-catchments in the study area where spatial layout optimization is to be carried out, and 'A' represents the number of sub-catchments. k RA represents the actual area of ​​bioretention facilities deployed in the k-th sub-catchment. k The maximum operational deployment area of ​​the bioretention facility representing the kth sub-catchment area; Construct a multi-objective function with runoff reduction effect, carbon emissions, and construction cost as objectives, as shown in the formula: In the formula: f 1 represents the objective function for maximizing runoff reduction, and n represents the number of rainfall events used to evaluate the runoff reduction effect at the system's outlets. Let be the reduction rate of the total outflow from the system outlet under the i-th rainfall event. Let be the peak discharge reduction rate of the system outlet under the i-th rainfall event; f 2. The objective function for minimizing the total carbon emissions from the construction of bioretention facilities in the region is EF. bio To optimize carbon emissions per unit area of ​​bioretention facilities; f 3 is the objective function for minimizing the total construction cost of the overall bioretention facility in the region. bio To optimize the construction cost per unit area of ​​bioretention facilities; The runoff reduction effect is calculated by comparing the total outflow and peak flow before and after facility installation, using the following formula: In the formula, The total outflow during the system discharge process before the bioretention facility is deployed. This refers to the total outflow from the system outlet after the bioretention facility is installed. The peak flow rate of the system outlet before the bioretention facility is deployed. The peak flow rate of the system outlet after the bioretention facility is installed; The area vectors of the sub-catchment areas are encoded as chromosome individuals. Through non-dominated sorting, crowding calculation, and selection, crossover, and mutation operations of the NSGA-II algorithm, a Pareto front solution set is formed, resulting in an optimized spatial layout scheme.

9. The structural and spatial layout optimization design method for coupling the Hydrus-1D and SWMM models according to claim 1, characterized in that, Step S5 specifically includes the following: The unified operating environment and data structure are initialized, and common variables are constructed to store rainfall process data, hydraulic parameters of soil and filler media, maximum deployable area of ​​sub-catchment areas, and outfall monitoring nodes. The vertical structural thickness combination and layered hydraulic parameters of the facility are transcribed into a Hydrus-1D model. The profile mesh and material mapping are reconstructed, boundary conditions are set, calculations are performed, flow sequences are extracted, and relevant indicators, carbon emissions, and costs are calculated. The SWMM model file is dynamically rewritten according to the decision variables of the sub-catchment area. In the SUBCATCHMENTS section, the equivalent impermeability is reduced based on the original impermeability and area. In the LID_USAGE section, the bioretention facility item is inserted, while keeping other hydraulic structure sections unchanged. The optimization process involves parallel processing of each generation of the population, and process pool scheduling is used to ensure computational efficiency and repeatability. After convergence, the Pareto front solution set and related indicators are output. Output representative solutions and form a comparison table. Verify the constraints such as the layout area of ​​a single sub-catchment area. Add penalty functions or eliminate candidate solutions that do not meet the constraints.

10. The structural and spatial layout optimization design method for coupling the Hydrus-1D and SWMM models according to claim 1, characterized in that, The optimal bioretention facility design scheme obtained in step S6 includes the optimal vertical structural parameter set h. * =[H * 1,H * 2], Optimal spatial layout parameter set a * =[a * 1,a * 2,…,a * K [ ], and the corresponding outflow process and objective function value of the discharge outlet under each rainfall process.

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