Sponge facility space layout optimization method for urban community rainfall flood regulation and storage

Abstract

A sponge facility spatial layout optimization method for urban community rainfall flood regulation and storage comprises the steps that firstly, multi-source data of a research area is collected, sub catchment subareas are divided, hydrological parameters are extracted, the current annual rainstorm runoff process is simulated through an SWMM model, and the regulation and storage requirements of all the sub catchment subareas are calculated; 2, two-dimensional hydrodynamic simulation is carried out through an SWMM coupling LISFLOOD-FP model, and a ponding depth distribution diagram is obtained. And 3, based on the multi-source data and the ponding depth distribution map, combining sponge facility layout conditions, constructing a suitability evaluation system, generating a comprehensive suitability score map, and dividing priority areas. And 4, constructing a regulation and storage target equation according to the regulation and storage demand and the suitability score map, solving a facility area combination meeting the regulation and storage demand, and screening out a minimum cost scheme. And 5, performing multi-objective optimization on the facility layout in combination with the ponding depth distribution diagram and the priority region, and screening out an optimal layout scheme. According to the method, the optimal facility layout is provided for each sub catchment area, and the regulation and storage efficiency and the space adaptability of sponge facilities are effectively improved.

Description

Technical Field

[0001] This invention belongs to the technical field of spatial optimization in sponge city construction, specifically relating to a method for optimizing the spatial layout of sponge facilities for stormwater storage in urban communities. Background Technology

[0002] With the continuous advancement of urbanization and the frequent occurrence of extreme weather events, most cities face severe pressure on stormwater storage and the risk of urban flooding. Since the concept of "sponge city" was proposed in 2013, pilot projects have been carried out in many cities, and since 2021, systematic and city-wide construction tasks have been promoted. However, the following problems still exist in the planning and implementation of sponge cities at this stage: First, the layout of facilities relies heavily on qualitative experience and the results of pilot projects, lacking a quantitative mechanism for identifying storage targets for the future design stage; second, the selection of facility types and spatial layout often focus on local areas, failing to systematically consider the heterogeneity of urban space and the integrity of the ecological pattern; third, the evaluation methods often remain at the level of comparing single-objective effects after completion, lacking optimization design and cost-benefit analysis throughout the entire process. Summary of the Invention

[0003] To address the problems of existing technologies, this invention provides a method for optimizing the spatial layout of sponge city facilities for stormwater storage and regulation in urban communities. The method aims to construct a stormwater storage objective function by comprehensively identifying stormwater storage targets, evaluating facility suitability, calculating storage capacity per unit area, and determining the deployment area. An initial layout is generated through random sampling of a spatial priority grid. A multi-objective optimization model is constructed using a landscape pattern index. The NSGA-II algorithm is employed to optimize the facility configuration structure, and the TOPSIS method is used to select the optimal solution. This achieves a systematic and quantitative design of sponge city facilities from target identification to layout optimization, effectively overcoming the subjectivity and post-planning issues inherent in traditional planning. It improves the storage efficiency and spatial adaptability of facilities, promoting the development of sponge city construction towards a comprehensive and standardized approach. This solves the current problems in sponge city construction, such as the difficulty in achieving stormwater total volume control targets and the lack of quantitative guidance for facility deployment.

[0004] To achieve the above objectives, the specific solution of the present invention is as follows:

[0005] A method for optimizing the spatial layout of sponge city facilities for stormwater storage in urban communities includes the following steps:

[0006] Step 1: Collect the first type of multi-source data for the study area. The first type of multi-source data includes current land use, digital elevation model, drainage network layout, and design storm. Based on the distribution of roads, buildings, and pipe networks on the underlying surface, divide the study area into sub-catchment zones and extract the hydrological parameters of area, slope, and impermeability of each sub-catchment zone. Calculate the design storm volume for a certain return period in the current year and perform time-history allocation. Use the SWMM model to simulate the runoff process of the secondary storm in the study area for a certain return period in the current year and calculate the total secondary storm control rate for each sub-catchment zone. Based on the target control rate of the total secondary storm volume in the future urban planning scenario, calculate the unit storage volume of each sub-catchment zone that still needs to be achieved by deploying sponge city facilities after deducting the runoff that can be directly discharged by the pipe network. Determine the storage demand of each sub-catchment zone and record the current situation without facility deployment.

[0007] Step 2: Based on Step 1, the SWMM coupled with the LISFLOOD-FP model is used to conduct a two-dimensional hydrodynamic simulation to obtain a spatial distribution map of water depth.

[0008] Step 3: Based on the digital elevation model and land use data from the first type of multi-source data in Step 1, and the spatial distribution map of water depth from Step 2, combined with the second type of multi-source data and the deployment conditions of various sponge facilities, the second type of multi-source data includes slope and spatial buffer distance. The deployable areas of various facilities are identified, and indicators such as elevation, slope, land use type, and spatial buffer distance are selected as suitability factors. The weight values ​​of each suitability factor in the overall suitability are calculated, and the consistency of the weight system is checked. The indicator layers are uniformly rasterized using GIS tools, and weighted and superimposed according to the weight values ​​to generate a comprehensive suitability score map for facility deployment. The comprehensive score results are divided into several levels, and raster layers are output with uniform spatial resolution. Based on the comprehensive suitability score map, the raster areas where sponge facilities can be deployed are identified, and priority areas are divided according to the score level.

[0009] Step 4: Based on the storage and regulation needs of each sub-catchment area determined in Step 1 and the comprehensive suitability score map of facility layout generated in Step 3, construct the storage and regulation target equation, establish the relationship between the facility layout area of ​​each sub-catchment area and the required total storage and regulation volume, impose conditional constraints on the storage and regulation target equation, solve for the sponge facility area combination that meets the storage and regulation needs, calculate the full life cycle cost corresponding to the sponge facility area combination, and select the minimum cost area combination scheme.

[0010] Step 5: Based on the minimum cost area combination scheme selected in Step 4, the landscape pattern index is introduced. Combined with the facility deployment grid and priority area determined in Step 3, and the spatial distribution map of water depth generated in Step 2, the facility grid layout is optimized in multiple objectives to select the optimal facility layout scheme that meets the water storage target and is suitable for the landscape pattern.

[0011] Step 6: Repeat steps 1 to 5 for each sub-catchment area to obtain the optimal facility layout scheme for each sub-catchment area.

[0012] Furthermore, it also includes the following steps:

[0013] Step 61: Simulation and verification of storage effect: Based on the optimal facility layout scheme obtained in Step 5, the facility type, spatial location and area configuration in the optimal facility layout scheme are converted into the input parameters required by the SWMM model. The SWMM model is used again to simulate and verify the storage effect of the optimal facility layout scheme of each sub-catchment obtained in Step 6 under the same design rainstorm scenario as in Step 1. The result is compared with the current situation without facility layout obtained in Step 1. The quantitative evaluation results of the optimal facility layout scheme described in Step 5 in terms of rainfall runoff control and flood risk mitigation are output.

[0014] Step 62: Repeat steps 1 to 61 to advance the construction of the next planning goal's urban community sponge facility type combination and its spatial layout.

[0015] Furthermore, the quantitative evaluation results of the optimal facility layout scheme described in step 61 in terms of rainfall runoff control and flood risk mitigation include the following steps:

[0016] Step 611, Construct a simulation verification model: Input the optimal facility layout scheme obtained in step 5, convert the facility type, spatial location and area configuration in the optimal facility layout scheme into the input parameters required by the SWMM model, set the LID facility attribute parameters, and obtain the updated SWMM model of the sub-catchment area.

[0017] Step 612: Run the updated SWMM model of the sub-catchment area, extract the key indicators of runoff depth and runoff control rate of the sub-catchment area under a certain return period, and compare and analyze them with the current situation without facility layout described in Step 1. Output the quantitative evaluation results of the optimal facility layout scheme described in Step 5 in terms of rainfall runoff control and flood risk mitigation, including the comparative analysis of key indicators of runoff depth and runoff control rate.

[0018] Furthermore, the calculation formula for the design rainfall amount for a certain return period in the current year mentioned in step 1 is as follows:

[0019] (1)

[0020] In the formula: q represents the design rainfall intensity, L / (s·ha); P represents the design rainfall return period, y; t represents the design rainfall duration, min; the time-history allocation adopts the Chicago method for the time-history allocation of rainfall duration;

[0021] The formula for calculating the total rainfall control rate of each sub-catchment zone is as follows: (2)

[0022] In the formula: R cr R represents the total rainfall control rate of each sub-catchment area; P represents the total runoff of the sub-catchment area in mm; and P represents the total rainfall in mm. Expressed as runoff coefficient;

[0023] The formula for calculating the unit storage capacity of each sub-catchment area, after deducting runoff that can be directly discharged through the pipe network, which still needs to be achieved by deploying sponge facilities, is as follows:

[0024] (3)

[0025] In the formula: This represents the additional unit storage capacity required after deducting the stormwater discharge from the pipeline network, expressed in cubic meters (m³). 3 / ha; This is expressed as the runoff coefficient of stormwater discharged from the pipe network. The value of this parameter is determined by urban planning, and according to the specifications, it can be taken as 0.2~0.4. This represents the runoff coefficient corresponding to the target control rate.

[0026] Furthermore, the method for obtaining the spatial distribution map of water depth in step 2 includes the following steps:

[0027] Step 21: Extract the overflow data at each node of the SWMM model described in Step 1, generate the overflow boundary file, and combine it with the DEM of the study area to generate an elevation file to drive the LISFLOOD-FP model for two-dimensional hydrodynamic model simulation.

[0028] Step 22: Configure the LISFLOOD-FP model parameter file, select the adaptive solver and set the simulation duration and output interval. After running the model, output the spatial distribution map of water depth.

[0029] Furthermore, the formula for calculating the weight of each suitability factor in the total suitability mentioned in step 3 is as follows:

[0030] (5),

[0031] In the formula, Indicates the weight value; This represents the normalized value of the importance score of the i-th indicator relative to the j-th indicator in the judgment matrix; n represents the matrix order, i.e., the number of indicators.

[0032] The consistency test includes calculating the maximum eigenvalue, consistency index, and consistency ratio of the judgment matrix A;

[0033] The formula for calculating the largest eigenvalue of the judgment matrix A is as follows:

[0034] (6),

[0035] In the formula, λ max represents the largest eigenvalue; AW represents the product of the judgment matrix A and the weight vector W; This represents the weight value; n represents the matrix order, i.e., the number of indicators.

[0036] The formula for calculating the consistency index CI is as follows:

[0037] (7),

[0038] The formula for calculating the consistency ratio CR is as follows:

[0039] (8),

[0040] In the formula: n represents the matrix order, i.e. the number of indicators; RI is the random consistency index, which needs to be determined by looking up a table based on the matrix order.

[0041] Furthermore, the formula for establishing the relationship between the facility layout area of ​​each sub-catchment and the required total storage capacity, as described in step 4, is as follows:

[0042] (12)

[0043] In the formula: express Zihuishui District No. The area of ​​such facilities, in m 2 V i Indicates the first Storage capacity per unit area of ​​such facilities, m 3 ; This indicates the additional storage capacity of the sponge city facilities required to achieve the 75% target control rate, taking into account the external discharge from the pipeline network, in m. 3 / ha;

[0044] The conditions for the target equation of water storage are as follows:

[0045] (1) The sum of the storage capacity of all facilities in the j-sub-catchment area shall not be less than the target storage capacity:

[0046] (13)

[0047] (2) The area of ​​Class I facilities in the j-sub-catchment area does not exceed the maximum deployable area, and the area is non-negative:

[0048] (14)

[0049] In the formula, The value is determined according to relevant standards, representing the maximum proportion of the facility layout area to the sub-catchment area.

[0050] (3) The sum of the areas of all combined facilities in sub-catchment area j shall not exceed the total impermeable surface area of ​​sub-catchment area:

[0051] (15)

[0052] The formula for calculating the total life-cycle cost corresponding to the area combination of the sponge city facilities is as follows:

[0053] (16)

[0054] In the formula: The unit area lifecycle cost of sponge city facilities is expressed in yuan. This represents the construction cost per unit area of ​​sponge city facilities, expressed in yuan. denoted as RMB, representing the operation and maintenance cost per unit area of ​​sponge city facilities over their service life; k represents the growth rate coefficient, which is determined based on the economic development level of the study area. Indicates the service life of sponge city facilities, in years; The residual value of sponge city infrastructure is expressed in yuan.

[0055] The total life-cycle cost corresponding to the sponge city facility area combination includes construction cost, operation and maintenance costs, residual value, and discount rate. The residual value calculation formula is as follows:

[0056] (17)

[0057] In the formula: This indicates the time interval between the last maintenance and management work and the facility's lifespan, calculated on an annual basis. Indicates facility lifespan, in years; This indicates the annual maintenance cost of sponge city facilities.

[0058] Furthermore, the method for obtaining the optimal facility layout scheme described in step 5 includes the following steps:

[0059] Step 51: Initial layout scheme construction: Using the grid area and priority area for sponge facilities determined in Step 3, the spatial distribution map of water depth generated in Step 2, and the minimum cost area combination scheme selected in Step 4, multiple initial layout solutions are generated by hierarchical random sampling in high priority areas as the initial population input for the NSGA-II algorithm.

[0060] Step 52: Multi-objective optimization model construction: Input the initial layout solution generated in step 51 and the sponge facility deployment grid area and priority area determined in step 3, select landscape pattern indicators such as patch density, shape index and cohesion index as optimization objectives, and embed the minimum cost area combination scheme determined in step 4 as hard constraints, and output the multi-objective optimization model, including optimization objectives and constraints.

[0061] Step 53: NSGA-II Algorithm Execution: Input the multi-objective optimization model from Step 52 and the initial layout solution generated in Step 51. Use the layout position encoding structure, set parameters such as population size, crossover and mutation probability, and maximum number of generations, generate a new generation of solution set through crossover and mutation operations, and evolve generation by generation by combining non-dominated sorting and crowding distance selection mechanism, and finally output the Pareto optimal solution set that satisfies the multi-objective performance.

[0062] Step 54: Optimal Solution Selection and Decision Support: Input the Pareto optimal solution set generated in Step 53, use the TOPSIS method to comprehensively evaluate and rank the Pareto front solution set, construct positive ideal solutions and negative ideal solutions after normalization based on landscape indicators, select the optimal facility layout scheme with the highest proximity, and finally output the optimal facility layout scheme.

[0063] Advantages of the present invention

[0064] This invention presents a method for optimizing the spatial layout of sponge city facilities at the urban community scale, enabling the systematic integration of water storage target identification, facility area combination calculation, spatial layout optimization, and ecological effectiveness evaluation during the planning stage. The method first simulates runoff depth and water accumulation depth under different design storm scenarios based on the SWMM and LISFLOOD-FP models, quantifying the water storage gap of each sub-catchment. Secondly, it constructs a suitability raster map of typical facilities such as green roofs, sunken green spaces, and bioretention units by combining multiple factors including DEM elevation, slope, land use type, and buffer distance. Then, it constructs an area objective function based on the water storage capacity per facility unit, sets multiple constraints, and solves for the facility combination area that satisfies the water storage target. Subsequently, it overlays the facility suitability and waterlogging risk raster, generates an initial raster layout scheme using a hierarchical priority sampling method, introduces landscape pattern indices including PD, LSI, and COHESION, constructs a multi-objective optimization function, and uses the NSGA-II algorithm to optimize the spatial configuration structure of facilities. Finally, it uses the TOPSIS method to perform multi-attribute screening on the Pareto solution set to obtain the optimal facility layout scheme. This method achieves quantitative optimization of stormwater storage targets and spatial layout schemes throughout the entire process, avoiding the subjectivity, post-evaluation, and regional fragmentation problems existing in the current construction of sponge city facilities, and has good replicability and scalability. Attached Figure Description

[0065] Figure 1 This is a flowchart of a method for optimizing the spatial layout of sponge facilities for stormwater storage in urban communities, as proposed in this invention.

[0066] Figure 2 (a) is a generalized map of the sub-catchment area of ​​City A;

[0067] Figure 2 (b) is a spatial distribution map of the control rate of sub-storms in each sub-catchment area of ​​City A during the 5-year return period (the control rate of the 5-year return design storm is set at 75%).

[0068] Figure 2 (c) is a spatial distribution map of the underlying surface storage capacity required in the study area under the condition of external drainage of the network (the control rate of the 5-year return period design rainstorm is 75%).

[0069] Figure 2 (d) is a spatial distribution map of waterlogging depth in the study area under a 5-year return period design rainstorm scenario;

[0070] Figure 3 This is a spatial distribution map of the suitability scores of the three types of sponge city facilities in the study area;

[0071] Figure 4 This is a schematic diagram showing the overlay and priority classification of facility suitability grid and waterlogging grid;

[0072] Figure 5 The Pareto frontier of the S1177 facility landscape pattern index in the Zishui River area;

[0073] Figure 6 It is the spatial distribution of facilities in the S1177 sub-catchment area under a 5-year return period;

[0074] Figure 7 This is a spatial distribution map of sponge city facilities across City A under a 5-year return period;

[0075] Figure 8 (a) is a simulated spatial distribution map of storm runoff in City A over a 5-year return period under optimized facility layout;

[0076] Figure 8 (b) is a spatial distribution map of the storm runoff control rate in City 5aA under optimized facility layout. Detailed Implementation

[0077] The present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. It should be noted that the specific embodiments are not intended to limit the scope of the present invention.

[0078] like Figures 1 to 8 The method for optimizing the spatial layout of sponge city facilities for stormwater storage and regulation in urban communities, as described in this specific embodiment, includes the following steps:

[0079] Step 1: Determining the underlying surface storage capacity target for urban community planning scenarios: For a specific sponge city construction community, first-type multi-source data is collected for the study area. This first-type multi-source data is mainly used to construct the SWMM hydrological model and identify the storage capacity target. The first-type multi-source data includes current land use, digital elevation model, drainage network layout, and design storm data. The SWMM model is constructed to quantitatively identify the storage capacity gap under different design storm scenarios. City A is selected as a specific example. The specific steps are as follows:

[0080] Step 11: Based on the distribution of roads, buildings, and pipe networks on the underlying surface of City A, 2596 sub-catchment zones were divided, with 4030 stormwater inlets (nodes) and 572 drainage outlets, covering an area ranging from 0.792 to 1306.61 ha. Hydrological parameters such as slope and impermeability were extracted for each sub-zone. The 5-year return period design rainfall P for the current year of 2020 was calculated, and the Chicago method was used to allocate the rainfall duration over time. The generalized sub-catchment zones are shown below. Figure 2 As shown in (a).

[0081] The formula for calculating the 5-year return period design rainfall P in City A for the current year 2020 is as follows:

[0082] (1),

[0083] In equation (1): q represents the design rainfall intensity, L / (s·ha); P represents the design rainfall recurrence period, y; t represents the design rainfall duration, min.

[0084] Step 12: Using the SWMM model, simulate the runoff process of the secondary rainstorm with a 5-year return period of 2020 for the urban study area as described in Step 11, and calculate the total secondary rainstorm control rate R of each sub-catchment area under this rainstorm scenario in the current year. cr The calculation is performed using the following formula:

[0085] (2),

[0086] In equation (2): R represents the total runoff of the sub-catchment area, in mm; P represents the total rainfall, in mm; It is expressed as the runoff coefficient.

[0087] Taking a 5A return period design storm control rate of 75% as an example, the overall control rate of sub-storms in each sub-catchment area of ​​City A is as follows: Figure 2 As shown in (b), it can be seen that under the 5a scenario in City A, the catchment areas of each region... The range was 10.0% to 60.2%, with an average of 29.14%, which is far from the target control rate of 75%.

[0088] Step 13. Based on the target control rate of 75% for the total amount of secondary rainstorms in City A's planning scenario, calculate the unit storage capacity that each sub-catchment still needs to achieve through the deployment of sponge city facilities after deducting runoff that can be directly discharged through the pipe network. (m) 3 / ha), the calculation formula is as follows:

[0089] (3),

[0090] In formula (3): This represents the additional unit storage capacity required after deducting the stormwater discharge from the pipeline network, expressed in cubic meters (m³). 3 / ha; This parameter represents the runoff coefficient of stormwater discharged from the pipe network. The value of this parameter is determined by urban planning, and according to the specifications, it can be taken as 0.2~0.4. In this study, it is determined to be 0.2 based on the interpolation of the impermeability of City A. The runoff coefficient corresponding to a 75% control rate is taken as 0.25; the spatial distribution of the underlying surface's water storage capacity under a 5-year design storm scenario is calculated as follows: Figure 2 As shown in (c).

[0091] The formula for step 11 above is implemented according to step 12 of Chinese patent CN202310625256.0, entitled "A Method for Evaluating the Total Rainfall Control Rate of Sponge City Construction". The formula for step 12 above is implemented according to step 3 of Chinese patent CN202310625256.0, entitled "A Method for Evaluating the Total Rainfall Control Rate of Sponge City Construction". The formula for step 13 above is implemented according to step 42 of Chinese patent CN202310625256.0, entitled "A Method for Evaluating the Total Rainfall Control Rate of Sponge City Construction".

[0092] Step 2: Based on Step 1, the SWMM coupled with the LISFLOOD-FP model is used to conduct a two-dimensional hydrodynamic simulation to obtain a spatial distribution map of waterlogging depth. This is to determine the spatial distribution of waterlogging depth in the study area under a specified rainstorm return period, identify high-risk areas with significant water storage needs, and provide a basis for subsequent facility spatial layout and optimization. The specific steps are as follows:

[0093] Step 21: Extract the overflow data at each node of the SWMM model described in Step 1, generate an overflow boundary file (.bdy), and combine it with the DEM of the study area to generate an elevation file (.dem.ascii), which is used to drive the LISFLOOD-FP model to perform two-dimensional hydrodynamic model simulation.

[0094] Step 22: Configure the LISFLOOD-FP model parameter file (.par), select the adaptive solver, and set the simulation duration to 180 minutes and the output interval to 3 minutes. After running the model, output the spatial distribution map of urban waterlogging depth under a 5-year design rainstorm scenario, as shown below. Figure 2 As shown in (d).

[0095] Step 3: Construction of a Suitability Evaluation System for Sponge Facilities at the Urban Community Scale: Based on the DEM and land use data from the first type of multi-source data in Step 1, and the spatial distribution map of water depth from Step 2, this step combines the second type of multi-source data and the deployment conditions of various sponge facilities for analysis. The second type of multi-source data includes slope and spatial buffer distance. This data is used for spatial suitability evaluation of sponge facilities. The slope data in the second type of multi-source data is generated by calculating the DEM, and the spatial buffer distance is set according to the facility type. The deployable areas for various types of facilities are clarified. The indicators of elevation, slope, land use type, and spatial buffer distance are selected as suitability factors. The weight values ​​of each suitability factor in the overall suitability are calculated, and the consistency of the weight system is checked. Using GIS tools, the indicator layers are uniformly rasterized and weighted according to the weight values ​​to generate a comprehensive suitability score map for facility deployment. The comprehensive score results are divided into several levels, and raster layers are output with a uniform spatial resolution. Based on the comprehensive suitability score map, the raster areas where sponge facilities can be deployed are identified, and priority areas are divided according to the score level.

[0096] This embodiment selects three types of sponge city facilities—green roofs, bioretention, and sunken green spaces—for spatial suitability analysis to determine their potential for deployment in City A, providing spatial input for subsequent screening and optimization of deployment area. The specific steps are as follows:

[0097] Step 31: Construct a suitability evaluation index system: Based on the basic requirements of sponge city facility deployment for topography, land use conditions, and environmental safety, and combined with the analysis of the topography of City A, four indicators were finally selected as suitability indicators: elevation, slope, land use type, and spatial buffer distance. Elevation data was sourced from the DEM; slope was calculated using spatial analysis tools; land use types were classified according to the current urban land use status (buildings, green spaces, cultivated land, etc.); spatial demand indicators were set according to facility type, with restrictions such as a building buffer zone ≥3m and a disaster point buffer zone ≥1000m. The scores for the suitability indicators corresponding to various facilities are shown in Table 1.

[0098] Table 1. Scoring Table for Suitability Indicators of Three Typical Sponge City Facilities:

[0099]

[0100] Step 32: Determine the importance of each factor using a weighting method: Construct a judgment matrix using expert scoring combined with the Analytic Hierarchy Process (AHP), calculate the weight of each factor in the overall suitability, and perform a consistency check on the weighting system. The formula for calculating the weight value of each suitability factor in the overall suitability is as follows:

[0101] (1) Construct a judgment matrix A using the 1-9 scale method, compare each indicator pairwise, and assign a score of 1-9 based on their importance to the target layer. The greater the importance of the former (indicator i) compared to the latter (indicator j), the higher the score value. a ij For scale;

[0102] (2) Normalize the judgment matrix to obtain the normalized matrix. The calculation formula is as follows:

[0103] (4),

[0104] In the formula, b ij This represents the normalized value of the importance score of the i-th indicator relative to the j-th indicator in the judgment matrix.

[0105] (3) Calculate the weight of each indicator As shown in the following formula:

[0106] (5),

[0107] In the formula, Indicates the weight value; This represents the normalized value of the importance score of the i-th indicator relative to the j-th indicator in the judgment matrix; n represents the matrix order, i.e., the number of indicators.

[0108] The consistency check includes calculating the largest eigenvalue λ of the judgment matrix A. max Consistency indicators CI and consistency ratio CR;

[0109] The formula for calculating the largest eigenvalue of the judgment matrix A is as follows:

[0110] (6),

[0111] In the formula, represents the largest eigenvalue; AW represents the product of the judgment matrix A and the weight vector W; This represents the weight value; n represents the matrix order, i.e., the number of indicators.

[0112] The formula for calculating the consistency index CI is as follows:

[0113] (7),

[0114] The formula for calculating the consistency ratio CR is as follows:

[0115] (8),

[0116] In the formula: AW is the product of the judgment matrix A and the weight vector W; n represents the matrix order, i.e., the number of indicators; RI is the random consistency index, which needs to be determined by looking up a table based on the matrix order. The standard table of random consistency index RI is shown in Table 2.

[0117] Table 2

[0118]

[0119] The calculated weights are as follows: land use type weight is 0.5166, elevation weight is 0.1235, slope weight is 0.2257, and spatial demand weight is 0.1341. The largest eigenvalue is 4.0458. The consistency index CI of the judgment matrix is ​​0.01527; the randomness index RI of the fourth-order matrix is ​​0.9; and the random consistency ratio CR = CI / RI = 0.0170 < 0.1. Therefore, the judgment matrix can be considered to have acceptable consistency, and the calculated weights are reasonable.

[0120] Step 33: Perform suitability weighted overlay analysis: Using GIS tools, all indicator layers are uniformly rasterized, and weighted overlays are performed according to weight values ​​to generate a comprehensive suitability score map for facility layout. This map is then uniformly converted into 6m×6m resolution raster cells. The comprehensive score results are divided into suitability levels: score 0–1: unsuitable; score 1–2: moderately suitable; score 2–2.5: suitable; score 2.5–3: most suitable. A raster layer with a uniform spatial resolution is output as input for subsequent layout area selection and optimization calculations.

[0121] The spatial distribution of suitability scores for three typical sponge city facilities is as follows: Figure 3 As shown, the number of grid units with a suitability score of 2.5-3 for sunken green spaces in City A is 215,290, covering an area of ​​25,834.8 hectares; these are mainly concentrated in the western, northeastern, and southeastern parts of the city, namely Xixiangtang, Xingning, and Yongning districts. The number of grid units with a suitability score of 2.5-3 for bioretention facilities is 285,648, covering a total area of ​​34,277.8 hectares; their spatial distribution trend is similar to that of sunken green spaces, but their distribution is more widespread and scattered, forming more spatial fragments within the city and exhibiting typical patchy characteristics. The total number of grid units in the most suitable area for green roofs is 251,111, corresponding to a total area of ​​approximately 904 hectares; these are mainly distributed in areas with roof slopes of 0-5°.

[0122] Step 4: Calculation of facility layout area configuration based on storage target: Based on the storage demand of each sub-catchment determined in Step 1 and the comprehensive suitability score map of facility layout generated in Step 3, construct the storage target equation, establish the relationship between the facility layout area of ​​each sub-catchment and the required total storage volume, impose condition constraints on the storage target equation, solve for the sponge facility area combination that meets the storage demand, calculate the life cycle cost (LCC) corresponding to the sponge facility area combination, and select the minimum cost area combination scheme as the feasible solution input for subsequent spatial layout optimization;

[0123] This embodiment further selects a single sub-catchment S1177 as a case study. The total area of ​​the S1177 sub-catchment is 8.59 ha, and the required storage capacity under a 1-year return period rainstorm scenario is 980.663 m³, which translates to a unit storage capacity of 114.16 m³ / ha.

[0124] Step 41, Calculate the unit storage capacity of various sponge city facilities: Based on relevant specifications or engineering data, the calculation formulas for the unit area storage capacity of the three types of facilities—green roofs, sunken green spaces, and bioretention units—are as follows:

[0125] (1) The formula for calculating the storage capacity per unit area of ​​green roof is as follows:

[0126] (9),

[0127] In the formula: Indicates the maximum water storage height, in meters (m). This indicates the average porosity of the planting soil and filler layers; This indicates the total depth of the planting soil and filler layers, in meters (m).

[0128] (2) The storage capacity per unit area of ​​sunken green space is as follows:

[0129] (10)

[0130] In the formula: Indicates the maximum water storage height, in meters (m). Indicates the hydraulic gradient of infiltration; for vertical infiltration... ; Represents the soil permeability coefficient, in m / s; Indicates the infiltration time, in minutes.

[0131] (3) The storage capacity per unit area of ​​the bioretention unit is as follows:

[0132] (11),

[0133] In the formula: This indicates the average porosity of the planting soil and filler layers; Indicates the total depth of the planting soil and filler layers, in meters (m). Indicates the vegetation volume fraction; Represents the soil permeability coefficient, in m / s; Indicates the average design water depth of the aquifer, in meters (m). Indicates the calculation time, in minutes; Indicates the maximum water storage height, in meters (m).

[0134] The specific parameters and calculation results of the storage capacity per unit area of ​​the bioretention unit are shown in Table 3.

[0135] Table 3

[0136]

[0137] Step 42, Construct the regulation and storage target equation: The relationship between the facility layout area of ​​each sub-catchment and the required total regulation and storage volume is expressed by the following equation:

[0138] (12),

[0139] In the formula: express Zihuishui District No. The area of ​​such facilities, in m 2 ; Indicates the first Storage capacity per unit area of ​​such facilities, m 3 ; This indicates the additional storage capacity of the sponge city facilities required to achieve the 75% target control rate, taking into account the external discharge from the pipeline network, in m. 3 / ha.

[0140] The objective equation above is subject to the following constraints:

[0141] (1) The sum of the storage capacity of all facilities in the j-sub-catchment area shall not be less than the target storage capacity:

[0142] (13)

[0143] (2) The area of ​​Class I facilities in the j-sub-catchment area does not exceed the maximum deployable area, and the area is non-negative:

[0144] (14)

[0145] In the formula The maximum proportion of the facility layout area to the sub-catchment area is determined according to relevant standards, with 0.3 for green roofs, 0.3 for sunken green spaces, and 0.2 for bioretention facilities.

[0146] (3) The sum of the areas of all combined facilities in sub-catchment area j shall not exceed the total impermeable surface area of ​​sub-catchment area:

[0147] (15)

[0148] Step 43: Based on the construction of the above-mentioned storage objective function and area constraints, the inequality equations are solved using an exhaustive method. The ranges of the three variables are set, and a constant step size traversal is performed. One unknown variable is solved for each variable. The traversal and combination methods are used to solve all possible facility area configuration combinations for sub-catchment S1177 under a 5-year design storm frequency, resulting in 1115 combined solutions. Since the calculated solution sets for the area of ​​sponge facilities required to meet the target storage capacity in each sub-catchment are numerous, and some extreme solutions exist, data cleaning is performed on the facility area solution sets here to ensure more reasonable subsequent research. The facility combination data in each sub-catchment area were screened one by one according to the following seven conditions: ① x1=0, x2 ≥Aimp×5%, x3≥Aimp×5%; ② x2=0, x1≥Aimp×5%, x1≥Aimp×5%; ③ x3=0, x1≥Aimp×5%, x2≥Aimp×5%; ④ x1=0, x2=0, x3≥Aimp×5%; ⑤ x1=0, x3=0, x2≥Aimp×5%; ⑥ x2=0, x3=0, x1≥Aimp×5%; ⑦ x1≥Aimp×5%, x2≥Aimp×5%, x3≥Aimp×5%.

[0149] Step 44: Calculate the Life Cycle Cost (LCC) corresponding to the sponge facility area combination obtained in Step 43, and select the minimum cost area combination scheme. The Life Cycle Cost (LCC) calculation formula is as follows:

[0150] (16)

[0151] In the formula: The unit area lifecycle cost of sponge city facilities is expressed in yuan. This represents the construction cost per unit area of ​​sponge city facilities, expressed in yuan. represents the operation and maintenance cost per unit area of ​​sponge city facilities over its service life, expressed in yuan; k represents the growth rate coefficient, taken as 5% based on the economic development level of the study area. This indicates the service life of the sponge city facility, in years, with a conservative estimate of 20 years. The residual value of the sponge city infrastructure is expressed in yuan.

[0152] The total life-cycle cost corresponding to the sponge city facility area combination includes construction cost, operation and maintenance costs, residual value, and discount rate. The residual value calculation formula is as follows:

[0153] (17)

[0154] In the formula: This indicates the time interval between the last maintenance and management work and the facility's lifespan, calculated on an annual basis. Indicates facility lifespan, in years; This indicates the annual maintenance cost of sponge city facilities.

[0155] Based on the "Design Atlas of Low Impact Development Rainwater Control and Utilization Engineering in Guangxi Zhuang Autonomous Region" and the engineering cost standards of City A, the construction and maintenance costs of three facilities (green roof, sunken green space, and bioretention unit) were determined. Using a growth rate coefficient k=5% and J2=e=20a to calculate the residual value SV, the unit area LCC cost was obtained as follows: green roof: 270 yuan / m²; sunken green space: 105 yuan / m²; bioretention unit: 940 yuan / m². Specific parameter values ​​are shown in Table 4.

[0156] Table 4

[0157]

[0158] For the area combinations that satisfy the conditions in step 4-3, calculate their corresponding total LCC cost. The facility area combination with the lowest total cost for sub-catchment area S1177 under the condition of meeting the 5-year rainstorm scenario storage requirements is: green roof area of ​​388.54 m². 2 The sunken green space covers an area of ​​2331.23 m². 2 The bioretention area is 317.32 m². 2 The corresponding total life cycle cost is 648,000 yuan.

[0159] Step 5: Based on the minimum cost area combination scheme selected in Step 4, and combined with the facility deployment grid and priority areas determined in Step 3, as well as the spatial distribution map of water depth generated in Step 2, the non-dominated sorting genetic algorithm (NSGA-II) is used to optimize the facility grid layout in multiple objectives to improve the synergistic performance of ecological pattern and spatial response, obtain a facility layout scheme that combines regulation and storage effect, cost-effectiveness and landscape connectivity, and thus select the optimal facility layout scheme with the highest proximity, and obtain the optimal facility layout scheme.

[0160] The method for obtaining the optimal facility layout scheme described in step 5 includes the following steps:

[0161] Step 51: The purpose of constructing the initial layout scheme is to generate multiple initial layout solutions as the initial population input for the NSGA-II algorithm. The specific operations are as follows:

[0162] Input: The grid areas and priority areas for sponge city facilities determined in step 3; the spatial distribution map of water depth generated in step 2; and the division of the facility deployment area into three priority levels, such as... Figure 4 As shown. Sampling is prioritized from areas defined as "most suitable + water depth ≥ 0.5m", and the minimum cost area combination scheme selected in step 4 is used as the target for facility grid deployment.

[0163] Method: In high-priority areas, the np.random.choice() function of the NumPy library is used to perform stratified random sampling according to the layout area constraint to generate multiple initial solutions that meet the facility area target;

[0164] Output: Multiple initial layout solutions are used as initial population inputs for the NSGA-II algorithm;

[0165] Step 52: Constructing a multi-objective optimization model aims to select multiple landscape pattern indicators as optimization objectives, taking the ecological patches formed in the spatial layout of facilities as the object. The specific operation is as follows:

[0166] Input: The initial layout solution generated in step 51 and the sponge facility deployment grid area and priority area determined in step 3;

[0167] Method: In this embodiment, three indices were selected from the aspects of landscape density, landscape, and structure: patch density (PD), shape index (LSI), and cohesion index (COHESION) as optimization targets, and the minimum cost area combination scheme determined in step 4 was embedded as a hard constraint.

[0168] The formulas for calculating patch density (PD), shape index (LSI), and cohesion index are as follows:

[0169] Patch density (PD) is used to describe the number and distribution density of patches in a region:

[0170] (18)

[0171] In the formula: for The number of patches of this type of facility Represented as the sub-catchment area serial number; For the first The total area of ​​the catchment area is m. 2 .

[0172] Shape Index (LSI): The shape index primarily focuses on the overall morphology of a patch. It is typically a single numerical indicator that uses a simple numerical value to express the regularity or irregularity of the patch shape.

[0173] (19)

[0174] In the formula: for The facility's The length of the boundary of each patch, n is... The total number of patches in the facility, i.e. for Total length of the boundaries of all patches in the landscape; For the first The total area of ​​the catchment area is m. 2 .

[0175] Cohesion Index: Used to describe the connectivity or cohesion between patches in a landscape. The cohesion index measures the degree of interconnection between patches in a landscape, reflecting the integrity and connectivity of the landscape.

[0176] (20)

[0177] In the formula: No. The first type of facility Area of ​​each patch (m2); No. The first type of landscape Perimeter of each patch (m); For the first The total area of ​​the catchment area is m. 2 .

[0178] For sponge city infrastructure, while too many small patches can enhance local biodiversity, they significantly increase maintenance costs and management complexity. Conversely, too low patch density can lead to uneven distribution and ineffective coverage of the entire sub-catchment. Therefore, a moderate patch density (PD) should be chosen to balance ecological benefits and coverage. A higher shape index (LSI) indicates more complex patch boundaries, increased contact with the surrounding environment, and a greater susceptibility to edge effects, which can exacerbate pollutant intrusion and infrastructure degradation. To improve infrastructure stability and resilience, patch boundary morphology should be controlled to maintain a moderately low LSI, avoiding extreme low values ​​that could weaken the ecological heterogeneity within patches. The cohesion index reflects the spatial connectivity between patches; a higher value indicates a more compact distribution, which is beneficial for the continuity of ecological processes and the overall function of the ecological network. Therefore, schemes with higher cohesion should be prioritized to enhance the overall ecological connectivity and system stability of the sub-catchment. The multi-objective optimization function can then be constructed as follows: (twenty one),

[0179] Output: A multi-objective optimization model, including the optimization objective and constraints.

[0180] Step 53: The purpose of running the NSGA-II algorithm is to generate a Pareto optimal solution set that satisfies multi-objective performance. The specific operation is as follows:

[0181] Input: The initial layout solution generated in step 51, with facility placement location as the decision variable; Step 52 uses patch density (PD), shape index (LSI), and cohesion index (COHESION) as optimization objectives, with the total facility placement area as a hard constraint embedded in the algorithm. In each generation of individual evolution, new individuals are generated through crossover and mutation operations, and the population is screened and updated based on non-dominated sorting and crowding distance to achieve continuous improvement in multi-objective performance.

[0182] Methods: A positional coding structure was adopted, with the optimal individual retention coefficient set to 0.3, the population size to 500, the maximum number of generations to 1000, the crossover probability to 0.8, and the mutation probability to 0.3. A new generation of solution sets was generated through crossover and mutation operations, and the evolution was carried out generation by generation by combining non-dominated sorting and crowding distance selection mechanisms.

[0183] Output: Output the optimal solution set that satisfies multi-objective performance, such as the Pareto front of the S1177 facility landscape pattern index in the sub-catchment area. Figure 5 As shown.

[0184] Step 54: Optimal Solution Screening and Decision Support aims to screen the optimal facility layout scheme from the Pareto front solution set. The specific operations are as follows:

[0185] Input: The Pareto optimal solution set generated in step 53;

[0186] Methods: The TOPSIS (Topology of Ideal Solutions) method was used to comprehensively evaluate and rank the Pareto front solution set. Positive and negative ideal solutions were constructed after normalization based on landscape indicators, and the optimal facility layout scheme with the highest degree of approximation was selected.

[0187] Output: The optimal facility layout scheme for sub-catchment S1177, which takes into account multiple objectives of "storage, cost, and landscape pattern", includes three types of facilities: green roofs, sunken green spaces, and bioretention units. Figure 6 As shown.

[0188] Step 6: Repeat steps 1 to 5 for each sub-catchment area in Haidian District to obtain the optimal facility layout scheme for different facility combination scenarios in the 2596 sub-catchments of the entire city of A, such as... Figure 7 As shown.

[0189] Step 61: Simulation Verification of Storage and Regulation Effect: Based on the optimal facility layout scheme obtained in Step 5, the SWMM model is used again to simulate and verify the storage and regulation effect of the optimal facility layout scheme for each sub-catchment obtained in Step 6 under a certain design storm scenario. This is compared with the current situation without facility deployment obtained in Step 1 to evaluate its actual effectiveness in rainfall runoff control and flood risk mitigation. Output the quantitative evaluation results of the optimal facility layout scheme described in Step 5 in terms of rainfall runoff control and flood risk mitigation; the specific steps are as follows:

[0190] Step 611, Construct a simulation verification model: Input the optimal facility layout scheme obtained in step 5, convert the facility type, spatial location and area configuration in the optimal facility layout scheme into the input parameters required by the SWMM model, set the LID facility attribute parameters, complete the SWMM model update of the sub-catchment area, and obtain the updated SWMM model of the sub-catchment area.

[0191] Step 612: Simulate and extract regulation and storage indicators, and compare and analyze the results: Run the updated SWMM model of the sub-catchment area, extract key indicators of runoff depth and runoff control rate of the sub-catchment area under a certain return period, and compare and analyze them with the current situation without facility deployment as described in Step 1. Output the quantitative evaluation results of the optimal facility layout scheme described in Step 5 in terms of rainfall-runoff control and flood risk mitigation, including the comparative analysis of key indicators of runoff depth and runoff control rate. The results show that under a 5-year return period, the average runoff depth of the sub-catchment area of ​​City A is 26.32 mm, and the runoff depth range is 19.83-37.97 mm. The average runoff depth under the current operating conditions is 58.5 mm, with a reduction of 50%, indicating a significant control effect. The average runoff control rate is 69.5%, and the runoff depth range is 56-74.7%, which is close to the set target of 75% runoff control rate, indicating that the facilities operate efficiently under low to medium rainfall intensity and basically achieve the expected regulation and storage target. The specific spatial distribution of the data is as follows: Figure 8 As shown.

[0192] Step 62: Repeat steps 1 to 61 to advance the construction of the next planning target's urban community sponge facility type combination and its spatial layout, so as to achieve systematic, whole-area, and whole-process scientific quantitative guidance for the sustainable construction of sponge cities.

[0193] This method is applicable to urban communities with various terrains such as plains and hills. It is not only applicable to City A, but can also be extended to other urban communities with similar terrain and climate characteristics.

Claims

1. A method for optimizing the spatial layout of sponge city facilities for stormwater storage and regulation in urban communities, characterized in that, Includes the following steps: Step 1: Collect the first type of multi-source data for the study area. The first type of multi-source data includes current land use, digital elevation model, drainage network layout, and design storm. Based on the distribution of roads, buildings, and pipe networks on the underlying surface, divide the study area into sub-catchment zones and extract the hydrological parameters of area, slope, and impermeability of each sub-catchment zone. Calculate the design storm volume for a certain return period in the current year and perform time-history allocation. Use the SWMM model to simulate the runoff process of the secondary storm in the study area for a certain return period in the current year and calculate the total secondary storm control rate for each sub-catchment zone. Based on the target control rate of the total secondary storm volume in the future urban planning scenario, calculate the unit storage volume of each sub-catchment zone that still needs to be achieved by deploying sponge city facilities after deducting the runoff that can be directly discharged by the pipe network. Determine the storage demand of each sub-catchment zone and record the current situation without facility deployment. Step 2: Based on Step 1, the SWMM coupled with the LISFLOOD-FP model is used to conduct a two-dimensional hydrodynamic simulation to obtain a spatial distribution map of water depth. Step 3: Based on the digital elevation model and land use data from the first type of multi-source data in Step 1, and the spatial distribution map of water depth from Step 2, combined with the second type of multi-source data and the deployment conditions of various sponge facilities, the second type of multi-source data includes slope and spatial buffer distance. The deployable areas of various facilities are identified, and indicators such as elevation, slope, land use type, and spatial buffer distance are selected as suitability factors. The weight values ​​of each suitability factor in the overall suitability are calculated, and the consistency of the weight system is checked. The indicator layers are uniformly rasterized using GIS tools, and weighted and superimposed according to the weight values ​​to generate a comprehensive suitability score map for facility deployment. The comprehensive score results are divided into several levels, and raster layers are output with uniform spatial resolution. Based on the comprehensive suitability score map, the raster areas where sponge facilities can be deployed are identified, and priority areas are divided according to the score level. Step 4: Based on the storage and regulation needs of each sub-catchment area determined in Step 1 and the comprehensive suitability score map of facility layout generated in Step 3, construct the storage and regulation target equation, establish the relationship between the facility layout area of ​​each sub-catchment area and the required total storage and regulation volume, impose conditional constraints on the storage and regulation target equation, solve for the sponge facility area combination that meets the storage and regulation needs, calculate the full life cycle cost corresponding to the sponge facility area combination, and select the minimum cost area combination scheme. Step 5: Based on the minimum cost area combination scheme selected in Step 4, the landscape pattern index is introduced. Combined with the facility deployment grid and priority area determined in Step 3, and the spatial distribution map of water depth generated in Step 2, the facility grid layout is optimized in multiple objectives to select the optimal facility layout scheme that meets the water storage target and is suitable for the landscape pattern. Step 6: Repeat steps 1 to 5 for each sub-catchment area to obtain the optimal facility layout scheme for each sub-catchment area.

2. The method according to claim 1, characterized in that, It also includes the following steps: Step 61: Simulation and verification of storage effect: Based on the optimal facility layout scheme obtained in Step 5, the facility type, spatial location and area configuration in the optimal facility layout scheme are converted into the input parameters required by the SWMM model. The SWMM model is used again to simulate and verify the storage effect of the optimal facility layout scheme of each sub-catchment obtained in Step 6 under the same design rainstorm scenario as in Step 1. The result is compared with the current situation without facility layout obtained in Step 1. The quantitative evaluation results of the optimal facility layout scheme described in Step 5 in terms of rainfall runoff control and flood risk mitigation are output. Step 62: Repeat steps 1 to 61 to advance the construction of the next planning goal's urban community sponge facility type combination and its spatial layout.

3. The method according to claim 2, characterized in that, The quantitative assessment results of the optimal facility layout scheme in step 61 regarding rainfall-runoff control and flood risk mitigation include the following steps: Step 611, Construct a simulation verification model: Input the optimal facility layout scheme obtained in step 5, convert the facility type, spatial location and area configuration in the optimal facility layout scheme into the input parameters required by the SWMM model, set the LID facility attribute parameters, and obtain the updated SWMM model of the sub-catchment area. Step 612: Run the updated SWMM model of the sub-catchment area, extract the key indicators of runoff depth and runoff control rate of the sub-catchment area under a certain return period, and compare and analyze them with the current situation without facility layout described in Step 1. Output the quantitative evaluation results of the optimal facility layout scheme described in Step 5 in terms of rainfall runoff control and flood risk mitigation, including the comparative analysis of key indicators of runoff depth and runoff control rate.

4. The method according to claim 1, characterized in that, The formula for calculating the design rainfall for a certain return period in the current year mentioned in step 1 is as follows: ，（1） In the formula: q represents the design rainfall intensity, L / (s·ha); P represents the design rainfall return period, y; t represents the design duration of the rainstorm, in min; the time-history allocation adopts the Chicago method for allocating the rainfall duration. The formula for calculating the total rainfall control rate of each sub-catchment zone is as follows: ，（2） In the formula: R cr R represents the total rainfall control rate of each sub-catchment area; P represents the total runoff of the sub-catchment area in mm; and P represents the total rainfall in mm. Expressed as runoff coefficient; The formula for calculating the unit storage capacity of each sub-catchment area, after deducting runoff that can be directly discharged through the pipe network, which still needs to be achieved by deploying sponge facilities, is as follows: ，（3） In the formula: This represents the additional unit storage capacity required after deducting the stormwater discharge from the pipeline network, expressed in cubic meters (m³). 3 / ha; This is expressed as the runoff coefficient of stormwater discharged from the pipe network. The value of this parameter is determined by urban planning, and according to the specifications, it can be taken as 0.2~0.

4. This represents the runoff coefficient corresponding to the target control rate.

5. The method according to claim 1, characterized in that, Step 2, which involves obtaining the spatial distribution map of water depth, includes the following steps: Step 21: Extract the overflow data at each node of the SWMM model described in Step 1, generate the overflow boundary file, and combine it with the DEM of the study area to generate an elevation file to drive the LISFLOOD-FP model for two-dimensional hydrodynamic model simulation. Step 22: Configure the LISFLOOD-FP model parameter file, select the adaptive solver and set the simulation duration and output interval. After running the model, output the spatial distribution map of water depth.

6. The method according to claim 1, characterized in that, The formulas for calculating the weight values ​​of each suitability factor in the overall suitability mentioned in step 3 are as follows: （5）， In the formula, Indicates the weight value; This represents the normalized value of the importance score of the i-th indicator relative to the j-th indicator in the judgment matrix; n represents the matrix order, i.e., the number of indicators. The consistency test includes calculating the maximum eigenvalue, consistency index, and consistency ratio of the judgment matrix A; The formula for calculating the largest eigenvalue of the judgment matrix A is as follows: （6）， In the formula, λ max represents the largest eigenvalue; AW represents the product of the judgment matrix A and the weight vector W; This represents the weight value; n represents the matrix order, i.e., the number of indicators. The formula for calculating the consistency index CI is as follows: （7）， The formula for calculating the consistency ratio CR is as follows: （8）， In the formula: n represents the matrix order, i.e. the number of indicators; RI is the random consistency index, which needs to be determined by looking up a table based on the matrix order.

7. The method according to claim 1, characterized in that, The formula for establishing the relationship between the facility layout area of ​​each sub-catchment and the required total storage capacity, as described in step 4, is as follows: ，（12） In the formula: express Zihuishui District No. The area of ​​such facilities, in m 2 V i Indicates the first Storage capacity per unit area of ​​such facilities, m 3 ; This indicates the additional storage capacity of the sponge city facilities required to achieve the 75% target control rate, taking into account the external discharge from the pipeline network, in m. 3 / ha; The conditions for the target equation of water storage are as follows: (1) The sum of the storage capacity of all facilities in the j-sub-catchment area shall not be less than the target storage capacity: ，（13） (2) The area of ​​Class I facilities in the j-sub-catchment area does not exceed the maximum deployable area, and the area is non-negative: ，（14） In the formula, The value is determined according to relevant standards, representing the maximum proportion of the facility layout area to the sub-catchment area. (3) The sum of the areas of all combined facilities in sub-catchment area j shall not exceed the total impermeable surface area of ​​sub-catchment area: ；（15） The formula for calculating the total life-cycle cost corresponding to the area combination of the sponge city facilities is as follows: ，（16） In the formula: The unit area lifecycle cost of sponge city facilities is expressed in yuan. This represents the construction cost per unit area of ​​sponge city facilities, expressed in yuan. denoted as RMB, representing the operation and maintenance cost per unit area of ​​sponge city facilities over their service life; k represents the growth rate coefficient, which is determined based on the economic development level of the study area. Indicates the service life of sponge city facilities, in years; The residual value of sponge city infrastructure is expressed in yuan. The total life-cycle cost corresponding to the sponge city facility area combination includes construction cost, operation and maintenance costs, residual value, and discount rate. The residual value calculation formula is as follows: ，（17） In the formula: This indicates the time interval between the last maintenance and management work and the facility's lifespan, calculated on an annual basis. Indicates facility lifespan, in years; This indicates the annual maintenance cost of sponge city facilities.

8. The method according to claim 1, characterized in that, The method for obtaining the optimal facility layout scheme described in step 5 includes the following steps: Step 51: Initial layout scheme construction: Using the grid area and priority area for sponge facilities determined in Step 3, the spatial distribution map of water depth generated in Step 2, and the minimum cost area combination scheme selected in Step 4, multiple initial layout solutions are generated by hierarchical random sampling in high priority areas as the initial population input for the NSGA-II algorithm. Step 52: Multi-objective optimization model construction: Input the initial layout solution generated in step 51 and the sponge facility deployment grid area and priority area determined in step 3, select landscape pattern indicators such as patch density, shape index and cohesion index as optimization objectives, and embed the minimum cost area combination scheme determined in step 4 as hard constraints, and output the multi-objective optimization model, including optimization objectives and constraints. Step 53: NSGA-II Algorithm Execution: Input the multi-objective optimization model from Step 52 and the initial layout solution generated in Step 51. Use the layout position encoding structure, set parameters such as population size, crossover and mutation probability, and maximum number of generations, generate a new generation of solution set through crossover and mutation operations, and evolve generation by generation by combining non-dominated sorting and crowding distance selection mechanism, and finally output the Pareto optimal solution set that satisfies the multi-objective performance. Step 54: Optimal Solution Selection and Decision Support: Input the Pareto optimal solution set generated in Step 53, use the TOPSIS method to comprehensively evaluate and rank the Pareto front solution set, construct positive ideal solutions and negative ideal solutions after normalization based on landscape indicators, select the optimal facility layout scheme with the highest proximity, and finally output the optimal facility layout scheme.

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