Underlying surface randomness-considered coal port low-impact development facility layout optimization method

Abstract

The invention belongs to the field of green port planning and operation, and discloses a coal port low-impact development facility layout optimization method considering underlying surface randomness. Comprising the following steps: collecting data; establishing a rainwater runoff model; constructing a response matrix; generating a representative underlying surface scene; establishing a multi-objective optimization model; solving the optimization model; and determining an optimal layout scheme. The coal port low-impact development facility layout optimization method provides a scientific basis for planning and construction of coal port rainwater collection facilities, considers the randomness of the underlying surface type of the coal port, and improves the accuracy and adaptability of the rainwater collection facility layout scheme. The utilization efficiency of water resources is improved, the operation cost is reduced, and green port construction is promoted.

Description

Technical Field

[0001] The present invention belongs to the field of green port planning and operation, relates to the layout optimization of rainwater collection facilities in coal ports, and particularly relates to a layout optimization method for low impact development facilities in coal ports considering the randomness of underlying surfaces. Background Art

[0002] With the intensification of the global water shortage problem, a large amount of water resources is consumed in the dust removal operations of ports, especially coal ports, which exacerbates the regional water shortage problem. At present, the rainwater recovery in coal ports mainly relies on gray facilities such as sewers and cannot cope with the change of rain runoff coefficient caused by the operation in coal yards. Secondly, low impact development facilities are widely used in urban rainwater recovery, green city construction, etc. due to their decentralized layout and large-scale recovery characteristics. The application of this facility in intensive operation areas such as ports, chemical industrial parks, and logistics parks has become a trend. The paper titled Residential demolition and its impact on vacant lot hydrology: Implications for the management of stormwater and sewer system overflows by Shuster et al. in 2014 mentioned that the existing layout optimization methods for low impact development facilities are mostly based on the assumption of fixed underlying surface types. Therefore, there is still a lack of relevant technical support for the layout of low impact development facilities in coal ports, and the randomness of the underlying surface in coal ports is not fully considered, which may lead to poor actual application effects.

[0003] Therefore, there is an urgent need for a layout optimization method for port rainwater collection facilities considering the randomness of underlying surfaces to improve rainwater collection efficiency and reduce construction costs. Summary of the Invention

[0004] The objective of the present invention is to provide an optimization method for the layout of low-impact development facilities in coal ports considering the randomness of underlying surfaces. By introducing changes in random underlying surface types and combining multi-objective optimization models and surrogate models, efficient layout optimization of rainwater collection facilities in coal ports is achieved. For multiple objectives, the Nash bargaining solution is used to achieve the best low-impact development layout in coal ports. The optimization method includes four main stages: First, the SWMM is used to simulate the rainwater runoff in coal ports. On this basis, a response matrix is established as a surrogate model to improve the calculation efficiency. Second, considering the investment of port operators and rainfall runoff control, a multi-objective stochastic optimization model for the layout of low-impact development facilities in coal ports is constructed. Then, the impact of the random underlying surface type of the port on rainwater runoff is evaluated using the rainwater runoff simulation results. Based on the clustering algorithm, cluster analysis is performed on the historical stacking data of the yard to generate five representative underlying surface type schemes. Finally, the NSGA-2 algorithm is used to seek a trade-off solution between the two objective functions in the case of representative surface types. The Nash bargaining solution is used to capture the interests of decision-makers, thereby determining a suitable layout scheme for rainwater collection facilities on the Pareto front.

[0005] The technical solution of the present invention:

[0006] An optimization method for the layout of low-impact development facilities in coal ports considering the randomness of underlying surfaces, the steps are as follows:

[0007] Step 1: Data collection and preprocessing;

[0008] (1) Collect the geographical information of the coal port, including the topographic map of the port and the functional division map of different regions;

[0009] (2) Collect meteorological data, including the rainfall, rainfall intensity and rainfall duration over the years;

[0010] (3) Obtain the rainwater pipe network layout map, including the distribution, pipe diameter and slope of the existing rainwater pipe network in the port;

[0011] (4) Collect the runoff coefficient data of different underlying surface types, including the runoff coefficients of coal piles, concrete floors, soils, and green areas under different rainfall conditions;

[0012] (5) Collect the construction cost and annual operation cost data of low-impact development facilities including green roofs, grassed swales, and permeable pavements;

[0013] (6) Collect the historical stacking data of the coal port yard, that is, the stacking and reclaiming operations of various goods in the yard;

[0014] (7) Collect the actual observed data of historical rainwater runoff in the coal port;

[0015] Sort out and analyze the collected data, and check the integrity and accuracy of the data;

[0016] Step 2: Establish a rainwater runoff model;

[0017] Use the Storm Water Management Model (SWMM) to dynamically simulate the rainfall runoff process and the hydrological performance of low impact development facilities; according to the geographical information, meteorological data, rainwater pipe network layout map of the coal port, and runoff coefficient data of different underlying surface types collected, establish the input files of the rainwater management model, including the division of sub-catchments, rainfall patterns and durations, connection relationships of rainwater pipe networks, and settings of different underlying surface types;

[0018] Verify the effectiveness of the rainwater management model, and adjust the parameters of the rainwater management model by comparing with the actual observed data of the historical rainwater runoff of the coal port obtained in Step 1, so that the rainwater management model can accurately simulate the rainwater runoff changes of the coal port under different rainfall scenarios;

[0019] Step 3: Construct a response matrix;

[0020] Run the rainwater management model to simulate several layout schemes of low impact development facilities with types, locations, and capacities, and obtain the rainwater runoff flows of different sub-catchments under each rainfall scenario and underlying surface type for each layout scheme of low impact development facilities; establish a response matrix, where the rows represent different layout schemes of low impact development facilities, the columns represent the combinations of different sub-catchment underlying surface types and rainfall scenarios, and the elements in the matrix represent the rainwater runoff flows of the sub-catchments corresponding to the layout schemes of low impact development facilities and rainfall scenarios; through the response matrix, calculate the total runoff volume under any layout scheme of low impact development facilities;

[0021] The steps to construct the response matrix are as follows:

[0022] (1) For each layout scheme of low impact development facilities, it is necessary to run the rainwater management model once in the research area of the coal port for runoff simulation analysis;

[0023] (2) For any layout scheme of low impact development facilities and rainfall scenario, construct a response matrix, where the elements along the diagonal are the runoff of each sub-catchment ;

[0024] (3) Construct a decision vector , where the elements are the area fractions assigned to each low impact development facility in the sub-catchment;

[0025] (4) Based on the input data of the area of each sub-catchment, obtain the area matrix A of the sub-catchments;

[0026] (5) Construct a connectivity matrix to describe the upstream and downstream relationships of all sub-catchments; if sub-catchment area j is upstream of sub-catchment area i, the non-diagonal element of the connectivity matrix is equal to 1, otherwise it is zero, and it is stipulated that the diagonal element ;

[0027] (6) Estimate the stormwater runoff flow at the outlet of each sub-catchment by summing the runoff of each sub-catchment and the stormwater runoff flows of all upstream areas:

[0028]

[0029] where represents converting the vector parameter into a diagonal matrix. As in the above formula, for the vector parameters and perform diagonal matrix conversion, and the diagonal elements in the diagonal matrix are ; is the correction factor for the layout scheme of low impact development facilities; is the duration of stormwater runoff simulation;

[0030] Step Four: Generate representative underlying surface type scenarios;

[0031] Use the K-medoids clustering algorithm to analyze the historical data of the coal port yard collected in Step One. Set the number of clusters generated by the clustering algorithm to 5, search and calculate the sum of the distances from the underlying surface type data points to the centroid of the dataset, divide the data points into 5 clusters, and the 5 real data centroids generated by the clustering operation are the representative underlying surface type scenarios;

[0032] Step Five: Establish a multi-objective programming model;

[0033] Take the total investment cost of low impact development facilities as objective function 1, including fixed costs, the construction cost of low impact development facilities, and the operating cost throughout the life cycle; consider the impact of the type, location, and area of different low impact development facilities on the total investment cost, and take the total runoff control rate of the coal port as objective function 2 to maximize the rainwater collection and control effect and reduce the impact of stormwater runoff on port operations and the surrounding environment; connect with the response matrix constructed in Step Three to form a multi-objective programming model based on the response matrix, and use the randomness of the underlying surface type as the constraint condition of the multi-objective programming model to ensure the feasibility and effectiveness of the optimization results under different underlying surface type scenarios; The objective function and constraints of the multi-objective programming model are expressed by formulas:

[0034] (1) Objective function 1:

[0035]

[0036] where The construction cost required to deploy the l-th low impact development facility per unit area at the candidate location j in the i-th sub-catchment; The fixed cost required to deploy the l-th low impact development facility at the candidate location j in the i-th sub-catchment; The operation cost required to deploy the l-th low impact development facility per unit area at the candidate location j in the i-th sub-catchment; The area of the l-th low impact development facility deployed at the candidate location j in the i-th sub-catchment; A 0-1 variable representing whether the l-th low impact development facility is deployed at the candidate location j in the i-th sub-catchment; The life cycle of the l-th low impact development facility; The discount rate;

[0037] (2) Objective function 2:

[0038]

[0039] Among them, Represents the k-th underlying surface type scenario, Represents the Probability of occurrence in the k-th underlying surface type scenario, Represents the total runoff of sub-catchment i when no low impact development facility is deployed, Represents the total runoff of sub-catchment i after deploying the low impact development facility; t represents the simulation time step;

[0040]

[0041] The above formula calculates the total runoff of sub-catchment i before constructing the low impact development facility;

[0042] Among them, And Are the slope function and roughness coefficient function in the k-th underlying surface type scenario; Is the area of sub-catchment i; Is the equivalent width of sub-catchment i; Is the k-th rainfall scenario;

[0043]

[0044] The above formula represents the total runoff of sub-catchment i after constructing the low impact development facility;

[0045]

[0046] The above formula defines the functional expression of the runoff of sub-catchment i at time step t;

[0047] Where, is the slope of sub-catchment i, is the roughness coefficient of sub-catchment i;

[0048]

[0049]

[0050] The above formula represents the relationship between slope, roughness coefficient and surface type, where u represents the u-th surface type; represents the slope; represents the roughness coefficient;

[0051] (3) Constraints:

[0052] (3.1) Regional area constraint:

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] They are the relationship constraints among the layout area of low-impact facilities, the available layout area of low-impact development facilities and the sub-catchment area respectively; is the area occupied by the u-th surface type at the candidate location j in the i-th sub-catchment;

[0059] (3.2) Low-impact development facility type constraint:

[0060]

[0061]

[0062] It is required that the type of rainwater collection facilities matches the surface type; indicates whether there is an area of the u-th surface type at the candidate location j in the i-th sub-catchment;

[0063] (3.3) Flow constraint:

[0064]

[0065] Ensure that the runoff of each sub-catchment at each time step is within a safe range, and are the lower and upper limits of the runoff volume;

[0066]

[0067] Define the relationship between the peak runoff volume and the runoff volume at each time step, where is the peak runoff volume of the i-th sub-catchment area;

[0068] (3.4) Logical constraint:

[0069]

[0070] Ensure that the area values of each facility can be obtained only after the low impact development facilities are built at the candidate locations, represents a number representing infinity;

[0071] Step Six: Solve the optimization model;

[0072] Use NSGA-2 as the optimization solution algorithm, set the parameters of the algorithm, run NSGA-2, solve the multi-objective optimization model, and obtain the Pareto front under different underlying surface type scenarios, that is, a set of low impact development facility layout schemes that achieve a balance between the total investment cost and the total runoff control rate of the coal port;

[0073] Step Seven: Determine the optimal low impact development facility layout scheme;

[0074] Select the optimal layout scheme on the Pareto front through the Nash bargaining solution; set the distance parameter of the Nash bargaining solution , find the point closest to the ideal solution on the Pareto front, which is the optimal layout scheme;

[0075] Use the Nash bargaining theory to simulate the negotiation process among stakeholders and select a final solution from a set of non-dominant solutions, expressed as the following formula:

[0076]

[0077]

[0078] where, is the distance function; is the distance parameter; and are the layout schemes, that is, the solutions; and mean the two objective functions in the model; is the set on the Pareto boundary. Given a certain value of, the point closest to the ideal point, that is, the Nash bargaining solution; if , at Among them, the target with a smaller deviation plays a more important role; if , the two targets have the same weight; if , in , the target with a larger deviation has a greater weight.

[0079] The system of the present invention includes a data processing module, a model establishment module, a scenario generation module, a response matrix construction module, an optimization model solution module, and a layout scheme determination module. Each module works together to optimize the layout of rainwater collection facilities in coal ports.

[0080] Advantages of the present invention:

[0081] 1. Considering the randomness of the underlying surface types in coal ports, it improves the accuracy and adaptability of the layout scheme of rainwater collection facilities.

[0082] 2. By means of the response matrix, it improves the calculation efficiency of the multi-objective optimization model and can obtain a reasonable layout scheme in a relatively short time.

[0083] 3. Using the Nash bargaining solution to balance the goals of different stakeholders makes the final layout scheme more feasible and acceptable.

[0084] 4. The method and system of the present invention provide a scientific basis for the planning and construction of rainwater collection facilities in coal ports, contribute to improving the water resource utilization efficiency, reducing the operation cost, and promoting the construction of green ports. Description of the Drawings

[0085] Figure 1 is the flowchart of the low-impact development layout optimization model for coal ports.

[0086] Figure 2 is the schematic diagram of each functional area in the research area.

[0087] Figure 3 is the schematic diagram of the sub-watershed division in the research area. Detailed Embodiments

[0088] The following further illustrates the detailed embodiments of the present invention in combination with the drawings and technical solutions.

[0089] Taking the layout optimization of rainwater collection facilities in a large coal port in northern China as an example, the optimization model is divided into five steps. The specific process is as Figure 1 shown.

[0090] Step 1: Data collection and preprocessing

[0091] Collect the geographical information of the case coal port (including topographic maps of the port, functional division maps of different areas, etc.), meteorological data (annual rainfall, rainfall intensity, rainfall duration for many years, etc.), rainwater pipe network layout maps, runoff coefficient data of different underlying surface types (coal piles, concrete ground, bare soil, green areas, etc.), and historical storage data of the coal port yard. Organize and analyze the collected historical data, check the integrity and accuracy of the data, and process the missing or abnormal data to ensure data quality.

[0092] The research area includes the first-phase and second-phase projects of the case coal port, covering an area of about 20 km 2 . The research area is divided into three parts: the coal terminal front area, the coal yard area, and the coal terminal auxiliary area. Each functional area in the research area is as Figure 2 shown. 1 represents soil; 2 represents green space; 3 represents concrete ground; 4 represents the main road; 5 represents the roof; 6 represents coal piles; 7 represents the auxiliary operation area; 8 represents the yard area; 9 represents the terminal front operation area. Obtain the layout map and rainwater pipe network map of the research area as the basic data for regional rainwater runoff simulation. Divide the research area into sub-catchments, and the topographic map of the sub-catchment division is as Figure 3 , and the areas of 12 coal yard areas are shown in Table 1 below, and the historical runoff coefficient data of different area types are shown in Table 2 below:

[0093] Table 1 Area data of coal yard areas

[0094]

[0095] Table 2 Historical runoff coefficient data of different area types in the research area

[0096]

[0097] The rainfall is designed with recurrence intervals of 1 year, 5 years, 10 years, 50 years, and 100 years, and the duration is 2 hours, which matches the average operation time of a single stacking or reclaiming task in the coal yard. The storm intensity duration-frequency formula for the research area:

[0098]

[0099] where q is the rainfall intensity (mm / minute), P is the rainfall recurrence interval (years), and t is the rainfall duration (minutes).

[0100] Based on the previous intermittent rainfall runoff monitoring data, the port operator obtained the runoff coefficients of specific sub-domains in the research area, as shown in Table 3 below.

[0101] Table 3 Runoff coefficients of some sub-domains in the research area

[0102]

[0103] Step 2: Establish a rainwater runoff model and a response matrix

[0104] Use the Storm Water Management Model (SWMM) to simulate the rainwater runoff changes of the coal port under different underlying surface scenarios. The collected geographic information, meteorological data, and rainwater pipe network layout maps are used as the input files for the SWMM, including the division of sub-catchments, the connection relationships of the rainwater pipe network, and the settings of different underlying surface types. Compare with the actual rainwater runoff observation data of the coal port and adjust the model parameters.

[0105] Select a sub-catchment and use 3 types of low impact development (LID) facilities to verify the effectiveness of the response matrix surrogate model. Under the 2-hour design rainfall in 1 year, check the effectiveness of the surrogate model without facility arrangements. The relationship between the flow rate of the sub-catchment and the area of a single LID facility shows an almost linear trend. R 2 > 0.95 indicates that the response matrix effectively simulates the results of LID facilities during rainfall events. Verify the effectiveness of the surrogate model in scenarios involving multiple facility layouts. For all combinations of LID facilities, the Nash-Sutcliffe efficiency coefficient is close to 1, indicating the effectiveness of the response matrix.

[0106] Step 3: Generate representative underlying surface scenarios

[0107] Use the clustering algorithm to analyze the historical storage data of the coal port yard, classify similar underlying surface types into the same category, and generate 5 representative underlying surface type scenarios. Use the clustering algorithm to select some key sub-watersheds and observe the representative water level lines at each water level interval. The clustering results of all sub-domain hydrographs are shown in Table 4 below.

[0108] Table 4 Clustering results of all sub-domain hydrographs in the study area

[0109]

[0110] Change the proportion of the yard area occupied by coal piles, analyze the impact of the change in the underlying surface on the rainwater runoff of the coal port, i.e., the utilization rate of the yard area, and simulate the rainwater runoff process of the yard. Under the 2-hour design storm in 1 year, establish 11 utilization rate scenarios, ranging from 0% to 100%, with equal intervals (10%). As the coal stockpile increases, the total runoff volume decreases significantly, and the area under the pollution discharge curve gradually decreases. The incremental accumulation of coal in the yard causes the total runoff volume to decrease from 48,000 m 3 to 14,100 m 3Around. Based on the historical dataset of the coal port yard operation process in 2019, the clustering method is used to generate representative scenarios of the yard underlying surface types. Five scenarios of coal and concrete underlying surfaces with the highest occurrence probabilities in the entire study area are obtained using the clustering method, as shown in Table 5 below. Since Scenario 4 in the table has a relatively high occurrence frequency, the port operator can optimize the layout of rainwater collection facilities under Scenario 4. Therefore, Scenario 4 can be used as a benchmark scenario to discuss the necessity of considering the randomness of the underlying surface.

[0111] Table 5 Representative Scenarios of Yard Underlying Surface Types (Percentage of Imperviousness)

[0112]

[0113] Step 4: Establish and Solve the Multi-Objective Optimization Model

[0114] Establish the multi-objective optimization model:

[0115] (1) Objective function setting

[0116] (1.1) Minimize the total investment cost: Calculate the total cost of low-impact development facilities, including construction costs, operation and maintenance costs, etc., considering the impacts of different facility types, layout locations, and areas on the cost. The formula is:

[0117]

[0118] (1.2) Maximize the total runoff control rate: Aim to maximize the rainwater collection and control effect and reduce the impact of rainwater runoff on port operations and the surrounding environment. The formula is:

[0119]

[0120] (2) Constraint condition setting:

[0121] (2.1) Area constraint: Ensure that the area of low-impact development facilities does not exceed the available space.

[0122] (2.2) Matching constraint between facility type and underlying surface: Ensure that the low-impact development facility type matches the underlying surface type.

[0123] (2.3) Flow constraint: Ensure that the runoff volume is within a safe range.

[0124] (2.4) Logic constraint: Ensure that the facility area has a value only after it is determined to be constructed.

[0125] Use NSGA-2 to solve the multi-objective optimization model, set the parameters of the algorithm, the population size is 100, the maximum number of iterations is 300, the crossover probability is 0.9, and the mutation probability is 0.1. Run NSGA-2 to obtain the Pareto front under different underlying surface scenarios.

[0126] NSGA-2 is coded in Python 3.10 with the parameter settings as follows: the maximum number of iterations \(I_{max}=300\), the crossover rate and mutation rate are 0.9 and 0.1 respectively. Under the 1-year 2-hour design storm, for every 10% increase in the runoff control rate before the inflection point, the total cost surges by approximately 2,302,950,000 yuan; for every 10% increase in the runoff control rate after the inflection point, the total cost surges by approximately 6,092,930,000 yuan. The port operator tends to select the layout of rainwater collection facilities near the inflection point in Scenario 4, and the total cost of the selected rainwater collection facilities layout is approximately 1.8 billion yuan.

[0127] By combining five representative scenarios with the proposed model and method, the corresponding Pareto fronts are generated. The available data are as follows: the solution sets of each scenario have consistent characteristics, the inflection point of the Pareto front appears in the interval of 48% - 50%, and the relationship between cost and runoff control rate changes significantly before and after the inflection point; for the change in the total cost of low-impact development layout plans when the runoff control rate ranges from 40% to 50% in the five scenarios, the inflection point also appears in the interval of 48% - 50%; the change in the total runoff control rate of the five scenarios when the total cost of low-impact development facilities ranges from 0.5 billion to 3 billion yuan.

[0128] Step 5: Determine the optimal layout plan

[0129] Select the optimal layout plan on the Pareto front through the Nash bargaining solution. Set the distance parameter \(\lambda\) of the Nash bargaining solution, and adjust the value of \(\lambda\) according to the degree of concern of different stakeholders such as the coal port management and the government for cost and runoff control rate. Find the point on the Pareto front that is closest to the ideal solution, which is the optimal layout plan.

[0130] Identify the Nash bargaining solution based on the distance parameter \(\lambda\) to balance the total runoff control rate and the total cost of rainwater collection facilities. The Pareto front and layout plan obtained by this method are more economical and efficient because the investment cost is lower than that in Scenario 4 at most rainwater collection rates. For example, about 100 million yuan can be saved at a rainwater collection rate of 49%. The Pareto front is located within its fluctuation range. The purple points represent the Nash bargaining solutions selected at different \(\lambda\) values, and their characteristics are similar to those of the Pareto front and are located within the same fluctuation range. Taking the Pareto front of the 1-year design rainfall considering the randomness of the yard underlying surface type as an example, when \(3.1\leqslant\lambda\leqslant5.0\), the total runoff control rate and the total cost of low-impact development facilities of the coal port are 50.98% and 1.636 billion yuan respectively. This solution shows that considering the representative scenarios of the yard underlying surface type, the expected values of the total runoff control rate and cost overrun are 50.98% and 1.636 billion yuan respectively.

Claims

1. A method for optimizing the layout of low-impact development facilities in coal ports considering the randomness of underlying surfaces, characterized in that The steps are as follows: Step 1: Data collection and preprocessing; Collect the geographical information, meteorological data, rainwater pipe network layout diagrams, runoff coefficient data of different underlying surface types, construction costs and annual operating costs of low impact development facilities, historical storage data of coal port yards, and actual observed data of historical rainwater runoff in coal ports; Step 2: Establish a rainwater runoff model; Use the Storm Water Management Model (SWMM) to dynamically simulate the rainfall runoff process and the hydrological performance of low impact development facilities; according to the collected geographical information, meteorological data, rainwater pipe network layout diagrams, and runoff coefficient data of different underlying surface types of the coal port, establish the input files of the rainwater management model, including the division of sub-catchments, rainfall patterns and durations, connection relationships of rainwater pipe networks, and settings of different underlying surface types; Step 3: Construct a response matrix; Run the rainwater management model to simulate several layout schemes of low impact development facilities with types, locations, and capacities, and obtain the rainwater runoff flows in different sub-catchments under different rainfall scenarios and underlying surface types for each layout scheme of low impact development facilities; establish a response matrix, where the rows represent different layout schemes of low impact development facilities, the columns represent combinations of different sub-catchment underlying surface types and rainfall scenarios, and the elements in the matrix represent the rainwater runoff flows of the sub-catchments corresponding to the layout schemes of low impact development facilities and rainfall scenarios; Calculate the total runoff volume under any layout scheme of low impact development facilities through the response matrix; Step 4: Generate representative underlying surface type scenarios; Use the K-medoids clustering algorithm to analyze the historical data of coal port yards collected in Step 1, set the number of clusters generated by the clustering algorithm to 5, search and calculate the sum of the distances from the underlying surface type data points to the dataset centroid, divide the data points into 5 clusters, and the clustering operation generates 5 real data centroids, which are the representative underlying surface type scenarios; Step 5: Establish a multi-objective programming model; Take the total investment cost of low impact development facilities as objective function 1, including fixed costs, construction costs of low impact development facilities, and operating costs throughout the life cycle; consider the influence of the types, locations, and areas of different low impact development facilities on the total investment cost, and take the total runoff control rate of the coal port as objective function 2 to maximize the rainwater collection and control effect and reduce the impact of rainwater runoff on port operations and the surrounding environment; Connect with the response matrix constructed in Step 3 to form a multi-objective programming model based on the response matrix, and take the randomness of the underlying surface type as a constraint condition of the multi-objective programming model to ensure the feasibility and effectiveness of the optimization results under different underlying surface type scenarios; Step 6: Solve the optimization model; Adopt NSGA-II as the optimization solution algorithm, set the parameters of the algorithm, run NSGA-II, solve the multi-objective optimization model, and obtain the Pareto front under different underlying surface type scenarios, that is, a set of layout schemes of low impact development facilities that achieve a balance between the total investment cost and the total runoff control rate of the coal port; Step 7: Determine the optimal layout scheme of low impact development facilities; Select the optimal layout plan on the Pareto front through the Nash bargaining solution; set the distance parameter of the Nash bargaining solution , and find the point on the Pareto front that is closest to the ideal solution, which is the optimal layout plan.

2. The method for optimizing the layout of low-impact development facilities in a coal port considering the randomness of underlying surfaces according to claim 1, characterized in that: (1) Collect the geographical information of the coal port, including the topographic map of the port and the functional division maps of different regions; (2) Collect meteorological data, including the rainfall, rainfall intensity and rainfall duration over the years; (3) Obtain the layout map of the rainwater pipe network, including the distribution, pipe diameter and slope of the existing rainwater pipe network in the port; (4) Collect the runoff coefficient data of different underlying surface types, including the runoff coefficients of coal piles, concrete floors, soils and green areas under different rainfall conditions; (5) Collect the construction cost and annual operation cost data of low-impact development facilities including green roofs, grassed swales and permeable pavements; (6) Collect the historical storage data of the coal port yard, that is, the stacking and reclaiming operations of various goods in the yard; (7) Collect the actual observed data of historical rainwater runoff in the coal port; Organize and analyze the collected data to check the integrity and accuracy of the data.

3. The method for optimizing the layout of low-impact development facilities in a coal port considering the randomness of underlying surfaces according to claim 2, characterized in that: The steps for constructing the response matrix are as follows: (1) For each layout plan of low-impact development facilities, it is necessary to run a rainwater management model once in the research area of the coal port for runoff simulation analysis; (2)For any low impact development facility layout plan and rainfall scenario, construct a response matrix, where the elements along the diagonal are the runoff of each sub-catchment ; (3) Construct a decision vector for each layout plan of low impact development facilities , where the elements are the area fractions assigned to each low impact development facility in the sub-catchment area; (4) Based on the input data of the area of each sub-catchment, obtain the area matrix A of the sub-catchments; (5) Construct a connectivity matrix , which describes the upstream and downstream relationships of all sub-catchments; if sub-catchment j is upstream of sub-catchment i, the non-diagonal element of the connectivity matrix is equal to 1, otherwise it is zero, and it is stipulated that the diagonal element ; (6) Estimate the rainwater runoff flow at the outlet of each sub-catchment by summing the runoff of each sub-catchment and the rainwater runoff flows of all upstream areas: , where represents converting the vector parameter into a diagonal matrix. As in the above formula, for the vector parameters and to perform diagonal matrix conversion, the diagonal elements in the diagonal matrix are ; is the correction factor for the layout scheme of low-impact development facilities; is the duration of rainwater runoff simulation.

4. The method for optimizing the layout of low-impact development facilities in a coal port considering the randomness of underlying surfaces according to claim 3, characterized in that: The objective function of the multi-objective programming model is expressed by the formula: (1) Objective function 1: , where is the construction cost required to deploy the l-th low impact development facility per unit area at the candidate location j in the i-th sub-catchment area; is the fixed cost required to deploy the l-th low impact development facility at the candidate location j in the i-th sub-catchment area; is the operation cost required to deploy the l-th low impact development facility per unit area at the candidate location j in the i-th sub-catchment area; is the area of the l-th low impact development facility deployed at the candidate location j in the i-th sub-catchment area; is a 0-1 variable representing whether the l-th low impact development facility is deployed at the candidate location j in the i-th sub-catchment area; is the life cycle of the l-th low impact development facility; is the discount rate; (2) Objective function 2: , where represents the th underlying surface type scenario, represents the probability of occurrence under the th underlying surface type scenario, represents the total runoff of sub - catchment i without the installation of low - impact development facilities, represents the total runoff of sub - catchment i after the installation of low - impact development facilities; t represents the simulation time step; , the above formula calculates the total runoff of sub - catchment i before the construction of low - impact development facilities; Among them, and are the slope function and roughness coefficient function under the k-th underlying surface type scenario; is the area of sub-catchment i; is the equivalent width of sub-catchment i; is the th rainfall scenario; , where the above equation represents the total runoff of sub-catchment i after the construction of low-impact development facilities; , which defines the functional expression of the runoff of sub-catchment i at time step t; Among them, is the slope of sub-catchment i, is the roughness coefficient of sub-catchment i; , the above formula represents the relationship among slope, roughness coefficient and surface type, where u represents the u-th surface type; represents slope; represents roughness coefficient.

5. The method for optimizing the layout of low-impact development facilities in a coal port considering the randomness of underlying surfaces according to claim 4, characterized in that: The constraints of the multi-objective programming model are expressed by the formula: (1) Regional area constraint: ， ， ， ， , which are the relationship constraints of the layout area of low-impact facilities, the layout area of low-impact development facilities, and the sub-catchment area respectively; is the area occupied by u types of surface in the candidate location j of the i-th sub-catchment; (2) Low-impact development facility type constraint: ， , it is required that the type of rainwater collection facility matches the surface type; indicates whether there is an area of u surface types at the candidate location j in the i-th sub-catchment area; (3) Flow constraint: Ensure that the runoff volume of each sub-catchment is within the safe range at each time step, and are the lower and upper limits of the runoff volume; , define the relationship between the peak runoff and the runoff at each time step, where is the peak runoff of the i-th sub-watershed; (4) Logic constraint: , ensure that the area values of each facility can only be obtained after building low-impact development facilities at the candidate locations, A number representing infinity.

6. The method for optimizing the layout of low-impact development facilities in a coal port considering the randomness of underlying surfaces according to claim 5, characterized in that: Use the Nash bargaining theory to simulate the negotiation process among stakeholders and select a final solution from a set of non-dominant solutions, which is expressed by the formula as follows: ， , where is a distance function; is a distance parameter; and are layout schemes, i.e., solutions; and mean two objective functions in the model; is a set on the Pareto boundary; given with a certain value, the point closest to the ideal point, i.e., the Nash bargaining solution; if , in , the objective with a smaller deviation plays a more important role; if , the two objectives have the same weight; if , in , the objective with a larger deviation has a greater weight.

Images