Bioretention facility design method based on numerical simulation and multi-objective optimization

Abstract

The invention discloses a bioretention facility design method based on numerical simulation and multi-objective optimization, and belongs to the technical field of rainwater management, and the method comprises the following steps: S1, obtaining a special background demand of a bioretention facility of a target area; s2: according to a filler selection layering model constructed by an analytic hierarchy process, inputting a special background demand into the filler selection layering model to obtain an internal optimal filler combination of the bioretention facility; s3, constructing a DRAINMOD hydrological model, and establishing a parameter space through BOX-Behnken experimental design to generate a plurality of groups of virtual working conditions; s4, simulating the multiple groups of virtual working conditions through a DRAINMOD hydrological model to obtain a simulation result; s5, on the basis of a sensitivity analysis method, key regulation and control parameters are determined according to simulation results; and S6, based on a simulation result, optimizing the key regulation and control parameters through a second-order polynomial regression model to obtain an optimal design parameter combination.

Description

Technical Field

[0001] This invention belongs to the field of rainwater management technology, specifically relating to a design method for bioretention facilities based on numerical simulation and multi-objective optimization. Background Technology

[0002] With the acceleration of urbanization, sponge city construction has become a key technological approach to alleviate urban flooding and control non-point source pollution. As a core component of low-impact development systems, the design rationality of bioretention facilities directly determines key indicators such as total stormwater runoff control rate, pollutant removal efficiency, and facility operation and maintenance cycle. Traditional design methods have significant limitations in adapting to complex climatic conditions and diverse site requirements.

[0003] Traditional bioretention facility design methods are centered on phased physical trials, employing a "site testing - parameter correction - expanded application" technical route. Implementation requires a 12-18 month on-site monitoring period, repeatedly verifying parameters such as filler ratio and structural layer thickness through physical models, ultimately forming regional design specifications. While this method ensures design reliability in specific areas, it suffers from three fundamental drawbacks: ① Physical trials are significantly affected by cyclical climate, requiring a single verification to cover a complete hydrological year, resulting in a development cycle of 2-3 years; ② Regional parameters are difficult to transfer across climate zones; ③ Multi-objective collaborative optimization capabilities are insufficient, making it difficult to simultaneously achieve balanced optimization of hydraulic performance, purification efficiency, and construction cost within the existing technological framework. A typical case shows that the construction cost of the design scheme produced by the traditional method is 42% higher than the theoretical optimal value.

[0004] Therefore, a design method for bioretention facilities based on numerical simulation and multi-objective optimization is needed to address the problems existing in current technologies. Summary of the Invention

[0005] In view of this, the present invention provides a design method for bioretention facilities based on numerical simulation and multi-objective optimization, which solves the problems of existing bioretention facility design methods that are based on phased physical experiments, have long experimental cycles, strong regional limitations, and high costs.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] This invention provides a design method for bioretention facilities based on numerical simulation and multi-objective optimization, comprising the following steps:

[0008] S1: Obtain the specific background requirements of bioretention facilities in the target area; among which, the specific background requirements include: the need for a balance between rainwater retention and infiltration, the limitations of the use of filler materials, and the specific requirements of water quality;

[0009] S2: Based on the hierarchical model for packing selection constructed by the analytic hierarchy process, the specific background requirements are input into the hierarchical model for packing selection to obtain the optimal packing combination for the internal bioretention facility;

[0010] S3: Construct the DRAINMOD hydrological model and generate multiple sets of virtual working conditions by establishing a parameter space through the BOX-Behnken experimental design;

[0011] S4: Simulate multiple sets of virtual working conditions using the DRAINMOD hydrological model to obtain simulation results;

[0012] S5: Based on sensitivity analysis, key control parameters are determined according to simulation results;

[0013] S6: Based on the simulation results, the key control parameters are optimized using a second-order polynomial regression model to obtain the optimal combination of design parameters.

[0014] As an embodiment of the present invention, the filler selection layered model includes: a target layer, a criterion layer, and a bottom layer; wherein, the criterion layer is constructed based on preset core parameters; the preset core parameters include: total runoff control rate, runoff delay time, peak flow control rate, peak lag time, total suspended solids reduction rate, soil moisture content decay rate, and construction cost;

[0015] The bottom layer is used to generate multiple filler combinations according to specific background requirements.

[0016] As an embodiment of the present invention, after establishing the hierarchical structure model, an expert scoring method is used to statistically analyze and construct pairwise comparison judgment matrices; the constructed pairwise comparison judgment matrices are then subjected to hierarchical single sorting and consistency checks, specifically including:

[0017] The elements of the pairwise comparison matrix are normalized column-wise to obtain the target matrix, as shown below:

[0018] A = (a ij ) m×m

[0019] B = (q ij ) m×m

[0020]

[0021] In the formula, A is the pairwise comparison judgment matrix, B is the target matrix, and a ij To compare elements in a matrix pairwise, q ij The elements in the target matrix;

[0022] Add the elements of the target matrix row by row to obtain a vector.

[0023] For vectors After normalization, the weight vector is obtained. As shown below:

[0024]

[0025] In the formula, α i For vectors The element in, ω i These are elements in the weight vector;

[0026] The largest eigenvalue of each pairwise comparison matrix is ​​calculated as follows:

[0027]

[0028] The consistency index is calculated as follows:

[0029]

[0030] In the formula, CI is the consistency index, CR is the consistency ratio, and RI is the randomness index;

[0031] Consistency results are obtained based on the consistency ratio.

[0032] As an embodiment of the present invention, the constructed DRAINMOD hydrological model is used to simulate the hydrological effects of bioretention facilities, and is based on the simulation of soil profile water volume changes and soil surface water volume changes; wherein, the soil profile water balance is as follows:

[0033] ΔV s =D+ET+DS-I

[0034] In the formula, ΔV s The change in soil profile water volume is represented by D, the drainage volume of the drainage pipe is represented by ET, the evapotranspiration volume is represented by DS, the lateral drainage volume and deep infiltration volume is represented by I, and the infiltration volume from the soil surface is represented by I.

[0035] The changes in soil surface water are shown below:

[0036] P = I + ΔS + RO

[0037] In the formula, P represents the change in soil surface water, ΔS represents the change in soil surface water storage, and RO represents the rainwater runoff.

[0038] As an embodiment of the present invention, multiple sets of virtual working conditions are simulated using the DRAINMOD hydrological model to obtain simulation results, including:

[0039] Obtain virtual working conditions for the target area; the virtual working conditions include: regional feature information, design parameters, and initial parameter data; the design parameters include: catchment area ratio, filler layer thickness, soil layer thickness, water storage layer height, drainage pipe spacing, and internal water storage height; the regional feature information includes: rainfall characteristics and geological parameters;

[0040] The virtual operating conditions are input into the DRAINMOD hydrological model for simulation, and the simulation results are obtained.

[0041] The beneficial effects of this invention are as follows: by constructing a stratified model for filler selection and a DRAINMOD hydrological model to simulate and test the filler selection and design parameters in the system design process, the optimal design parameters are determined. This eliminates the need for phased physical tests during the design process, solving the problems of existing bioretention facility design methods that rely on phased physical tests, have long experimental cycles, strong regional limitations, and high costs.

[0042] Other advantages, objectives, and features of the invention will be set forth in the following description and will be apparent to those skilled in the art in some respects, or may be learned by practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0043] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0044] Figure 1 This is a schematic diagram of the process of the present invention;

[0045] Figure 2 This is a schematic diagram of the layered model for selecting fillers according to the present invention;

[0046] Figure 3 This is a radar chart showing the score of the hierarchical analysis process in this invention.

[0047] Figure 4 This is a comparison chart of simulated and actual values ​​of the biological retention system of the present invention;

[0048] Figure 5 The simulation results of DRAINMOD of the present invention are shown in the figure.

[0049] Figure 6 This is a graph showing the performance and influencing factors of the response surface model of this invention;

[0050] Figure 7 This is a comparison diagram of the optimized hydrological characteristic curves of the present invention;

[0051] Figure 8 This is a comparison chart of moisture content changes during dry and rainy seasons according to the present invention;

[0052] Figure 9 This is a graph showing the variation of TSS removal rate during dry / rainy seasons according to the present invention. Detailed Implementation

[0053] like Figure 1 ~to Figure 9 As shown, this invention provides a design method for bio-retention facilities based on numerical simulation and multi-objective optimization, comprising:

[0054] S1: Obtain the specific background requirements of bioretention facilities in the target area; among which, the specific background requirements include: the need for a balance between rainwater retention and infiltration, the limitations of the use of filler materials, and the specific requirements of water quality;

[0055] S2: Based on the hierarchical model for packing selection constructed by the analytic hierarchy process, the specific background requirements are input into the hierarchical model for packing selection to obtain the optimal packing combination for the internal bioretention facility;

[0056] S3: Construct the DRAINMOD hydrological model and generate multiple sets of virtual working conditions by establishing a parameter space through the BOX-Behnken experimental design;

[0057] S4: Simulate multiple sets of virtual working conditions using the DRAINMOD hydrological model to obtain simulation results;

[0058] S5: Based on sensitivity analysis, key control parameters are determined according to simulation results;

[0059] S6: Based on the simulation results, the key control parameters are optimized using a second-order polynomial regression model to obtain the optimal combination of design parameters.

[0060] The working principle of the above technical solution is as follows: In the design of layout schemes for bioretention facilities, traditional bioretention facility design methods are mostly based on phased physical experiments, requiring a large number of repeated experiments to screen fillers and adjust structural parameters. This type of method faces significant challenges in special geographical scenarios (such as offshore islands and remote areas), with the following problems: Long experimental cycle: Optimization of filler ratios and adjustment of structural layer parameters require multiple physical constructions and rainfall simulations, resulting in low project implementation efficiency; Strong regional limitations: Due to differences in soil permeability and rainfall characteristics, the same scheme needs to be re-tested and adapted when transplanted across regions, making it impossible to form a universal technical standard; High cost: In complex scenarios... The challenges of transporting and collecting data, coupled with insufficient deployment of high-precision monitoring instruments, make it difficult to support the data demands of multi-objective collaborative optimization. To design suitable solutions for the target region, the following steps were taken: First, the specific background requirements of bioretention facilities in the target region were identified. Then, a stratified packing selection model was constructed using the analytic hierarchy process (AHP) to input the specific background requirements into the model, yielding the optimal packing combination for the bioretention facility. Next, a parameter space was established using the BOX-Behnken experimental design to generate multiple sets of virtual operating conditions, which were then simulated using the constructed DRAINMOD hydrological model to obtain simulation results. Finally, sensitivity analysis was used, combined with the simulation results, to select... The key control parameters in the design parameters are extracted; finally, the key control parameters are optimized by the second-order polynomial regression model to obtain the optimal combination of design parameters; among them, when obtaining the special background requirements of the bioretention facilities in the target area, they are generally obtained from the following three aspects: 1. The balance requirement of rainwater retention and infiltration; 2. The limitations of the use of filler material; 3. The special characteristics of water quality; taking the special background requirements of the bioretention facilities of coral islands as an example, the special background requirements are as follows: (1) The balance requirement of rainwater retention and infiltration: the soil of coral islands is mainly composed of coral sand. Although its excellent permeability can meet the infiltration requirements of the bioretention system, the excessively high permeability coefficient makes the pure coral sand system present (1) Weak water retention capacity, with only about 14.2% of runoff retained in the pure matrix system; (2) Limitations of filler material: Unlike the diverse soil types available in inland areas, the main filler material for coral islands must be local coral sand to ensure the economic efficiency and feasibility of the project; however, the physicochemical properties of coral sand, such as mineral composition, cation exchange capacity (only 0.3 cmol / kg) and organic matter content (<0.5%), are significantly different from those of conventional inland soils; (3) Special characteristics of water quality: Inland stormwater runoff is mainly polluted by heavy metals, TP, TN, COD and suspended particulate matter, while coral islands are far from land-based pollution sources, and runoff pollutants during periods of high-intensity rainfall are concentrated in solid suspended matter;

[0061] The beneficial effects of the above technical solution are as follows: By constructing a stratified model for filler selection and a DRAINMOD hydrological model, the filler selection and design parameters in the system design process are simulated and tested to determine the optimal design parameters. This eliminates the need for phased physical tests during the design process, solving the problems of existing bioretention facility design methods that rely on phased physical tests, resulting in long experimental cycles, strong regional limitations, and high costs.

[0062] In one embodiment, the fill material is selected using a layered model, including: a target layer, a criterion layer, and a bottom layer; wherein, the criterion layer is constructed based on preset core parameters; the preset core parameters include: total runoff control rate, runoff delay time, peak flow control rate, peak lag time, total suspended solids reduction rate, soil moisture content decay rate, and construction cost;

[0063] The bottom layer is used to generate multiple filler combinations according to specific background requirements;

[0064] After establishing the hierarchical structure model, expert scoring was used to statistically analyze and construct pairwise comparison judgment matrices. The constructed pairwise comparison judgment matrices were then subjected to hierarchical single-ordering and consistency checks, specifically including:

[0065] The elements of the pairwise comparison matrix are normalized column-wise to obtain the target matrix, as shown below:

[0066] A = (a ij ) m×m

[0067] B = (q ij ) m×m

[0068]

[0069] In the formula, A is the pairwise comparison judgment matrix, B is the target matrix, and a ij To compare elements in a matrix pairwise, q ij The elements in the target matrix;

[0070] Add the elements of the target matrix row by row to obtain a vector.

[0071] For vectors After normalization, the weight vector is obtained. As shown below:

[0072]

[0073] In the formula, α i For vectors The element in, ω i These are elements in the weight vector;

[0074] The largest eigenvalue of each pairwise comparison matrix is ​​calculated as follows:

[0075]

[0076] The consistency index is calculated as follows:

[0077]

[0078] In the formula, CI is the consistency index, CR is the consistency ratio, and RI is the randomness index;

[0079] The consistency result is obtained by judging the consistency ratio;

[0080] The working principle and beneficial effects of the above technical solution are as follows: In the process of constructing a hierarchical model for filler selection based on the Analytic Hierarchy Process (AHP), the target layer is constructed with the optimal filler combination as the objective. Then, the soil-filler combination system with the best comprehensive performance is selected through manual statistical screening, and the criterion layer is constructed using multi-dimensional evaluation indicators such as total runoff control rate (P1), runoff delay time (P2), peak flow control rate (P3), peak lag time (P4), total suspended solids reduction rate (P5), soil moisture content decay rate (P6), and construction cost (P7). The bottom layer is constructed by randomly generating various filler combinations based on special background requirements. Specifically, based on special background requirements, the limitations or must-use fillers, required functional requirements (retention and infiltration, special water treatment), and number of filler layers are determined. Then, various fillers are selected according to the requirements, and multiple fillers are randomly combined to obtain multiple filler combinations. After establishing the hierarchical structure model of the filler selection stratification model, a pairwise comparison judgment matrix is ​​constructed through expert scoring and statistical analysis. Then, a hierarchical single sorting and consistency check are performed on the constructed pairwise comparison judgment matrices. When obtaining the consistency result based on the consistency ratio, there are two situations: when CR < 0.1, it indicates that the consistency of judgment matrix A is acceptable; when CR ≥ 0.1, it indicates that a logical error occurred when constructing judgment matrix A. The RI value can be found in the RI table. By meeting the special background needs of the target area, the designed bioretention facility scheme can make full use of local materials and achieve strong targeted pollutant removal.

[0081] Similarly, taking the design process of the aforementioned coral island as an example, after obtaining specific background requirements, a structure was constructed as follows: Figure 2The stratified model of the packing combination shown is constructed by pairwise comparison matrices of each evaluation index and subjected to consistency test. The calculation shows that the maximum eigenvalue of the matrix is ​​7.272, the consistency index (CI) is 0.045, the randomness index (RI) is 1.341, and the consistency ratio (CR) is 0.034 (CR = 0.045 / 1.341 = 0.034 < 0.1), indicating that the judgment matrix has good consistency (Table 1).

[0082] Table 1. Pairwise comparison judgment matrix and evaluation index weights

[0083]

[0084]

[0085] Under the baseline rainfall conditions (rainfall intensity 40 mm / h, rainfall duration 1 hour, and pre-drying time 1 day), none of the seven bioretention facilities experienced overflow, demonstrating consistent control over rainwater runoff. Therefore, the hydrological effect indicator was ineffective in the analytic hierarchy process (AHP) comparison. To fully utilize all evaluation indicators, experimental data under the most unfavorable rainfall conditions (rainfall intensity 80 mm / h, rainfall duration 1 hour, and pre-drying time 1 day) were used as the simulation scenario to calculate the evaluation indicator values ​​for devices A1–A3, B1–B3, and C. The total cost was calculated based on peat moss at ¥3.6 / L, laterite at ¥1.6 / kg, vermiculite at ¥16 / kg, biochar at ¥34 / kg, and coconut coir at ¥1 / L; the costs of coral sand and laterite were negligible.

[0086] Table 2 shows the initial evaluation index values ​​for bioretention facilities with different filler combinations. Among them, the overflow ratio, the rate of decrease in the moisture content of the planting soil layer, and the total cost are negatively correlated with the final score. Therefore, in order to facilitate the use of the analytic hierarchy process, the rate of decrease in the moisture content of the planting soil layer is converted into the water holding capacity of the planting soil layer, and the total cost is converted into the remaining funds. The adjusted evaluation index values ​​are shown in Table 3, and the standardized evaluation index values ​​are shown in Table 4.

[0087] Table 2. Initial Evaluation Indicators and Corresponding Values

[0088]

[0089] Table 3. Adjusted values ​​of evaluation indicators

[0090]

[0091]

[0092] Table 4. Standardized Evaluation Indicator Values

[0093]

[0094] Using experimental data under heavy rainfall conditions (rainfall intensity 80 mm / h, rainfall duration 1 hour, and prior drought days ADD = 1 day) as a simulation scenario, the evaluation values ​​of devices A1-A3, B1-B3, and C were calculated. To facilitate optimization using the analytic hierarchy process (AHP), the soil moisture content decay rate was converted to soil water retention capacity, and the total construction cost was expressed using remaining funds. The final evaluation score was obtained by multiplying the standardized evaluation index values ​​by their corresponding weights. Figure 3 The results showed that, except for devices A3 and B3 which had significant defects, the overall performance of each device in controlling rainfall and runoff was relatively similar. The core indicator currently limiting performance was the rate of water content decay, with the B series showing the best improvement effect. Device B1 scored the highest at 0.164, followed by device C at 0.154, then devices B2, A2, B3, and A3, with A3 scoring the lowest. Therefore, the bioretention system using "coral sand + laterite" as the soil layer and "coral sand + vermiculite" as the filler layer exhibited the best overall performance.

[0095] In one embodiment, the constructed DRAINMOD hydrological model is used to simulate the hydrological effects of bioretention facilities, and is based on the simulation of changes in soil profile water volume and soil surface water volume; wherein, the soil profile water balance is as follows:

[0096] ΔV s =D+ET+DS-I

[0097] In the formula, ΔV s The change in soil profile water volume is represented by D, the drainage volume of the drainage pipe is represented by ET, the evapotranspiration volume is represented by DS, the lateral drainage volume and deep infiltration volume is represented by I, and the infiltration volume from the soil surface is represented by I.

[0098] The changes in soil surface water are shown below:

[0099] P = I + ΔS + RO

[0100] In the formula, P represents the change in soil surface water, ΔS represents the change in soil surface water storage, and RO represents the rainwater runoff.

[0101] Multiple virtual operating conditions were simulated using the DRAINMOD hydrological model, and the simulation results are as follows:

[0102] Obtain virtual working conditions for the target area; the virtual working conditions include: regional feature information, design parameters, and initial parameter data; the design parameters include: catchment area ratio, filler layer thickness, soil layer thickness, water storage layer height, drainage pipe spacing, and internal water storage height; the regional feature information includes: rainfall characteristics and geological parameters;

[0103] The virtual operating conditions are input into the DRAINMOD hydrological model for simulation, and the simulation results are obtained.

[0104] The working principle of the above technical solution is as follows: Simulation results are obtained by using the constructed DRAINMOD hydrological model to simulate multiple virtual operating conditions. The constructed DRAINMOD hydrological model can predict seepage paths and pollution interception efficiency by inputting regional characteristic information such as rainfall characteristics and geological parameters of the target area; and identifies key system parameters based on parameter sensitivity analysis. The DRAINMOD hydrological model simulates the hydrological effects of bioretention facilities mainly based on two water balance principles. Specifically, the groundwater drainage volume D needs to be indirectly calculated through the drainage rate. The drainage rate is calculated differently depending on whether there is water accumulation on the soil surface: without water accumulation, the Hooghoudt steady-state equation is used; with water accumulation, the Kirkham formula is used. E T is calculated using the steady-state Thornth-Waite empirical formula or the Peman-Monteith equation, and compared with the actual soil moisture content. If PET < actual soil moisture content, then ET = PET; if PET > actual soil moisture content, then ET = actual soil moisture content. Lateral drainage and deep infiltration DS are calculated using Darcy's law or the Dupuit-Forchheimer assumption to determine their corresponding fluxes, and then the calculation is performed. Soil surface infiltration I is calculated by predicting the infiltration rate using the Green-Ampt equation. For example, based on the simulation results, the sensitivity analysis of the design parameters is performed: according to the experimental conditions, air temperature and rainfall data are input into the model, and the total runoff control rate is the core output parameter of the sensitivity analysis (Table 5).

[0105] Table 5 Sensitivity Analysis of Model Input Parameters

[0106]

[0107] Note: |SN|≥1 indicates high sensitivity, 1≥|SN|≥0.2 indicates sensitivity, 0.2≥|SN|≥0.05 indicates moderate sensitivity, and 0.05≥|SN|≥0 indicates no sensitivity.

[0108] The results show that the model is insensitive to rainfall intensities of 10-40 mm / h. This may be because the rainfall runoff in this range is relatively small, and the bioretention facilities can completely absorb the runoff, resulting in no change in the output and thus exhibiting parameter insensitivity. Table 3 shows the sensitivity analysis results under a rainfall intensity of 80 mm / h. Under the condition of a rainfall intensity of 80 mm / h, the parameters of catchment area ratio R, filler layer thickness D1, soil layer thickness D2, water storage layer height H1, drainage pipe spacing L, and internal water storage height H2 affect the total diameter.

[0109] The flow control rate exhibits high sensitivity, indicating a significant impact on model performance. In contrast, changes in parameters Re, KR, and K have minimal impact on runoff reduction rate, suggesting low sensitivity of these parameters. Therefore, when constructing a bioretention system model, it is crucial to ensure the accuracy of R, H1, and L, as they play a key role in system reliability. Specifically, R and H1 are set as initial design parameters for the bioretention facility, with values ​​of 10 cm and 15 cm respectively, while k uses empirical values. The design values ​​for H2, D1, and D2 are all 40 cm. Since only a single drainage pipe is installed within the facility, parameter L is defined as the system diameter and set to 20 cm. For parameters with low sensitivity, Re is set to 25 mm, KR is determined to be 0.0035 cm / h through variable head infiltration tests, and k is measured to be 50.67 cm / h through constant head infiltration tests. Then, the model is calibrated and validated: this study compares simulated and measured values ​​under different rainfall scenarios to determine the coefficient of determination R... 2 The relative error (RE) and Nash efficiency coefficient (NSE) were used as evaluation indicators to calibrate and validate the runoff generation module and the infiltration module. The main input parameters of the model are as follows: R = 10, H1 = 15cm, L = 20cm, Re = 25cm, k = 300cm / d, H2 = 40cm, KR = 0.0035cm / h, D1 = 40cm, D2 = 40cm, and K = 50.67cm / h. Figure 4 (a) shows the comparison results between the simulated flow rate and the actual flow rate of the flow generation module. Figure 4 (b) Shows the comparison results between the simulated infiltration volume and the actual infiltration volume of the infiltration module; R after the runoff generation model of the catchment area is calibrated. 2 The three evaluation indicators, RE, and NSE, were 0.999, -0.015, and 0.931, respectively; the R-value of the bioretention system model after calibration was... 2 The three evaluation indices, RE, and NSE, were 0.996, -0.018, and 0.941, respectively. In summary, the calibrated bioretention system model demonstrated good simulation performance for both runoff generation and infiltration processes, indicating high model reliability. Subsequently, the runoff generation and infiltration modules within the catchment area were validated sequentially using rainfall intensities of 20, 30, 50, and 70 mm / h. By comparing the simulated and actual runoff volumes under four different conditions, the Re... 2 RE and NSE were 1.000, 0.041, and 0.921, respectively; a comparison between simulated and actual infiltration volumes of the bioretention system showed that R... 2 The coefficient of performance (COP) is 0.993, RE is 0.060, and NSE is 0.808. These results indicate that the model simulation is reliable and ready for use. Further analysis of the simulation results: After validation, the DRAINMOD hydrological model generated the influence of six main parameters (R, H1, D1, D2, H2, and L) on the stormwater runoff control effect of the bioretention system under different rainfall intensities. The results are as follows: Figure 5 As shown in the figure, the total runoff reduction rate (TRRR) of the bioretention system is affected by multiple parameters: the catchment area ratio (R) is significantly negatively correlated with it (TRRR decreases by 66.3% when R increases from 5 to 25), because the overflow surges as the catchment area expands; the water storage layer height (H1) increases TRRR under high rainfall intensity (80 mm / h) by extending the water storage time (TRRR reaches 76.4% when H1 = 25 cm), but excessive elevation may lead to the risk of plant root immersion; the thickness of the filler layer (D1) and soil layer (D2) improves rainwater interception capacity by increasing porosity, but its effect on improving TRRR is limited (only promotes a slight increase in TRRR under 80 mm / h rainfall). In addition, the internal water storage height (H2) and the spacing between drainage pipes (L) cause TRRR to fluctuate nonlinearly due to dynamic water level changes and differences in drainage efficiency; considering all factors, D1, D2, and H2 have a weak effect on improving the system's runoff management capacity. To balance runoff control, pollutant removal, ensuring sufficient water retention in the substrate layer to support plant growth, and preventing excessive root immersion, the study proposes a combined parameter of "30cm soil layer + 40cm filler layer + 40cm internal water storage height." However, R, H1, and L have significantly different impacts on the system's TRRR and require further optimization and adjustment.

[0110] Finally, parameter optimization based on response surface methodology: Response surface analysis was used to optimize the three parameters of the bioretention system—catchment ratio (R), aquifer height (H1), and drainage pipe spacing (L)—under conditions of 80 mm / h rainfall intensity, 1-hour rainfall duration, and 1-day anterior drought duration (ADD). The study used simulation results from the DRANIMMOD hydrological model, fitted the experimental results with a second-order model, and verified the model's reliability through analysis of variance and significance tests. Specifically, based on the DRANIMMOD simulation results, the multiple quadratic regression equations for the total runoff reduction rate (TRRR) and various influencing factors, established using response surface methodology, are as follows:

[0111] Y=-0.1332*A+0.0528*B-0.0326*C-0.0102*AB+0.0116*AC-0.0268*BC+0.0377*A 2 +0.0134*B 2 +0.0432*C 2 +0.466

[0112] In the formula, A represents R, B represents H1, and the unit is cm; C represents L, and the unit is cm.

[0113] Normal probability plot ( Figure 6(a) shows the fit between the external residuals and the expected normal distribution. The data points are highly consistent with the reference line, indicating that the residuals are approximately normally distributed, satisfying the basic assumptions of regression analysis. Although slight deviations at both ends are noteworthy, the overall distribution meets the requirements of normality. (Scatter plot of external residuals and predicted values) Figure 6 (b) shows that most residuals are within the critical threshold of ±4.82 and are randomly distributed near the zero line, confirming that the model has homogeneity of variance and that there are no obvious outliers in the data; the comparison chart of actual and predicted values ​​( Figure 6 In (c), the data points are densely distributed near the 45-degree reference line, intuitively reflecting the model's high prediction accuracy and verifying its strong ability to capture the inherent patterns of the data. Through response surface interaction analysis (fixing parameters at the center value and examining pairwise interaction effects), a three-dimensional response surface plot ( Figure 6 (df) reveals a key principle: when the catchment area ratio (R=10) and aquifer height (H1=20cm) work synergistically, the total runoff reduction rate can reach a peak of 70.5%. Figure 6 (d) shows that increasing R significantly weakens the effect, while increasing H1 only slightly enhances the effect, highlighting the dominance of R; under the interaction of drain pipe spacing (L=10cm) and R=10 ( Figure 6 (e)), the initial increase in L leads to a sharp drop in efficiency, which then stabilizes, further confirming the priority effect of R; while when H1 = 20cm and L = 10cm ( Figure 6 (f)) The total runoff reduction rate reached 70.5%, and the increase of H1 can rapidly improve efficiency, reflecting its stronger influence compared to L;

[0114] In summary, R, H1, and L all significantly affect the total runoff reduction rate, with their importance ranked as R > H1 > L. The interaction effect between H1 and L is significant, while the interaction effect between R and other parameters is not significant. After calibrating the fitted equations, the optimal design parameters for the bioretention system were obtained with the goal of maximizing the total runoff reduction rate (TRRR): a catchment area ratio (R) of 10.113, aquifer height (H1) of 19.62 cm, and drain pipe spacing (L) of 17.85 cm. Under these conditions, the simulated total runoff reduction rate reaches 71.8%.

[0115] After the above design scheme was adopted to set up and actually run the bioretention system of the coral island, the results are as follows:

[0116] Figure 7This paper compares the hydrological characteristic curves of the bioretention system before and after design parameter optimization. The results show that the system did not overflow under all rainfall scenarios except for a rainfall intensity of 80 mm / h. Under a rainfall intensity of 80 mm / h, the optimized bioretention system achieved a total runoff reduction rate (TRRR) of 67.7%, which is highly consistent with the model prediction of 71.8% and significantly higher than the unoptimized 60.0% runoff reduction rate. The runoff delay time increased from 19 minutes to 28 minutes. Regarding peak flow control, the optimized system increased the peak flow reduction rate from 42.9% to 46.4%, and delayed the peak arrival time to 28 minutes, demonstrating superior hydrological control performance. Overall, under the same rainfall conditions, the optimized bioretention system extended the overall retention time of runoff before it reached the outlet. This improvement may stem from reducing the filler layer thickness from 80 cm to 70 cm, reducing the potential energy of the rainwater runoff and thus decreasing the outflow rate. However, the optimized system exhibited a slightly higher flow velocity than before optimization. This may be due to the soil layer thickness being reduced from 40cm to 30cm, resulting in a reduction in pore volume and thus lowering the system's water-holding capacity.

[0117] (2) Changes in water content in bioretention systems under actual rainfall scenarios

[0118] Figure 7 Figures (a) and (b) illustrate the dynamic response and differences in soil moisture content of the bioretention system under different climatic conditions during the rainy and dry seasons. The combined experimental results from both seasons show that system A exhibits significantly better water retention capacity and stability than system B under extreme hydrological conditions, and demonstrates unique advantages in soil depth dependence, drought resistance, and water retention capacity.

[0119] In a 30-day rainy season simulation, System A exhibited a prominent vertical stratification water-holding capacity: the water content in the 10cm soil layer was 21.6%, and the water content in the 30cm deep soil layer reached 37.5%, representing increases of 7.6% and 20.6% respectively compared to the corresponding depths of System B (14.0% and 16.9%). This significant difference indicates that the positive impact of soil depth on water-holding capacity is particularly pronounced in System A. Its deeper soil layers, through an effective water storage and slow release mechanism, form a "reservoir" effect during heavy rainfall, preventing rapid water loss from the shallower layers. Furthermore, System A demonstrated an adaptive advantage to changes in rainfall intensity; regardless of fluctuations in rainfall intensity, the water content in each layer remained consistently higher than in System B. This characteristic allows it to sustain the water supply needs of plant roots over a long period. Especially in special environments such as coral islands with high evaporation and frequent sudden rainfall, the system's strong water-holding capacity can buffer fluctuations in water supply and ensure vegetation survival. In the 30-day dry season experiment, System A also demonstrated excellent drought resistance: after 10 consecutive days of drought stress from D1 to D10, System A maintained a water content of 17.2% and 31.2% at depths of 10cm and 30cm, respectively, while the water content of System B plummeted to 11.3% (10cm) and 11.7% (30cm) during the same period. After the extreme rainfall on D10, System A rapidly reached near-saturation (20.7% and 36.0%), and during the subsequent 12 days (D10-D22) of natural drying, its water content only decreased linearly to 19.4% (-6.3%) and 33.5% (-6.9%), with equivalent daily water loss rates of 0.53% (10cm) and 0.58% (30cm). System B exhibited rapid primary water loss during this stage, with its water content plummeting from 14.5% and 16.7% to 12.1% (-16.6%) and 13.1% (-21.8%) within the same time period. The average daily water loss rate reached 1.38% (10cm) and 1.82% (30cm), which is 2.6-3.1 times that of System A. This indicates that System A not only efficiently absorbs rainwater but also achieves gradual water release through capillary action and adsorption-locking mechanisms in deep soil.

[0120] (3) TSS removal efficiency of the optimized bioretention system

[0121] Figure 9 Experimental results show that the bioretention system exhibits excellent TSS retention performance in both the rainy and dry seasons: during the experiment, the total suspended solids concentration in the treated effluent remained below 4 mg / L, and the overall TSS removal rate consistently exceeded 98.7%. These findings reveal that the packing medium of this system possesses both strong physical retention and chemical adsorption properties.

[0122] The beneficial effects of the above technical solution are as follows: By using the above technical solution, the optimal packing combination is determined through the packing combination layered model, and the optimal design parameters are determined by combining the DRAINMOD hydrological model. This solves the problems existing in the design methods of biotherapy facilities, such as the disconnect between packing and structure (the selection of packing ratio is not synchronously associated with structural parameters such as soil depth and drainage pipe layout, resulting in an imbalance between the system's water retention capacity and pollutant interception efficiency), fragmented model application (hydrological models such as DRAINMOD are mostly used for single-function simulation and are not deeply coupled with optimization methods such as analytic hierarchy process and response surface methodology, making it difficult to achieve global optimization of parameter space), and lack of sensitivity to key parameters (insufficient dynamic weight allocation of core control factors such as permeability coefficient and catchment area ratio, resulting in the design scheme being prone to failure under extreme rainfall).

[0123] Meanwhile, the above design method, through a four-order closed-loop technical system of "decision model + hydrological simulation + parameter optimization + hierarchical verification," achieved the following objectives:

[0124] 1. Rapid deployment: The entire process is digitalized, reducing the traditional 6-8 month field trial cycle to 2-3 weeks;

[0125] 2. Scenario Adaptation: Based on the dynamic regulation mechanism of soil infiltration in specific regions, it is highly compatible with the needs of permeable soils and regional hydrology;

[0126] 3. Low-cost implementation: By utilizing local soil materials and numerical simulation technology, construction and monitoring costs can be reduced by up to 60%.

[0127] In one embodiment, the method further includes: designing a dry / rainy season cycle test based on actual regional rainfall conditions to verify and optimize the actual system's capabilities. Model parameters are then corrected in real-time using feedback data (error <5%), forming a closed-loop optimization process.

[0128] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.

Claims

1. A design method for bioretention facilities based on numerical simulation and multi-objective optimization, characterized in that, Includes the following steps: S1: Obtain the specific background requirements of bioretention facilities in the target area; among which, the specific background requirements include: the need for a balance between rainwater retention and infiltration, the limitations of the use of filler materials, and the specific requirements of water quality; S2: Based on the hierarchical model for packing selection constructed by the analytic hierarchy process, the specific background requirements are input into the hierarchical model for packing selection to obtain the optimal packing combination for the internal bioretention facility; S3: Construct the DRAINMOD hydrological model and generate multiple sets of virtual working conditions by establishing a parameter space through the BOX-Behnken experimental design; S4: Simulate multiple sets of virtual working conditions using the DRAINMOD hydrological model to obtain simulation results; S5: Based on sensitivity analysis, key control parameters are determined according to simulation results; S6: Based on the simulation results, the key control parameters are optimized using a second-order polynomial regression model to obtain the optimal combination of design parameters.

2. The design method for a bioretention facility based on numerical simulation and multi-objective optimization according to claim 1, characterized in that, The fill material selection uses a layered model, including: target layer, criterion layer, and bottom layer; among which, the criterion layer is constructed based on preset core parameters; the preset core parameters include: total runoff control rate, runoff delay time, peak flow control rate, peak lag time, total suspended solids reduction rate, soil moisture content decay rate, and construction cost; The bottom layer is used to generate multiple filler combinations according to specific background requirements.

3. The design method for a bioretention facility based on numerical simulation and multi-objective optimization according to claim 2, characterized in that, After establishing the hierarchical structure model, expert scoring was used to statistically analyze and construct pairwise comparison judgment matrices. The constructed pairwise comparison judgment matrices are subjected to hierarchical single sorting and consistency checks, specifically including: The elements of the pairwise comparison matrix are normalized column-wise to obtain the target matrix, as shown below: A=(a ij ) m×m B=(a ij ) m×m In the formula, A is the pairwise comparison judgment matrix, B is the target matrix, and a ij To compare elements in a matrix pairwise, q ij The elements in the target matrix; Add the elements of the target matrix row by row to obtain a vector. For vectors After normalization, the weight vector is obtained. As shown below: In the formula, α i For vectors The element in, ω i These are elements in the weight vector; The largest eigenvalue of each pairwise comparison matrix is ​​calculated as follows: The consistency index is calculated as follows: In the formula, CI is the consistency index, CR is the consistency ratio, and RI is the randomness index; Consistency results are obtained based on the consistency ratio.

4. The design method for a bioretention facility based on numerical simulation and multi-objective optimization according to claim 1, characterized in that, The constructed DRAINMOD hydrological model is used to simulate the hydrological effects of bioretention facilities. It is based on the simulation of changes in soil profile water volume and soil surface water volume; the soil profile water balance is shown below: ΔV s =D+ET+DS-I In the formula, ΔV s The change in soil profile water volume is represented by D, the drainage volume of the drainage pipe is represented by ET, the evapotranspiration volume is represented by DS, the lateral drainage volume and deep infiltration volume is represented by I, and the infiltration volume from the soil surface is represented by I. The changes in soil surface water are shown below: P = I + ΔS + RO In the formula, P represents the change in soil surface water, ΔS represents the change in soil surface water storage, and RO represents the rainwater runoff.

5. The design method for a bioretention facility based on numerical simulation and multi-objective optimization according to claim 1, characterized in that, Multiple virtual operating conditions were simulated using the DRAINMOD hydrological model, and the simulation results are as follows: Obtain virtual working conditions for the target area; the virtual working conditions include: regional feature information, design parameters, and initial parameter data; the design parameters include: catchment area ratio, filler layer thickness, soil layer thickness, water storage layer height, drainage pipe spacing, and internal water storage height; the regional feature information includes: rainfall characteristics and geological parameters; The virtual operating conditions are input into the DRAINMOD hydrological model for simulation, and the simulation results are obtained.

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