Hydraulic optimization simulation for reducing confluence and controlling the overflow pollution of storage ponds based on the Storm Water Management Model and Non-dominated Sorting Genetic Algorithm-II

Many cities in the world, especially the old urban areas, adopt combined drainage systems, and sewage overflows often occur in rainy seasons (Blum et al. 2019). On the one hand, this causes ponding on roads, affects traffic, and even endangers the safety of people's lives and property. The overflow of sewage is large in volume and poor in quality. Without any treatment, it is directly discharged into the receiving water body, causing pollution to the urban water body. At present, the sewage treatment rate in some large- and medium-sized cities has exceeded 80%, but the water quality of urban rivers is still poor; one of the most important reasons is that the combined overflow pollution has not been effectively controlled (Schertzinger et al. 2019). Some cities have transformed the original direct discharge confluence drainage system into an intercepting confluence drainage system (Sun et al. 2021a, 2021b) by intercepting part of the rainwater runoff to the sewage treatment plant to reduce the pollution load of confluence overflow. The interception multiple is generally 1–5, but the early design of the sewage treatment plant did not consider the flow during rainy days, so although most of the sewage is intercepted at the sewage treatment plant during rainy days, it exceeds the treatment load of the sewage treatment plant. A large amount of sewage is discharged into the receiving water body without any treatment. At the same time, because the lower limit of the design standard is often taken in the construction of a drainage system, the standard is generally low, coupled with an increase in extreme weather in recent years and a sharp increase in the impervious areas in the process of rapid urbanization, resulting in a sharp increase in the pollution load of combined overflow, which has become one of the main pollution sources of many urban water bodies (Arianna et al. 2019). The effective control of confluence overflow pollution has become a top priority to solve urban water environmental problems. Urban water pollution has become a shackle restricting the sustainable development of cities, among which the non-point source pollution caused by the first rain erosion has become the main source of water pollution. In all kinds of initial rainwater pollution control measures, the rainwater reservoir has been widely used in European and American countries for its advantages of strong applicability and good economy. However, it is difficult to determine the volume of the storage tank accurately, and the use and development of the storage tank are limited.

The research scholars in related fields on reducing the hydraulic pollution of combined overflow have become mature. Sun studied the control-oriented quality modeling method of a sewage pipe network (Sun et al. 2021a, 2021b). Total suspended solids were selected as the quality index because it was easy to estimate by measuring turbidity and was related to other quality indexes. For different components in the sewage pipe network, the model equation was independent, which allowed extended use. To ensure the accuracy of the proposed model, a calibration procedure and sensitivity analysis were proposed using the data generated by virtual reality simulation. Then, based on the proposed model, a quality-based model predictive control was developed. Li et al. conducted a risk assessment on the heavy metal pollution of water resources in Chengdu (Li et al. 2021) and studied the total concentration and reduction changes in heavy metals and antibiotics during the production of reclaimed water. The possible health risks to the ecological environment and human body were assessed. Alisawi took the Karbala case as an example and used the rainwater management model (SWMM5) to study the sewer overflow mitigation strategy during festivals and rainfall (Alisawi 2020).

As a non-point source pollution control measure, the regulation and storage tank have a good effect and high operability. In many cities at home and abroad, combined overflow pollution control methods have been applied extensively. The storage tank is a flood prevention and storage facility (Saplioglu et al. 2019), which can regulate and store a large amount of rainwater and sewage generated during rainfall, so as to achieve the purposes of peak shaving, reduction, and pollution reduction (Shi et al. 2020). Regulation refers to what occurs when the excessive flow value generated by rainfall exceeds the carrying capacity of the pipe network, and the excess part enters the regulating and storage pool to reduce the inflow of the downstream pipe section. Detention storage refers to the short-term storage of rainwater and sewage in the early stage of rainfall, peak flow, and other processes, and its treatment or discharge when rainfall stops or water quality is stable. The rainwater and sewage stored in the storage tank can achieve a certain removal effect on particulate pollutants, and after a period of precipitation, pollutants are adsorbed on its surface, so as to reduce the pollution and its impact on the downstream water body. The regulation and storage facilities are generally configured in combination with the closure facilities or treatment facilities, which can be arranged above or below the ground. The facilities are in the form of a pool and pipe culvert. By storing mixed sewage, the storage tank can also purify the sewage.

Abderrahmane et al. (2021) studied the influence of highway traffic on the contamination of roadside soil with heavy metals. This paper summarizes the harm of lead to the human body and its existing form in the soil, introduces the environmental quality standard of soil lead, analyzes the influence of highway traffic on soil lead pollution, and puts forward the prevention and control countermeasures of soil road source lead pollution in combination with the actual situation in China. Scharnberg et al. (2020) studied the optical and structural characterization of Bi₂FexNbO₇ nanoparticles for environmental applications. The Bi₂FexNbO₇ photocatalyst was synthesized by solid-state reaction synthesis. Its structure and photocatalytic performance were studied by XRD, SEM, TEM, UV visible diffuse reflection, and other characterization methods. Buaisha et al. (2020) studied heavy metal removal investigation in conventional activated sludge systems. The content changes of Cu, Zn, Pb, Cd, Hg, and As in sewage and sludge in different treatment sections of the traditional activated sludge process of a sewage treatment plant and their morphological distribution characteristics in sewage were studied to further understand the removal of heavy metals in different treatment sections. The removal rate of Hg in the sewage of the whole process was the largest, averaging 76.4%, and the removal rate of Pb was the smallest, averaging 29.7%. The removal rates of heavy metals in different treatment sections vary greatly. The maximum removal rate of Zn is 55.4% from the influent to the effluent of the primary sedimentation tank, followed by Hg and Cu, with average removal rates of 40.0 and 34.2%; none of the above methods can effectively reduce the hydraulic pollution caused by confluence overflow. Ismail et al. (2022) studied the use of industrial waste desulfurization gypsum (flue gas desulfurization gypsum, FGDG) as an adsorbent, and under the conditions of static adsorption, the adsorption process of FGDG on various heavy metal ions and the coexistence of various heavy metal ions were investigated under the aspects of temperature and pH value. Mufrodi et al. (2023) studied the reaction of carbon dioxide gas absorption with the suspension of calcium hydroxide in a slurry reactor. The amount of carbon dioxide (CO₂) absorption and calcium ion (Ca²⁺) concentration besides the pH of the aqueous solution were observed during the CO₂ absorption to precipitate calcium carbonate (CaCO₃) from calcium hydroxide (Ca(OH)₂). A reaction rate-limiting effect of an amount of CO₂ absorption without any organic additives in the early stage of the precipitation was observed, which was attributed to an interruption effect of bicarbonate ion (HCO⁻³) on the precipitation of CaCO₃. Raji & Packialakshmi (2022) assessed the wastewater pollutants retaining for a soil aquifer treatment using batch column experiments. Soil aquifer treatment systems are increasingly seen as a relatively inexpensive and complementary water quality enhancement process, which may be particularly relevant in water scarcity scenarios. In this context, a set of soil-column experiments were conducted aiming to replicate the conditions of infiltration basins using soil as a depuration media for wastewater quality increment previous to managed aquifer recharge.

Therefore, the hydraulic optimization method for the reduction of overflow pollution in the combined reservoir system based on SWMM and NSGA-II is studied, which provides a theoretical reference for the hydraulic optimization of the reduction of overflow pollution in the combined reservoir system. The planned area of each sub-basin in the study area was input into the SWMM to calculate the simulated value of rainwater and flood and the volume of the regulated reservoir under the existing planning conditions. The multiple linear regression method is used to establish the proxy function of reservoir capacity, total runoff, and engineering cost. The NSGA-II was used to optimize the reservoir model. Based on the principle of determining the reservoir volume by the rainstorm intensity formula in Wuhan, the rainstorm intensity in Wuhan was calculated. The saturation function model and exponential scour model were used to describe the accumulation and scour processes of pollutants, and the hydrological and water quality parameters were determined. The coupled optimization proxy model was established to improve the initial population, crossover operator, and NSGA-II. This method can effectively reduce the hydraulic pollution caused by combined overflow. For the reduction rate of total runoff, the reduction rate after optimization is greater than that before optimization; for the peak flow reduction, the reduction rate after optimization is greater than that before optimization, but the change in the return period has no significant influence on the optimization range. The main advantage of this method is that the tank volume is determined based on the actual location of the study area, the tank volume is simulated, and the model parameters are corrected by the Monte Carlo method to prevent water overflow from the drainage pipe and effectively reduce the hydraulic pollution caused by the combination overflow.

The planned area of the regulation and storage tanks in each subcatchment area in the study area is the input for the SWMM to calculate the stormwater simulation value and adjust the storage tank volume under the existing planning. The agency function between the volume of the storage tank and the total runoff and construction cost is established by using a multiple linear regression method. The agent model is optimized by the NSGA-II. The non-dominated solution is substituted into the SWMM for calculation, and the rationality of the optimization result is analyzed.

The purpose of the model method is to dynamically simulate rainfall–runoff through the SWMM and simulate the rainwater operation on each subcatchment area with runoff components (Hou et al. 2020), including receiving the runoff generated by rainfall and the pollutant load caused by scouring. Then, the runoff attributes entering the regulation and storage tank system through pipe channels and other facilities are calculated by the calculus component, so as to deduce the best regulation and storage volume.

The SWMM is a computer model of urban storm management developed by the National Environmental Protection Agency in the 1970s. The model can simulate the complete urban rainfall–runoff, including surface runoff and the flow in the drainage network, the accumulation and scouring of surface pollutants, and the process of combined sewage overflow. It is an effective tool for the analysis of pollution characteristics of combined overflow and the planning and design of combined drainage pipelines.

The topographic data in the catchment area mainly adopt the 1:2,000 topographic map. According to the direction of the actual roads, the distribution of blocks, and the flow direction of surface runoff, the simulated area was artificially divided into any number of water-collection sub-regions of different areas. According to the topographic map, the average slope and generalized width of each catchment subarea are calculated. Assuming that the rainfall in the whole area is uniform, the rainwater in each subdistrict flows into the nearest pipe network node, and then according to the pipe network data and the division results of the above catchment area, the pipeline information is entered into the model. The main pipes of the drainage pipeline are made from reinforced concrete. The pipe generalization result obtained from this is that in several catchment subareas, the drainage network is generalized into n nodes and n–1 pipelines.

Hydraulic model parameters include the initial depression depth of the permeable ground, the initial depression depth of the impervious ground, and the Manning coefficient of the permeable ground (Malicki et al. 2019). These parameters need to be determined according to the actual situation and with reference to the parameters provided in the manual. The Houghton model is selected as the infiltration model, and the maximum infiltration rate, minimum infiltration rate, and attenuation coefficient are 76 mm·h⁻¹, 3.3 mm·h⁻¹, and 2 h⁻¹, respectively. The initial depression depth of impervious ground is 1.5 mm. The roughness coefficient of impervious ground is 0.015. The initial depression depth of permeable ground is 5 mm. The roughness coefficient of permeable ground is 0.02. The material of the drainage main is reinforced concrete. By consulting the SWMM user manual and referring to the relevant research simulation results, the Manning coefficient of the pipeline is proposed to be 0.01. The percentage of impervious surfaces without depression water storage is 25%. The confluence model adopts the nonlinear reservoir model. Dynamic wave is selected for the hydraulic model.

In the process of determining hydrological parameters, they are selected according to the user manual of SWMM (Baek et al. 2020). The main hydraulic parameters' inputs include the Manning coefficient, depression water storage, and infiltration model. According to the research results of relevant scholars, the attenuation coefficient of the research area α is 31/h, and the maximum and minimum infiltration rates and are 76.0 and 3.2 mm/h, respectively. The values of water storage of permeable surface and non-permeable surface depressions are 5.04 and 1.51 mm, respectively. Manning coefficients of impervious surface, permeable surface, and pipeline are 0.013, 0.400, and 0.011, respectively. Surface confluence and dynamic wave are selected as the basic conditions of the nonlinear reservoir model and hydrodynamic model to calculate water quality and quantity.

Considering the strong scouring force and short residence time of runoff after entering the pipeline, the assumptions of ‘rapid and complete mixing’ and ‘no attenuation of pollutants’ after runoff entering the pipeline of the storage tank can be approximately regarded as the actual flow process. For typical pollutants, chemical oxygen demand, total suspended solids, total nitrogen, and total phosphorus are selected as representative factors of water quality changes in the simulation process (Vasantharaj et al. 2021). According to the actual situation of the study area, three land use types, roads, roofs, and green spaces, are set up. The saturation function model and exponential scouring model are selected to describe the accumulation and scouring processes of pollutants. The sweeping frequency of the road is set as once per day, the sweeping removal rate is set as 70%, and the drought days in the early stage are set as 5 d. The concentration values of chemical oxygen demand, total suspended solids, total nitrogen, and total phosphorus brought in by rainwater runoff are 25, 10, 1.8, and 0.1 mg/L, respectively.

Through the above process, the working process of the typical rainfall storage tank is simulated, and the volume of the storage tank is determined in combination with the discharge target.

The proxy model is a mathematical model that uses the proxy method to fit discrete data. The most representative agent models include the RSM model, Kriging agent model, and RBF agent model. Referring to the concept of the agency model, the agency function between the storage pond and the total runoff and construction cost is established by using a multiple linear regression method (Wang et al. 2019). Among them, multiple regression analysis is a common analysis method to study the relationship between a dependent variable and multiple independent variables. It is widely used in the fields of complex system engineering such as atmosphere and hydrology.

The regress function in MATLAB is called to establish and solve the above multiple regression equation (Diveev et al. 2021), and the R² obtained is close to 1, indicating that the regression equation is relatively significant and can be used for proxy function calculation.

Set the constraints of the model: the optimization process is based on the known planning data, which has the advantages of fewer constraints and easy implementation. Specific constraints are as follows:

The NSGA-II layers all individuals and calculates the congestion distance allocated to each one. The larger the congestion distance, the more ‘sparse’ the area the individual is in (Liu & Chen 2019). When comparing the advantages and disadvantages of individuals, those with smaller levels will be regarded as better, and individuals with a larger crowding distance at the same level will be better. The algorithm was improved to improve the global search ability and population diversity of the traditional NSGA-II and avoid the population falling into the local Pareto optimal solution set.

The initial population P is obtained by random initialization. According to formula (9), N individuals in the initial population P (N is the population number) are reverse generated into N reverse individuals to obtain the reverse population ⁠. The fitness values of all individuals in are calculated and sorted, and N individuals with good fitness values are selected as the new initial population. The probability of finding a better initial population can be improved, so as to suppress the premature phenomenon of the algorithm.

The proposed improved NSGA-II steps are as follows:

• Initialization: Input the network parameters, randomly generate the initial population with population size N, use the reverse learning method to obtain the reverse population ⁠, calculate the fitness values of all individuals in and sort them, and select N individuals with good fitness values as the new initial population ⁠.

• Fast non-dominated sorting: According to the fast non-dominated sorting strategy, compare the objective function values of each individual in ⁠, rank each individual hierarchically, and calculate the crowding distance of each individual in each level (Aguilar-Mamani et al. 2021).

• Tournament selection: Through the tournament criteria, randomly select N/2 individuals in the population for comparison, and select the optimal individuals from them, which are repeated N times to form the parent population ⁠.

• Generation of progeny population: Use the arithmetic crossover operator and polynomial mutation operator to crossover and mutate the parent population and generate the offspring population ⁠.

• Population mixing: Mix the parent population and the offspring population Q into an intermediate population with a population size of ⁠, and quickly make the non-dominated sorting of intermediate population ⁠.

• Population regeneration: In an empty population with a population size of N, add a set of non-dominated individuals at levels 1, 2 … in turn until level i is further added, and the population size will exceed N. Fill the individuals in the level one by one according to the crowding distance from large to small until the population size is equal to N, forming a new species group ⁠.

• Return to step (3) and stop the iteration after the maximum number of iterations.

The new species group is the Pareto optimal solution set of the optimization problem.

To study the applications of a hydraulic optimization method based on the SWMM and NSGA-II for regulation and for storage tanks to reduce the overflow pollution of the combined system, a part of the northeast of a city is selected as the research area. The method in this paper is used to optimize the hydraulic simulation to reduce the overflow pollution of a combined system in the study area, and the results are as follows.

The study area contains seasonal lakes. The terrain in the basin is mostly plain and has hilly lands, with a total basin area of 15.7 km², belonging to the subtropical monsoon climate area. The region has four distinct seasons: mild climate, abundant rainfall, and sufficient sunlight. The annual average precipitation is 1,599.0 mm, and the annual average runoff is 8,520 × 10⁴ m³. According to the reference principles for the division of subcatchment areas, when dividing the catchment areas, it has to meet the conditions such as the whole area of the subcatchment area is located on the same side of the watershed, the number of underlying surface types contained in a single subcatchment area is small, the shape of the subcatchment area is regular, the length:width ratio is appropriate, and a single building is located in the same subcatchment area, to comprehensively consider the distribution of the watershed, land use type, building distribution, and other factors. The study area is divided into 88 subcatchment areas, with the area of each subcatchment ranging from 0.012 to 0.065 km² with a total of 54 rainwater inspection wells and 72 rainwater pipes and channels.

According to the analysis in Figure 4, the regulating reservoir starts to collect the sewage caused by rain erosion in about 5 min. At the beginning, the rainfall was small, and the rainfall that entered the storage tank before 25 min increased very slowly, which was reflected in the very gentle slope of the storage tank curve, because the rainwater pipeline system had a certain peak regulating effect. During the period of 25–60 min, the rainwater collected by the inlets in the far and near catchment areas begins to converge to the storage tank, so the rainfall in the storage tank begins to increase rapidly, which is reflected in the straight-line rise of the slope of the storage curve. After 60 min, the regulation and storage rainfall reaches the maximum value, and then the regulation and storage rainfall remains unchanged. The volume of regulation and storage tank No. 1 is 10,889 m³, and the volume of regulation and storage tank No. 2 is 12,231 m³. For the convenience of construction, the volume of the regulation and storage tank is rounded off, so the volumes of regulation and storage tank No. 1 and regulation and storage tank No. 2 are set to be 11,000 and 13,000 m³, respectively.

The model calculation is carried out according to the determined parameters, and three monitoring sections are selected at the upper, middle, and lower positions of the road near the study area. During the whole rainfall process, the hydrological and water quality indicators including water level, flow rate, chemical oxygen demand, total suspended solids, total nitrogen, total phosphorus, pH value, and other indicators are monitored synchronously, the monitoring results and calculation results are compared, and the parameters are adjusted to make the results meet the principle of minimum relative deviation, so as to obtain the optimal value of parameters.

The Monte Carlo method is used to calibrate the model parameters by using the rainfall data on 6 April 2021. The final parameter results are shown in Tables 1 and 2.

During the rain on 3 April 2021 and 6 April 2021, the Nash coefficients of various indicators are shown in Table 3.

It can be seen from Table 3 that the coupling optimization model constructed in the proposed method is more reliable in the process of runoff and water quality simulation. This is because the coupling optimization model is established by using the method proposed in this paper, and the proxy function between the storage capacity, total runoff, and total cost is established by using the multiple linear regression method, which is transformed into the optimization model aiming at the minimum total runoff and total cost.

The changes in total runoff and peak discharge reduction rate before and after optimization are shown in Table 4.

It can be found that the method in this paper has a certain optimization effect on the construction of the regulation and storage tank for the combined overflow pollution:

• For the reduction rate of total runoff, the reduction rate after optimization is greater than that before optimization, and the shorter the return period, the greater the optimization range.

• For the peak flow reduction rate, the reduction rate after optimization is greater than that before optimization, but the change in the return period has no significant impact on the optimization range.

• For the construction cost, the cost after optimization increases slightly, but compared with the optimization range of total runoff and peak discharge reduction rate, the increase in the construction cost is small. This is because this method uses reverse learning mechanism to improve the NSGA-II, solve the optimization model, and obtain the non-dominated solution of the agent model. The non-dominated solution is substituted into the SWMM for calculation, and the rationality of the optimization result is analyzed.

According to the analysis of Figure 5, in the whole water inflow process, the concentration of total suspended solids in the inlet water of the storage tank increases rapidly to a peak value of 122 mg/L in 0–30 min. Considering that in the actual confluence process, the most advanced water entering the storage tank is the precipitation that directly falls into the nearest inlet to the storage tank, and this part of precipitation does not participate in the surface scouring, the initial concentration of pollutants in the inlet water of the storage tank is 0. As the surface runoff enters the rainwater inlet and converges in the storage tank, the initial effect begins to reflect. A larger number of high-pollution load rainwater and a small amount of clean water directly enter the rainwater inlet before converging, resulting in a rapid increase in the concentration of influent pollutants. These are also the research results for load-related research studies by scholars and other scholars on the obviously different pollution and scouring transport laws of rainwater runoff at the source catchment surface and after passing through the rainwater pipeline system. With the increase in the rainfall duration (30–60 min), runoff carries a large number of pollutants into the storage tank, and the inflow is also increasing synchronously, so the concentration of pollutants in the storage tank is still declining to a stable value of 65 mg/L. At 60 min, the storage capacity reaches the maximum. At this time, the intercepting valve in front of the intercepting well will automatically close, the storage tank will no longer have water, the concentration of total suspended solids in the tank will remain stable, and the subsequent water will overflow from the drain. It can be seen that the regulation and storage tank with the volume determined by the model method have a significant effect on reducing the non-point source pollution caused by the initial rainwater scouring. When the return period is 1a, the regulation and storage tank can control the total suspended solid concentration to 65 mg/L when it rains for 60 min, reaching the first-class discharge standard of the integrated sewage discharge standard (GB8978-1996). This also shows that the proposed method can effectively achieve the purpose of reducing the hydraulic pollution caused by combined overflow. This is because the coupling optimization model is established by the method of this paper, and the proxy function between the reservoir volume and the total runoff and the total cost is established by using the multiple linear regression method, which is transformed into an optimization model with the goal of minimizing the total runoff and the total cost.

A hydraulic optimization method based on the SWMM and NSGA-II to reduce overflow pollution in a composite tank system is studied. The SWMM was established to simulate rainfall–runoff dynamically, and the internal runoff component of the SWMM was used to simulate the stormwater movement in each basin, including storm runoff and scour pollution load. By using a multiple linear regression method, the proxy function of the reservoir capacity, total runoff, and total cost is established and transformed into an optimization model aiming at minimum total runoff and total cost. The NSGA-II algorithm is improved by using the reverse learning mechanism, hoping to provide a new idea for the overflow pollution control of the combined system by studying the overflow pollution control method of the combined system. When the rainfall is 60 min, the total suspended solid concentration can be controlled at 65 mg/L by adjusting the tank. The comprehensive sewage discharge standard (GB8978-1996) level 1 is met. With the increase in the rainfall duration (30–60 min), runoff brought a large number of pollutants into the tank, and the inflow also increased at the same time, so the concentration of pollutants in the tank still decreased steadily to 65 mg/L. After 60 min, the storage tank capacity reaches the maximum. However, this method has some shortcomings; that is, it does not analyze the overflow pollution of an urban integrated system pipe network in a complex environment. There is no analysis and discussion on the multiple correspondence between the dilution ratio of sewage, sewage treatment plant capacity, pollutant removal efficiency, discharge standard, and overflow discharge load. In the future development, the complex factors affecting the overflow pollution of an urban integrated pipe network should be considered to reduce the water pollution caused by confluence overflow. Furthermore, the storage tank volume should be determined and the pollution reduction effect should be improved. Also, a series of technical problems such as pipe network connection, construction geology, construction, and operation management of underground large-capacity pumping stations should be solved.

All relevant data are included in the paper or its Supplementary Information.

The authors declare that there is no conflict.