The effective operation of pumping stations plays a crucial role in urban flood management. However, challenges persist in optimizing pumping station operations, including inaccuracies in characterizing flood propagation and the high computational costs associated with optimization. This study introduces a novel optimization approach for pumping station operation that integrates a hydrodynamic model with evolutionary algorithms, leveraging data-driven technology. The method iteratively computes operation rules using the adaptive particle swarm optimization (APSO) algorithm to identify optimal solutions. The hydrodynamic model accurately simulates flood propagation and provides hydraulic parameters for the objective function and constraints of the APSO algorithm. With the predictive capability of the Kriging model, the optimization enhances efficiency by reducing the frequency of calls to the hydrodynamic model. A study case of a flood management digital twin experimental platform was then taken for the application. Compared to initial operation rules, the objective function value of the proposed method is reduced by 28.7, 32.5, and 25%, respectively, under varying magnitudes of unsteady flood inflows, demonstrating high performances in both flood mitigation and operation cost control. Moreover, the method only requires 70 calls to the hydrodynamic model to formulate the decision operation rule.

  • Optimal operation of pumping stations considering the effects of floods on urban flood control and drainage systems.

  • Integrating a hydrodynamic model with an evolutionary algorithm.

  • Applying the proposed approach to the digital twin experimental platform for flood management.

Under the compounded effects of global climate change and anthropogenic activities, the frequency of extreme meteorological events has surged (Kumar et al. 2023), and the annual distribution of runoff in the basin is uneven (Zaghloul et al. 2022). This has led to a notable increase in flood disasters, imposing significant constraints on urban development, causing substantial economic losses, and imparting profound social ramifications (Liu et al. 2023; Yan et al. 2023; Jonkman et al. 2024). Moreover, these events have the potential to endanger the safety of individuals and their property. Many nations have acknowledged the importance of integrating urban flood prevention and drainage systems, strengthening the operation and management of flood control projects, and enhancing flood prevention and emergency response capabilities to combat flood challenges (Hanazaki et al. 2022; Ke et al. 2024). This is especially crucial in cities with complex river systems and dense hydraulic engineering, where flood processes are intricate (Sun et al. 2024). The combination of heavy rainfall and river overflow frequently results in river water levels exceeding those of urban drainage systems. In such a situation, pumping stations play a crucial role in urban flood control, presenting challenges in their operation and management (Wang et al. 2022; Yi & Zou 2023).

Due to the constraints of flood control, ecological protection, energy consumption, financial investment, and public impact, the traditional decision-making approach of pumping station operation has been difficult to meet the demands of intelligent and refined management (Wang et al. 2023; Zhao et al. 2023). Relying on experience-based decision-making models is time-consuming and labor-intensive, which affects the optimal effectiveness of pumping station operations. With the advancement of computer technology and data science, the study of digital twin technology has garnered significant attention (Tao & Qi 2019). Numerous researchers have leveraged digital twin technology in flood management to address flood inundation challenges, establishing it as a prominent research focus in the field (Bartos & Kerkez 2021; Henriksen et al. 2023; Ranjbar et al. 2024). By leveraging comprehensive monitoring and basic information, along with insights from relevant disciplines in the basin, digital twin flood management simulates and reproduces the correlation and dynamic changes of water flow and associated physics as well as decision-making factors in the virtual environment (Huang et al. 2022). This facilitates rapid, precise, and intelligent analysis of natural water flow simulation and prediction, hydraulic engineering scheduling, as well as their respective effects. The pumping station serves as a pivotal component of the urban flood control and drainage system (UFCDS). The establishment of the digital twin management platform relies on the intelligent decision-making operation of the pumping stations to provide accurate analysis and calculation capabilities for flood forecasting and flood control planning.

Inspired by biological principles, evolutionary algorithms (EAs) achieve global optimization by simulating natural phenomena or physical processes, and have been widely applied in recent years (Choi 2022; Pasandideh & Yaghoubi 2023; Singh et al. 2023). When integrated with physical process model simulations to compute flood propagation, EAs serve as solvers for key parameters such as flow rate and water level, thereby facilitating the optimal solution of operation rules. Despite their effectiveness compared to traditional optimization methods, EAs remain fundamentally stochastic search algorithms with constraints. The iterative optimization process requires multiple calls to the solver to address objective functions and constraints, resulting in significant computational costs. Some researchers have used mathematical formulas or simplified hydrological models to calculate the flooding process as an optimization solver, aiming to reduce computational costs (Yazdi & Khazaei 2019; Wang et al. 2021). However, due to the neglect of strict momentum conservation, these methods can only provide a simplified depiction of the physical flooding process. Despite enhancing optimization efficiency, this method falls short of accurately describing the intricate dynamics of flood propagation, posing challenges in ensuring the precision of optimization outcomes (Ming et al. 2020). In contrast, hydrodynamic models are able to reliably predict the entire process of flood and calculate the spatial-temporal variation of flood flow, depth, and velocity by solving two-dimensional shallow water equations (SWEs). These models are used to quantify the flood process in the objective function. However, employing hydrodynamic models as optimization solvers is computationally too expensive, with individual design scenario simulations often taking tens of minutes or even hours (Zhou 2024). This limitation restricts the feasibility of conducting numerous costly evaluation calculations when directly coupled with EAs. In some studies, a coupled graphics processing unit has been employed to enhance the computational efficiency of hydrodynamic models (Zhao & Liang 2022; Wang et al. 2024). However, this approach still falls short of meeting the demands for optimizing solutions with EAs. Consequently, challenges persist in the optimization operations of pumping stations, particularly regarding accurately characterizing flood processes while enhancing solution efficiency.

Over the past decades, EAs have gained widespread popularity as a tool for optimization (Chen et al. 2010; Dash et al. 2022). Most studies on EAs operate under the implicit assumption that evaluating the objectives and constraints of candidate solutions is straightforward and low-cost. However, in numerous practical optimization problems, such low-cost evaluation functions are nonexistent. Instead, the assessment of objectives and constraints frequently depends on physical experiments or numerical simulations, which are often costly and difficult to optimize (Jin et al. 2019). With the recent advancements in data-driven (DD) and machine learning (ML) technologies, a surrogate model is constructed using the data-driven evolutionary optimization (DDEO) method to replace the original time-consuming numerical model, significantly reducing the number of calls to the original model (Huang et al. 2021; Yu et al. 2024). Coupled with EAs, efficient global optimization can be achieved through effective model management strategies. Particularly, an online DDEO method can prove highly advantageous for experimental or numerical simulations where objective or constraint functions are computationally expensive (Zhen et al. 2023). In recent years, DDEO has been developed in various fields as promising methods for optimal design and operation management (Saini et al. 2023; Vondracek et al. 2023). However, its application in flood management remains relatively limited.

This study leveraged the flood management digital twin experimental platform to provide real measurement data and establish a corresponding two-dimensional hydrodynamic model for simulating flood propagation. Based on the DDEO method, a Kriging model-assisted adaptive particle swarm optimization (KAAPSO) solution framework was proposed to address the UFCDS management, with a primary focus on optimizing pump operations. Through the evaluation and demonstration of the optimization results, the study ensured the accuracy of flood physical processes while significantly reducing optimization calculation costs. The study highlights the feasibility and potential applications of flood management digital twin platforms based on the hydrodynamic model and the DDEO method, providing fresh insights into urban flood management, particularly in the context of pumping station operation.

Description of the digital twin experimental platform

The digital twin experimental platform was located at the Xi'an University of Technology and was designed according to the concept of urban river and lake flood control and drainage systems (Figure 1). The experimental platform with a total length of 2.6 m and a width of 1.2 m, included three parts: a physical model, a control system, and a virtual digital twin. The physical model simulated flooding inflows through the water supply system, with flooding subsequently directed into the inner lake through the upstream channel. The inner lake and the outer river are connected via the drainage gate. When the water level of the outer river is lower than that of the inner lake, flooding is discharged freely through the gate. Conversely, when the water level of the outer river is higher than that of the inner lake, the gates are closed to prevent the river water from entering the lake. The upstream section of the inner river is regarded as the outfall of the municipal pipe network. If the water level of the section is higher than the outfall height, it signifies that flooding in the upstream urban area cannot be promptly discharged. In such situations, pumping station serves as essential drainage facilities. The pumping station is composed of three drainage pumps with a rated flow rate of 3,600 m3/h. The operation of the pumps is automatically controlled by the variation of the lake water level. The entire water flow channel of the physical model is constructed using reinforced glass, facilitating visualization, and preventing erosion (Figure 2).
Figure 1

General view of the digital twin experimental platform.

Figure 1

General view of the digital twin experimental platform.

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Figure 2

Schematic diagram of the experimental setup.

Figure 2

Schematic diagram of the experimental setup.

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The virtual digital twin enables real-time data monitoring, component control, and flood evolution propagation demonstration. Control components such as pumps, drainage gates, and the data measurement units transmit signals to the programable logic controller (PLC) via cables, which are then relayed to the web-based virtual digital twin for integration. The virtual digital twin can also transmit control signals to the PLC to automatically operate the control components. In the experiment, an electromagnetic flowmeter is used to obtain the flow rate variation of the water supply pump, with the frequency of the inverter motor controlled based on the flow sensor's negative feedback. Two ultrasonic level gauges are used to measure the water level variation non-contact (Figure 2). Moreover, the running time and switches of the drainage pumps are recorded and transmitted to the virtual digital twin via the PLC for statistical analysis.

Data required and test conditions

A digital elevation model (DEM) of the physical model was acquired with a horizontal resolution of 510−3m, comprising almost 110,000 cells (Figure 3). DEM is essential to establish a hydrodynamic model for flood simulation. The Manning coefficient for the reinforced glass water flow channel is suggested as 8.510−3s/m1/3 (Jiang et al. 2023).
Figure 3

DEM of the physical model.

Figure 3

DEM of the physical model.

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The inflow data utilized for model validation comprise both steady inflows, with a flow rate of 10 m3/h, and unsteady inflows (Figure 4). The discharge patterns include free outflow when the gate is open and pumping station discharge when the gate is closed. Each drainage pattern employs a different initial control water level of the inner lake HL. Table 1 shows four combinations of different inflows and drainage patterns. The operation of the drainage pumps is automatically regulated based on the HL. The water level of pumps on is 50, 55, and 60 cm in turn, and off is 55, 50, and 45 cm, and the outfall height is set at 9 cm.
Table 1

Different cases for model validation

CaseInflow patternDischarge patternInitial HL (cm)
V1 Steady Free outflow 25 
V2 Unsteady Free outflow 25 
V3 Steady Pump discharge 45 
V4 Unsteady Pump discharge 45 
CaseInflow patternDischarge patternInitial HL (cm)
V1 Steady Free outflow 25 
V2 Unsteady Free outflow 25 
V3 Steady Pump discharge 45 
V4 Unsteady Pump discharge 45 
Figure 4

The unsteady validation inflow hydrograph.

Figure 4

The unsteady validation inflow hydrograph.

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To model flooding in the river, three stepped unsteady inflows of varying magnitudes are considered, designated as QH, QM, and QL representing high, medium, and low discharges, respectively (Figure 5). The experimental conditions are designed to simulate a scenario where the water level of the outer river is higher than the level of the inner lake, leading to flooding discharge by the drainage pumping station. Before the experiment, the drainage gate was conventionally open, and the inner lake water level was 45 cm.
Figure 5

Three unsteady inflow hydrographs for modelling flooding.

Figure 5

Three unsteady inflow hydrographs for modelling flooding.

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Two initial operation rules were developed focusing on flood control O1 and pump operation costs O2, respectively (Table 2). The minimum operating water level of the pump units is 30 cm, and the switching on and off of each pump is controlled at 5 cm intervals. When mainly focusing on flood control, the inner lake water level can be pre-reduced to the lowest storage level of 30 cm before the flood peak, and all pumps are uniformly switched off to reduce the water level as soon as possible when the water level drops to 30 cm. When the main objective is to control operation costs, the inner lake water level is pre-reduced to 40 cm. The operational model entails the sequential activation and deactivation of all pumps, aiming to minimize pump switches and thus reduce operation costs (Li et al. 2022).

Table 2

Pumping station initial operation rules

Initial rulePre-reduced (cm)PumpOn (cm)Off (cm)
O1 30 P1 35 30 
P2 40 30 
P3 45 30 
O2 40 P1 45 40 
P2 50 45 
P3 55 50 
Initial rulePre-reduced (cm)PumpOn (cm)Off (cm)
O1 30 P1 35 30 
P2 40 30 
P3 45 30 
O2 40 P1 45 40 
P2 50 45 
P3 55 50 

The river-lake water system serves as both the recipient of the municipal drainage network and the natural flood storage area within the urban city, collectively forming the UFCDS. During the flood season, challenges arise, such as the lack of coordination between municipal drainage and the river-lake water system, resulting in backwater impacts leading to upstream water level rise and impeding the discharge of rainwater from urban pipe networks. The drainage pumping station is a pivotal water engineering facility within the UFCDS, and its operation serves as the linchpin of flood management. Strengthening pumping station scheduling as the core of the UFCDS can ensure flood discharge safety, alleviate the flood protection pressure of upstream cities, and control the operation and maintenance cost of pumping stations.

Formulation of optimization models

Suppose that there are M pump units in the drainage pumping station. The control program for the pumps is pre-written and stored in the PLC before the flood event, remaining unchanged during operation. Each pump has two water levels to control start and stop, respectively, resulting in 2M pump control variables. In this study, the objective function is to minimize the peak water level HR in the upstream river and reduce the operation and maintenance cost EP of the pumping station. The selected upstream river section contains urban drainage network outfalls. When the water level exceeds the height of the outfalls, urban rainwater cannot be discharged promptly, leading to urban waterlogging. Considering the importance of flood control, the multi-objective optimization problem is transformed into a single-objective optimization problem using normalized weight (Wang et al. 2021). In the objective function, the violation of the constraints is considered a penalty term. The expression of the objective function is as follows:
(1)
(2)
where w0 is a linear weight for balancing the relationship between the peak water level HR and the pumping operation and maintenance cost EP. Violationh represents the penalty term in the objective function, which limits the variables that may be illegal constraints in the optimization process and is composed of upstream river section water level and the pump switches limit. Hc is the height of the municipal pipe network outfalls. Sh is the sum of the pump limit switches per hour and is set to 12 (Ministry of Housing and Urban-Rural Development of the People's Republic of China/ State Administration for Market Regulation 2021). Sm is the switches of the mth pump. The α1 and α2 represent the penalty factors, respectively.
The operation cost is usually the power consumption, which is expressed in this study by the operating time of the pumping station. Frequent switching on and off of the pumping machine can lead to a reduction in service life, and the maintenance cost is expressed in terms of the number of pump switches. The Ep is expressed as follows:
(3)
where Tm is the operating time of thw mth pump and ko is the magnitude weight.
Subject to:
(4)
(5)
(6)
where the control water level HL is kept between the maximum warning water level Hmax and the minimum allowable water level Hmin. am and bm are decision variables, which represent the control water level when the mth pump is on and off, respectively. Δh represents the increment of water level.

Optimization framework

The optimization framework comprises three main modules: a numerical module (hydrodynamic model), an optimization module (adaptive particle swarm optimization (APSO) algorithm), and an assisted module (Kriging surrogate model) (Cressie 1990). The hydrodynamic model simulates the dynamic flood propagation and provides reliable hydraulic parameters to the optimization module for fitness evaluation. The APSO algorithm is optimized by iterative algorithm population evolution. In the process of population evolution, the Kriging surrogate model is constructed to predict the individual fitness value of the offspring to complete the accelerated convergence. The proposed framework is illustrated in Figure 6, and the description of each module is as follows.
Figure 6

Flowchart of the optimization framework.

Figure 6

Flowchart of the optimization framework.

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Hydrodynamic model with coupled pumping station

To accurately reflect the physical processes of flood propagation, this study uses the GPU accelerated surface water flow and transport model (GAST) model for simulating floods, which is a numerical model developed by the State Key Laboratory of Eco-hydraulics in the Northwest Arid Region of China (Imran et al. 2024; Li et al. 2024). The model takes the 2D SWEs as the governing equation, its conservation scheme can be expressed in vector form as:
(7)
(8)
(9)
where t represents the time. x and y are the Cartesian coordinates. q denotes the vector of conserved flow variables consisting of h, uh, and vh, which are the water depth and unit-width discharges in the x- and y-directions. F and G are the flux vectors in the x- and y-directions, respectively. g is gravity. S is the source vector that may be further subdivided into net rain source terms i, slope source terms Sb and friction source terms Sf; Z represents the bed elevation. Cf depends on the Manning coefficient and can be expressed as Cf = gn2/h1/3, where n is the Manning coefficient.

The hydraulic information exchange area of the drainage pumping station is situated on the ground surface. Hydraulic information exchange is facilitated through the inner boundary treatment method of the 2D hydrodynamic model. The implementation steps are outlined as follows:

Step 1: Pump grid marking. Mark the position of the drainage pump to be processed in the hydrodynamic model terrain file. In this scenario, the drainage pump terrain grid cell is marked as 20, and the pump outlet grid cell is marked as 21 (Figure 7).
Figure 7

Schematic diagram of the inner boundary method of the drainage pumps.

Figure 7

Schematic diagram of the inner boundary method of the drainage pumps.

Close modal

Step 2: Pump discharge information exchange. Stop the pump grid and pump discharge outlet grid Harten-Lax-van Leer Contact (HLLC) Riemann solver for fluxes calculation. The variation of grid cell water depth in the same time step is calculated by the given pump discharge QP. For the inner river computational domain, this variation should be subtracted as the water depth value at the subsequent time step. Conversely, for the outer river computational domain, this variation should be added. The average water depth of six adjacent grids is selected as the threshold for pump control, avoiding excessive fluctuations in the threshold level within a single-cell grid under fine grid resolution.

APSO algorithm

The particle swarm optimization (PSO) algorithm, inspired by the swarm foraging behavior of birds, is an evolutionary algorithm renowned for its adaptability and rapid convergence in addressing complex optimization problems (Wang et al. 2018). Each particle in the population represents a potential solution to the optimization problem. In each iteration, the velocities and positions of particles for the ith particle in the dth-dimensional search space are updated as follows:
(10)
(11)
where c1 and c2 are personal and global learning constants, respectively, both set to 2.05 (Wu et al. 2022); ω is the inertia weight; r1 and r2 are the random numbers in (0, 1); pbestid is the best personal experience of the ith particle in the dth dimensional, and gbestd is the best experience among all particles in the dth dimensional; xid and Vid represent the position and velocity of the ith particle in the dth dimensional, respectively.
To enhance the global search capability of the PSO algorithm in the early stage and its local search capability in the later stage, an adaptive weight is introduced to construct the APSO algorithm (Zhan et al. 2009).
(12)
where f is the current fitness value. fmin and fm are the minimum and average fitness values, respectively. ωmin and ωmax are the minimum and maximum weights and set to 0.4 and 0.9 (Zhan et al. 2009).

Kriging model and surrogate management

The Kriging model consists of a regression model and a nonparametric Gaussian random process (Kleijnen 2009), which is expressed as follows:
(13)
where y(x) is the response value. fj(x) is the known regression basis function, and βj is the corresponding regression coefficient. Z(x) is a static random process with zero mean, variance σ2z, and covariance Cov[Z(xj), Z(xk)] =σ2zR(xj,xk), which represents the systematic deviation between the regression term and the response. R(xj,xk) is a correlation function of θ and represents the spatial correlation between different sample points xj and xk. The Kriging model can calculate the predicted value of an unknown function and can also calculate the error associated with the predicted value. It exhibits strong local prediction capabilities and effectively addresses nonlinear and complex problems.
The Kriging model is coupled to the APSO algorithm as a surrogate to assist population evolution and construct the KAAPSO algorithm. The Kriging model is used to predict the fitness values of all offspring populations, and the most promising particle is selected as a sample point by combining the infill criterion. In this study, a hybrid infill criterion is used (Li et al. 2022), which effectively balances agent efficiency and accuracy.
(14)
where MP(x) and EI(x) represent the minimize prediction criterion and expected improvement criterion, respectively. ξ is a predefined threshold to determine whether the EI(x) should be used.

Only the selected sample points are calculated by the hydrodynamic model, which avoides excessive calls of the hydrodynamic model to improve the calculation efficiency. This approach ensures that the particles guiding the evolution undergo realistic evaluation. Importantly, the Kriging model is not static during optimization, instead, it is dynamically updated through the continuous addition of sample points to improve predictive accuracy.

Validation of hydrodynamic model

Figure 8 illustrates a comparison between the simulated and measured values of the upstream section water level HR and the inner lake water level HL for different validation cases. The simulation results align closely with the experimental measurements, with all the Nash–Sutcliffe efficiency values exceeding 0.95 (Moriasi et al. 2015). The operation status of three drainage pumps P1, P2, and P3 is compared in Table 3. The absolute error between the measured and simulated values of the running time is less than 5%, and the number of switches for each pump is the matches. These comparison results indicated that the selected parameters are reasonable and demonstrate that the model effectively simulates the hydrodynamic process.
Table 3

Comparison of measured and simulated pump operation status

CasePumpRunning time
Switches
Measured (s)Simulated (s)Error (%)MeasuredSimulated
V3 P1 138 135 −2.2 
P2 124 120 −3.2 
P3 52 52 
V4 P1 308 307 −0.3 
P2 267 271 1.5 
P3 181 185 2.2 
CasePumpRunning time
Switches
Measured (s)Simulated (s)Error (%)MeasuredSimulated
V3 P1 138 135 −2.2 
P2 124 120 −3.2 
P3 52 52 
V4 P1 308 307 −0.3 
P2 267 271 1.5 
P3 181 185 2.2 
Figure 8

Validation results of different cases, (a) V1, (b) V2, (c) V3, and (d) V4.

Figure 8

Validation results of different cases, (a) V1, (b) V2, (c) V3, and (d) V4.

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Optimal operation of pumping station

The Online Kriging-Assisted Adaptive Particle Swarm Optimization Algorithm (OKAAPSO) method was used to optimize the pumping operation rules during the three experimental floods. An initial population of 30 particles was randomly generated by parallel computation. Considering that the time to call the hydrodynamic model for a real evaluation is approximately 12 min, the maximum number of iterations was set to 70, that is, 70 times of sample filling is needed to find the optimal solution. For each flooding process, it took 12 × 70 = 840 min to obtain the optimal operation rule. Therefore, sufficient response time remained available to address the risk of flooding. Figure 9 illustrates the convergence curve of the high discharge flooding QH.
Figure 9

Sample convergence curve for the QH hydrograph.

Figure 9

Sample convergence curve for the QH hydrograph.

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Table 4 shows the optimized operation rules of the pump under various flood inflow conditions. The pump operation rules entail sequential activation and deactivation. With the decrease in flood inflow discharge, the maximum pre-reduced level of the inner lake gradually increases, which is 33, 36, and 39.5 cm under the QH, QM, and QL flood inflows, respectively. This demonstrates that the proposed optimization method can accurately optimize the pumping station operation rules under different inflows.

Table 4

Pumping station optimal operation rules for different inflow hydrographs

InflowsPre-reduced (cm)PumpOn (cm)Off (cm)
QH 33 P1 36.5 33 
P2 40 33.5 
P3 40 35.5 
QM 36 P1 43.5 36 
P2 48.5 37 
P3 50.5 45.5 
QL 39.5 P1 44 39.5 
P2 54.5 47.5 
P3 56 50 
InflowsPre-reduced (cm)PumpOn (cm)Off (cm)
QH 33 P1 36.5 33 
P2 40 33.5 
P3 40 35.5 
QM 36 P1 43.5 36 
P2 48.5 37 
P3 50.5 45.5 
QL 39.5 P1 44 39.5 
P2 54.5 47.5 
P3 56 50 

The results of the proposed OKAAPSO algorithm for three inflows are compared with those of the initial rules in Figure 10. The optimized operation rules effectively balance the drainage capacity and the pumping station costs. Across all three inflows, the inner lake control water level HL is higher under rule O1 compared to rule O2. Following optimization, HL is lowest for QH, intermediate for QM and highest for QL inflow. In both QH and QM inflows, HL is the highest using the initial rule O2, which focuses on the pumping station cost reduction. This leads to backwater conditions, causing the upstream section level HR to exceed the height of the pipe network outfall. However, the optimized operation rules appropriately raise HL to save more costs while ensuring that HR does not exceed the limited water level. A comparison of the objective function values calculated for different operation rules (Table 5) indicates that the optimized objective function values have a different degree of decrease compared to the initial rules. Operation rules that exceed the limited water level are reflected in the objective function, resulting in an increase in the function value due to constraint violations. Based on the minimum value of the objective function calculated for the initial rules, the objective function value decreases by 28.7, 32.5, and 25%, respectively, in QH, QM, and QL flood inflow after optimization. This indicates that the proposed optimization method can effectively find the optimal solution under the given constraints.
Table 5

Comparison of the objective function of optimal and initial rules

Operation ruleObj
QHQMQL
O1 10.11 8.84 7.33 
O2 87.28 7.45 5.15 
Opt 7.21 5.97 3.86 
Operation ruleObj
QHQMQL
O1 10.11 8.84 7.33 
O2 87.28 7.45 5.15 
Opt 7.21 5.97 3.86 
Figure 10

Comparison of the results of optimal and initial rules, (a) HL comparison of QH hydrograph, (b) HR comparison of QH hydrograph, (c) HL comparison of QM hydrograph, (d) HR comparison of QM hydrograph, (e) HL comparison of QL hydrograph, and (f) HR comparison of QM hydrograph.

Figure 10

Comparison of the results of optimal and initial rules, (a) HL comparison of QH hydrograph, (b) HR comparison of QH hydrograph, (c) HL comparison of QM hydrograph, (d) HR comparison of QM hydrograph, (e) HL comparison of QL hydrograph, and (f) HR comparison of QM hydrograph.

Close modal

Comparing the running time and the switches of the pumps (Table 6), the optimized running time also shows a balance between drainage capacity and cost. The switches are all controlled within reasonable limits, especially in the QL, the switches are reduced to 3 times. This reduction indicates a significant improvement in optimization effectiveness.

Table 6

Comparison of the pump operation status of optimal and initial rules

InflowsSwitches
Running time (min)
O1O2OptO1O2Opt
QH 13 27.00 25.64 26.85 
QM 14 24.13 22.69 23.52 
QL 11 21.85 20.32 19.66 
InflowsSwitches
Running time (min)
O1O2OptO1O2Opt
QH 13 27.00 25.64 26.85 
QM 14 24.13 22.69 23.52 
QL 11 21.85 20.32 19.66 

The mainstream method for flood propagation is accurate simulation and drainage engineering scheduling analysis. However, due to the complexity of pumping station operation rules, it is difficult to meet the operational optimality requirements by scenario simulation analysis. On the other hand, EAs are suitable for solving complex optimization problems but require multiple calls to the solver of the objective function and constraints. By employing DDEO algorithms, the advantages of both approaches can be effectively combined. The hydrodynamic model is utilized to solve the hydraulic parameters required for pump station operation, thereby addressing the issue of imprecise calculations in the flood propagation process. The hydrodynamic model is used as the solver for the objective function and constraints of the optimization algorithm. By leveraging the predictive capabilities of ML models, the number of calls to the hydrodynamic model can be reduced, thereby addressing the issue of high computational costs in optimization. To validate the feasibility of this method in the field of flood management, the operation rules of pump stations under three unsteady flood conditions were optimized. The flood risk of the river channel and the power consumption of the pumps were analyzed before and after optimization. The results indicate that under different flood inflow conditions, the optimized operation rules vary in their emphasis on flood risk and pump power consumption within the objective function.

Analysis of Figure 8 reveals that there remains an error between the hydrodynamic model simulation results and the measured data. The error may arise from the accuracy of the DEM and the precision of water level and flow data collection. The finer the DEM grid resolution, the more accurate the flood simulation results, but finer grids also introduce additional computational burdens (Ma et al. 2023). Currently, a grid resolution of 510−3m is selected, which can effectively achieve accurate flood process simulation within an acceptable time frame. Although proportional-integral-derivative (PID) control was added to the unsteady inflow, flow fluctuations are still inevitable. Throughout the experiment, the water level exceeded 3 cm, thereby avoiding measurement errors caused by surface tension.

The objective function of pump station optimization encompasses flood control and operational costs. The optimization results obtained in Figure 10 effectively demonstrate the tradeoffs between these two objectives. After optimization, the water level in the inner lake remains at the lowest control level before the flood peak, thereby creating more storage space for the incoming flood peak. This also reflects that the optimized scheme, based on ‘pre-discharge before the flood season,’ further achieves ‘pre-discharge before the peak’ through pump control according to different flood flow processes, thus minimizing the backwater effect to the greatest extent.

Based on the above conclusions, this work designed a novel drainage pumping station operation optimization method, which is based on the hydrodynamic model-driven evolutionary algorithm. When forecasted flood data are obtained from the ministry of water resources, it first constructs a corresponding hydrodynamic model to calculate the flood process. Then, an optimization algorithm is used to solve the operation of the pumping station. From the optimal results shown in Figure 10, it can be observed that the method proposed in this paper has significant potential in providing operations for flood control and drainage projects.

Although the proposed approach demonstrated effectiveness in the experimental case study, its limitations must be acknowledged. Notably, the operation optimization still requires calling the hydrodynamic model for almost a hundred real evaluations. Moreover, for a single flood event, only the operation rule corresponding to that particular event can be determined. This limitation becomes more pronounced when dealing with complex and variable flood events encountered in flood digital twin platforms. To address these challenges, future research could focus on constructing a database by pre-optimizing the operation rules for multiple design and historical flood events. This database could then be leveraged to develop ML models to meet the timeliness requirements for decision-making.

The operation of the pumping station is important in flood management and the development of the digital twin platform. This study proposes a novel optimization method for the operation of drainage pumping stations focusing on balancing flood mitigation and operational costs. Using DD technology, the method enables the combination of the hydrodynamic model with a coupled pumping station and APSO algorithms under limited computational resources. The hydrodynamic model is used to accurately represent the flooding physical processes and generate hydraulic characteristics for the APSO algorithm. The substantial reduction in the number of evaluations is attributed to the integration of the Kriging model into the optimization process, which assists the APSO algorithm in reducing the call to the hydrodynamic model. Simultaneously, this approach effectively addresses the challenges associated with inaccurate descriptions of flooding propagation and time-consuming optimization of pump operation.

The proposed method has been implemented in a digital twin experimental platform with a river and lake flood control and drainage system. The results show that the optimized operation rules effectively achieve the optimal solution of the objective function under the constraints. Under the inflow flooding conditions with different discharges of high, medium, and low, the optimized integrated objective function values decreased by 28.7, 32.5, and 25%, respectively. This reduction demonstrates the significant optimization effectiveness of the method. Consequently, this method provides a refined operation rule for pumping stations, contributing to the management of the UFCDS.

This work is partly supported by the Key science and technology projects of Power China (DJ-ZDXM-2022-41), the Major science and technology projects of Power China Northwest Engineering Corporation Limited (XBY-ZDKJ-2022-9), the National Natural Science Foundation of China (42307108), and the Postdoctoral Research Project of Shaanxi Province (2023BSHGZZHQYXMZZ52).

X. L. and J. H. conceptualized the whole study and developed the methodology; X. L. and S. W. wrote the original draft preparation; X. L., S. X., and T. Z. helped on material preparation, collection, and analysis; Y. L. and H. M. supervised the work; Y. L. and T. Z. rendered support in funding acquisition; Y. G. guided for manuscript revision.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.

Bartos
M.
&
Kerkez
B.
(
2021
)
Pipedream: An interactive digital twin model for natural and urban drainage systems
,
Environmental Modelling & Software
,
144
.
doi:10.1016/j.envsoft.2021.105120
.
Chen
W. N.
,
Zhang
J.
,
Chung
H. S. H.
,
Zhong
W. L.
,
Wu
W. G.
&
Shi
Y. H.
(
2010
)
A novel set-based particle swarm optimization method for discrete optimization problems
,
IEEE Transactions on Evolutionary Computation
,
14
(
2
),
278
300
.
doi:10.1109/tevc.2009.2030331
.
Cressie
N.
(
1990
)
The origins of Kriging
,
Mathematical Geology
,
22
(
3
),
239
252
.
Dash
S. S.
,
Sahoo
B.
&
Raghuwanshi
N. S.
(
2022
)
An adaptive multi-objective reservoir operation scheme for improved supply-demand management
,
Journal of Hydrology
,
615
.
doi:10.1016/j.jhydrol.2022.128718
.
Hanazaki
R.
,
Yamazaki
D.
&
Yoshimura
K.
(
2022
)
Development of a reservoir flood control scheme for global flood models
,
Journal of Advances in Modeling Earth Systems
,
14
(
3
).
doi:10.1029/2021ms002944
.
Henriksen
H. J.
,
Schneider
R.
,
Koch
J.
,
Ondracek
M.
,
Troldborg
L.
,
Seidenfaden
I. K.
&
Stisen
S.
(
2023
)
A new digital twin for climate change adaptation, water management, and disaster risk reduction (HIP digital Twin)
,
Water
,
15
,
1
.
doi:10.3390/w15010025
.
Huang
P. F.
,
Wang
H. D.
&
Jin
Y. C.
(
2021
)
Offline data-driven evolutionary optimization based on tri-training
,
Swarm and Evolutionary Computation
,
60
.
doi:10.1016/j.swevo.2020.100800
.
Huang
Y.
,
Yu
S.
,
Luo
B.
,
Li
R.
,
Li
C.
&
Huang
W.
(
2022
)
Development of the digital twin Changjiang River with the pilot system of joint and intelligent regulation of water projects for flood management
,
Journal of Hydraulic Engineering
,
53
(
3
),
253
269
.
Imran
M.
,
Hou
J. M.
,
Wang
T.
,
Li
D. L.
,
Gao
X. J.
,
Noor
R. S.
&
Ojeda
M. G. V.
(
2024
)
Assessment of the impacts of rainfall characteristics and land use pattern on runoff accumulation in the Hulu River Basin, China
,
Water
,
16
(
2
).
doi:10.3390/w16020239
.
Jiang
J.
,
Liu
R.
&
Zhou
X.
(
2023
)
Study on the influence of flow velocity on dynamic characteristics and tail vortex structure of moored spherical submersible
,
Periodical of Ocean University of China
,
53
(
10
),
55
62
.
Jin
Y. C.
,
Wang
H. D.
,
Chugh
T.
,
Guo
D.
&
Miettinen
K.
(
2019
)
Data-driven evolutionary optimization: An overview and case studies
,
IEEE Transactions on Evolutionary Computation
,
23
(
3
),
442
458
.
doi:10.1109/tevc.2018.2869001
.
Jonkman
S. N.
,
Curran
A.
&
Bouwer
L. M.
(
2024
)
Floods have become less deadly: An analysis of global flood fatalities 1975–2022
,
Natural Hazards
, 120, 6327–6342.
doi:10.1007/s11069-024-06444-0
.
Ke
E. T.
,
Zhao
J. C.
,
Zhao
Y. L.
,
Wu
J. Z.
&
Xu
T.
(
2024
)
Coupled and collaborative optimization model of impervious surfaces and drainage systems from the flooding mitigation perspective for urban renewal
,
Science of the Total Environment
,
917
.
doi:10.1016/j.scitotenv.2024.170202
.
Kleijnen
J. P. C.
(
2009
)
Kriging metamodeling in simulation: A review
,
European Journal of Operational Research
,
192
(
3
),
707
716
.
doi:10.1016/j.ejor.2007.10.013
.
Kumar
A.
,
Kumar
S.
,
Rautela
K. S.
,
Shekhar
S.
,
Ray
T.
&
Thangavel
M.
(
2023
)
Assessing seasonal variation and trends in rainfall patterns of Madhya Pradesh, Central India
,
Journal of Water and Climate Change
,
14
(
10
),
3692
3712
.
doi:10.2166/wcc.2023.280
.
Li
X.
,
Hou
J. M.
,
Chai
J.
,
Du
Y. E.
,
Han
H.
,
Fan
C.
&
Qiao
M. X.
(
2022
)
Multisurrogate assisted evolutionary algorithm-based optimal operation of drainage facilities in urban storm drainage systems for flood mitigation
,
Journal of Hydrologic Engineering
,
27
(
11
).
doi:10.1061/(asce)he.1943-5584.0002214
.
Li
X. Y.
,
Hou
J. M.
,
Pan
Z. P.
,
Li
D. L.
,
Luan
G. X.
,
Fan
C.
&
Duan
C. H.
(
2024
)
Response of urban floods to two coupling modes of surface and pipe flow models
,
Hydrological Sciences Journal
,
69
(
3
),
365
376
.
doi:10.1080/02626667.2023.2279205
.
Liu
W.
,
Feng
Q.
,
Engel
B. A.
,
Yu
T. F.
,
Zhang
X.
&
Qian
Y. G.
(
2023
)
A probabilistic assessment of urban flood risk and impacts of future climate change
,
Journal of Hydrology
,
618
.
doi:10.1016/j.jhydrol.2023.129267
.
Ma
Y. Y.
,
Hou
J. M.
,
Liu
W.
,
Li
B. Y.
,
Wang
T.
&
Wang
F.
(
2023
)
Refined three-dimensional river channel reconstruction method based on coarse DEMs for flood simulation
,
Environmental Modeling & Assessment
,
28
(
5
),
787
802
.
doi:10.1007/s10666-023-09887-0
.
Ming
X. D.
,
Liang
Q. H.
,
Xia
X. L.
,
Li
D. M.
&
Fowler
H. J.
(
2020
)
Real-time flood forecasting based on a high-performance 2-D hydrodynamic model and numerical weather predictions
,
Water Resources Research
,
56
(
7
).
doi:10.1029/2019wr025583
.
Ministry of Housing and Urban-Rural Development of the People's Republic of China/State Administration for Market Regulation
(
2021
)
Standard for Design of Outdoor Wastewater Engineering
.
Beijing
:
Ministry of Housing and Urban-Rural Development of the People's Republic of China/ State Administration for Market Regulation
.
Moriasi
D. N.
,
Gitau
M. W.
,
Pai
N.
&
Daggupati
P.
(
2015
)
Hydrologic and water quality models: Performance measures and evaluation criteria
,
Transactions of the Asabe
,
58
(
6
),
1763
1785
.
Pasandideh
I.
&
Yaghoubi
B.
(
2023
)
Optimal reservoir operation using new SChoA and choA-PSO algorithms based on the entropy weight and TOPSIS methods
,
Iranian Journal of Science and Technology-Transactions of Civil Engineering
,
47
(
1
),
519
533
.
doi:10.1007/s40996-022-00931-9
.
Ranjbar
R.
,
Segovia
P.
,
Duviella
E.
,
Etienne
L.
,
Maestre
J. M.
&
Camacho
E. F.
(
2024
)
Digital twin of Calais canal with model predictive controller: A simulation on a real database
,
Journal of Water Resources Planning and Management
,
150
(
5
).
doi:10.1061/jwrmd5.Wreng-6266
.
Saini
B. S.
,
Chakrabarti
D.
,
Chakraborti
N.
,
Shavazipour
B.
&
Miettinen
K.
(
2023
)
Interactive data-driven multiobjective optimization of metallurgical properties of microalloyed steels using the DESDEO framework
,
Engineering Applications of Artificial Intelligence
,
120
.
doi:10.1016/j.engappai.2023.105918
.
Singh
R. K.
,
Kumar
S.
,
Pasupuleti
S.
,
Villuri
V. G. K.
&
Agarwal
A.
(
2023
)
Evaluating evolutionary algorithms for simulating catchment response to river discharge
,
Journal of Water and Climate Change
,
14
(
8
),
2736
2754
.
doi:10.2166/wcc.2023.083
.
Sun
H.
,
Zhang
X. W.
,
Ruan
X. J.
,
Jiang
H.
,
Shou
W. C.
,
Song
Y. Z.
&
Zhen
J. N.
(
2024
)
Mapping compound flooding risks for urban resilience in coastal zones: A comprehensive methodological review
,
Remote Sensing
,
16
(
2
).
doi:10.3390/rs16020350
.
Tao
F.
&
Qi
Q. L.
(
2019
)
Make more digital twins
,
Nature
,
573
(
7775
),
490
491
.
doi:10.1038/d41586-019-02849-1
.
Vondracek
D.
,
Padovec
Z.
,
Mares
T.
&
Chakraborti
N.
(
2023
)
Optimization of dome shape for filament wound pressure vessels using data-driven evolutionary algorithms
,
Materials and Manufacturing Processes
,
38
(
15
),
1899
1910
.
doi:10.1080/10426914.2023.2187823
.
Wang
D. S.
,
Tan
D. P.
&
Liu
L.
(
2018
)
Particle swarm optimization algorithm: An overview
,
Soft Computing
,
22
(
2
),
387
408
.
doi:10.1007/s00500-016-2474-6
.
Wang
X.
,
Tian
W. C.
&
Liao
Z. L.
(
2021
)
Offline optimization of sluice control rules in the urban water system for flooding mitigation
,
Water Resources Management
, 35, 949–962.
doi:10.1007/s11269-020-02760-9
.
Wang
X. J.
,
Xia
J. Q.
,
Zhou
M. R.
,
Deng
S. S.
&
Li
Q. J.
(
2022
)
Assessment of the joint impact of rainfall and river water level on urban flooding in Wuhan City, China
,
Journal of Hydrology
,
613
.
doi:10.1016/j.jhydrol.2022.128419
.
Wang
X. N.
,
Ma
X. M.
,
Liu
X. L.
,
Zhang
L. K.
,
Tian
Y.
&
Ye
C.
(
2023
)
Research on optimal operation of cascade pumping stations based on an improved sparrow search algorithm
,
Water Science and Technology
,
88
(
8
),
1982
2001
.
doi:10.2166/wst.2023.308
.
Wang
X. H.
,
Hou
J. M.
,
Pan
X. X.
,
Chen
G. Z.
,
Gao
X. J.
&
Zhang
Z. A.
(
2024
)
A novel approach to determine spatial prioritization of flooding mitigation practices based on coupled hydrodynamic and rainfall-tracking model
,
Journal of Water and Climate Change
,
15
(
3
),
1184
1203
.
doi:10.2166/wcc.2024.532
.
Yan
R.
,
Liu
L. L.
,
Liu
W. L.
&
Wu
S. H.
(
2023
)
Quantitative flood disaster loss-resilience with the multilevel hybrid evaluation model
,
Journal of Environmental Management
,
347
.
doi:10.1016/j.jenvman.2023.119026
.
Yazdi
J.
&
Khazaei
P.
(
2019
)
Copula-based performance assessment of online and offline detention ponds for urban stormwater management
,
Journal of Hydrologic Engineering
,
24
(
9
).
doi:10.1061/(asce)he.1943-5584.0001810
.
Yu
L. Q.
,
Ren
C. L.
&
Meng
Z. Y.
(
2024
)
A surrogate-assisted differential evolution with fitness-independent parameter adaptation for high-dimensional expensive optimization
,
Information Sciences
,
662
.
doi:10.1016/j.ins.2024.120246
.
Zaghloul
M.
,
Ghaderpour
E.
,
Dastour
H.
,
Farjad
B.
,
Gupta
A.
,
Eum
H.-I.
&
Hassan
Q.
(
2022
)
Long term trend analysis of river flow and climate in Northern Canada
,
Hydrology
,
9
,
197
.
doi:10.3390/hydrology9110197
.
Zhan
Z. H.
,
Zhang
J.
,
Li
Y.
&
Chung
H. S. H.
(
2009
)
Adaptive particle swarm optimization
,
IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics
,
39
(
6
),
1362
1381
.
doi:10.1109/tsmcb.2009.2015956
.
Zhao
J. H.
&
Liang
Q. H.
(
2022
)
Novel variable reconstruction and friction term discretisation schemes for hydrodynamic modelling of overland flow and surface water flooding
,
Advances in Water Resources
,
163
.
doi:10.1016/j.advwatres.2022.104187
.
Zhao
F. L.
,
Qiu
B. Y.
,
Wang
H. J.
&
Yan
T. X.
(
2023
)
Energy saving based on a multi-objective optimization model of the tidal pumping station along the coastal area
,
Journal of Cleaner Production
,
421
.
doi:10.1016/j.jclepro.2023.138513
.
Zhen
H. X.
,
Gong
W. Y.
,
Wang
L.
,
Ming
F.
&
Liao
Z. W.
(
2023
)
Two-stage data-driven evolutionary optimization for high-dimensional expensive problems
,
Ieee Transactions on Cybernetics
,
53
(
4
),
2368
2379
.
doi:10.1109/tcyb.2021.3118783
.
Zhou
K.
(
2024
)
Study of the hydrologic and hydrodynamic coupling model (HHDCM) and application in urban extreme flood systems
,
Applied Water Science
,
14
(
4
), 67.
doi:10.1007/s13201-024-02132-3
.
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