ABSTRACT
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.
HIGHLIGHTS
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.
INTRODUCTION
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.
EXPERIMENTAL STUDY
Description of the digital twin experimental platform
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
Case . | Inflow pattern . | Discharge pattern . | Initial HL (cm) . |
---|---|---|---|
V1 | Steady | Free outflow | 25 |
V2 | Unsteady | Free outflow | 25 |
V3 | Steady | Pump discharge | 45 |
V4 | Unsteady | Pump discharge | 45 |
Case . | Inflow pattern . | Discharge pattern . | Initial HL (cm) . |
---|---|---|---|
V1 | Steady | Free outflow | 25 |
V2 | Unsteady | Free outflow | 25 |
V3 | Steady | Pump discharge | 45 |
V4 | Unsteady | Pump discharge | 45 |
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).
Initial rule . | Pre-reduced (cm) . | Pump . | On (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 rule . | Pre-reduced (cm) . | Pump . | On (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 |
METHOD
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
Optimization framework
Hydrodynamic model with coupled pumping station
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 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
Kriging model and surrogate management
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.
RESULTS AND DISCUSSION
Validation of hydrodynamic model
Case . | Pump . | Running time . | Switches . | |||
---|---|---|---|---|---|---|
Measured (s) . | Simulated (s) . | Error (%) . | Measured . | Simulated . | ||
V3 | P1 | 138 | 135 | −2.2 | 2 | 2 |
P2 | 124 | 120 | −3.2 | 2 | 2 | |
P3 | 52 | 52 | 0 | 2 | 2 | |
V4 | P1 | 308 | 307 | −0.3 | 2 | 2 |
P2 | 267 | 271 | 1.5 | 2 | 2 | |
P3 | 181 | 185 | 2.2 | 2 | 2 |
Case . | Pump . | Running time . | Switches . | |||
---|---|---|---|---|---|---|
Measured (s) . | Simulated (s) . | Error (%) . | Measured . | Simulated . | ||
V3 | P1 | 138 | 135 | −2.2 | 2 | 2 |
P2 | 124 | 120 | −3.2 | 2 | 2 | |
P3 | 52 | 52 | 0 | 2 | 2 | |
V4 | P1 | 308 | 307 | −0.3 | 2 | 2 |
P2 | 267 | 271 | 1.5 | 2 | 2 | |
P3 | 181 | 185 | 2.2 | 2 | 2 |
Optimal operation of pumping station
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.
Inflows . | Pre-reduced (cm) . | Pump . | On (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 |
Inflows . | Pre-reduced (cm) . | Pump . | On (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 |
Operation rule . | Obj . | ||
---|---|---|---|
QH . | QM . | QL . | |
O1 | 10.11 | 8.84 | 7.33 |
O2 | 87.28 | 7.45 | 5.15 |
Opt | 7.21 | 5.97 | 3.86 |
Operation rule . | Obj . | ||
---|---|---|---|
QH . | QM . | QL . | |
O1 | 10.11 | 8.84 | 7.33 |
O2 | 87.28 | 7.45 | 5.15 |
Opt | 7.21 | 5.97 | 3.86 |
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.
Inflows . | Switches . | Running time (min) . | ||||
---|---|---|---|---|---|---|
O1 . | O2 . | Opt . | O1 . | O2 . | Opt . | |
QH | 13 | 7 | 9 | 27.00 | 25.64 | 26.85 |
QM | 14 | 8 | 7 | 24.13 | 22.69 | 23.52 |
QL | 11 | 6 | 3 | 21.85 | 20.32 | 19.66 |
Inflows . | Switches . | Running time (min) . | ||||
---|---|---|---|---|---|---|
O1 . | O2 . | Opt . | O1 . | O2 . | Opt . | |
QH | 13 | 7 | 9 | 27.00 | 25.64 | 26.85 |
QM | 14 | 8 | 7 | 24.13 | 22.69 | 23.52 |
QL | 11 | 6 | 3 | 21.85 | 20.32 | 19.66 |
DISCUSSION
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.
CONCLUSIONS
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.
FUNDING
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).
AUTHOR CONTRIBUTIONS
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 AVAILABILITY STATEMENT
Data cannot be made publicly available; readers should contact the corresponding author for details.
CONFLICT OF INTEREST
The authors declare there is no conflict.