Multi-level dynamic zoning design to improve the restorative capability of resilience: An emergence response in water contamination flushing

Sustainable urban development needs to be supported by the urban water distribution systems (WDSs) (UN 2015). However, climate change, extreme droughts, and population growth have stressed freshwater supply worldwide (Salehi 2022). Recent studies show that 25% of large cities are experiencing some levels of water stress (Lund Schlamovitz & Becker 2021). In order to cope with the problem of water stress, in addition to actively expanding non-conventional water sources (Singh et al. 2020; Singh 2021; Singh & Samsher 2021, 2024), the need for water security to improve the emergency response capability of the WDS to cope with failures and to reduce the impacts of abnormal accidents, so as to enhance the reliability and resilience of the system (Mahmoud et al. 2018), has become a priority objective of WDS management.

Against the widespread use of zoning in WDSs, improving the emergency response capabilities of zoning networks has become increasingly important. However, the conventional district metered areas (DMAs) bounded by closed valves are used for pressure management and leakage control (Saldarriaga et al. 2019; Bui et al. 2020; Spedaletti et al. 2022; Marlim & Kang 2024), their permanent closed boundaries actually decreases structural redundancy, which reduces space of emergency response actions to cope with system failure or emergency events for resilience improvement (Wright et al. 2014). Meanwhile, with the development of the Internet of Things and communication technology, the conventional WDS is gradually transformed into a smart WDS (Gupta et al. 2020), in which the smart valves play an important role in the intelligent regulation of the valves state and the degree of opening to control and adjust the water flow through remote control. This requires us to re-examine the approach of DMA design, which evolves from fixed DMAs design to dynamic DMAs design which integrates dynamic adjustments of DMAs boundary smart valves to enable rapid and effective response to pressure management (Ulusoy et al. 2022) and various accidents flexibly (Wright et al. 2014; Di Nardo et al. 2015; Mahmoud et al. 2018; Strickling et al. 2020).

Dynamic DMAs offer a transformative approach to WDS management, transcending the capabilities of conventional static DMAs. Their key advantages lie not only in enhanced leakage management and pressure regulation but also in the dynamic adaptability of boundaries and hydraulic states during system failures. This dynamic capability mitigates the negative impact of fault isolation on overall network performance, enables rapid emergency responses, and ultimately fosters greater system resilience. Wright et al. (2015) successfully implemented the dynamic DMA structure in a real WDS and verified its advantages in increasing the average zone pressure (AZP). The advantages of dynamic DMAs have also been approved in many other applications, such as water supply capacity in firefighting events (Di Nardo et al. 2016), resilience improvement (Giudicianni et al. 2020b; Ulusoy et al. 2022), and response strategies in case of pipe bursts (Mahmoud et al. 2018; Trapiello et al. 2023). Therefore, this article investigates dynamic DMA design to facilitate the development of smart WDS.

Conventional DMA design in WDSs unfolds in two critical stages (Bui & Kang 2023): node clustering and boundary segmentation. The first stage, node clustering, aims to group interconnected nodes with similar spatial and hydraulic characteristics into cohesive clusters. This process minimizes inter-cluster connections while striving for balanced cluster sizes, aligning with concepts like graph partitioning in computational science and community detection in complex network theory (Saldarriaga et al. 2019). Consequently, many relevant algorithms from these fields are readily applied to DMA node clustering, including graph partition methods (Di Nardo et al. 2013; Liu & Han 2018; Zevnik et al. 2019) and recent advances in community detection algorithms (Zeidan et al. 2021; Shao et al. 2024; Sharma et al. 2022). Other methods have also emerged including graph neural networks (Rong et al. 2022), transport function-based clustering (Creaco et al. 2022), and topology-distance-based clustering (Du et al. 2023). The second phase of DMA design, boundaries segmentation, focuses on optimizing the placement of valves and flowmeters within the boundary pipes, guided by the results of the node clustering phase. Optimal booster pump configuration can also be determined in the stage (Bui & Kang 2023). This stage aims to achieve a delicate balance: meeting operational requirements for accurate water flow measurement and satisfactory hydraulic performance for leakage control, all while minimizing the cost of DMA implementation (Liu & Lansey 2020; Sharma et al. 2022). This multi-faceted challenge has attracted researchers to employ diverse optimization methods, including single-objective evolutionary algorithms (Spizzo et al. 2023), multi-objective evolutionary algorithms (Zhang et al. 2017; Liu & Lansey 2020), multi-criteria assessment (Liu & Han 2018; Bui et al. 2021), and heuristic algorithms (Liu & Han 2018; Creaco et al. 2019; Pesantez et al. 2019; Zevnik et al. 2019).

There are also some technical requirements during the DMA design process, including suitable sizes for DMA (Morrison et al. 2007) and the connectedness of each district to transmission mains (Ferrari et al. 2014), the former has received sufficient attention, but many DMA design methods do not meet the requirements of the latter. In DMA design, transmission mains primarily serve as water transportation to districts, while distribution pipes in DMAs distribute water to users. Differentiation between transmission mains and distribution pipes is a crucial cornerstone of effective DMA design (Tian et al. 2022). Failing to recognize these functional disparities can lead to costly mismatches, which use transmission mains as DMA inlet boundaries. Therefore, several researchers have explored DMA partitioning based on the functional classification of transmission mains and distribution pipes based in different pipe thresholds (Ferrari et al. 2014; Rahman & Wu 2018; Zhang et al. 2019). Recognizing the impact of transmission mains diameter thresholds on DMA size and meter/valve requirements, Zhang et al. (2021) introduced a method to optimize this threshold, minimizing boundary pipes, average path distance to transmission main nodes, and unmetered water volume.

Current methods of dynamic DMA design are mainly merging existing conventional DMA structures to improve the performance of WDSs. Scarpa et al. (2016) divided WDS into water supply areas based on locations of water sources. Their study investigated the impact of dynamically aggregating these areas with multiple sources on water quality, reliability, and firefighting capabilities. Similarly, Giudicianni et al. (2020a) utilized a multi-scale method to represent existing DMAs, employing community detection algorithms to identify aggregation schemes while preserving original boundaries. Subsequently, they optimized valve and flowmeter locations using a genetic algorithm. Bui et al. (2022) proposed a novel two-step method for dynamic DMAs. This approach first determines optimal DMA structures for various scenarios, followed by integrating valve adjustments within these structures to create adaptive DMAs capable of handling diverse operational anomalies.

However, a critical gap exists between the potential and the current reality of dynamic DMAs. Firstly, it is difficult to determine suitable dynamic DMA meeting engineering criteria in one step for large-scale complex WDS depending on computationally demanding optimization algorithms. Without classification of transmission mains and distribution pipes, the generated DMAs will include the two types of pipes, making it difficult to effectively manage pipe failures and control water pollution by adjusting boundary valves dynamically to improve system resilience. Secondly, the studies on dynamic emergency response focus on pipe bursts and fire accidents, there is limited literature on responsive actions in the case of a contamination threat, the relevant literature focuses only on the optimal placement of hydrants (Shafiee & Berglund 2015; Moghaddam et al. 2020; Shoorangiz et al. 2023). A combination strategy of water network partitioning, pipe valve closure for contamination isolation and flushing water from hydrants should be applied to develop a more effective response strategy for decision-makers to reduce and eventually eliminate the contamination (Eliades et al. 2023). This article tackles these limitations by proposing a novel three-level hierarchical partitioning method. This approach differentiates water source areas (WSAs), pressure management areas (PMAs), and dynamic DMAs, each fulfilling distinct roles within the network. Crucially, this partitioning is anchored in the fundamental classification of transmission and distribution functionalities, significantly enhancing partitioning speed and efficiency. Further, each level serves a specific purpose: WSAs facilitate water quality management, PMAs enable efficient pressure regulation and control, and dynamic DMAs focus on localized leakage control and emergency response. This targeted approach effectively alleviates the operational and management challenges associated with complex water distribution networks. Furthermore, a coupled emergency response strategy of WDS zoning, valve closure, hydrant flushing, and dynamic DMA adjustment is proposed to isolate the contaminated area and perform flushing while also adjusting the DMA boundary of low-pressure areas to increase AZP, thereby reducing the adverse impacts of flushing effectively, and improving the resilience of the WDS.

For complex water networks with multiple sources, ensuring reliable water supply and stable quality presents a significant challenge. While individual nodes may receive water from one or several sources depending on their location, water utilities seek to maintain a balanced supply area for each source to achieve these objectives. This necessitates accurately defining the actual water supply area for each source during network partitioning. Existing infrastructure, particularly pump station operation and water tank boundaries, should ideally remain unaltered unless compelling circumstances necessitate changes. Determining these areas with precision is crucial for preserving network integrity and achieving both reliable water supply and consistent water quality.

To identify water supply areas with precision, the following criterion is employed: a node is unequivocally considered to reside within the supply area dominated by water source ‘r’ if and only if its corresponding percentage flow value within the SD-FCM surpasses a predetermined threshold. By applying this criterion, the methodology constructs a comprehensive map of supply areas, each unequivocally associated with a specific water source.

In multi-source networks, some nodes exhibit the characteristic of receiving water from multiple sources concurrently. To pinpoint the primary WSA for such nodes, the Dijkstra algorithm (Dijkstra 1959) is strategically employed. This algorithm operates on a node weight adjacency matrix, constructed using pipe lengths as weights. By calculating the shortest distances from each available water source to these nodes, the algorithm designates the source with the minimum distance as the primary water source for each node.

To effectively distinguish between transmission mains and distribution pipes within each WSA, this article employs a robust two-pronged approach. First, pipes are sorted in ascending order of diameter. Leveraging the Pareto principle, a diameter threshold is strategically set at the point encompassing 80% of the pipes, serving as a primary criterion for classification. Second, to account for potential anomalies where downstream pipe diameters exceed upstream diameters due to design or maintenance interventions, the Breadth-First Search (BFS) algorithm is applied to find these transmission mains. Initiating from each water source, this algorithm explores interconnected pipes, ultimately pinpointing the transmission mains within the WSA. The judicious selection of distinct transmission main thresholds forms a cornerstone of efficient partitioning schemes that align with the network's unique hydraulic requirements and cost constraints (Zhang et al. 2021).

The nodes situated along the transmission mains are designated as water source points. The water distribution network is separated by several areas termed as IPAs by the transmission mains. Because each IPA is connected to only a few water source points, which can be taken as the root nodes of the depth-first search (DFS) algorithm, and DFS explores as far as possible along each branch before backtracking. Tian et al. (2022) demonstrated the ability of DFS to determine IPAs. DFS is also used to determine IPAs in this study.

The water distribution network is divided into a number of IPAs, and design of PMA and DMA are performed in each IPA, respectively, and the divide-and-conquer strategy effectively reduces the size of the zoning and the decision variables, and improves the zoning efficiency.

Within the realm of pressure management, the PBI stands as a metric, quantifying pressure distribution uniformity within a designated area. A lower PBI value gracefully mirrors a more harmonious pressure area, offering a fertile ground for optimization of pressure levels and subsequent bolstering of water leak control initiatives. Within the confines of this study, a PBI value below or equal to λ is considered as a PMA, with the value of λ determined on a case-by-case basis, signifying its suitability for refined pressure management strategies. Conversely, areas exhibiting PBI values that exceed this threshold are composed of multiple PMAs within their boundaries, necessitating further extraction of main distribution pipes with larger diameters and the subsequent determination of IPAs, persist until the distinguished formation of PMAs that gracefully satisfy the PBI requirement. For PMAs with few pressure variations, even if the PBI value meets the requirements, the size of PMA can be large. For this case, a reasonable size of PMA can be determined based on the network structure, demand patterns, etc., and then a reasonable size of PMA can be obtained by utilizing the main distribution pipe extraction.

For PMAs exceeding the designated DMA size threshold, further refinement through internal DMA design is crucial. This process, involving clustering of DMA nodes and optimization of DMA boundaries, ensures effective leakage management within these DMAs. The presence of water flow interchange between adjacent DMAs, termed dependent DMAs, emerges as a key outcome of this approach. By strategically carving out dependent DMAs within each PMA, on the one hand, pressure management is more stable with fixed boundaries and on the other hand, decision variables for DMA design are greatly reduced, which improves the computational efficiency of DMA design.

In this article, the greedy modularity maximization algorithm (Clauset et al. 2004) is applied to identify the clustering structure of the undirected graph G, which is implemented via the python-based NetworkX (Aric et al. 2008). The algorithm begins with each node in its own community and repeatedly joins the pair of communities that lead to the largest modularity until no further increase in modularity is possible.

Following the clustering of DMA nodes, the subsequent stage demands the identification of DMA inter-boundary pipes, accompanied by a rigorous determination of optimal locations for DMA inlets with flowmeters, and boundary valves within these boundary pipes. While flowmeters are essential for precise water metering within DMA inlets, an excessive number of these devices can lead to a surge in construction costs and hinder effective pressure regulation. Conversely, a conservative approach to inlet placement, necessitating the closure of DMA boundary valves, can inadvertently reduce the available flow paths from source to DMA. This reduction carries the potential to exacerbate hydraulic head loss, induce undesirable pressure drops within DMAs, and ultimately compromise the reliability of WDS. To navigate this delicate balance between cost and reliability, the boundary optimization challenge is formed as a multi-objective optimization problem in this study. The objective is to minimize the total cost associated with flowmeters and maximize the reliability of the WDS while simultaneously meeting the head constraint.

The optimization of the boundary pipes is conducted using the non-dominated sorting genetic algorithm (NSGA-II) (Deb et al. 2002). This algorithm helps determine the installation locations of valves and the flowmeter while meeting the minimum service head constraint.

Effective DMA design demands adherence to a multitude of technical requirements (Liu & Lansey 2020). Therefore, comprehensively evaluating each resulting Pareto solution from the DMA boundary optimization encompassing multiple technical criteria is crucial for identifying the optimal configuration. Recognizing the limitations inherent in static DMA boundaries, such as potential reductions in AZP, water quality deterioration, and diminished network redundancy, this framework leverages three key evaluation indicators: AZP deviation, water quality deviation, and network resilience deviation. These metrics serve as tools for assessing the performance of each Pareto-optimal alternative, ultimately guiding the selection of the most effective DMA configuration. The three evaluation indicators are as follows:

Conventional fixed DMAs have many shortcomings that make it difficult to adapt to future water supply requirements, such as increasing the pressure in the water supply network and responding to abnormal incidents. In order to solve these problems, a subset of valves must be endowed with the capability for strategic opening and closing, enabling dynamic aggregation or separation of DMAs as required. This dynamic adaptability holds the potential to enhance water pressure in daily operations and minimize failure consequences under abnormal accidents. Dynamic DMA design is proposed to simultaneously meet the demand for network restructuring for daily operation and dynamic emergency response. Specifically, the daily operation achieves pressure control and leakage management through different DMA boundary adjustments during daytime and nighttime. In case of system failure, the scope of failure impact is controlled and the speed of response is improved by temporarily changing the DMA boundaries. However, a comprehensive retrofit of all boundary valves would incur a considerable financial burden. To strike a balance between functionality and cost-effectiveness, this study proposes a judicious valve selection process guided by AZP criteria, which shall be elucidated forthwith:

• (1) In the event of a singular boundary valve existing between two adjacent DMAs, it shall be designated as a dynamic open/close valve.

• (2) In scenarios where multiple boundary valves reside between adjacent DMAs, a selection process is employed to identify those that warrant dynamic control capabilities. Considering the limited number of valves, the enumeration method is applied to evaluate a comprehensive array of possible valve combinations. Each combination is then subjected to rigorous hydraulic simulation to calculate its associated AZP by (16). The objective of this process is to pinpoint the specific valve configuration that yields the best enhancement effect of AZP, thereby maximizing water pressure within the aggregated DMAs. For a certain number of dynamic valves, the combination with the largest AZP is identified and the AZP enhancement effect is calculated using Equation (17). The optimal dynamic valve combinations for different numbers of dynamic valves can be obtained using the above method. From this, dynamic valve combinations that satisfy the AZP enhancement thresholds can be obtained for decision-makers to choose.

  

  (16)

  

  (17)

  where nn is the total number of nodes in the two merging DMAs; P_i,cDMA is the pressure of node i after the aggregation of two DMAs, mH₂O; denotes the maximum AZP of the aggregated areas under the combination of i dynamic valves, mH₂O; denotes the average AZP of the aggregated areas without dynamic valves, mH₂O; and is the AZP enhancement threshold determined on a case-by-case scenario.

This study determines DMA size based on nodal demands, aiming for each DMA to serve 500–5,000 households. Considering an average household size of 2.3 persons, this corresponds to an estimated population of 1,150–11,500 per DMA. Further accounting for a per capita water demand of 114.794 L/day or 0.001328 L/s, each DMA is designed to supply a total demand ranging from 1.5279 to 15.2793 L/s. This approach aligns with established best practices for DMA sizing, striking a delicate balance between operational efficiency and cost-effectiveness.

In this study, once the positions of DMA inlets, fixed boundary valves, and dynamic boundary valves have been determined, the dynamic response under the scenarios of contamination in the WDS is examined. These scenarios are taken as examples to analyze the emergency response of other DMAs aggregation when the contaminated area is flushed. The study considers two realistic contamination scenarios to provide a comprehensive understanding of potential contamination events in an actual water distribution network:

(1) Local contamination incident characterizing by its confinement within a DMA, exclusively impacting the distribution network while leaving the transmission network unaffected. This scenario allows for a focused response strategy that involves isolating the contaminated DMA by strategically closing its inlets, thereby temporarily restricting water service within that designated area. Notably, this isolation procedure typically exerts minimal impact on the broader WDS and neighboring DMAs. However, the subsequent flushing process, which necessitates a higher flow of water to effectively remove contaminants, does hold the potential to cause disruptions within the network and potentially affect surrounding DMAs.

(2) Global contamination encompassing both the distribution network and transmission mains, affecting a significantly larger area. This widespread contaminant presence necessitates a more extensive response strategy. Contaminated DMAs and the impacted transmission mains are consequently shut down, resulting in localized water service interruptions within isolated DMAs. Furthermore, this shutdown disrupts the normal flow paths from the water source, leading to a reduction in water supply pressure for surrounding uncontaminated DMAs. The subsequent flushing process, requiring a high-flow rate for effective contaminant removal, further amplifies these disruptions, impacting both the remaining transmission mains and operating DMAs.

Contamination incidents within water networks pose a significant threat to public health and safety. Therefore, effective response strategies are critical to mitigate their impact. This includes implementing rapid and effective measures to isolate the contaminated area to prevent the spread of a contaminant once it enters the distribution network and flushing the contaminated water through hydrants to make the system return back to normal state swiftly (Xin et al. 2017). The coupled emergency response strategy of WDS zoning, valve closure, hydrant flushing, and dynamic DMA adjustment offers a compelling solution for achieving both objectives. The boundary valves within DMAs can be readily closed to effectively isolate the contamination, preventing its further spread. Additionally, dynamically adjustable valves between DMAs enable aggregation of DMAs suffering from low pressure during flushing of the contaminated area, minimizing the potential adverse effects of high-flow flushing, thereby facilitating a rapid and controlled recovery. The dynamic emergency response based on valve operation and flushing after contamination is performed in the following steps:

• (1) Upon locating the contamination source and extent of the contamination by water quality simulation, isolation of the contaminated region is first conducted by closing all designated boundaries where water flow connects the contaminated area to its surroundings to halt the potential spread of contaminants, safeguarding other districts within the network.

• (2) Start flushing the contaminated area using unidirectional flushing by opening its inlets and selecting flushing nodes at the end of the isolated region with significant water demands to flow one way from larger diameter to smaller diameter water mains. Due to the presence of branch pipes, it is supposed that flushing nodes are the end nodes of branch pipes, hydrant scheduling for contaminated water evacuation is not needed, but for loop network hydrant scheduling is required (Hu et al. 2022). At the same time, consumers are warned (Strickling et al. 2020) and other demand nodes within the isolated area should be prohibited from accessing water during flushing to prevent human contamination.

• (3) Two distinct flushing strategies are employed within this investigation to evaluate their efficacy in contaminant removal and elucidate the optimal approach for decontamination efforts. These strategies comprise (a) a sequential DMA flushing program, after completing one DMA flushing and restoration, move on to the next DMA for flushing and (b) a simultaneous multi-DMA flushing program, the contaminated DMAs start flushing simultaneously and the flushing progress is monitored in real-time monitoring.

• (4) While each isolated DMA undergoes flushing, hydraulic simulation is performed to evaluate the impact of flushing and determine the critical threshold to select affected DMAs requiring dynamic aggregation operations, and then open the dynamic valves of those DMAs to mitigate adverse effects of network flushing and improve the water supply effectiveness of the WDS.

• (5) Once the network flushing is completed and the WDS is restored to its normal state, all boundaries are returned to their original state.

Harnessing a percentage flow matrix derived from trace simulations and Dijkstra's shortest path algorithm, the water network system is partitioned into two WSAs, each corresponding to a distinct water source. Visual representations of these WSAs, encompassing Reservoir A and Reservoir B, are presented in Figure 6. Notably, the WSA associated with Reservoir A (WSA A) comprises 15,199 demand nodes and 15,280 pipes, while the WSA affiliated with Reservoir B (WSA B) encompasses 3,173 demand nodes and 3,199 pipes.

Subsequent to the separation of WSAs for each water source, an extraction process is undertaken to identify the transmission mains. The Pareto principle is used to determine the diameter threshold of transmission mains for each area separately, specifically 300 mm for WSA A and 400 mm for WSA B. The extracted transmission mains are prominently illustrated with bold red lines in Figure 6.

Subsequently, the number of DMAs within each PMA is determined based on both the desired demand range within individual DMAs and the total demand within the PMA. For the PMA at the center of the network, where the pipe connections are more complex, a smaller DMA size is used for the DMA design in order to facilitate pressure control. While for peripheral PMAs, a larger DMA scale is used. The number of DMAs for different PMAs are given in Table 2. To achieve DMA design, a community structure detection algorithm, designed to maximize modularity, is employed to cluster nodes into DMAs.

Following the identification of node clusters as DMAs, the boundary pipes separating individual DMAs are determined accordingly. To optimize the placement of DMA inlets and boundary valves, a multi-objective optimization algorithm, NSGA-II, is employed. The variables for PMA4, PMA5, PMA6, PMA7, and PMA8 are 10, 27, 3, 6, and 15, respectively. It can be seen that for each PMA, there are fewer decision variables, which is due to the fact that the number of boundary pipes between DMAs has decreased through transmission pipe extraction and node clustering, which also shows the advantage of the multi-level zoning method proposed in this article in reducing the amount of computation. Considering the small number of decision variables, the population size was set to 100 for NSGA-II undergoing 1,000 evolutionary generations, with a crossover coefficient of 0.85 and a mutation rate of 0.001. This optimization process yields Pareto fronts showcasing optimal DMA boundary configurations within each PMA. However, due to the limited number of boundary pipes within each PMA, the generated number of partitioning scenarios is relatively small. For PMA4, PMA5, PMA6, PMA7, and PMA8, where multiple DMA solutions emerge, a multi-criteria evaluation is undertaken, adhering to the methodology outlined in Section 2.3.3, where ⁠, ⁠, and are all set to be 1/3, indicating that they have the same importance, to select the optimal DMA design solution based on the performance evaluation index F. The results of this evaluation are comprehensively presented in Table 3 and choose Solution 4 for PMA4, Solution 3 for PMA5, Solution 2 for PMA6, Solution 3 for PMA7, and Solution 1 for PMA8. For the remaining PMAs, NSGA-II identifies a singular, optimal solution, rendering additional multi-criteria evaluation unnecessary.

Table 4 comprehensively details the pre- and post-partitioning differences in PMA boundary structure, hydraulic characteristics, and water quality performance. The number of DMA boundaries consists of the number of source points and the number of boundary pipes of each PMA. For the 66 boundary pipes identified, a total of 41 flowmeters and 25 valves are to be installed. Notably, following the implementation of the optimized DMA design, PMA5 and PMA8 demonstrate obvious pressure reductions exceeding 30 and 20%, respectively, compared with their initial pre-partitioning state.

Using the proposed optimization method, dynamic valves are carefully selected from among the identified DMA boundary valves to facilitate the flexible aggregation and separation of DMAs in response to varying operational needs. The partial branch structure of the water network system in this case results in a relatively streamlined DMA partition configuration, requiring a limited number of boundary valves. This fortunate circumstance enables the designation of all boundary valves as dynamic valves, 25 dynamic valves, effectively realizing a fully dynamic DMA structure within the system.

The independent DMA is only connected to the water transmission pipes, and the structure is simple and easy to control, so it will not be analyzed separately in this article. Next, this article focuses on the dynamic aggregation of dependent DMAs within a PMA. We focus on optimizing DMA operation throughout the daily cycle to achieve adaptable pressure control and efficient leakage management. During peak demand hours (8:00–22:00), strategic DMA aggregations are implemented to augment the hydraulic capacity of the network and bolster its resilience index, ensuring adequate water supply. Conversely, during off-peak hours (22:00–8:00), DMA separations come into play, prioritizing pressure management within individual DMAs for effective leakage control.

Table 5 presents a comparative analysis of the hydraulic performance for dynamic DMAs with boundary adjustments and fixed DMAs without adjustments during daytime operation. Notably, implementing dynamic adjustments yields a substantial minimum pressure increase of 4.54 m compared with the fixed configuration. This significant improvement primarily stems from mitigating the adverse hydraulic impacts introduced by PMA5 and PMA8 partitions, as detailed in Table 4. Overall, dynamic adjustments result in an average pressure increase of 3.96 m and a commendable 2.1% boost in system reliability. Importantly, the analysis reveals a commendable 8.6% boost in water quality due to dynamic adjustments.

Table 5 further elucidates the hydraulic performance of fixed DMAs during nighttime operation. Notably, the implementation of adjusted pump speeds with a head drop during the night leads to an average pressure reduction of 2.82 m compared with daytime levels. This pressure decrease demonstrably reduces leakage losses within the network, providing valuable insights and a crucial reference point for optimizing dynamic adjustments during nighttime hours in future studies.

In response to a contamination event within a DMA, it is assumed that the contamination is detected at 11:00 a.m., and the contamination source is also pinpointed with affected scope as illustrated in Figure 13. The DMA layout reveals that the contamination encompasses DMA9, DMA12, DMA14, and DMA18. Prompt containment measures necessitate the isolation of these four DMAs by closing their inlets and severing any boundary connections with neighboring DMAs. To facilitate effective decontamination, a 3-h isolation period is assumed prior to initiating flushing operations within the contaminated DMAs.

After isolating the contaminated DMAs, flushing nodes are selected. According to Equation (18), each flushing node is assigned a specified flushing flow rate during the flushing process, while the water demand of other nodes in the isolated DMAs is adjusted to zero. The isolated DMAs are divided into multiple flushing subareas based on the criterion of whether the isolated subarea has an inlet connected to a transmission main. DMA9 and DMA12, each connected to distinct transmission mains, constitute separate flushing subareas. However, DMA14 and DMA18, both situated downstream of DMA9 and receiving water solely through DMA9, are grouped together with DMA9 as a single, unified flushing subarea.

Within this study, the flushing process unfolded through a sequenced flushing strategy, DMA9 followed by DMA12. The simulation found that flushing DMA9 had no effect on other DMAs, so there was no need to adjust other DMA boundaries. In contrast, when flushing DMA12, three DMAs were affected by low pressure, so dynamic aggregation needed to be used to reduce the effect of low pressure. The dynamic DMA aggregations were implemented as shown in Table 6 and hydraulic performance during dynamic DMA aggregation can be referred to Supplementary Table S1.

In the contamination event on the transmission main, detection occurs at 2:00 a.m., prompting swift identification of the source and the extent of the affected area, as visualized in Figure 13. The DMA layout reveals a widespread contamination spanning a total of 10 DMAs: DMA8, DMA9, DMA10, DMA11, DMA12, DMA15, DMA16, DMA17, DMA46, and DMA47, along with three independent DMAs, iDMA1, iDMA2, and iDMA3. To safeguard the integrity of the unaffected network, immediate isolation of these 13 DMAs is paramount. This involves the closure of all inlets supplying the contaminated zone and any boundary valves connecting it to neighboring DMAs. The simulation assumes a 3-h preparation window for isolation before the commencement of flushing operations within the affected DMAs.

Following the swift isolation of the contaminated DMAs, a flushing process commences. Spearheading this operation is the selection of flushing nodes; each assigned a specific flow rate in accordance with Equation (18). Simultaneously, to simulate the suspension of contaminated water consumption, demand at all other nodes within the isolated area is precisely adjusted to zero. To optimize flushing efficiency, the isolated area undergoes a subdivision into 12 distinct flushing subareas based on the criterion: the presence or absence of inlets directly connected to transmission mains. Notably, DMA11, positioned downstream of DMA16 and receiving its entire water supply through DMA16, necessitates a coordinated flushing approach. Therefore, these two DMAs are flushed as a unified flushing subarea, while the remaining DMAs undergo individualized flushing.

Within the framework of this study, a carefully orchestrated sequential flushing approach was employed to decontaminate the affected areas. The planned sequence prioritized efficiency, proceeding in the following order: iDMA1, iDMA2, iDMA3, DMA9, DMA10, DMA12, DMA46, DMA47, DMA17, DMA15, DMA16, and culminating with DMA8. This prioritization was based on the anticipated flushing time for each contaminated area individually, with those requiring shorter durations receiving precedence. iDMA1, iDMA2, and iDMA3 are directly connected to transmission mains, isolating and flushing the three DMAs have little impact on other DMAs, and they are not taken into consideration next.

Flushing of DMA9, DMA10, DMA12, DMA46, DMA47, DMA17, and DMA15 in sequence has little impact on other DMAs, while flushing DMA16 and DMA8 will result in low pressure in DMA50, then DMA50 and DMA49 are aggregated, the hydraulic performance during dynamic DMA aggregation is shown in Supplementary Table S4.

This article proposes a multi-level dynamic zoning design method and a coupled emergency response strategy during water contamination.

The multi-level design method involves employing partition of WSAs, which are further subdivided into multiple independent PMAs consisting of several dependent DMAs with flow exchanges. WSAs are determined by SD-FCM and shortest path algorithm, while identification PMAs are based on transmission mains extraction and PBI. The greedy modularity maximization algorithm and NSGA-II are used to optimize the DMA boundaries, and the optimal DMA solution is obtained by multi-criteria evaluation. The enumeration method coupled with AZP enhancement assessment is applied to determine the location of dynamic valves for dynamic DMAs.

The advantage of dynamic DMAs is validated on emergency response during contamination flushing. A coupled emergency response strategy of WDS zoning, valve closure, hydrant flushing, and dynamic DMA adjustment is proposed to improve the restorative capability of resilience. Specifically, when contamination is identified, the contaminated DMAs are isolated by closing the inlets and valves to stop the pollution from spreading further. While flushing the contaminated area, dynamic valves are opened to aggregate the DMAs suffering from low pressure caused by high flushing flow to reduce the impact of flushing. Two indicators are proposed to measure the resilience: the change of AZP (⁠⁠) and the number of contaminated people (Pop). Two contamination scenarios including local and global contamination and two flushing methods of sequential flushing and simultaneous flushing were also compared.

Our findings indicate that although sequential flushing has a longer flushing time, the impact of low flushing flow on the hydraulic performance of the WDS is also lower. Additionally, the capacity requirement for the pump station is not as high as that of simultaneous flushing. On the other hand, simultaneous flushing exhibits a fast recovery efficiency, but the higher flushing flow has a larger impact on the network, resulting in greater hydraulic performance challenges. The quick recovery effect of simultaneous flushing comes at the cost of a higher impact on the network, necessitating a higher pump station capacity to meet the pumped flow requirements. This increased capacity may lead to higher initial investment in pump station construction.

The dynamic DMA design method proposed in this article can effectively improve the resilience recovery during contamination flushing. The following studies can analyze other failure scenarios, such as pipe bursts caused by earthquakes. In addition, the performance of other optimization algorithms for design of WSA, PMA, and dynamic DMA can be analyzed. Dynamic scheduling of emergency response is also a very important research topic.

This research was funded by the Science Research Project of Hebei Education Department (ZD2022055) and the Key Research and Development Program of Hebei Province (No. 21375401D).

J.L.: Conceptualization, Methodology, Validation, Funding Acquisition, Writing – Review and Editing. H.W.: Writing – Original Draft, Software, Formal Analysis. Q.Z.: Visualization, Resources, Project Administration, Writing – Review and Editing. Y.W.: Investigation, Formal Analysis. D.Z.: Supervision, Funding Acquisition. D.W.: Supervision, Resources. Y.H.: Writing – Review and Editing, Resources.

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

The authors declare there is no conflict.