Optimal Segmentation Approach for Reducing Water Outage Damage Considering Urbanization in Water Distribution Systems

Abstract

Damage due to abnormal conditions in water distribution systems is attributable to direct causes, such as facility deterioration, as well as indirect causes, including inadequate management, natural disasters, and negligence of a manager. Such damage can be prevented from being spread by closing a shut-off valve to isolate the incident area, although additional damage may occur in the area isolated by the control valve due to water outage, thus requiring a structural solution. Therefore, this study proposed an optimal segment division technique that minimizes the damage due to water outage occurring in the isolated area by installing a shut-off valve at an appropriate location through an optimal valve location determination model designed based on various urban development scenarios. The proposed technique was applied to a benchmark network and J-city network in Korea for performance verification. This technique can be used to select the number of installable valves and find the optimal valve locations according to the urban development scenario.

1. Introduction

Urban development and water distribution systems (WDSs) are closely interconnected. WDSs are functionally linked to urban development and play a critical role in supporting the progress of cities and ensuring a stable quality of life. In particular, WDSs are one of the crucial factors that impact urban planning. Additionally, WDSs should be appropriately designed during urban development, and expansion and improvement should be carried out in alignment with long-term urban planning. For these reasons, the planning of urban development and of WDSs are mutually interdependent. The stable operation of WDSs plays a significant role in ensuring the sustainable development of the city and the well-being of its residents [1,2].

Since WDSs are infrastructure that can be directly related to life, robustness needs to be improved for stable water supply even under abnormal conditions (e.g., leakage, pipe breakage, extreme demand conditions such as fire water). Robustness refers to the ability of the system to maintain its functionality even under abnormal conditions, and it is a component that contributes to resilience [3]. Lansey et al. [4] suggested that WDSs’ robustness can be improved through measures such as increasing the pipe diameter and installing additional shut-off valves. The enhancement of robustness through the installation of additional valves is associated with the partitioning of segments. Segments refer to the areas in the WDSs that are isolated based on the location of the shut-off valves, including system components such as pipes and nodes within those segments [5]. When abnormal situations occur, it may be necessary to close valves for system repairs or maintenance. However, closing valves can cause damage from undelivered water in segment. Since larger segments can cause more significant damage, research has been conducted to improve robustness through the installation of additional valves.

Jun [6] proposed a method for evaluating valve efficiency based on the connected components and demand quantity to consider the effects of valve location. To improve upon the errors in the conventional reliability calculation method, which only considers the damaged conduit, a revised reliability calculation method was proposed to account for unintended isolations that occur when the only available supply pipe is blocked by other segments [7]. Furthermore, Jun and Loganathan [8] introduced the segment identification algorithm (SIA), which efficiently explores the damaged area through a matrix representing the connections of components such as nodes, pipes, and valves. Choi et al. [9] suggested a system for enhancing the robustness of WDSs by installing additional valves. Their study employed a multicriteria decision-making process considering social, economic, and hydraulic significance to prioritize the division of segments explored through the SIA. Additionally, the optimal locations of additional valves were determined using the Monte Carlo simulation, which takes into account the resident population of the isolated area and the valve failure rate. When the proposed technique was applied to an actual WDS, the damage to the resident population was reduced by up to 50% through the installation of additional valves. Lim and Kang [10] proposed an enhanced exploration technique to overcome the limitations where unintended isolations are not detected in a branch network. This technique explores unintended isolation through a link-based adjacency matrix representing the connections of pipelines. To minimize the damage caused by water outages, an optimal valve location determination model was proposed, considering the extent of the damage from undelivered water and valve installation cost [11,12]. These studies were conducted with a focus on installing additional valves and dividing segments to minimize the damage from undelivered water caused by abnormal situations.

However, as WDSs are designed and expanded in tandem with urban development, research should focus on segment partitioning and the installation of additional valves, considering the current forms of urban development, such as (1) planned city developments and (2) urban expansion, to enhance the robustness of the WDSs. Planned cities require a high level of completion in their final design proposals due to their emphasis on long-term planning and development. In addition, since the design of WDSs according to the expansion of the city is carried out through several stages over many years, an optimal design plan for each stage is required. Therefore, this study suggested the optimal segment division considering the urban development forms of (1) planned city developments and (2) urban expansion. In this study, the optimal segment division was proposed, which quantified the damage from undelivered water through the SIA and selected the optimal valve location using an optimization algorithm to minimize the damage. The objective function of the optimization algorithm was to minimize the damage, with the decision variables being the valve locations. The constraints considered were the efficiency of the segment deviation (ESDs).

2. Optimal Segment Division Approach Based on Urbanization

The optimal segment division technique based on scenarios was proposed in this study for reducing the damage derived from the water outage that occurs in the isolated area by determining the locations for dividing large-scale segments and reinforcing the WDS through additional shut-off valves. The proposed technique determines the optimal valve location in four steps. Figure 1 shows the process of dividing segments based on the optimal valve location.

In Step 1, the damage from undelivered water occurring in the WDS is identified quantitatively based on the component information and a hydraulic analysis model of WDSs (e.g., EPANET 2.2) [13] that has been verified and corrected. The relevant data are obtained using EPANET 2.2, scientific programming language (MATLAB) [14], and the EPANET toolkit [15]. The information, including the ID, location, and demand number of the components constituting the network, such as nodes, pipes, and valves, is used as an input in the optimal valve location determination model. The segments in which damage from undelivered water occurs are explored by building a matrix representing the connection status of the components and valve locations based on the collected information. Valves are closed to create isolated areas, which are referred to as “segments” [5]. These segments act as isolated zones, and the segment is blocked in terms of the water supply to allow for the system repairs. The damage from undelivered water can be identified according to the segment configuration through the closure of shut-off valves. In the WDS, the damage from undelivered water can be divided into direct damage and indirect damage [16]. Direct damage means the damage from undelivered water through valve closing (i.e., segment, unintended isolation), while indirect damage means damage such as pressure drop and supply shortage in surrounding nodes due to valve closing for the repair or maintenance of pipes. Damage from undelivered water caused by the valve closing occurs not only in the segment but also in unintended isolations. Jun and Loganathan [8] define an unintended isolation as an area where the pipe is unintentionally blocked when isolating the segment. To quantify the damage from undelivered water, this study considered as the sum of undelivered water demand in the segment and unintended isolation. The degree of damage from undelivered water becomes the criterion for deciding the reinforcement priority of isolated areas; if the damage from undelivered water in a particular area exceeds 10% of the entire damage, the area is selected as a large-scale segment. The selected large-scale segments can be divided through additional shut-off valves, and then the conduit belonging to the selected area is set as the candidate for installing the valve. The optimal valve location for minimizing the damage from undelivered water is explored among the group of candidates.

2.1. Segment Identification and Large-Scale Segment Selection

Segments refer to the areas isolated by a shut-off valve in the WDS and the areas where damage from undelivered water occurs due to the suspension of the water supply when the valve installed near the incident location is closed due to abnormal conditions. The demand quantity of nodes belonging to a segment can be converted into the degree of damage from undelivered water, which then becomes the quantitative criterion for determining the priority of installing additional shut-off valves. However, due to the complex composition of WDSs, an efficient method is required to explore segment locations and assess the degree of damage from undelivered water.

Therefore, this study utilized the segment identification algorithm (SIA) proposed by Jun and Loganathan [8] to systematically analyze the degree of damage from undelivered water and identify the segment locations. The SIA explores segments by constructing a Nord-ark matrix (NAM), valve location matrix (VLM), and valve deficiency matrix (VDM) consisting of nodes (rows) and pipes (columns). The NAM represents the connections between nodes and pipes, where “1” indicates that the node and conduit at each location are connected, and “0” indicates otherwise. The VLM is a matrix of the same size as the NAM, where “1” indicates the location of a valve installed between a node and the conduit, and “0” indicates otherwise. The VDM represents the locations where a valve is not installed, based on the difference between the NAM and VLM, with “1” indicating the absence of a valve and “0” indicating the presence of a valve. The SIA proceeds as follows. (1) Construct the NAM, VLM, and VDM using the location information of the components constituting the WDS. (2) Save the column number by identifying the locations with a value of “1” in the VDM. (3) Save the row number with a value of “1” by exploring the saved column number in the row direction. (4) Save the column number with a value of “1” by exploring the numbers saved in (3) in the column direction or terminate the exploration if location information is not available. (5) Save the numbers of the saved nodes and pipes as segment components. (6) Set the value of the saved components to “0” to distinguish the explored segments and repeat this process until all the components of the VDM have a value of “0”.

Figure 2 and

Table 1. Components of the identified segments for the example network.

Segment No.	Pipes	Nodes	Damage (CMH)	UI(CMH)
Seg. 1	P1, P2, P4	N1	50	0
Seg. 2	P5, P6	N3, N4	150	150
Seg. 3	P7, P8	N5, N6	150	0
Seg. 4		N2	50	0
Seg. 5	P3		0	0

present the network created to demonstrate the application results of the SIA, where the assumed demands of the node and valve locations are depicted. This network has six nodes connected to a reservoir and four installed valves. Figure 2 is an example to describe the concept of the segment, the unintended isolation, and the derived damage from undelivered water.

In Table 1, the maximum damage from undelivered water caused by vale closing is identified as Segment 2. Segment 2 directly includes Node 3 and Node 4 (150 CMH), and the closing of Valve 3 causes unintentional isolation, leading to damage from undelivered water to Node 5 and Node 6 (150 CMH). This caused the most damage from undelivered water among the segments, comprising a total undelivered water demand of 300 CMH. The maximum damage from undelivered water can be reduced from 300 CMH to 150 CMH by installing an additional valve on Pipe 5.

In this study, large-scale segments were selected to determine the priority of damage reduction. While installing additional shut-off valves at all the nodes is effective in preventing damage spread and minimizing its extent, prioritization is necessary when there are limitations in the installation period and the number of valves that can be installed. Therefore, isolated areas encompassing at least 10% of the total demand in terms of the damage from undelivered water were identified as large-scale segments. Subsequently, an optimal valve location was determined to minimize the damage for segments with the highest damage from undelivered water among the selected segments.

2.2. Segment Division Scenarios Considering Urbanization

This study proposed an optimal segment division technique for valve installation based on different urban development scenarios and installation periods, as depicted in Figure 3. The first scenario, applicable to urban expansion (Scenario 1), involves simultaneously installing multiple valves. This approach is suitable for promptly isolating incident areas caused by abnormal conditions, preventing damage from spreading or becoming prolonged. It is also suitable for planned city development areas that are clearly defined according to their purpose. The second scenario, applicable to planned city construction (Scenario 2), entails sequential valve installation divided into installation periods. It allows for adjusting the number of installable valves based on changes in the budget. This study proposed an optimal segment division technique based on various urban development scenarios. To propose the optimal segment division technique, the objective function considered the maximum damage from undelivered water (direct damage). The reason for consideration of the direct damage is the presence or absence of residence of persons under the scenario. In Scenario 1, residents install a limited number of valves at once for optimal segmentation before inhabiting, so only direct damage is considered. In Scenario 2, as the city expands over time, not only direct damage but also indirect damage (e.g., pressure drop and supply shortage) occurs. Therefore, for a quantitative comparison of the performance of the two scenarios, direct damage was considered as damage from water outage.

2.3. Determination of Optimal Valve Location

The location of additional shut-off valves for segment division was determined using the Harmony Search (HS) algorithm, which was proposed by Geem et al. [17]. The HS is an optimization algorithm that mimics the process of musicians playing various instruments to create a harmonious performance, analogous to finding the optimal solution through iterative calculations. The algorithm involves several key parameters: Harmony Memory Size (HMS), which determines the number of memories that can be saved; Harmony Memory Considering Rate (HMCR), which governs the global search through random or existing memories; and Pitch Adjusting Rate (PAR), which facilitates the local search by adjusting the generated memories. The HS algorithm is executed as follows:

(1)

An initial solution is generated based on the specified HMS.

(2)

The HMCR is applied to the initial solution, resulting in the creation of a new solution.

(3)

The PAR is applied to the new memory, adjusting the solution further.

(4)

The generated memory is compared to the existing memory and evaluated based on whether it minimizes or maximizes the objective function. If necessary, the memory is replaced.

(5)

The algorithm continues until the stopping conditions, such as the maximum number of iterations, are met. The solution that satisfies the constraints and objective function is selected as the optimal solution.

This is a simplified explanation of the HS algorithm and its steps. This algorithm is a metaheuristic optimization method that can be applied to various optimization problems, including determining the optimal location of additional shut-off valves in the context of segment division.

The optimal valve location determination model developed in this study follows the procedure illustrated in Figure 4, using the Harmony Search (HS) algorithm. The following is an overview of the steps involved. (1) Randomly select locations for the number of valves to be installed in the pipes within the previously selected large-scale segments. (2) Calculate the damage from undelivered water for the segments that have been divided by the valves installed at the respective locations. (3) Explore new valve locations using the HMCR or PAR and calculate the damage from undelivered water for the divided segments. (4) If the newly selected valve location results in a greater reduction in damage from undelivered water compared to the previously selected valve location, add it to the list of candidates. (5) In Scenario 1, stop the execution if the optimal location is determined for the set number of valves or within the set number of iterations. In Scenario 2, as the number of valves being installed is divided according to the period, explore a new location if the valve location of the previous year has been selected.

The objective function of the optimization algorithm used in the study is to minimize the maximum damage from undelivered water demand. The damage from undelivered water is calculated as the sum of the segment and unintended isolation demand. Equation (1) shows the objective function for the maximum damage from undelivered water demand.

$$\mathit{Minimize}\mathit{MD}=\sum ({ND}_{si}+{ND}_{uj})$$

(1)

where MD = maximum damage from undelivered water demand, ND_si = i-th nodal demand in segment, and ND_uj = j-th nodal demand in the unintended isolation

In addition, the decision variables in this study are the location and number of the additional valves. Since the valve locations can be installed at the end of both sides of the pipes belonging to the segment, if the number of pipes is 10, the optimal valve location according to the number is selected from a total of 20 valve installation location candidates. The constraints of this study considered the efficiency of the segment divisions (ESDs) to determine the optimal valve location. Generally, the constraints are used with a specific range, such as thresholds. However, ESDs are not applied as constraints with specific thresholds. Thus, the penalty points according to whether the constraints are satisfied are not applied. Choi et al. [9] reported that the damage from undelivered water can be reduced by up to 50% by installing additional valves. In optimal segment division through the addition of a shut-off valve, the valve position should be selected to maximize ESDs and minimize the maximum damage from undelivered water that occurs in the segment simultaneously. ESDs mean the ratio of maximum damage reduced after segmentation to the maximum damage from undelivered water, as shown in Equation (2).

$$E{SD}_s=\frac{({MD}_{b.}-{Std.\_D}_{a.})}{{MD}_{b.}}\times 100(\mathrm{\%})$$

(2)

where ESDs = efficiency of the segment divisions, MD_b. = maximum damage from the undelivered water demand before the segment division, and Std._D_a. = standard deviation of the damage after the segment division

ESDs are considered as a constraint for post-processing when the fitness value (minimize the maximum damage from undelivered water) is the same. Figure 5 shows an example of how ESDs are applied as a constraint.

In Figure 5, there are four Harmony Memory (HM) and four fitness values. Among the fitness values (maximum damage from undelivered water) according to the HM, the fitness for 1–3 is the same at 400 CMH. In this case, the maximum damage from the undelivered water demand for HM 1–3 is the same at 400 CMH, although the undelivered water demand for the other segments varies. Therefore, the superiority among these solutions is same if it is considered only the objective function. Thus, this study performed the post-processing (i.e., considering the maximum ESDs) to derive a superior solution from among the same fitness. Through using ESDs as the post-processing, the 1st solution with the highest ESDs value (92%) can achieve excellent performance in both aspects: minimizing the maximum damage from undelivered water demand and the equitable segment division aspect.

3. Application and Results

In this study, an optimal segment division technique was proposed to minimize the damage from undelivered water in water distribution systems (WDSs) under abnormal conditions. The technique was evaluated using two real-world networks: Hanoi network [18] and J-city network. By applying the proposed technique to these networks, the performance and applicability of the technique were assessed based on a comparison of the results obtained for different scenarios of urban development. The results of the study provide insights into the effectiveness of the optimal segment division technique in mitigating the damage from undelivered water under various urban development scenarios. The comparison of the results helps understand the impacts of different development plans on the performance of the WDSs and the effectiveness of the proposed technique in minimizing the damage.

3.1. Description of Study Networks

In this study, the proposed optimal segment division technique was applied to both the Hanoi network (Figure 6) and J-city network (Figure 7), which represent real-world water distribution systems. The networks have different characteristics in terms of the number of pipes, flow supply, nodes, and shut-off valve installations. For the Hanoi network, which consists of 34 pipes, 19,194 CMH of flow is supplied to 31 nodes from 1 reservoir. The original Hanoi network has no located valve. However, in order to verify the proposed methodology, the initial valve locations were randomly set, and the derived initial valve locations were used as the initial solution for both scenarios. Using the proposed technique, four large-scale segments were selected from among the seven segments based on the assessment of the potential damage from undelivered water. On the other hand, the J-city network is more complex, with 327 pipes supplying 38,564 CMD of flow to 277 nodes from one reservoir. In addition, since J-city is the real-world WDS, the location of the actually installed shut-off valve was set as the initial solution. In this network, a total of 72 initial valves were installed. In this case, the selection of the large-scale segment was based on the need for future additional shut-off valves due to the anticipated population growth and increased water supply demand in the planned city development region. For the parameters of the HS, this study performed a sensitivity analysis of parameters such as the HMCR and PAR. Since, the HMCR and PAR are probability values, the HMCR was varied from 0.7 to 0.95 and the PAR was varied from 0.05 to 0.3 at 0.05 intervals. Using these parameters set, the sensitivity analysis was performed 20 times independently and found the best parameters set and applied. By applying the proposed technique to these networks, this study aimed to evaluate the performance and applicability of the technique in mitigating damage from undelivered water under different urban development scenarios.

3.1.1. Benchmark Network: Hanoi Network

In this study, two methodologies were suggested based on different urban development scenarios to compare the application results of the proposed optimal segment division technique. Figure 8 shows the application results of the methodology in the context of urban development in Hanoi network. The number of additional shut-off valves was set as 10, and the division results of the top 3 segments were derived for analysis.

In Scenario 1, the valves were installed sequentially, one at a time, to evaluate the changes in the damage from undelivered water as the number of valves increased. The results showed that installing two valves in Seg. 1, which had the highest damage from undelivered water, resulted in the highest damage reduction rate of 18%. The damage from undelivered water decreased as more valves were installed, and the lowest damage reduction effect of 5 CMH was observed when all 10 additional shut-off valves were installed. However, installing 9 shut-off valves resulted in a damage reduction effect of 9% (1865 CMH), satisfying the stopping conditions of the proposed technique.

In Scenario 2, the installation period was set to five years, and the changes in the damage from undelivered water were examined as the number of valves increased each year. The number of installed valves each year was randomly set. For the Hanoi network, the results in the first year were the same as those in Scenario 1 since the valve location was identical. As the number of valves increased, installing all 10 additional valves led to maximum damage from undelivered water of 15% (2935 CMH) of the total demand, which was 6% higher than the final result in Scenario 1 (9%, 1860 CMH). In Scenario 2, the optimal valve location was explored considering the valves installed in the previous year, resulting in different valve locations compared to Scenario 1. However, the number of installed valves in the large-scale segments matched between the two scenarios (Seg. 1: 6 valves, Seg. 2 and 3: 1 valve). These comparisons highlight the effectiveness of the proposed optimal segment division technique in reducing the damage from undelivered water under different urban development scenarios.

3.1.2. Real-World Network: J-City Network

The proposed technique was initially applied to the Hanoi network, but due to its limited components, such as nodes, pipes, and valves, the results were not as diverse. To provide a more comprehensive analysis, the proposed technique was then applied to the J-city network, which has a more complex structure and represents an actual drainage pipe network. For the J-city network, Figure 9 showed that installing 1 additional shut-off valve resulted in the highest reduction rate, reducing the damage from undelivered water from 32% (12,201 CMD) to 20% (7651 CMD). Interestingly, installing six or eight additional shut-off valves produced the same damage reduction results as installing five or seven additional shut-off valves, respectively. This observation can be attributed to the intricate nature of the J-city network, which requires additional valves to effectively divide the segments. In the J-city network, the existing 4 large-scale segments were divided into 13 segments, and a total of 10 valves were installed over a 5-year period using Scenario 2. The number of valves installed each year was randomly determined. In the first year, one additional shut-off valve was installed, which yielded the same result as in Scenario 1, with a 25% reduction in damage. However, as the number of valves increased, a 17% reduction rate (6507 CMD) was achieved, which was 5% higher than the result of installing 10 additional shut-off valves in Scenario 1 (9%, 3764 CMD). This difference can be attributed to the exploration of the optimal valve locations in Scenario 2, considering the locations of existing valves when dividing the large-scale segments. The application of the proposed technique to the J-city network demonstrates its effectiveness in minimizing the damage from undelivered water under various urban development scenarios. The results highlight the importance of considering the network’s complexity and the number of valves required for effective segment division.

4. Conclusions

In this study, an optimal segment division technique was proposed to minimize the damage from undelivered water and reinforce water distribution systems (WDSs) under various scenarios of urban development. The technique involved quantitatively calculating the damage from undelivered water in isolated areas through the segment isolation analysis (SIA) and selecting large-scale segments exceeding 10% of the total demand as priorities for valve locations. The optimal valve location was determined using the Harmony Search (HS) algorithm, considering the minimization of the maximum damage from undelivered water. Constraints such as ESDs were imposed to deduce the maximum segment division results. The proposed technique was applied to the Hanoi network and the J-city network, considering different urban development scenarios. Scenario 1 involved simultaneously installing the installable valves, while Scenario 2 involved sequentially installing valves by year. In the Hanoi network, the application of Scenario 1 with nine additional shut-off valves resulted in maximum damage from undelivered water of 9% (1860 CMH), satisfying the stopping conditions. However, in Scenario 2 with varying the number of installed valves over a five-year period, the maximum damage from undelivered water reached 15% (2935 CMH), which was 6% higher than in Scenario 1. Similarly, in the J-city network, Scenario 1 with 10 additional shut-off valves resulted in a maximum damage from undelivered water of 9% (3764 CMD), satisfying the stopping conditions. In contrast, Scenario 2 yielded a maximum damage from undelivered water of 17% (6507 CMD), which was 6% higher than in Scenario 1.

From the above analysis of the failure to satisfy the stopping conditions under the same number of valves, it was observed that Scenario 1 explored the optimal location by resetting the valve location as the number of installable valves increased. In contrast, Scenario 2 explored the optimal valve location by considering the location determined in the previous year. Although Scenario 2 did not yield better results than Scenario 1, it provided more flexibility in taking actions based on the available budget during WDS improvement projects. Decision-makers can choose between the two scenarios based on their advantages and disadvantages.

To improve the performance of the optimal segment division technique, future studies should conduct further research to set different ratios for selecting large-scale segments based on the network size. Additionally, improvements can be made by appropriately selecting the optimal valve location based on factors such as the extent of the damage from undelivered water, minimum valve installation cost, and the probability of pipe breakage due to deterioration, considering the input from field technicians and the demands of the WDS facility maintenance manager. Indirect damage due to the pressure drop caused by water outage will be quantified using pressure-driven analysis, and a model that can be considered simultaneously with direct damage will be developed. These improvements can help minimize the damage from undelivered water caused by natural disasters and inadequate decision-making in WDS management.