Three methodologies were considered to improve WDSs robustness through optimal valve installation: (1) the segment finding algorithm, (2) the critical segment selection technique and (3) the determination of valve locations.
The segment finding algorithm can identify the segment as well as unintentional isolation. To replace the previous technique used for selecting the segments to be divided, a multicriteria decision technique that considers hydraulic, social and socio-economic criteria is used to evaluate the critical segment selection technique. In this chapter, a new valve location determination technique to ensure reinforcement, that could replace an engineer’s experience when deciding an additional valve installation location to improve the segment’s robustness, is proposed. This technique analyzes pipe and valve failures to determine the optimal valve location.
2.1. Valve Location Determination to Improve System Robustness
Regionalizing the WDSs while considering the segment concept is a core approach for constructing robust WDSs and efficient management. Therefore, more efficient and robust construction techniques are needed than the approach that uses engineers’ experience to optimize the segmentation of the WDSs.
This study proposes a framework of the optimal valve installation approach for robust water distribution network segmentation. This technique uses basic valve location information to identify all segments of the WDSs and organize pipe and node lists included within them. The importance of each segment is then quantified considering hydraulic, social and socio-economic factors and the weight of each factor is then calculated. The priority of the segment is determined by the weighted utopian approach, applying various system factors with different weights. Finally, the optimal valve position is determined considering the probability pipe and valve failure. The procedure can be detailed as follows.
Step 1: Data collection
Data that can quantify the segment’s importance (EPANET input file, location of the valve, demand data, location of important facilities, the number of water users, the type of residence) are collected.
Step 2: Segment identification
The segments in the whole WDSs are identified using the segment identification algorithm and the nodes, pipes and valves in each segment are listed.
Step 3: Weight calculation
The weights of each factor are calculated using the data collected in step 1 (data that quantify the attributes for multicriteria decision-making) and the expected damage of each segment during system failure is quantified.
Step 4: Prioritization of each segment
The weighted utopian approach is applied to determine segment priority and the highest priority segment to be divided is selected. In this case, each factor’s weight, which was calculated in step 3, is applied to each segment.
shows a model for determining segment priority for division. The model regards factors related to segment importance as (1) hydraulic, (2) social and (3) socio-economic importance. Before determining the weights of each factor in the model, a questionnaire survey analysis is conducted to evaluate the relative importance and the targets are experts in the WDSs field.
(1) Hydraulic importance: The WDSs are complex and interacts with various hydraulic components, such as pipes, nodes, valves and sources. It can determine priority according to the properties of the hydraulic components within the segment. In this model, three criteria are considered: undelivered demand (the number of water users), increasing head loss to isolate the segment and the number of valves required to isolate the segment.
(2) Social importance: The WDSs are inseparable from social activities and social importance factors, such as important facilities including government offices and medical facilities, composition of ages, restoration infrastructure (equipment, workforce, system) and secondary damage caused by restoration (traffic congestion, blackout, communication damage) can be criteria for judging importance.
(3) Socio-economic importance: Economic activity is closely related to water supply. In this model, we consider two factors, the average income level and the characteristics of the water user (residential, commercial and industrial districts as criteria for determining the economic importance of the segment).
Step 5: Search for optimal valve location
Finally, the optimal valve locations and the number of additional valves are determined. This process starts with the highest priority segment identified in Step 4. The candidate valve locations are set based on engineering knowledge from among all potential locations. In the installable location candidates, the additional valve is installed and the performance of the segmented segments (i.e., the number of water user, undelivered demand) is evaluated. The number of additional valves is determined simultaneously with the selection of the valve locations. First, the relationship between the number of additional valves and the maximum damage under pipe failure situations is determined as shown in Figure 2
. Then, the proper number of additional valves is determined from a marginal effect analysis using Figure 2
that yield optimal efficiency with additional valve installation. The determined number of valves can increase or decrease depending on the additional requirements of the decision maker.
To evaluate the efficiency of the additional valve, Monte Carlo simulation is conducted considering the valve operation success ratio and pipe failure analysis. The valve operation ratio indicates the probability that a valve operates successfully when the valve is closed due to pipe failure. At that time, if a valve fails and cannot be closed, the segment will be expanded up to the neighboring valves successfully closed. For example, if pipe 6 fails, valves 1 and 2 are closed to isolate pipe 3, pipe 6 and node 6. However, if valve 2 malfunctions as indicated in Figure 3
, the segment is expanded to cover pipe 3, pipe 6, pipe 8, node 4, node 5 and node 6, increasing the undelivered demand. Therefore, the valve operating rate is considered in this chapter because this factor can be used to evaluate reasonably the damage in the present WDSs.
2.2. Segment Identification Algorithm
The segment finding algorithm was developed by Jun et al. [14
] and introduced three matrices (i.e., the node-arc, valve location and valve deficiency matrices) to identify a segment based on valve location in WDSs. These three matrices have the same configuration, in which a row represents a node and a column represents a pipe. Figure 4
presents an example of segment identification.
The node-arc matrix shows the relationship between the nodes and pipes that constitute the WDSs. If there are nodes corresponding to both ends of the pipe, the value is 1; if not, the value is 0. Table 2
(a) is an example of a node-arc matrix.
Valve Location Matrix
The valve location matrix indicates the position of the drain valve. If the valve is located at one end nodes of the pipe, the value is 1; if not, the value is 0. Table 2
(b) is an example of a valve location matrix.
Valve Deficiency Matrix
The valve deficiency matrix is composed of the difference between the node-arc and valve location matrices and indicates points with and without installed valves. A matrix value of “1” indicates that no valve is installed at that point, while “0” indicates that there is a valve. An example of a valve deficiency matrix is presented in Table 2
(c). The segment finding algorithm is based on the valve deficiency matrix and repeats row and column searches to identify all the segments of the WDSs. To understand the segment search process, the following is an explanation of the identification process of Seg. 1. First, a column search is performed on P3 in the matrix to find “1.” At this time, a value of “1” is found at point (N2, P3). A row search is then performed on N2 to find “1.” As a result of the row search, “1” is found at P5. As P5 is found on the N2 row, rather than P3, a column search is performed for P5. After the column search, “1” is not found in row P5; therefore, the search process is finished. The segment identification then shows that N2 is within Seg. 1 after the column search and P3 and P5 are included in Seg. 1 as a result of the row search. Therefore, Seg. 1 is composed of P3, P5 and N2. The segment can be found based on the pipe in a similar manner. If all columns and rows in the valve deficiency matrix are “0”, the pipe or node can be identified as an independent segment.
As a follow-up to the segment search algorithm, Jun et al. [14
] proposed an optimal segment design technique for WDSs. This technique automated segment and unintentional isolation identification; it can be applied to large-scale WDSs and suggests an efficient method of segmenting one that is over-designed. However, when selecting segments to be divided, only the population is considered and the optimal valve location is selected based on the experience of the engineer, not by a mathematical algorithm.
Therefore, this study proposes a new criterion for evaluating segment importance, as well as the number of water users and a multicriteria decision technique is used to prioritize segments that should be divided.
Multicriteria decision techniques can determine the priorities of the segments that need to be divided and a new valve location determination technique is proposed that could replace the engineer’s experience when the additional valve installation location for the highest priority segment is decided.
2.3. Critical Segment Selection Technique
In the existing optimal valve location determination technique, only the number of water users is considered when selecting the segment to be divided. This makes the selection process more efficient. Moreover, the selection of the valve location for optimal segmentation is based on the experience of the engineer, rather than a quantitative approach using a mathematical algorithm.
However, as WDSs performance and behavior is closely related to social and economic activities, the segments to be reinforced should be selected considering various criteria, including social and economic aspects as well as hydraulic.
Therefore, in this section, the segment to be divided by installing more valves is determined considering several criteria, including social, socio-economic and hydraulic factors, using multicriteria decision-making techniques. The multicriteria decision-making model applied in this study is the weighted utopian approach [15
] that combines a weighting method and multi-criteria decision-making.
2.3.1. Weighted Utopian Approach
Decision problems are prioritized according to comparisons between alternatives (i.e., the diversity of alternatives, the evaluation criteria of the decision maker, or the objective of the decision) and the best alternative is then selected. When considering various decision factors, most cases have a trade-off relationship. Therefore, a compromise need to be presented that meets both conflicting standards.
When making decisions, the weight of each factor cannot be the same and the most important factor in decision-making is the method by which the weight that represents the relative importance among those factors is determined. However, the utopian approach proposed by Xanthopulos et al. [16
] assumed that the weight of each factor is the same; therefore, it cannot reflect realistic decision-making and risks the production of results different from reality. To overcome the limitations of the existing utopian approach, Yoo et al. [15
] proposed a weighted utopian approach that combines weight determination techniques with the utopian approach. As the weighted utopian approach can simultaneously consider various weighting methods, it can not only identify a reasonable alternative but also allow flexible coping by broadening the choice of alternatives according to the situation.
If there are two factors (F1 and F2) used for decision-making, the alternative factor can be expressed as Figure 5
a by normalizing the two factors to values between 0 and 1. In this case, the weight of each factor has the same value and the coordinate of the utopian point is (1, 1). However, after calculating the weights of F1 and F2 following various weighting determination approaches, the weighted coordinate is that shown in Figure 5
b. For example, when the weights of F1 and F2 are 0.6 and 0.4, respectively, the coordinates of the utopian point are (0.6, 0.4). The Euclidean distance is commonly used to determine the distance between a utopian point and an alternative and the formula to calculate it is shown in Figure 5
b. The priority of the alternatives is determined in the order of the shortest Euclidean distance.
2.3.2. Determination Weight Factor Approaches
The most important task in decision-making and prioritization is the determination of each factor’s weight, which represents the relative importance of different factors.
Many previous studies [17
] have calculated the relative weights of each factor using the multicriteria decision-making technique. This study applies seven of these approaches (Table 3
) to calculate relative weight in multicriteria decision-making.