This paper presents a comparative analysis of three partitioning methods, including Fast Greedy, Random Walk, and Metis, which are commonly used to establish the district metered areas (DMAs) in water distribution systems. The performance of the partitioning methods is compared using a spectrum of evaluation indicators, including modularity, conductance, density, expansion, cuts, and communication volume, which measure different topological characteristics of the complex network. A complex water distribution network EXNET is used for comparison considering two cases, i.e., unweighted and weighted edges, where the weights are represented by the demands. The results obtained from the case study network show that the Fast Greedy has a good overall performance. Random Walk can obtain the relative small cut edges, but severely sacrifice the balance of the partitions, in particular when the number of partitions is small. The Metis method has good performance on balancing the size of the clusters. The Fast Greedy method is more effective in the weighted graph partitioning. This study provides an insight for the application of the topology-based partitioning methods to establish district metered areas in a water distribution network.Recent research has focused on the development of topology-based partitioning methods (e.g., graph theory, Metis, and Random Walk) to consider more network attributes. Most recently, Perelman et al. [3] developed a network partitioning approach from a practical perspective, in which the distribution network is partitioned based on the backbone transmission pipes identified in the first step. The Metis partitioning method [11] was used to divide the network topology into DMAs. Moreover, the water sources should be regarded as the main control elements for network partitioning [12] so that the source supply areas have the least influence on the hydraulic performance of the isolated zones and the finer communities are further divided by a graph partitioning method. Wright et al. [13] introduced the concept of dynamically-controlled DMAs for burst identification and leakage estimation, and it can be used to improve system resilience to permanent valve closures. The Walktrap algorithm, which is also referred to as Random Walk [14,15], was used to trap the walker in the dense cluster, and partition the water distribution network accordingly [16]. The aforementioned studies are the straightforward applications to network partitioning, however, the mechanism, characteristic, and applicability of the graphical partitioning methods (i.e., Metis, Random Walk) are not properly addressed. Moreover, there is no comprehensive comparison of the various topology partitioning algorithms and, therefore, it is difficult to determine which algorithm is more suitable and, thus, should be used for WDS partitioning in practice.Network partitioning can be assessed using hydraulic indicators and topological indicators. Additionally, economic criteria can also be used to consider the costs and benefits involved by the...

Fast detection of pipe burst in water distribution systems (WDSs) could improve customer satisfaction, increase the profits of water supply and more importantly reduce the loss of water resources. Therefore, sensor placement for pipe burst detection in WDSs has been a crucial issue for researchers and practitioners. This paper presents an economic evaluation indicator named as net cost based on cost–benefit analysis to solve the optimal pressure sensor placement problem. The net cost is defined as the sum of the normalized optimal detection uncovering rate and investment cost of sensors. The optimal detection uncovering rate and the optimal set of sensor locations are determined through a single-objective optimization model that maximizes the detection coverage rate under a fixed number of sensors. The optimal number of sensors is then determined by analyzing the relationship between the net cost and the number of sensors. The proposed method is demonstrated to be effective in determining both the optimal number of sensors and their locations on a benchmark network Net3. Moreover, the sensor accuracy and pipe burst flow magnitude are shown to be key uncertainties in determining the optimal number of sensors.

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Resilience has currently attracted increasing interest in the optimization of water distribution systems (WDSs). Most research mainly focuses on optimal design problems. However, the system operation has not been investigated adequately regarding resilience. Therefore, we proposed an integral format of the demand-weighted modified resilience index (IMRI), which can capture the overall resilient performance throughout the operational period. This indicator was incorporated into the multi-objective operation optimization model as one of the objectives. Two benchmark networks were considered as case studies. The resulting Pareto fronts show a clear competing relationship between cost and resilience. Operating conditions in pumps, reservoirs and tanks at each regulation step were characterized by methods of resilience decomposition, which proved valuable intuitively for resilience regulation. A framework for explicit resilience assessment was also developed to examine directly the overall performance in statistics about those optimal solutions obtained. Explicit resilience results show that the IMRI can effectively quantify the resilience of system operation in the temporal dimension. Furthermore, scheduling more pumps, higher trigger-on levels of tanks and a wider range of trigger-level control could yield a more resilient solution to the operation of WDSs.

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