Planners and engineers attempting to improve the resilience of water distribution systems face numerous challenges regarding the allocation and placement of redundancy so as to reduce the likelihood and impact of asset failures and take into consideration the growing demand for clean water, now and into the future. Water distribution systems may be represented as networks of multiple nodes (e.g. reservoirs, storage tanks and hydraulic junctions) interconnected by physical links (e.g. pipes) where the connectivity patterns of this network affects its reliability, efficiency and robustness to failures. In this paper we employ the link-node representation of water infrastructures and exploit a wide range of advanced and emerging network theory metrics and measurements to study the building blocks of the systems and quantify properties such as redundancy and fault tolerance, in order to establish relationships between structural features and performance of water distribution systems. We study the water distribution network of a growing city from a developing country and explore network expansion strategies that are aimed to secure and promote structural invulnerability, subject to design and budget constraints.

Resilience enhancing expansion strategies for water distribution systems: A network theory approach

This paper explores a variety of strategies for understanding the formation, structure, efficiency and vulnerability of water distribution networks. Water supply systems are studied as spatially organized networks for which the practical applications of abstract evaluation methods are critically evaluated. Empirical data from benchmark networks are used to study the interplay between network structure and operational efficiency, reliability and robustness. Structural measurements are undertaken to quantify properties such as redundancy and optimal-connectivity, herein proposed as constraints in network design optimization problems. The role of the supply-demand structure towards system efficiency is studied and an assessment of the vulnerability to failures based on the disconnection of nodes from the source(s) is undertaken. The absence of conventional degree-based hubs (observed through uncorrelated non-heterogeneous sparse topologies) prompts an alternative approach to studying structural vulnerability based on the identification of network cut-sets and optimal connectivity invariants. A discussion on the scope, limitations and possible future directions of this research is provided.

Complex network analysis of water distribution systems

This paper explores a variety of strategies for understanding the formation, structure, efficiency, and vulnerability of water distribution networks. Water supply systems are studied as spatially organized networks for which the practical applications of abstract evaluation methods are critically evaluated. Empirical data from benchmark networks are used to study the interplay between network structure and operational efficiency, reliability, and robustness. Structural measurements are undertaken to quantify properties such as redundancy and optimal-connectivity, herein proposed as constraints in network design optimization problems. The role of the supply demand structure toward system efficiency is studied, and an assessment of the vulnerability to failures based on the disconnection of nodes from the source(s) is undertaken. The absence of conventional degree-based hubs (observed through uncorrelated nonheterogeneous sparse topologies) prompts an alternative approach to studying structural vulnerability based on the identification of network cut-sets and optimal-connectivity invariants. A discussion on the scope, limitations, and possible future directions of this research is provided.

A water distribution system, represented as a spatially organized graph, is a complex network of multiple interconnected nodes and links. The overall robustness of such a system, in addition to the reliability of individual components, depends on the underlying network structure. This paper presents a deterministic network-based approach to study the relationship between the structure and function of water distribution systems and to critically review the application of structural measurements in the analysis of vulnerability and robustness of such systems. Benchmark water supply networks are studied, and their level of resistance to random failures and targeted attacks on their bridges and cut-sets are explored. Qualitative concepts such as redundancy, optimal connectivity, and structural robustness are quantified. Among other measurements, two metrics of meshedness coefficient and algebraic connectivity are found of great use toward quantifying redundancy and optimal connectivity, respectively. A brief ...

Applying Network Theory to Quantify the Redundancy and Structural Robustness of Water Distribution Systems

The management of existing water supply networks can be substantially improved by permanent water district metering (WDM) which is one of the most efficient techniques for water loss detection and pressure management. However, WDM may compromise water system performance, since some pipes are usually closed to delimit districts in order not to have too many metering stations, to decrease costs and simplify water balance. This may reduce the reliability of the whole system and not guarantee the delivery of water at the different network nodes. In practical applications, the design of district meter areas (DMAs) is generally based on empirical approaches or on limited field experiences. In this work a design support methodology (DSM) is proposed, which helps to identify the position of flow meters and of boundary valves needed to define permanent DMAs. The DSM is based on graph theory and is applied to a test case.

A heuristic design support methodology based on graph theory for district metering of water supply networks

An integer goal programming based approach to maximize reliability in water distribution networks is developed. Previous work has shown that graphs which are inherently the most invulnerable to failure have the same number of links incident at each node, i.e. they are regular in degree. The converse of this statement is not true. Regular graphs can contain weaknesses such as bridges, articulation nodes, and even total disconnections. The integer goal programming formulation in this paper is combined with a procedure which recognizes both explicit and implicit articulation points within the water distribution network to ensure that such weaknesses are excluded from the final solution. The integer program component of the approach attempts to maximize regularity within the network. In the goal programming context this is achieved by minimizing the sum of the deviations, at each node, in terms of the number of links incident upon it, from the average number of links incident on a node over the whole...

P. Jacobs

Papers

Optimization of redundancy in water distribution networks using graph theoretic principles