Complex Networks Theory for Evaluating Scaling Laws and WDS Vulnerability for Potential Contamination Events

Abstract

In the last few years, water utilities have recognized the importance of evaluating the safety of water distribution networks from the potential risks of contamination, arising from failures or from intentional (targeted) or random attacks. Research literature has been recently focused on the optimal design of efficient detection systems, generally expressed as the problem of the optimal placement of monitoring sensors. In this paper, we introduce a methodology for calculating an index of vulnerability that represents the tendency of an injected contaminant to spread over the network. Epanet quality simulations are performed in order to determine the distribution function of the number of potentially contaminated nodes. The results show how such distribution is overall fitted by a stretched exponential law. The comparison with an auto-similar, tree-like network (described by a power-law) allows the determination of the Vulnerability Index, which quantifies how “far” the behavior of a given system deviates from pure scale-freeness. It is analytically calculated by a two-fold approximation of the stretched exponential and provides an alternative way of evaluating robustness against random water contamination. Different networks can then be directly compared, in order to assess and prioritize control measures and interventions.

Evaluation of the vulnerability in water distribution systems through targeted attacks

“…More recently, a methodology for calculating an index of vulnerability that represents the tendency of an injected contaminant to spread over the network was introduced, this index compares the behavior of the network to a scale-free network and allows to rank different networks in terms of their resistance to contamination (Nicolini 2020). Mortula et al conducted an integrated network and hydraulic analysis for identifying critical nodes that can be impacted by water shortages and proposing managerial action to reduce network vulnerability, diversify water sources, and reduce possibilities of contamination (Mortula et al 2020).…”

Urban Water Management: A Pragmatic Approach

“…This special issue consists of 10 papers that cover a wide range of research topics related to urban water systems. The specific topics include (Figure 1): operating procedure [4], system failure [5,6], water quality [7][8][9], capacity [10], demand [11,12], and energy and climate [13].…”

“…In Nicolini [6], a complex networks theory-based methodology for evaluating a synthetic vulnerability index for comparing the robustness of different WDNs with regard to the number of nodes where a contaminant could be accidentally injected is proposed. In the paper the possible causes of the contamination events are pointed out: transients giving rise to negative pressure, and rehabilitation work requiring the temporary isolation and emptying of a certain number of pipes.…”