Topological attributes of network resilience: A study in water distribution systems

Abstract

Resilience has been increasingly pursued in the management of water distribution systems (WDSs) such that a system can adapt to and rapidly recover from potential failures in face of a deep uncertain and unpredictable future. Topology has been assumed to have a great impact on resilience of WDSs, and is the basis of many studies on assessing and building resilience. However, this fundamental assumption has not been justified and requires investigation. To address this, a novel framework for mapping between resilience performance and network topological attributes is proposed. It is applied to WDSs here but can be adaptable to other network systems. In the framework, resilience is comprehensively assessed using stress-strain tests which measure system performance on six metrics corresponding to system resistance, absorption and restoration capacities. Six key topological attributes of WDSs (connectivity, efficiency, centrality, diversity, robustness and modularity) are studied by mathematical abstraction of WDSs as graphs and measured by eight statistical metrics in graph theory. The interplay between resilience and topological attributes is revealed by the correlations between their corresponding metrics, based on 85 WDSs with different sizes and topological features. Further, network variants from a single WDS are generated to uncover the value of topological attribute metrics in guiding the extension/rehabilitation design of WDSs towards resilience. Results show that only certain aspects of resilience performance, i.e. spatial and temporal scales of failure impacts, are strongly influenced by some (not all) topological attributes, i.e. network connectivity, efficiency, modularity and centrality. Metrics for describing the topological attributes of WDSs need to be carefully selected; for example, clustering coefficient is found to be weakly correlated with resilience performance compared to other metrics of network connectivity (due to the grid-like structures of WDSs). Topological attribute metrics alone are not sufficient to guide the design of resilient WDSs and key details such as the location of water sources also need to be considered.

Dynamical stability of water distribution networks

“…As supplementary materials of Ref. [18], the full network structure and properties of system components (e.g., pipes, nodal demands, elevations) were made open to the public in the EPANET2 format, except for the one network. For completeness, we have made the complete data for all the networks and their system components used in the present study available in the MATLAB format at Github, alongside the code for calculating the local stability index.…”

“…The eight structural properties of the network that we measured in our previous study [18] and used in the present article for comparison purposes are as follows. The link density is given by 2M/ [N(N − 1)].…”

“…The heterogeneity is that in the degree and given by N i=1 (k i − k ) 2 / k , where k i is the degree of the ith node and k = N i=1 k i /N is the average degree of the node. The version of the spectral gap used in [18] is given by the difference between the two largest eigenvalues of L. The modularity is a quantity representing the quality of community structure detected in the network and approximate modularity maximisation was carried out using Newman's algorithm [47].…”

Review of the Quantitative Resilience Methods in Water Distribution Networks

“…Resilience metrics in network methods are divided into two groups: network connectivity [75,119,121,137,138] and network redundancy [100,104,[139][140][141]. Network connectivity was proposed for dividing DMAs [75,121,137].…”

“…Network connectivity was proposed for dividing DMAs [75,121,137]. The most widely used network-redundancy metrics are the link density and node degree from complex network theory [104,[140][141][142][143], which focus on the network topology. Yazdani et al [139] expressed the pressure and flow requirements in WDNs using the demand-based node degree.…”