scholarly journals A Novel Graph-Based Vulnerability Metric in Urban Network Infrastructures: The Case of Water Distribution Networks

Water ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1502
Author(s):  
Andrea Ponti ◽  
Antonio Candelieri ◽  
Ilaria Giordani ◽  
Francesco Archetti
Keyword(s):  
Water Distribution ◽  
Transport Theory ◽  
Optimal Transport ◽  
Probability Distributions ◽  
Distribution Networks ◽  
Power Grids ◽  
Water Distribution Networks ◽  
Urban Network ◽  
Input Space ◽  
Optimal Transport Theory

The key contribution of this paper is to embed the analysis of the network in a framework based on a mapping from the input space whose elements are nodes of a graph or the entire graph into an information space whose elements are probability distributions associated to objects in the input space. Specifically, a node is associated to the probability distribution of its node-to-node distances and the whole graph to the aggregation of these node distributions. In this space two distances are proposed for this analysis: Jensen-Shannon and Wasserstein, based respectively on information theory and optimal transport theory. This representation allows to compute the distance between the original network and the one obtained by the removal of nodes or edges and use this distance as an index of the increase in vulnerability induced by the removal. In this way a new characterization of vulnerability is obtained. This new index has been tested in two real-world water distribution networks. The results obtained are discussed along those which relate vulnerability to the loss of efficiency and those given by the analysis of the spectra of the adjacency and Laplacian matrices of the network. The models and algorithms considered in this paper have been integrated into an analytics framework which can also support the analysis of other networked infrastructures among which power grids, gas distribution, and transit networks are included.

scholarly journals Probabilistic measures of edge criticality in graphs: a study in water distribution networks

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Andrea Ponti ◽  
Antonio Candelieri ◽  
Ilaria Giordani ◽  
Francesco Archetti
Keyword(s):  
Water Distribution ◽  
Transport Theory ◽  
Optimal Transport ◽  
Probability Distributions ◽  
Distribution Networks ◽  
Power Grids ◽  
Water Distribution Networks ◽  
Centrality Measures ◽  
Optimal Transport Theory ◽  
Critical Components

AbstractThe issue of vulnerability and robustness in networks have been addressed by several methods. The goal is to identify which are the critical components (i.e., nodes/edges) whose failure impairs the functioning of the network and how much this impacts the ensuing increase in vulnerability. In this paper we consider the drop in the network robustness as measured by the increase in vulnerability of the perturbed network and compare it with the original one. Traditional robustness metrics are based on centrality measures, the loss of efficiency and spectral analysis. The approach proposed in this paper sees the graph as a set of probability distributions and computes, specifically the probability distribution of its node to node distances and computes an index of vulnerability through the distance between the node-to-node distributions associated to original network and the one obtained by the removal of nodes and edges. Two such distances are proposed for this analysis: Jensen–Shannon and Wasserstein, based respectively on information theory and optimal transport theory, which are shown to offer a different characterization of vulnerability. Extensive computational results, including two real-world water distribution networks, are reported comparing the new approach to the traditional metrics. This modelling and algorithmic framework can also support the analysis of other networked infrastructures among which power grids, gas distribution and transit networks.

Vulnerability and robustness of networked infrastructures: beyond typical graph-based measures

2021 ◽  
Author(s):  
Andrea Ponti ◽  
Antonio Candelieri ◽  
Francesco Archetti
Keyword(s):  
Probability Distribution ◽  
Water Distribution ◽  
Probability Distributions ◽  
Linear Optimization ◽  
Minimum Energy ◽  
Real Life ◽  
Distribution Networks ◽  
Wasserstein Distance ◽  
Water Distribution Networks ◽  
Wasserstein Distances

<p>The issue of vulnerability and robustness in networked systems can be addressed by several methods. The most widely used are based on a set of centrality and connectivity measures from network theory which basically relate vulnerability to the loss of efficiency caused by the removal of some nodes and edges. Another related view is given by the analysis of the spectra of the adjacency and Laplacian matrices of the graph associated to the networked system.</p><p>The main contribution of this paper is the introduction of a new set of vulnerability metrics given by the distance between the probability distribution of node-node distances between the original network and that resulting from the removal of nodes/edges. Two such probabilistic measures have been analysed: Jensen-Shannon (JS) divergence and Wasserstein (WST) distance, aka the Earth-Mover distance: this name comes from its informal interpretation as the minimum energy cost of moving and transforming a pile of dirt in the shape of one probability distribution to the shape of the other distribution. The cost is quantified by the amount of dirt moved times the moving distance. The Wasserstein distance can be traced back to the works of Gaspard Monge in 1761 and Lev Kantorovich in 1942. Wasserstein distances are generally well defined and provide an interpretable distance metric between distributions. Computing Wasserstein distances requires in general the solution of a constrained linear optimization problem which is, when the support of the probability distributions is multidimensional, very large.</p><p>An advantage of the Wasserstein distance is that, under quite general conditions, it is a differentiable function of the parameters of the distributions which makes possible its use to assess the sensitivity of the network robustness to distributional perturbations. The computational results related to two real-life water distribution networks confirm that the value of the distances JS and WST is strongly related to the criticality of the removed edges. Both are more discriminating, at least for water distribution networks, than efficiency-based and spectral measures. A general methodological scheme has been developed connecting different modelling and computational elements, concepts and analysis tools, to create an analysis framework suitable for analysing robustness. This modelling and algorithmic framework can also support the analysis of other networked infrastructures among which power grids, gas distribution and transit networks.</p>

scholarly journals Leak localization in water distribution networks using classifiers with cosenoidal features

2020 ◽  
Vol 53 (2) ◽  
pp. 16697-16702
Author(s):  
I. Santos-Ruiz ◽  
J. Blesa ◽  
V. Puig ◽  
F.R. López-Estrada
Keyword(s):  
Water Distribution ◽  
Distribution Networks ◽  
Water Distribution Networks ◽  
Leak Localization

scholarly journals Bottom-Up Generation of Peak Demand Scenarios in Water Distribution Networks

2020 ◽  
Vol 13 (1) ◽  
pp. 31
Author(s):  
Enrico Creaco ◽  
Giacomo Galuppini ◽  
Alberto Campisano ◽  
Marco Franchini
Keyword(s):  
Water Distribution ◽  
Distribution Networks ◽  
Water Distribution Networks ◽  
Peak Demand ◽  
Long Time ◽  
Cross Correlations ◽  
User Demand ◽  
One Year ◽  
The One ◽  
Best Fit

This paper presents a two-step methodology for the stochastic generation of snapshot peak demand scenarios in water distribution networks (WDNs), each of which is based on a single combination of demand values at WDN nodes. The methodology describes the hourly demand at both nodal and WDN scales through a beta probabilistic model, which is flexible enough to suit both small and large demand aggregations in terms of mean, standard deviation, and skewness. The first step of the methodology enables generating separately the peak demand samples at WDN nodes. Then, in the second step, the nodal demand samples are consistently reordered to build snapshot demand scenarios for the WDN, while respecting the rank cross-correlations at lag 0. The applications concerned the one-year long dataset of about 1000 user demand values from the district of Soccavo, Naples (Italy). Best-fit scaling equations were constructed to express the main statistics of peak demand as a function of the average demand value on a long-time horizon, i.e., one year. The results of applications to four case studies proved the methodology effective and robust for various numbers and sizes of users.

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