Abstract
This paper compares two different representations (primal-mapping and dual-mapping) and applies a range of topological metrics to analysis the vulnerability of an urban drainage network (UDN) against structural failures, which is examined in the Elster Creek catchment. Based on the node degree distribution, the properties of the dual graph are similar to a scale-free network while the primal graph behaves like a random network. Further, the results show that the structure of the dual graph has better connectivity and redundancy compared to the structure of the primal graph. To identify vulnerabilities this paper test’s a new centrality metrics, that modifies betweenness centrality based on the UDN’s performance. This new metric ranks the most vulnerable conduit in the UDN. To validate the ranking a hydrodynamic model is used as a reference. The results show the significance of the structural metric in identifying critical components of the UDN and suggest a dual representation is an appropriate method for investigating vulnerabilities of an UDN against structural failures.
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Notes
- 1.
\( p_{k} \approx k^{ - \gamma } \).
- 2.
\( p_{k} = \left( {\begin{array}{*{20}c} {N - 1} \\ k \\ \end{array} } \right)p^{k} \left( {1 - p} \right)^{N - 1 - k} \).
- 3.
\( p_{k} = e^{ - \left\langle k \right\rangle } \frac{{\left\langle k \right\rangle^{k} }}{k!} \).
- 4.
\( UDNBC^{'} = \frac{{UDNBC - UDNBC_{min} }}{{UDNBC_{max} - UDNBC_{min } }} \).
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The Australian Government, Department of Education and Training - Research Training Program (RTP) funded this work.
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Hajiamoosha, P., Urich, C. (2020). A Network Theoretical Approach to Identify Vulnerabilities of Urban Drainage Networks Against Structural Failures. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 882. Springer, Cham. https://doi.org/10.1007/978-3-030-36683-4_73
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