Integrating Topological and Hydraulic Attributes for Robustness Analysis of Water Distribution Networks

Researchers are recognizing that the robustness evaluation of Water Distribution Networks (WDNs) is of great importance for reducing the impact of disruptive events. Yet, very few methods to measure the robustness of WDNs have been developed. These methods mainly focus on either the topological features or the hydraulic attributes of WDNs and fail to provide a comprehensive picture of the robustness characteristics of WDNs. The work described herein proposes a new robustness index to measure the heterogeneity of WDNs drawing on informational entropy theory. The paper attempts to shift away from an exclusive topological viewpoint or a pure hydraulic approach, towards a combined topological and hydraulic analysis. The main emphasis is on the influence of an individual node on the overall network performance. The use of the proposed index is illustrated with a real-world WDN of an Australian town. The results highlight the significance of integrating the topological and hydraulic metrics for a reliable assessment of robustness in WDNs. ARTICLE INFO Received May 1, 2018 Received in revised form May 2018 Accepted June 22, 2018

[1]  Yuejin Tan,et al.  Heterogeneity of Scale-free Networks , 2007 .

[2]  Jan Vreeburg,et al.  Robustness of the Drinking Water Distribution Network Under Changing Future Demand , 2014 .

[3]  Joong Hoon Kim,et al.  Robustness-Based Design of Water Distribution Systems , 2014 .

[4]  Yuehui Zhang,et al.  Network connectivity entropy and its application on network connectivity reliability , 2013 .

[5]  Paul Jeffrey,et al.  Resilience enhancing expansion strategies for water distribution systems: A network theory approach , 2011, Environ. Model. Softw..

[6]  Paul Jeffrey,et al.  Water distribution system vulnerability analysis using weighted and directed network models , 2012 .

[7]  John Doyle,et al.  Complexity and robustness , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[8]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[9]  Evangelos Pournaras,et al.  Improving robustness of complex networks via the effective graph resistance , 2014 .

[10]  Orazio Giustolisi,et al.  Extended Period Simulation Analysis Considering Valve Shutdowns , 2008 .

[11]  João Ricardo Sato,et al.  Measuring network's entropy in ADHD: A new approach to investigate neuropsychiatric disorders , 2013, NeuroImage.

[12]  Giovanni Francesco Santonastaso,et al.  Resilience and entropy as indices of robustness of water distribution networks , 2012 .

[13]  R. Solé,et al.  Information Theory of Complex Networks: On Evolution and Architectural Constraints , 2004 .

[14]  C Pozrikidis Node degree distribution in spanning trees , 2016 .

[15]  Kevin C. Desouza,et al.  Measuring agility of networked organizational structures via network entropy and mutual information , 2010, Appl. Math. Comput..

[16]  Frank Schultmann,et al.  Integrating entropy theory and cospanning tree technique for redundancy analysis of water distribution networks , 2018, Reliab. Eng. Syst. Saf..

[17]  Enrico Zio,et al.  Evaluation of the robustness of critical infrastructures by Hierarchical Graph representation, clustering and Monte Carlo simulation , 2016, Reliab. Eng. Syst. Saf..

[18]  B. S. Manoj,et al.  Link Influence Entropy , 2017 .

[19]  T. Killingback,et al.  Attack Robustness and Centrality of Complex Networks , 2013, PloS one.

[20]  Symeon E. Christodoulou,et al.  Topological Robustness and Vulnerability Assessment of Water Distribution Networks , 2017, Water Resources Management.

[21]  G. Puccini,et al.  Robustness-based design of water distribution networks , 2016 .

[22]  Frank Schultmann,et al.  System Dynamics Modelling Process in Water Sector: a Review of Research Literature , 2018, Systems Research and Behavioral Science.

[23]  T. Tanyimboh Informational Entropy: a Failure Tolerance and Reliability Surrogate for Water Distribution Networks , 2017, Water Resources Management.

[24]  Frank Schultmann,et al.  The four Rs performance indicators of water distribution networks:A review of research literature , 2017 .

[25]  Panos M. Pardalos,et al.  A New Network Robustness Topology Measure based on Information Theory , 2014, ArXiv.

[26]  Antonietta Simone,et al.  Classification of infrastructure networks by neighborhood degree distribution , 2016, ArXiv.

[27]  Chao Li,et al.  Entropy theory‐based criterion for hydrometric network evaluation and design: Maximum information minimum redundancy , 2012 .

[28]  Yizhang Jiang,et al.  The evaluation of complex networks' robustness based on entropy measure , 2014 .

[29]  S. Bhatt,et al.  Entropy-Based Redundancy Measures in Water-Distribution Networks , 1991 .

[30]  Antonietta Simone,et al.  Network structure classification and features of water distribution systems , 2017 .

[31]  Vijay P. Singh,et al.  Entropy Theory and its Application in Environmental and Water Engineering: Singh/Entropy Theory and its Application in Environmental and Water Engineering , 2013 .

[32]  Chonghui Guo,et al.  Entropy optimization of scale-free networks’ robustness to random failures , 2005, cond-mat/0506725.

[33]  Paul Jeffrey,et al.  Complex network analysis of water distribution systems , 2011, Chaos.

[34]  Paul Jeffrey,et al.  Applying Network Theory to Quantify the Redundancy and Structural Robustness of Water Distribution Systems , 2012 .

[35]  J. Ser,et al.  A Critical Review of Robustness in Power Grids Using Complex Networks Concepts , 2015 .

[36]  Tao Zhou,et al.  A limited resource model of fault-tolerant capability against cascading failure of complex network , 2007, 0708.4023.