ROBUSTNESS AND VULNERABILITY ANALYSIS OF WATER DISTRIBUTION NETWORKS USING GRAPH THEORETIC AND COMPLEX NETWORK PRINCIPLES

Water distribution systems are regarded as large sparse graphs with complex network characteristics. Topological aspects of system resilience, viewed as the antonym to structural vulnerability, are assessed in connection with the network architecture, robustness and loop redundancy. Deterministic techniques from complex networks and spectral graph theory are utilized to quantify well-connectedness and estimate loop redundancy in the studied benchmark networks. By using graph connectivity and expansion properties, system robustness against node/link failures and isolation of the demand nodes from the source(s) are assessed and network tolerance against random failures and targeted attacks on their bridges and cut sets are analyzed. Among other measurements, two metrics of meshed-ness and algebraic connectivity are proposed as candidates for quantification of redundancy and robustness, respectively, in optimization design models. A brief discussion on the scope and relevance of the provided measurements in the analysis of resilience of water distribution networks is presented.

[1]  Uri Shamir,et al.  A methodology for least-cost design of invulnerable water distribution networks , 1990 .

[2]  A. P. Masucci,et al.  Random planar graphs and the London street network , 2009, 0903.5440.

[3]  I. C. Goulter,et al.  Evaluation of methods for decomposition of water distribution networks for reliability analysis , 1988 .

[4]  Ake J Holmgren,et al.  Using Graph Models to Analyze the Vulnerability of Electric Power Networks , 2006, Risk analysis : an official publication of the Society for Risk Analysis.

[5]  Fei Xue,et al.  Analysis of structural vulnerabilities in power transmission grids , 2009, Int. J. Crit. Infrastructure Prot..

[6]  Guy Theraulaz,et al.  Topological patterns in street networks of self-organized urban settlements , 2006 .

[7]  Ezio Todini,et al.  Looped water distribution networks design using a resilience index based heuristic approach , 2000 .

[8]  Istvan Lippai.  Colorado Springs Utilities Case Study: Water System Calibration / Optimization , 2005 .

[9]  Thomas M. Walski,et al.  Water distribution valve topology for reliability analysis , 1993 .

[10]  Michel Bruneau,et al.  A Framework to Quantitatively Assess and Enhance the Seismic Resilience of Communities , 2003 .

[11]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[12]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[13]  Stephen P. Boyd,et al.  Growing Well-connected Graphs , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[14]  Gábor Csárdi,et al.  The igraph software package for complex network research , 2006 .

[15]  I. C. Goulter.  Current and future use of systems analysis in water distribution network design , 1987 .

[16]  Avi Ostfeld,et al.  Incorporating reliability in optimal design of water distribution networks—review and new concepts , 1993 .

[17]  Larry W. Mays,et al.  Battle of the network models: Epilogue , 1987 .

[18]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[19]  Enrico Zio,et al.  Service Reliability Analysis of a Tramway Network , 2007 .

[20]  Jochen Deuerlein,et al.  Decomposition Model of a General Water Supply Network Graph , 2008 .

[21]  Rajiv Gupta,et al.  Extended Use of Linear Graph Theory for Analysis of Pipe Networks , 2000 .

[22]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[23]  Avi Ostfeld,et al.  WATER DISTRIBUTION SYSTEMS CONNECTIVITY ANALYSIS , 2005 .

[24]  Ernesto Estrada,et al.  Network robustness to targeted attacks. The interplay of expansibility and degree distribution , 2006 .

[25]  G. Chartrand,et al.  Graphs & Digraphs , 1986 .

[26]  Avi Ostfeld,et al.  Reliability analysis of water distribution systems , 2004 .

[27]  Leonardo Dueñas-Osorio,et al.  Cascading failures in complex infrastructure systems , 2009 .

[28]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[29]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994 .

[30]  Z Kapelan,et al.  Risk- and robustness-based solutions to a multi-objective water distribution system rehabilitation problem under uncertainty . , 2006, Water science and technology : a journal of the International Association on Water Pollution Research.

[31]  L. da F. Costa,et al.  Characterization of complex networks: A survey of measurements , 2005, cond-mat/0505185.

[32]  Jakobus E. van Zyl,et al.  Operational Optimization of Water Distribution Systems using a Hybrid Genetic Algorithm , 2004 .

[33]  Zoran Kapelan,et al.  Least-Cost Design of Water Distribution Networks under Demand Uncertainty , 2005 .

[34]  Massimo Marchiori,et al.  LOCATING CRITICAL LINES IN HIGH-VOLTAGE ELECTRICAL POWER GRIDS , 2005, The Random and Fluctuating World.

[35]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[36]  I. Goulter,et al.  OPTIMIZATION OF REDUNDANCY IN WATER DISTRIBUTION NETWORKS USING GRAPH THEORETIC PRINCIPLES , 1989 .

[37]  A. Jamakovic,et al.  On the relationship between the algebraic connectivity and graph's robustness to node and link failures , 2007, 2007 Next Generation Internet Networks.

[38]  H. Kesavan,et al.  Graph-Theoretical Models for Pipe Network Analysis , 1972 .

[39]  M. A. Muñoz,et al.  Optimal network topologies: expanders, cages, Ramanujan graphs, entangled networks and all that , 2006, cond-mat/0605565.

[40]  Avi Ostfeld.  Reliability analysis of regional water distribution systems , 2001 .

[41]  B. Mohar.  THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .