Abstract
Very recently, a new set of local indices for urban water networks has been proposed by the authors, within a mathematical framework which is unprecedented for this field, as far as we know. Such indices can be viewed as the “elementary bricks” that can be used to construct as many global (and local) indices as one needs or wants, where the glue, or mortar, is given by the mathematical tools of the aforementioned framework coming mostly from linear algebra and vector analysis. In this paper, after a brief description of the setting as explained above, we recover, through new formulations, some well-known global indicators like the resilience index \(I_r\) introduced by Todini. Then we also give some explicit numerical computations and examples, sometimes with the help of the hydraulic software EPANET 2.0.12.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
The linear algebra foundation, in this case, is clear even from the name: MATrix LABoratory.
- 2.
Our value for \(I_{r}\) is very close to 0.47, the one computed in [21, Tab. 3].
- 3.
The result, this time, agrees perfectly with 0.48 calculated in [21, Tab. 3].
- 4.
Being the two WDNs so similar and being dimension and complexity so small, a “criticality” of one WDN with respect to the other must obviously be understood in an appropriate sense...
References
Alperovits, E., Shamir, U.: Design of optimal water distribution systems. Water Resour. Res. 13, 885–900 (1977)
Bonora, M., Caldarola, F., Muranho, J., Sousa, J., Maiolo, M.: Numerical experimentations for a new set of local indices of a water network. In: Sergeyev, Y. D. and Kvasov, D. E. (eds.) Proceedings of the 3rd International Conference “Numerical Computations: Theory and Algorithms”. Lecture Notes in Computer Science. vol. 11973. Springer, New York (2020). https://doi.org/10.1007/978-3-030-39081-5_42
Caldarola, F., Maiolo, M.: Local indices within a mathematical framework for urban water distribution systems. Cogent Eng. 6, 1643057 (2019). https://doi.org/10.1080/23311916.2019.1643057
Carini, M., Maiolo, M., Pantusa, D., Chiaravalloti, F., Capano, G.: Modelling and optimization of least-cost water distribution networks with multiple supply sources and users. Ricerche di Matematica 67(2), 465–479 (2018)
Di Nardo, A., Di Natale, M.: A heuristic design support methodology based on graph theory for district metering of water supply networks. Eng. Optim. 12, 193–211 (2011)
Di Nardo, A., Di Natale, M.: A design support metodology metodology for district metering of water supply networks. Water Distrib. Syst. Anal. 2010, 870–887 (2012)
Di Nardo, A., et al.: Redundancy features of water distribution systems. Proc. Eng. 186, 412–419 (2017)
Di Nardo, A., Di Natale, M., Santonastaso, G.: A comparison between different techniques for water network sectorization. Water Sci. Technol.: Water Supply 14, 961–970 (2014)
Di Nardo, A., Di Natale, M., Santonastaso, G., Tzatchkov, V., Alcocer-Yamanaka, V.: Water network sectorization based on graph theory and energy performance indices. J. Water Resour. Plann. Manage. 140, 620–629 (2014)
Di Nardo, A., Di Natale, M., Santonastaso, G., Tzatchkov, V., Alcocer-Yamanaka, V.: Performance indices for water network partitioning and sectorization. Water Sci. Technol.: Water Supply 15, 499–509 (2015)
Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, Cambridge (2012)
Maiolo, M., Carini, M., Capano, G., Piro, P.: Synthetic sustainability index (SSI) based on life cycle assessment approach of low impact development in the Mediterranean area. Cogent Eng. 4, 1410272 (2017)
Maiolo, M., Martirano, G., Morrone, P., Pantusa, D.: Assessment criteria for a sustainable management of water resources. Water Pract. Technol. 1(1): wpt2006012 (2006). https://doi.org/10.2166/wpt.2006.012
Maiolo, M., Mendicino, G., Pantusa, D., Senatore, A.: Optimization of drinking water distribution systems in relation to the effects of climate change. Water 9, 803 (2017). https://doi.org/10.3390/w9100803
Maiolo, M., Pantusa, D.: A methodological proposal for the evaluation of potable water use risk. Water Pract. Technol. 10, 152–163 (2015)
Maiolo, M., Pantusa, D.: An optimization procedure for the sustainable management of water resources. Water Sci. Technol.: Water Supply 16, 61–69 (2016). https://doi.org/10.2166/ws.2015.114
Maiolo, M., Pantusa, D.: Combined reuse of wastewater and desalination for the management of water systems in conditions of scarcity. Water Ecol. 72, 116–126 (2017)
Maiolo, M., Pantusa, D.: Infrastructure vulnerability index of drinking water supply systems to possible terrorist attacks. Cogent Eng. 5, 1456710 (2018)
Maiolo, M., Pantusa, D., Chiaravalloti, F., Carini, M., Capano, G., Procopio, A.: A new vulnerability measure for water distribution network. Water 10, 1005 (2019)
Shin, S., et al.: A systematic review of quantitative resilience measures for water infrastructure systems. Water 10, 164 (2018)
Todini, E.: Looped water distribution networks design using a resilience index based on heuristic approach. Urban Water 12, 115–122 (2000)
Aknowledgments
This work is partially supported by the research projects “origAMI, Original Advanced Metering Infrastructure”, CUP J48C17000170006, POR Calabria FESR-FSE 2014–2020, and “I-BEST”, CUP B28I17000290008, PON “Innovazione e competitività” 2014/2020 MiSE Horizon 2020.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Caldarola, F., Maiolo, M. (2020). Algebraic Tools and New Local Indices for Water Networks:Some Numerical Examples. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11973. Springer, Cham. https://doi.org/10.1007/978-3-030-39081-5_44
Download citation
DOI: https://doi.org/10.1007/978-3-030-39081-5_44
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-39080-8
Online ISBN: 978-3-030-39081-5
eBook Packages: Computer ScienceComputer Science (R0)