IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v409y2021ics0096300320306792.html
   My bibliography  Save this article

A mathematical investigation on the invariance problem of some hydraulic indices

Author

Listed:
  • Caldarola, Fabio
  • Maiolo, Mario

Abstract

In recent decades many mathematical models, both theoretical and computational, have been applied to hydraulic networks with considerable success, and recently this trend appears to be growing exponentially. Yet there are important problems of a mathematical nature that have very often had little consideration in this field, such as that of the invariance of the models with respect to the reference adopted. In this paper, a mathematical framework new in the field is used and, starting from the discussion of the invariance problem of local indices, the behavior of some widespread global ones that evaluate the resilience of a network will be investigated from both a theoretical and computational point of view. The authors also give suitable changing formulas in the local and global case and describe the conditions that ensure invariance. Through a mathematical-like formalization of the hydraulic network concept, the new framework finally allows to find a series of mathematical solutions to problems of this kind, two of which will be provided in the text.

Suggested Citation

  • Caldarola, Fabio & Maiolo, Mario, 2021. "A mathematical investigation on the invariance problem of some hydraulic indices," Applied Mathematics and Computation, Elsevier, vol. 409(C).
  • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300320306792
    DOI: 10.1016/j.amc.2020.125726
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320306792
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2020.125726?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dai, Jiangyu & Wu, Shiqiang & Han, Guoyi & Weinberg, Josh & Xie, Xinghua & Wu, Xiufeng & Song, Xingqiang & Jia, Benyou & Xue, Wanyun & Yang, Qianqian, 2018. "Water-energy nexus: A review of methods and tools for macro-assessment," Applied Energy, Elsevier, vol. 210(C), pages 393-408.
    2. Caldarola, Fabio, 2018. "The Sierpinski curve viewed by numerical computations with infinities and infinitesimals," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 321-328.
    3. João Marques & Maria Cunha & Dragan Savić & Orazio Giustolisi, 2017. "Water Network Design Using a Multiobjective Real Options Framework," Journal of Optimization, Hindawi, vol. 2017, pages 1-13, January.
    4. Manuel Herrera & Edo Abraham & Ivan Stoianov, 2016. "A Graph-Theoretic Framework for Assessing the Resilience of Sectorised Water Distribution Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(5), pages 1685-1699, March.
    5. D’Ambrosio, Claudia & Lodi, Andrea & Wiese, Sven & Bragalli, Cristiana, 2015. "Mathematical programming techniques in water network optimization," European Journal of Operational Research, Elsevier, vol. 243(3), pages 774-788.
    6. Agathoklis Agathokleous & Chrystalleni Christodoulou & Symeon E. Christodoulou, 2017. "Topological Robustness and Vulnerability Assessment of Water Distribution Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(12), pages 4007-4021, September.
    7. Sergeyev, Yaroslav D., 2007. "Blinking fractals and their quantitative analysis using infinite and infinitesimal numbers," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 50-75.
    8. Manuel Herrera & Edo Abraham & Ivan Stoianov, 2016. "A Graph-Theoretic Framework for Assessing the Resilience of Sectorised Water Distribution Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(5), pages 1685-1699, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yu, Juanya & Sharma, Neetesh & Gardoni, Paolo, 2024. "Functional connectivity analysis for modeling flow in infrastructure," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    2. Xiang He & Yongbo Yuan, 2019. "A Framework of Identifying Critical Water Distribution Pipelines from Recovery Resilience," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(11), pages 3691-3706, September.
    3. Tiedmann, Helena R. & Faust, Kasey M. & Sela, Lina, 2024. "Looking beyond individual failures: A system-wide assessment of water infrastructure resilience to extreme events," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    4. C. Giudicianni & A. Nardo & R. Greco & A. Scala, 2021. "A Community-Structure-Based Method for Estimating the Fractal Dimension, and its Application to Water Networks for the Assessment of Vulnerability to Disasters," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(4), pages 1197-1210, March.
    5. Ardalan Izadi & Farhad Yazdandoost & Roza Ranjbar, 2020. "Asset-Based Assessment of Resiliency in Water Distribution Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(4), pages 1407-1422, March.
    6. Alessandro Pagano & Raffaele Giordano & Ivan Portoghese, 2022. "A Pipe Ranking Method for Water Distribution Network Resilience Assessment Based on Graph-Theory Metrics Aggregated Through Bayesian Belief Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(13), pages 5091-5106, October.
    7. Elisabeth Vogel & Zoya Dyka & Dan Klann & Peter Langendörfer, 2021. "Resilience in the Cyberworld: Definitions, Features and Models," Future Internet, MDPI, vol. 13(11), pages 1-18, November.
    8. Johannes Stübinger & Lucas Schneider, 2020. "Understanding Smart City—A Data-Driven Literature Review," Sustainability, MDPI, vol. 12(20), pages 1-23, October.
    9. Wu, Jason & Baker, Jack W., 2020. "Statistical learning techniques for the estimation of lifeline network performance and retrofit selection," Reliability Engineering and System Safety, Elsevier, vol. 200(C).
    10. Hadi Alizadeh & Ayyoob Sharifi, 2020. "Assessing Resilience of Urban Critical Infrastructure Networks: A Case Study of Ahvaz, Iran," Sustainability, MDPI, vol. 12(9), pages 1-20, May.
    11. Bruno Brentan & Silvia Carpitella & Daniel Barros & Gustavo Meirelles & Antonella Certa & Joaquín Izquierdo, 2021. "Water Quality Sensor Placement: A Multi-Objective and Multi-Criteria Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(1), pages 225-241, January.
    12. Liu, Wei & Song, Zhaoyang, 2020. "Review of studies on the resilience of urban critical infrastructure networks," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    13. Tiku T. Tanyimboh & Anna M. Czajkowska, 2021. "Entropy maximizing evolutionary design optimization of water distribution networks under multiple operating conditions," Environment Systems and Decisions, Springer, vol. 41(2), pages 267-285, June.
    14. Carlo Giudicianni & Manuel Herrera & Armando Nardo & Kemi Adeyeye, 2020. "Automatic Multiscale Approach for Water Networks Partitioning into Dynamic District Metered Areas," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(2), pages 835-848, January.
    15. Liu, Wei & Song, Zhaoyang & Ouyang, Min, 2020. "Lifecycle operational resilience assessment of urban water distribution networks," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    16. Liu, Wei & Song, Zhaoyang & Ouyang, Min & Li, Jie, 2020. "Recovery-based seismic resilience enhancement strategies of water distribution networks," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    17. Tohmé, Fernando & Caterina, Gianluca & Gangle, Rocco, 2020. "Computing Truth Values in the Topos of Infinite Peirce’s α-Existential Graphs," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    18. Kulkarni, Onkar & Dahan, Mathieu & Montreuil, Benoit, 2022. "Resilient Hyperconnected Parcel Delivery Network Design Under Disruption Risks," International Journal of Production Economics, Elsevier, vol. 251(C).
    19. Tiku T. Tanyimboh & Anna M. Czajkowska, 2018. "Joint Entropy Based Multi-Objective Evolutionary Optimization of Water Distribution Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(8), pages 2569-2584, June.
    20. Bárbara Brzezinski Azevedo & Tarcísio Abreu Saurin, 2018. "Losses in Water Distribution Systems: A Complexity Theory Perspective," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(9), pages 2919-2936, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300320306792. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.