Fractal Geometry in Designing and Operating Water Networks

• Autorzy: Iwanek Małgorzata , Kowalski Dariusz , Kowalska Beata , Suchorab Paweł

Identyfikatory

DOI

10.12911/22998993/123501

• Języki publikacji: EN

Abstrakty

EN

Fractals are self-similar sets that cannot be easily described by classical geometry. Fractal sets have been implemented in almost all areas of human activity since they were introduced to science by Mandelbrot in 1982. For the last 10 years, the interest in fractal geometry has increased by the issues connected with water distribution networks (WDNs). The aim of this paper was to review the application of fractal geometry in designing and operating WDNs. Treating a WDN as a fractal pattern enables its description and classification, simplifies the assessment of a network reliability, helps to solve the problems of routing and dimensioning WDN, as well as enables to select the places to locate measurement points in a network to control water quality, pressure in pipes and water flow rate. Moreover, the application of tree-shaped fractal patterns to reflect WDNs helps to solve the problems of their optimization. Fractal geometry can be also applied to investigate the results of WDNs failures connected with leakage of water to the ground. Using fractal dimension of a pattern created by points reflecting places of water outflow on the soil surface after a prospective pipe breakage enables to determine the zone near a pipe, where the outflow of water on the soil surface is possible. It is an important approach for the security of humans and existing infrastructure. Usage of fractal geometry in description, optimisation and operation analysis of WDNs still continues, which confirms the efficiency of fractal geometry as a research tool. On the other hand, it can be supposed that fractal geometry possibilities have still not been fully used.

Słowa kluczowe

EN

water distribution network; fractal feature; tree-shaped pattern; fractal dimension

• Wydawca: Polskie Towarzystwo Inżynierii Ekologicznej ; Lublin University of Technology
• Czasopismo: Journal of Ecological Engineering
• Rocznik: 2020
• Tom: Vol. 21, nr 6
• Strony: 229--236
• Opis fizyczny: Bibliogr. 45 poz., rys.

Twórcy

autor

Iwanek Małgorzata

• Lublin University of Technology, Faculty of Environmental Engineering, ul. Nadbystrzycka 40B, 20-618 Lublin, Poland

autor

Kowalski Dariusz

• Lublin University of Technology, Faculty of Environmental Engineering, ul. Nadbystrzycka 40B, 20-618 Lublin, Poland

autor

Kowalska Beata

• Lublin University of Technology, Faculty of Environmental Engineering, ul. Nadbystrzycka 40B, 20-618 Lublin, Poland

autor

Suchorab Paweł

• Lublin University of Technology, Faculty of Environmental Engineering, ul. Nadbystrzycka 40B, 20-618 Lublin, Poland

Bibliografia

• 1. Azoumah Y., Bieupoude P., Neveu P. 2012. Optimal design of tree-shaped water distribution network using constructal approach: T-shaped and Y-shaped architectures optimization and comparison. International Communications in Heat and Mass Transfer 39(2), 182–189.
• 2. Bakker, M., Jung, D., Vreeburg, J., Van de Roer, M., Lansey, K., & Rierveld, L. 2014. Detecting pipe bursts using Heuristic and CUSUM methods. Procedia Engineering, 70, 85–92.
• 3. Barnsley M., Hutchinson J., Stenflo Ö. 2005. A fractal valued random iteration algorithm and fractal hierarchy. Fractals 13(02), 111–146.
• 4. Bejan A. 1996. Street network theory of organization in nature. J. Adv. Transportation 30(2), 85–107.
• 5. Ben-Mansour R., Habib M.A., Khalifa A., YoucefToumi K., Chatzigeorgiou, D. 2012. Computational fluid dynamic simulation of small leaks in water pipelines for direct leak pressure transduction. Computers & Fluids, 57, 110–123.
• 6. Berardi L., Liu S., Laucellii,D., Xu S., Xu P., Zeng W., Giustolisi O. 2014. Energy saving and leakage control in Water Distribution Networks: A joint research project between Italy and China. Procedia Engineering, 70, 152–161.
• 7. Bieupoude P., Azoumah Y., Neveu P. 2011. Environmental optimization of tree-shaped water distribution networks. Water resources management VI. Proc. of the sixth International Conference on Sustainable Water Resources Management, 99–109.
• 8. Csányi G., Szendrői B. 2004. Fractal–small-world dichotomy in real-world networks. Physical Review E, 70(1), 016122.
• 9. Deidda D., Sechi G. M., Zucca R. 2014. Finding economic optimality in leakage reduction: a costsimulation approach for complex urban supply systems. Procedia Engineering, 70, 477–486.
• 10. Di Nardo A., Di Natale M., Giudicianni C., Greco R., Santonastaso G.F. 2018. Complex network and fractal theory for the assessment of water distribution network resilience to pipe failures. Water Science and Technology: Water Supply, 18(3), 767–777.
• 11. Diao K., Butler D., Ulanicki B. 2017. Fractality in water distribution networks. Computing and Control for the Water Industry, Sheffield.
• 12. Eliades D. G., Polycarpou M.M. 2012. Leakage fault detection in district metered areas of water distribution systems. Journal of Hydroinformatics, 14(4), 992–1005.
• 13. Falconer K. J. 1990: Fractal Geometry: Mathematical Foundations and Applications. John Wiley, Chichester.
• 14. Gao L., Hu Y., Di Z. 2008. Accuracy of the ballcovering approach for fractal dimensions of complex networks and a rank-driven algorithm. Phys. Rev. E, 78, 046109.
• 15. Grzenda M., Sudoł M., Gębski W. 2010. Modelowanie systemu dystrybucji wody na przykładzie dużej aglomeracji miejskiej. Gaz, woda i technika sanitarna, 3, 2–6.
• 16. Hassan M.K., Kurths J. 2002. Can randomness alone tune the fractal dimension? Physica A, 315, 342–352.
• 17. Iwanek M., Suchorab P., Karpińska-Kiełbasa M. 2017. Suffosion holes as the results of breakage of buried water pipe. Periodica Polytechnica – Civil Engineering 4(61), 700–705.
• 18. Iwanek M. 2018. Metoda wyznaczania zasięgu stref zagrożenia powodowanego przez rozszczelnienie podziemnych przewodów wodociągowych. Monografie, 146, Wydawnictwo Komitetu Inżynierii Środowiska PAN, Lublin.
• 19. Iwanek M., Suchorab P. 2017. The assessment of water loss from a damaged distribution pipe using the FEFLOW software. ITM Web of Conferences, 15, 03006
• 20. Kadetova A.V., Rybchenko A.A., Trzhcinsky Y.B. 2007. Technogenic change of the geological environment of urban areas (by the example of Irkutsk town). Δελτίον της Ελληνικής Γεωλογικής Εταιρίας (Bulletin of the Geological Society of Greece), 40(3), 1440–1448.
• 21. Kansal M.L., Devi S. 2007. An improved algorithm for connectivity analysis of distribution networks. Reliability Engineering and System Safety, 92, 1295–1302.
• 22. Khomenko V.P. 2009. Suffosion hazard: today’s and tomorrow’s problem for cities. Engineering geology for tomorrow’s cities, Geological Society. Engineering Geology Special Publication, London.
• 23. Kim J.S., Goh K.-I., Kahng B., Kim D. 2007. A boxcovering algorithm for fractal scaling in scale-free networks. Chaos 17, 026116.
• 24. Kowalski D. 2011. Nowe metody opisu struktur sieci wodociągowych do rozwiązywania problemów ich projektowania i eksploatacji. Monografie, 88, Wydawnictwo Komitetu Inżynierii Środowiska PAN, Lublin.
• 25. Kowalski D., Kowalska B., Kwietniewski M. 2015. Monitoring of water distribution system effectiveness using fractal geometry. Bulletin of the Polish Academy of Sciences Technical Sciences, 63(1), 155–161.
• 26. Kudrewicz J. 2015. Fraktale i chaos. Wydawnictwo WNT, Warszawa.
• 27. Kutyłowska M., Hotloś H. 2014. Failure analysis of water supply system in the Polish city of Głogów. Engineering Failure, 41, 23–29.
• 28. Kwietniewski M., Gębski W., Wronowski N. 2005. Monitorowanie sieci wodociągowych i kanalizacyjnych, Wyd. Polskie Zrzeszenie Inżynierów i Techników Sanitarnych, Warszawa.
• 29. Mandelbrot B. B. 1982. The Fractal Geometry of Nature. W.H. Freeman and Co., New York.
• 30. Mandelbrot B.B. 1975. Stochastic models for the earth’s relief, the shape and fractal dimension of coastlines, and the number area rule for islands. Proceedings of the National Academy of Sciences of the United States of America, 72 (10), 2825–2828.
• 31. Mielcarzewicz E. 2000. Obliczanie systemów zaopatrzenia w wodę, Arkady, Warszawa.
• 32. Murray C.D. 1926a. The physiological principle of minimum work applied to the angle of branching of arteries. J.Gen.Physiol., 9, 835–841.
• 33. Murray C.D. 1926b. The Physiological Principle of Minimum Work: I. The Vascular System and the Cost of Blood Volume. Proceedings of the National Academy of Sciences of the United States of America, 12(3), 207–214.
• 34. Newman M.E.J. 2004. Analysis of weighted networks. Phys. Rev. E, 70, 056131.
• 35. Pauliuk S., Venkatesh G., Brattebø H., Müller D.B. 2014. Exploring urban mines: Pipe length and material stocks in urban water and wastewater networks. Urban Water Journal, 11(4), 274–283.
• 36. Peitgen H.-O., Jürgens H., Sanpe D. 1997. Granice chaosu. Fraktale. Część 1. PWN, Warszawa.
• 37. Song C., Havlin S. Makse H. A. 2005. Self-similarity of complex networks, Nature, 433, 392–395.
• 38. Song C., Havlin S., Makse H.A. 2006. Origins of fractality in the growth of complex networks, Nature Physics, 2, 275–281.
• 39. Song C., Gallos L.K., Havlin S., Makse H.A. 2007. How to calculate the fractal dimension of a complex network: the box covering algorithm. Journal of Statistical Mechanics: Theory and Experiment, 2007(03), P03006.
• 40. Suchorab P., Kowalski D. 2019. Routing of branched water distribution networks using fractal geometry and graph theory. MATEC Web of Conferences, 252, 02001.
• 41. Vargas K., Saldarriaga J. 2019a. Analysis of Fractality in Water Distribution Networks Using Hydraulic Criteria. World Environmental and Water Resources Congress 2019: Hydraulics, Waterways, and Water Distribution Systems Analysis, 564–572.
• 42. Vargas K., Saldarriaga J. 2019b. Potential District Metered Area Identification in Water Distribution Networks Using Hydraulic Criteria and the Box Covering Algorithm. World Environmental and Water Resources Congress 2019: Hydraulics, Waterways, and Water Distribution Systems Analysis, 573–586.
• 43. Wei D.J., Liu Q., Zhang H.X., Hu Y., Deng Y., Mahadevan S. 2013. Box-covering algorithm for fractal dimension of weighted networks. Scientific reports, 3(1), 1–8.
• 44. Zeng F., K. Li. 2013. Reliability Analysis of Fractal Water Distribution Networks Based on Basic Patterns, Proceedings of the 2013 Georgia Water Resources Conference, 2013, University of Georgia.
• 45. Zeng F., Li X., Li K. 2017. Modeling complexity in engineered infrastructure system: Water distribution network as an example. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(2), 023105.