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A Tsallis entropy-based redundancy measure for water distribution networks

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  • Singh, Vijay P.
  • Oh, Juik

Abstract

A measure of redundancy inherent in the layouts of water distribution networks is developed using the Tsallis entropy. Both the local redundancy at a node and the global redundancy due to the redundancies at adjacent nodes are derived. The redundancy measure is applied to layouts reported in the literature and is compared with the Shannon entropy-based measure. Using the values reported in the literature, it is shown that there is almost a one-to-one relation between the Shannon entropy and the Tsallis entropy-based redundancy and reliability and this relation allows to specify the reliability of a network whose redundancy is known. Hence, the redundancy measure can also be employed in the water distribution network design.

Suggested Citation

  • Singh, Vijay P. & Oh, Juik, 2015. "A Tsallis entropy-based redundancy measure for water distribution networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 360-376.
    • Handle: RePEc:eee:phsmap:v:421:y:2015:i:c:p:360-376
    DOI: 10.1016/j.physa.2014.11.044
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    References listed on IDEAS

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    1. Rubinstein, Reuven Y., 1997. "Optimization of computer simulation models with rare events," European Journal of Operational Research, Elsevier, vol. 99(1), pages 89-112, May.
    2. Niven, Robert K., 2004. "The constrained entropy and cross-entropy functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(3), pages 444-458.
    3. Önder Ekinci & Haluk Konak, 2009. "An Optimization Strategy for Water Distribution Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(1), pages 169-185, January.
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    Citations

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    Cited by:

    1. 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.
    2. Wang, Yumin & Zhu, Guangcan, 2021. "Evaluation of water quality reliability based on entropy in water distribution system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    3. 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).
    4. Tiku T. Tanyimboh, 2017. "Informational Entropy: a Failure Tolerance and Reliability Surrogate for 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(10), pages 3189-3204, August.
    5. Zarghami, Seyed Ashkan & Gunawan, Indra & Schultmann, Frank, 2018. "Integrating entropy theory and cospanning tree technique for redundancy analysis of water distribution networks," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 102-112.
    6. Tiku T. Tanyimboh & Anna Czajkowska, 2018. "Self-Adaptive Solution-Space Reduction Algorithm for Multi-Objective Evolutionary Design 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(10), pages 3337-3352, August.
    7. Arash Malekian & Ali Azarnivand, 2016. "Application of Integrated Shannon’s Entropy and VIKOR Techniques in Prioritization of Flood Risk in the Shemshak Watershed, Iran," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(1), pages 409-425, January.
    8. Arash Malekian & Ali Azarnivand, 2016. "Application of Integrated Shannon’s Entropy and VIKOR Techniques in Prioritization of Flood Risk in the Shemshak Watershed, Iran," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(1), pages 409-425, January.
    9. Zhang, Juan & Li, Yong & Yuan, Hongqiang & Du, Guofeng & Zhang, Mingyuan, 2024. "A demand-based three-stage seismic resilience assessment and multi-objective optimization method of community water distribution networks," Reliability Engineering and System Safety, Elsevier, vol. 250(C).
    10. Tiku T. Tanyimboh & Calvin Siew & Salah Saleh & Anna Czajkowska, 2016. "Comparison of Surrogate Measures for the Reliability and Redundancy of Water Distribution Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(10), pages 3535-3552, August.

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