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Open AccessArticle

How Are Various Surrogate Indicators Consistent with Mechanical Reliability of Water Distribution Systems: From a Perspective of Many-Objective Optimization

1
School of Civil and Transportation Engineering, Guangdong University of Technology, Guangzhou 510006, China
2
International Department, the Affiliated High School of South China Normal University, Guangzhou 510000, China
3
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
4
School of Environment, Tsinghua University, Beijing 100084, China
*
Authors to whom correspondence should be addressed.
Water 2019, 11(8), 1669; https://doi.org/10.3390/w11081669
Received: 21 June 2019 / Revised: 14 July 2019 / Accepted: 25 July 2019 / Published: 12 August 2019
(This article belongs to the Section Urban Water Management)
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Abstract

Exploring the trade-off between cost and system reliability of water distribution systems (WDSs) has been focused for two decades. Due to the intensive computation associated with the reliability analysis, it is popular in the research community to replace this procedure by using surrogate indicators. However, the discussion on the correlation among different types of such indicators is generally lacking, which implies that a deeper understanding of this aspect is needed. This paper proposes a novel methodology of investigating the relationships among many commonly used surrogate indicators for measuring the mechanical reliability of WDSs. In particular, the optimal design of WDSs is formulated as a many-objective optimization problem, using cost and each surrogate indicator as an individual goal. Two benchmark design problems of different scales and complexities are considered for verifying the proposed method. The well-known multi-objective evolutionary algorithm (MOEA), namely Borg that is suitable for coping with problems involving many objectives, is used to obtain the best approximation to the Pareto-optimal fronts for both cases. Afterward, the one-pipe burst testing is conducted to quantify the correlation between mechanical reliability and surrogate indicators. Results suggest that investigating the correlation of surrogate indicators from the perspective of many-objective optimization provides a direct and efficient way of distinguishing better indicators from worse ones. Resilience-based surrogate indicators and the Redundancy indicator that only depends on nodal pressures are highly related to the mechanical reliability of WDSs. In contrast, entropy-based indicators exhibit poor performance in reflecting the mechanical reliability. These insights contribute to the selection of more appropriate surrogate indicators for the optimal design of WDSs for researchers and practitioners. View Full-Text
Keywords: water distribution system; mechanical reliability; resilience; surrogate indicators; many-objective optimization water distribution system; mechanical reliability; resilience; surrogate indicators; many-objective optimization
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Wang, Q.; Huang, W.; Wang, L.; Zhan, Y.; Wang, Z.; Wang, X.; Zhan, X.; Liu, S. How Are Various Surrogate Indicators Consistent with Mechanical Reliability of Water Distribution Systems: From a Perspective of Many-Objective Optimization. Water 2019, 11, 1669.

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