Quadratic head loss approximations for optimisation problems in water supply networks

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Title: Quadratic head loss approximations for optimisation problems in water supply networks
Author(s): Pecci, F
Abraham, E
Stoianov, II
Item Type: Journal Article
Abstract: This paper presents a novel analysis on the accuracy of quadratic approximations for Hazen--Williams head loss formula, which enables the control of constraint violations in optimisation problems for water supply networks. The two smooth polynomial approximations considered here minimise the absolute and relative errors, respectively, from the original non-smooth Hazen--Williams head loss function over a range of flows. Since the quadratic approximations are used to formulate head loss constraints for different optimisation problems, we are interested in quantifying and controlling their absolute errors, which affect the degree of constraint violations of candidate feasible solutions. We derive new exact analytical formulae for the absolute errors as a function of the approximation domain, pipe roughness and relative error tolerance. We assess the efficacy of the quadratic approximations in mathematical optimisation for optimal pressure regulation in an operational water supply network. We propose a strategy on how to choose the approximation domain for each pipe such that the optimisation results are sufficiently close to the exact hydraulic feasibility region. By using simulations with multiple parameters, the approximation errors are shown to be consistent with our analytical predictions.
Publication Date: 17-Apr-2017
Date of Acceptance: 2-Jan-2017
URI: http://hdl.handle.net/10044/1/44287
DOI: https://dx.doi.org/10.2166/hydro.2017.080
ISSN: 1464-7141
Publisher: IWA Publishing
Start Page: 493
End Page: 506
Journal / Book Title: Journal of Hydroinformatics
Volume: 19
Issue: 4
Sponsor/Funder: Engineering & Physical Science Research Council (E
Funder's Grant Number: EP/P004229/1
Copyright Statement: © 2017 The Authors. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/).
Keywords: Science & Technology
Technology
Life Sciences & Biomedicine
Physical Sciences
Computer Science, Interdisciplinary Applications
Engineering, Civil
Environmental Sciences
Water Resources
Computer Science
Engineering
Environmental Sciences & Ecology
Hazen-Williams
modelling
optimisation
pipe friction
water supply networks
HAZEN-WILLIAMS EQUATION
OPTIMAL-DESIGN
PROPER USE
LIMITATIONS
ALGORITHMS
TOPOLOGY
FRICTION
MODELS
Environmental Engineering
0905 Civil Engineering
Publication Status: Published
Open Access location: http://dx.doi.org/10.2166/hydro.2017.080
Appears in Collections:Faculty of Engineering
Civil and Environmental Engineering



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