Water Distribution System Analysis: Newton-Raphson Method Revisited

Spiliotis, Mike; Tsakiris, George

doi:10.1061/(asce)hy.1943-7900.0000364

Cited by 31 publications

(26 citation statements)

References 8 publications

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“…Also, a comparative analysis of several DDA computational solution methods for gas and water distribution networks is available in Brkic (2011). Recently Spiliotis and Tsakiris (2011) proposed a DDA implementation of the Newton-Raphson method using a pipe discharge formula derived by combining the Darcy-Weisbach pipe friction head loss formula and the Colebrook-White function for the friction factor (see e.g. Eq.…”

mentioning

confidence: 99%

“…4.16 in Chadwick et al 2004). The procedure (Brkic 2012, Spiliotis andTsakiris 2012a) has the advantages that it avoids the iterative solution of the Colebrook-White function and benefits from the extra accuracy of the Darcy-Weisbach pipe friction head loss formula compared to empirical approximations such as the Hazen-Williams formula. It should be noted that the design optimization approach proposed here follows the convention that demands are known with reasonable certainty.…”

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confidence: 99%

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Penalty-Free Feasibility Boundary Convergent Multi-Objective Evolutionary Algorithm for the Optimization of Water Distribution Systems

Siew

Tanyimboh

2012

Water Resour Manage

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This version is available at https://strathprints.strath.ac.uk/43222/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. AbstractThis paper presents a new penalty-free multi-objective evolutionary approach (PFMOEA) for the optimization of water distribution systems (WDSs). The proposed approach utilizes pressure dependent analysis (PDA) to develop a multi-objective evolutionary search. PDA is able to simulate both normal and pressure deficient networks and provides the means to accurately and rapidly identify the feasible region of the solution space, effectively locating global or near global optimal solutions along its active constraint boundary. The significant advantage of this method over previous methods is that it eliminates the need for ad-hoc penalty functions, additional "boundary search" parameters, or special constraint handling procedures. Conceptually, the approach is downright straightforward and probably the simplest hitherto. The PFMOEA has been applied to several WDS benchmarks and its performance examined. It is demonstrated that the approach is highly robust and efficient in locating optimal solutions. Superior results in terms of the initial network construction cost and number of hydraulic simulations required were obtained. The improvements are demonstrated through comparisons with previously published solutions from the literature.

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Penalty-Free Feasibility Boundary Convergent Multi-Objective Evolutionary Algorithm for the Optimization of Water Distribution Systems

Siew

Tanyimboh

2012

Water Resour Manage

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“…Looped network of pipes: The use of the accurate explicit approximations should be prioritized over the use of the iterative solution in the calculation of looped networks of pipes, since in that way, double iterative procedures, one for the Colebrook equation and one for the solution of the whole looped system of pipes, can be avoided [63][64][65][66][67].…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Brkić¹,

Ćojbašić²

2017

Preprint

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This paper presents evolutionary optimization of explicit approximations of the empirical Colebrook's equation that is used for the calculation of the turbulent friction factor (λ), i.e., for the calculation of turbulent hydraulic resistance in hydraulically smooth and rough pipes including the transient zone between them. The empirical Colebrook's equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of the inner pipe surface (ε/D). It is implicit in the unknown friction factor (λ). The implicit Colebrook's equation cannot be rearranged to derive the friction factor (λ) directly, and therefore, it can be solved only iteratively [λ = f(λ, R, ε/D)] or using its explicit approximations [λ ≈ f(R, ε/D)], which introduce certain error compared with the iterative solution. The optimization of explicit approximations of Colebrook's equation is performed with the aim to improve their accuracy, and the proposed optimization strategy is demonstrated on a large number of explicit approximations published up to date where numerical values of the parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After that improvement, the computational burden stays unchanged while the accuracy of approximations increases in some of the cases very significantly.

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“…The use of the accurate explicit approximations should be prioritized over the use of iterative solution in calculation of looped networks of pipes since in that way double iterative procedures, one for the Colebrook equation and one for the solution of the whole looped system of pipes, can be avoided [63][64][65][66][67].…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Brkić¹,

Ćojbašić²

2017

Preprint

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Today, Colebrook's equation is mostly accepted as an informal standard for modeling of turbulent flow in hydraulically smooth and rough pipes including transient zone in between. The empirical Colebrook's equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of inner pipe surface (ε/D). It is implicit in unknown friction factor (λ). Implicit Colebrook's equation cannot be rearranged to derive friction factor (λ) directly and therefore it can be solved only iteratively [λ=f(λ, R, ε/D)] or using its explicit approximations [λ≈f(R, ε/D)]. Of course, approximations carry in certain error compared with the iterative solution where the highest level of accuracy can be reached after enough number of iterations. The explicit approximations give a relatively good prediction of the friction factor (λ) and can reproduce accurately Colebrook's equation and its Moody's plot. Usually, more complex models of approximations are more accurate and vice versa. In this paper, numerical values of parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After this improvement computational burden stays unchanged while accuracy of approximations increases in some of the cases very significantly.

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Water Distribution System Analysis: Newton-Raphson Method Revisited

Cited by 31 publications

References 8 publications

Penalty-Free Feasibility Boundary Convergent Multi-Objective Evolutionary Algorithm for the Optimization of Water Distribution Systems

Penalty-Free Feasibility Boundary Convergent Multi-Objective Evolutionary Algorithm for the Optimization of Water Distribution Systems

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

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Water Distribution System Analysis: Newton-Raphson Method Revisited

Cited by 31 publications

References 8 publications

Penalty-Free Feasibility Boundary Convergent Multi-Objective Evolutionary Algorithm for the Optimization of Water Distribution Systems

Penalty-Free Feasibility Boundary Convergent Multi-Objective Evolutionary Algorithm for the Optimization of Water Distribution Systems

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Evolutionary Optimization of Colebrook&rsquo;s Turbulent Flow Friction Approximations

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Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations