Preprint Article Version 1 This version is not peer-reviewed

Symbolic Regression Based Genetic Approximations of the Colebrook Equation for Flow Friction

Version 1 : Received: 29 August 2018 / Approved: 30 August 2018 / Online: 30 August 2018 (05:05:59 CEST)

A peer-reviewed article of this Preprint also exists.

Praks, P.; Brkić, D. Symbolic Regression-Based Genetic Approximations of the Colebrook Equation for Flow Friction. Water 2018, 10, 1175. Praks, P.; Brkić, D. Symbolic Regression-Based Genetic Approximations of the Colebrook Equation for Flow Friction. Water 2018, 10, 1175.

Journal reference: Water 2018, 10, 1175
DOI: 10.3390/w10091175

Abstract

Widely used in hydraulics, the Colebrook equation for flow friction relates implicitly to the input parameters; the Reynolds number, Re and the relative roughness of inner pipe surface, ε/D with the output unknown parameter; the flow friction factor, λ; λ=f(λ, Re, ε/D). In this paper, a few explicit approximations to the Colebrook equation; λ≈f(Re, ε/D), are generated using the ability of artificial intelligence to make inner patterns to connect input and output parameters in explicit way not knowing their nature or the physical law that connects them, but only knowing raw numbers, {Re, ε/D}→{λ}. The fact that the used genetic programming tool does not know the structure of the Colebrook equation which is based on computationally expensive logarithmic law, is used to obtain better structure of the approximations which is less demanding for calculation but also enough accurate. All generated approximations are with low computational cost because they contain a limited number of logarithmic forms used although for normalization of input parameters or for acceleration, but they are also sufficiently accurate. The relative error regarding the friction factor λ, in best case is up to 0.13% with only two logarithmic forms used. As the second logarithm can be accurately approximated by the Padé approximation, practically the same error is obtained also using only one logarithm.

Subject Areas

Colebrook equation; flow friction; turbulent flow; genetic programming; symbolic regression; explicit approximations

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