1472996
doi
10.3390/w10091175
oai:zenodo.org:1472996
Brkić, Dejan
Symbolic Regression-Based Genetic Approximations of the Colebrook Equation for Flow Friction
Praks, Pavel
info:eu-repo/semantics/openAccess
Free for private use; right holder retains other rights, including distribution
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 an inner pipe surface, ε/D with an unknown output 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 an 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 a better structure of the approximations, which is less demanding for calculation but also enough accurate. All generated approximations have low computational cost because they contain a limited number of logarithmic forms used for normalization of input parameters or for acceleration, but they are also sufficiently accurate. The relative error regarding the friction factor λ, in in the 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.
Zenodo
2018-09-02
info:eu-repo/semantics/article
1472995
1579533535.56917
4507546
md5:12c8c12ce4386bc090ffbc72580bf00e
https://zenodo.org/records/1472996/files/article.pdf
public