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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F18%3A10240152" target="_blank" >RIV/61989100:27740/18:10240152 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mdpi.com/2073-4441/10/9/1175" target="_blank" >https://www.mdpi.com/2073-4441/10/9/1175</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/w10091175" target="_blank" >10.3390/w10091175</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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, epsilon/D with an unknown output parameter; the flow friction factor, ; = f (, Re, epsilon/D). In this paper, a few explicit approximations to the Colebrook equation; approximate to f (Re, epsilon/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, epsilon/D}{}. 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 , 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 Pade approximation, practically the same error is obtained also using only one logarithm.

Název v anglickém jazyce

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

Popis výsledku anglicky

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, epsilon/D with an unknown output parameter; the flow friction factor, ; = f (, Re, epsilon/D). In this paper, a few explicit approximations to the Colebrook equation; approximate to f (Re, epsilon/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, epsilon/D}{}. 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 , 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 Pade approximation, practically the same error is obtained also using only one logarithm.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20302 - Applied mechanics

Projekt

—

Návaznosti

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Water

ISSN

2073-4441

e-ISSN

—

Svazek periodika

10

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

14

Strana od-do

—

Kód UT WoS článku

000448821900067

EID výsledku v databázi Scopus

2-s2.0-85052812202