Colebrook's Flow Friction Explicit Approximations Based on Fixed-Point Iterative Cycles and Symbolic Regression

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F19%3A10242723" target="_blank" >RIV/61989100:27740/19:10242723 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mdpi.com/2079-3197/7/3/48" target="_blank" >https://www.mdpi.com/2079-3197/7/3/48</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/computation7030048" target="_blank" >10.3390/computation7030048</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Colebrook's Flow Friction Explicit Approximations Based on Fixed-Point Iterative Cycles and Symbolic Regression

Popis výsledku v původním jazyce

The logarithmic Colebrook flow friction equation is implicitly given in respect to an unknown flow friction factor. Traditionally, an explicit approximation of the Colebrook equation requires evaluation of computationally demanding transcendental functions, such as logarithmic, exponential, non-integer power, Lambert W and Wright omega functions. Conversely, we herein present several computationally cheap explicit approximations of the Colebrook equation that require only one logarithmic function in the initial stage, whilst for the remaining iterations the cheap Pade approximant of the first order is used instead. Moreover, symbolic regression was used for the development of a novel starting point, which significantly reduces the error of internal iterations compared with the fixed value staring point. Despite the starting point using a simple rational function, it reduces the relative error of the approximation with one internal cycle from 1.81% to 0.156% (i.e., by a factor of 11.6), whereas the relative error of the approximation with two internal cycles is reduced from 0.317% to 0.0259% (i.e., by a factor of 12.24). This error analysis uses a sample with 2 million quasi-Monte Carlo points and the Sobol sequence.

Název v anglickém jazyce

Colebrook's Flow Friction Explicit Approximations Based on Fixed-Point Iterative Cycles and Symbolic Regression

Popis výsledku anglicky

The logarithmic Colebrook flow friction equation is implicitly given in respect to an unknown flow friction factor. Traditionally, an explicit approximation of the Colebrook equation requires evaluation of computationally demanding transcendental functions, such as logarithmic, exponential, non-integer power, Lambert W and Wright omega functions. Conversely, we herein present several computationally cheap explicit approximations of the Colebrook equation that require only one logarithmic function in the initial stage, whilst for the remaining iterations the cheap Pade approximant of the first order is used instead. Moreover, symbolic regression was used for the development of a novel starting point, which significantly reduces the error of internal iterations compared with the fixed value staring point. Despite the starting point using a simple rational function, it reduces the relative error of the approximation with one internal cycle from 1.81% to 0.156% (i.e., by a factor of 11.6), whereas the relative error of the approximation with two internal cycles is reduced from 0.317% to 0.0259% (i.e., by a factor of 12.24). This error analysis uses a sample with 2 million quasi-Monte Carlo points and the Sobol sequence.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Computation

ISSN

2079-3197

e-ISSN

—

Svazek periodika

7

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

12

Strana od-do

—

Kód UT WoS článku

000487943500002

EID výsledku v databázi Scopus

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