NDLI: Hybrid Models for Solving the Colebrook–White Equation Using Artificial Neural Networks

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Hybrid Models for Solving the Colebrook–White Equation Using Artificial Neural Networks

Content Provider	MDPI
Author	Cahyono, Muhammad
Copyright Year	2022
Description	This study proposes hybrid models to solve the Colebrook–White equation by combining explicit equations available in the literature to solve the Colebrook–White equation with an error function. The hybrid model is in the form of $fH=fo-eA.fH$ is the friction factor value f predicted by the hybrid model, $fo$ is the value of f calculated using several explicit formulas for the Colebrook–White equation, and $eA$ is the error function determined using the neural network procedures. The hybrid equation consists of a series of hyperbolic tangent functions whose number corresponds to the number of neurons in the hidden layer. The simulation results showed that the hybrid models using five hyperbolic tangent functions could produce reasonable predictions of friction factors, with the maximum absolute relative error (MAXRE) around one tenth, or ten times lower than that produced by the corresponding existing formula. The simplified hybrid models are also given using four and three tangent hyperbolic functions. These simplified models still provide accurate results with MAXRE of less than 0.1%.
Starting Page	211
e-ISSN	23115521
DOI	10.3390/fluids7070211
Journal	Fluids
Issue Number	7
Volume Number	7
Language	English
Publisher	MDPI
Publisher Date	2022-06-21
Access Restriction	Open
Subject Keyword	Fluids Hardware and Architecturee Colebrook–white Equation Friction Factor Explicit Approximation Artificial Neural Networks Hybrid Model
Content Type	Text
Resource Type	Article

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