Selection of ψ-Caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique

The paper considers the usage of genetic programming technique to select an analytic form of functional parameter of the ψ-Caputo fractional derivative. We study one-dimensional space–time fractional water transport equation with such derivatives with respect to both time and space variables that ge...

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Autor principal:	Vsevolod Bohaienko
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Moisture transport Fractional differential equation Parameters identification ψ-Caputo derivative Genetic programming Applied mathematics. Quantitative methods T57-57.97
Acceso en línea:	https://doaj.org/article/782b9a5ffec24964bbd3c2554a3d30df
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id	oai:doaj.org-article:782b9a5ffec24964bbd3c2554a3d30df
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spelling	oai:doaj.org-article:782b9a5ffec24964bbd3c2554a3d30df2021-12-04T04:36:24ZSelection of ψ-Caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique2666-720710.1016/j.rico.2021.100068https://doaj.org/article/782b9a5ffec24964bbd3c2554a3d30df2021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666720721000394https://doaj.org/toc/2666-7207The paper considers the usage of genetic programming technique to select an analytic form of functional parameter of the ψ-Caputo fractional derivative. We study one-dimensional space–time fractional water transport equation with such derivatives with respect to both time and space variables that generalizes the classical Richards equation. Having water head values measured by Watermark sensors as inputs, the statement of parameters identification problem is performed. The forms of functional parameters are represented as trees and found using a genetic programming algorithm. We compare the accuracy of field data description by the model with fixed and variable forms of derivatives’ functional parameters and obtained up to 30% increase in accuracy for the training dataset and up to 15% increase for the testing dataset when the considered method was used to select parameters’ forms.Vsevolod BohaienkoElsevierarticleMoisture transportFractional differential equationParameters identificationψ-Caputo derivativeGenetic programmingApplied mathematics. Quantitative methodsT57-57.97ENResults in Control and Optimization, Vol 5, Iss , Pp 100068- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Moisture transport Fractional differential equation Parameters identification ψ-Caputo derivative Genetic programming Applied mathematics. Quantitative methods T57-57.97
spellingShingle	Moisture transport Fractional differential equation Parameters identification ψ-Caputo derivative Genetic programming Applied mathematics. Quantitative methods T57-57.97 Vsevolod Bohaienko Selection of ψ-Caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique
description	The paper considers the usage of genetic programming technique to select an analytic form of functional parameter of the ψ-Caputo fractional derivative. We study one-dimensional space–time fractional water transport equation with such derivatives with respect to both time and space variables that generalizes the classical Richards equation. Having water head values measured by Watermark sensors as inputs, the statement of parameters identification problem is performed. The forms of functional parameters are represented as trees and found using a genetic programming algorithm. We compare the accuracy of field data description by the model with fixed and variable forms of derivatives’ functional parameters and obtained up to 30% increase in accuracy for the training dataset and up to 15% increase for the testing dataset when the considered method was used to select parameters’ forms.
format	article
author	Vsevolod Bohaienko
author_facet	Vsevolod Bohaienko
author_sort	Vsevolod Bohaienko
title	Selection of ψ-Caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique
title_short	Selection of ψ-Caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique
title_full	Selection of ψ-Caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique
title_fullStr	Selection of ψ-Caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique
title_full_unstemmed	Selection of ψ-Caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique
title_sort	selection of ψ-caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/782b9a5ffec24964bbd3c2554a3d30df
work_keys_str_mv	AT vsevolodbohaienko selectionofpscaputoderivativesfunctionalparametersingeneralizedwatertransportequationbygeneticprogrammingtechnique
_version_	1718372919922393088

Selection of ψ-Caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique

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