Modeling of the friction factor in pressure pipes using Bayesian Learning Neural Networks
The model proposed by Colebrook-White for calculating the coefficient of friction has been universally accepted by establishing an implicit transcendental function. This equation determines the friction coefficient for fully developed flows, that is, for turbulent flows with a Reynolds Number hig...
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| Format: | Online |
| Language: | spa |
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Universidad Pedagógica y Tecnológica de Colombia
2022
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| Subjects: | |
| Online Access: | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/13241 |
| _version_ | 1801706351008677888 |
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| author | Ladino Moreno, Edgar Orlando García Ubaque, Cesar Augusto García-Vaca, María Camila |
| author_facet | Ladino Moreno, Edgar Orlando García Ubaque, Cesar Augusto García-Vaca, María Camila |
| author_sort | Ladino Moreno, Edgar Orlando |
| collection | OJS |
| description |
The model proposed by Colebrook-White for calculating the coefficient of friction has been universally accepted by establishing an implicit transcendental function. This equation determines the friction coefficient for fully developed flows, that is, for turbulent flows with a Reynolds Number higher than 4000. In the present study, a Neural Network was developed from the approach of the Bayesian Regularization Backpropagation method to estimate the coefficient of friction. A set of 200,000 input data (inputs) was established for the relative roughness (ε/D) and the Reynolds Number (Re) and 200,000 output data (outputs) for the friction coefficient. The neuronal architecture that performed best corresponded to two hidden layers with 25 neurons each (2-25-25-1). Network performance was evaluated using mean square error, regression analysis, and the cross-entropy function. The neural model obtained presented a mean square error of 7.42E-13 and a relative error equal to 0.0035 % for the training data. Finally, the Bayesian Regularization backpropagation network demonstrated the ability to calculate the coefficient of friction for turbulent flows with an approximation of 10E-7 concerning the Colebrook-White equation.
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| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-13241 |
| institution | Revista Ciencia en Desarrollo |
| language | spa |
| publishDate | 2022 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-132412023-06-26T20:42:54Z Modeling of the friction factor in pressure pipes using Bayesian Learning Neural Networks Modelado del factor de fricción en tuberías a presión Utilizando Redes Neuronales de Aprendizaje Bayesiano Ladino Moreno, Edgar Orlando García Ubaque, Cesar Augusto García-Vaca, María Camila Coeficiente fricción, Colebrook-White, Regularización Bayesiana, Red Neuronal Artificial Artificial Neural Network, Bayesian Regularization, Coefficient of friction, Colebrook & White The model proposed by Colebrook-White for calculating the coefficient of friction has been universally accepted by establishing an implicit transcendental function. This equation determines the friction coefficient for fully developed flows, that is, for turbulent flows with a Reynolds Number higher than 4000. In the present study, a Neural Network was developed from the approach of the Bayesian Regularization Backpropagation method to estimate the coefficient of friction. A set of 200,000 input data (inputs) was established for the relative roughness (ε/D) and the Reynolds Number (Re) and 200,000 output data (outputs) for the friction coefficient. The neuronal architecture that performed best corresponded to two hidden layers with 25 neurons each (2-25-25-1). Network performance was evaluated using mean square error, regression analysis, and the cross-entropy function. The neural model obtained presented a mean square error of 7.42E-13 and a relative error equal to 0.0035 % for the training data. Finally, the Bayesian Regularization backpropagation network demonstrated the ability to calculate the coefficient of friction for turbulent flows with an approximation of 10E-7 concerning the Colebrook-White equation. El modelo propuesto por Colebrook-White para el cálculo del coeficiente de fricción ha sido aceptado universalmente estableciendo una función trascendental implícita. Esta ecuación determina el coeficiente de fricción para flujos completamente desarrollados, es decir, para flujos turbulentos con un Número de Reynolds superior a 4000. En el presente estudio se desarrolló una Red Neuronal a partir del enfoque del método de Retropropagación de Regularización Bayesiana para estimar el coeficiente de fricción. Se estableció un conjunto de 200,000 datos de entrada (inputs) para la rugosidad relativa (ε/D) y el Número de Reynolds (Re) y 200,000 datos de salida (outputs) para el coeficiente de fricción. La arquitectura neuronal que mejor se desempeñó correspondió a dos capas ocultas con 25 neuronas cada una (2-25-25-1). Se evaluó el rendimiento de la red utilizando el error medio cuadrático, el análisis de regresión y la función de entropía cruzada. El modelo neuronal obtenido presentó un error medio cuadrático de 7.42E-13 y un error relativo igual a 0.0035 % para los datos de entrenamiento. Finalmente, la red de retropropagación de Regularización Bayesiana demostró la capacidad de calcular el coeficiente de fricción para flujos turbulentos con una aproximación de 10E-7 con respecto a la ecuación de Colebrook-White. Universidad Pedagógica y Tecnológica de Colombia 2022-01-29 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/13241 10.19053/01217488.v13.n1.2022.13241 Ciencia En Desarrollo; Vol. 13 No. 1 (2022): Vol. 13 Núm. 1 (2022): Vol 13, Núm.1 (2022): Enero-Junio; 9-23 Ciencia en Desarrollo; Vol. 13 Núm. 1 (2022): Vol. 13 Núm. 1 (2022): Vol 13, Núm.1 (2022): Enero-Junio; 9-23 2462-7658 0121-7488 spa https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/13241/12517 |
| spellingShingle | Coeficiente fricción, Colebrook-White, Regularización Bayesiana, Red Neuronal Artificial Artificial Neural Network, Bayesian Regularization, Coefficient of friction, Colebrook & White Ladino Moreno, Edgar Orlando García Ubaque, Cesar Augusto García-Vaca, María Camila Modeling of the friction factor in pressure pipes using Bayesian Learning Neural Networks |
| title | Modeling of the friction factor in pressure pipes using Bayesian Learning Neural Networks |
| title_alt | Modelado del factor de fricción en tuberías a presión Utilizando Redes Neuronales de Aprendizaje Bayesiano |
| title_full | Modeling of the friction factor in pressure pipes using Bayesian Learning Neural Networks |
| title_fullStr | Modeling of the friction factor in pressure pipes using Bayesian Learning Neural Networks |
| title_full_unstemmed | Modeling of the friction factor in pressure pipes using Bayesian Learning Neural Networks |
| title_short | Modeling of the friction factor in pressure pipes using Bayesian Learning Neural Networks |
| title_sort | modeling of the friction factor in pressure pipes using bayesian learning neural networks |
| topic | Coeficiente fricción, Colebrook-White, Regularización Bayesiana, Red Neuronal Artificial Artificial Neural Network, Bayesian Regularization, Coefficient of friction, Colebrook & White |
| topic_facet | Coeficiente fricción, Colebrook-White, Regularización Bayesiana, Red Neuronal Artificial Artificial Neural Network, Bayesian Regularization, Coefficient of friction, Colebrook & White |
| url | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/13241 |
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