Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks
The fifth-degree polynomial equation determines the diameter in pressurized drinking water systems. The input variables are Q: flow (m3/s), H: pressure drop (m); L: pipe length (m); ε: roughness (m), ϑ: kinematic viscosity (m2/s), and Ʃk: sum of minor loss coefficients (dimensionless). After applyin...
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| Format: | Online |
| Language: | eng |
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Universidad Pedagógica y Tecnológica de Colombia
2022
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| Online Access: | https://revistas.uptc.edu.co/index.php/ingenieria/article/view/14037 |
| _version_ | 1801706098367922176 |
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| author | García-Ubaque, Cesar-Augusto Ladino-Moreno, Edgar-Orlando García-Vaca, María-Camila |
| author_facet | García-Ubaque, Cesar-Augusto Ladino-Moreno, Edgar-Orlando García-Vaca, María-Camila |
| author_sort | García-Ubaque, Cesar-Augusto |
| collection | OJS |
| description | The fifth-degree polynomial equation determines the diameter in pressurized drinking water systems. The input variables are Q: flow (m3/s), H: pressure drop (m); L: pipe length (m); ε: roughness (m), ϑ: kinematic viscosity (m2/s), and Ʃk: sum of minor loss coefficients (dimensionless). After applying the energy equation for a hydraulic system composed of two tanks connected to a pipe of constant diameter and accepting the Colebrook-White and the Darcy-Weisbach equations, an undetermined expression is obtained since more unknowns than equations are established. This problem is solved by implementing a nested loop for the coefficient of friction and the diameter. This article proposes an Artificial Neural Network (ANN) implementing the Levenberg-Marquardt backpropagation method to estimate the diameter from the log-sigmoidal transfer function under stationary flow conditions. The training signals set consists of 5,000 random data that follow a normal distribution, calculated in Visual Basic (®Excel). The statistics used for the network evaluation correspond to the mean square error, the regression analysis, and the cross-entropy function. The architecture with the best performance had a hidden layer with 25 neurons (6-25-1) presenting an MSE equal to 5.41E-6 and 9.98E+00 for the Pearson Correlation Coefficient. The cross-validation of the neural scheme was carried out from 1,000 independent input signals from the training set, obtaining an MSE equal to 6.91E-6. The proposed neural network calculates the diameter with a relative error equal to 0.01% concerning the values obtained with ®Epanet, evidencing the generalizability of the optimized system. |
| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-14037 |
| institution | Revista Facultad de Ingeniería |
| language | eng |
| publishDate | 2022 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-140372022-11-18T19:26:00Z Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks Determinación del diámetro interior de tuberías a presión para sistemas de agua potable utilizando redes neuronales artificiales García-Ubaque, Cesar-Augusto Ladino-Moreno, Edgar-Orlando García-Vaca, María-Camila Artificial Neural Network cold chain. Darcy-Weisbach Levenberg-Marquardt pipeline hydraulics Colebrook-White Darcy-Weisbach hidráulica de tuberías Levenberg-Marquardt red neuronal artificial The fifth-degree polynomial equation determines the diameter in pressurized drinking water systems. The input variables are Q: flow (m3/s), H: pressure drop (m); L: pipe length (m); ε: roughness (m), ϑ: kinematic viscosity (m2/s), and Ʃk: sum of minor loss coefficients (dimensionless). After applying the energy equation for a hydraulic system composed of two tanks connected to a pipe of constant diameter and accepting the Colebrook-White and the Darcy-Weisbach equations, an undetermined expression is obtained since more unknowns than equations are established. This problem is solved by implementing a nested loop for the coefficient of friction and the diameter. This article proposes an Artificial Neural Network (ANN) implementing the Levenberg-Marquardt backpropagation method to estimate the diameter from the log-sigmoidal transfer function under stationary flow conditions. The training signals set consists of 5,000 random data that follow a normal distribution, calculated in Visual Basic (®Excel). The statistics used for the network evaluation correspond to the mean square error, the regression analysis, and the cross-entropy function. The architecture with the best performance had a hidden layer with 25 neurons (6-25-1) presenting an MSE equal to 5.41E-6 and 9.98E+00 for the Pearson Correlation Coefficient. The cross-validation of the neural scheme was carried out from 1,000 independent input signals from the training set, obtaining an MSE equal to 6.91E-6. The proposed neural network calculates the diameter with a relative error equal to 0.01% concerning the values obtained with ®Epanet, evidencing the generalizability of the optimized system. El diámetro en sistemas a presión de agua potable es posible determinarlo mediante una ecuación polinómica de quinto grado. Como variables de entrada se tiene: Q: caudal (m3/s), H: pérdida de carga (m); L: longitud de la tubería (m); ε: rugosidad (m), : viscosidad cinemática (m2/s) y Ʃk: sumatoria de coeficientes de pérdidas menores (adimensional). Aplicado la ecuación de la energía para un sistema hidráulico compuesto por dos tanques conectados con una tubería de diámetro constante y aceptando la ecuación de Colebrook-White y la ecuación de Darcy-Weisbach se obtiene una expresión subdeterminada debido a que se establecen más incógnitas que ecuaciones. Este problema se soluciona implementando un bucle anidado para el coeficiente de fricción y el diámetro. Este artículo propone una Red Neuronal Artificial (RNA) implementando el método de Retropropagación Levenberg-Marquardt para estimar el diámetro a partir de la función de transferencia log-sigmoidal, esto bajo condiciones estacionarias de flujo. El conjunto de las señales de entrenamiento está conformado por 5,000 datos aleatorios que siguen una distribución normal, calculados en Visual Basic (®Excel). Los estadísticos utilizados para la evaluación de la red corresponden al error medio cuadrático, el análisis de regresión y la función de entropía cruzada. La arquitectura que demostró un mejor redimento correspondió a una capa oculta con 25 neuronas (6-25-1) presentando un MSE igual a 5.41E-6 y 9.98E+00 para el Coeficiente de Correlación de Pearson. La validación cruzada del esquema neuronal se realizó a partir de 1,000 señales de entrada independientes del conjunto de entrenamiento obteniendo MSE igual 6.91E-6. La red neuronal propuesta calcula el diámetro con un error relativo igual a 0.01% con respecto a los valores obtenidos a partir de ®Epanet, evidenciando la capacidad de generalización del sistema optimizado. Universidad Pedagógica y Tecnológica de Colombia 2022-03-25 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf text/xml https://revistas.uptc.edu.co/index.php/ingenieria/article/view/14037 10.19053/01211129.v31.n59.2022.14037 Revista Facultad de Ingeniería; Vol. 31 No. 59 (2022): January-March 2022 (Continuous Publication); e14037 Revista Facultad de Ingeniería; Vol. 31 Núm. 59 (2022): Enero-Marzo 2022 (Publicación Continua); e14037 2357-5328 0121-1129 eng https://revistas.uptc.edu.co/index.php/ingenieria/article/view/14037/11574 https://revistas.uptc.edu.co/index.php/ingenieria/article/view/14037/11680 Copyright (c) 2022 Cesar-Augusto García-Ubaque, Edgar-Orlando Ladino-Moreno, María-Camila García-Vaca http://creativecommons.org/licenses/by/4.0 |
| spellingShingle | Artificial Neural Network cold chain. Darcy-Weisbach Levenberg-Marquardt pipeline hydraulics Colebrook-White Darcy-Weisbach hidráulica de tuberías Levenberg-Marquardt red neuronal artificial García-Ubaque, Cesar-Augusto Ladino-Moreno, Edgar-Orlando García-Vaca, María-Camila Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks |
| title | Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks |
| title_alt | Determinación del diámetro interior de tuberías a presión para sistemas de agua potable utilizando redes neuronales artificiales |
| title_full | Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks |
| title_fullStr | Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks |
| title_full_unstemmed | Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks |
| title_short | Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks |
| title_sort | determination of the inside diameter of pressure pipes for drinking water systems using artificial neural networks |
| topic | Artificial Neural Network cold chain. Darcy-Weisbach Levenberg-Marquardt pipeline hydraulics Colebrook-White Darcy-Weisbach hidráulica de tuberías Levenberg-Marquardt red neuronal artificial |
| topic_facet | Artificial Neural Network cold chain. Darcy-Weisbach Levenberg-Marquardt pipeline hydraulics Colebrook-White Darcy-Weisbach hidráulica de tuberías Levenberg-Marquardt red neuronal artificial |
| url | https://revistas.uptc.edu.co/index.php/ingenieria/article/view/14037 |
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