Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks
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Universidad Pedagógica y Tecnológica de Colombia
2022
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| author | Cesar-Augusto García-Ubaque |
| author_facet | Cesar-Augusto García-Ubaque |
| contents | Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks Cesar-Augusto García-Ubaque Edgar-Orlando Ladino-Moreno María-Camila García-Vaca Ingeniería White Darcy Weisbach Colebrook Marquardt 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. 2022 artículo científico 0121-1129 https://www.redalyc.org/articulo.oa?id=413971146005 https://www.redalyc.org/journal/4139/413971146005/ https://www.redalyc.org/journal/4139/413971146005/html/ https://www.redalyc.org/journal/4139/413971146005/413971146005.epub https://www.redalyc.org/journal/4139/413971146005/movil 10.19053/01211129.v31.n59.2022.14037 en http://www.redalyc.org/revista.oa?id=4139 Facultad de Ingeniería application/pdf Universidad Pedagógica y Tecnológica de Colombia Facultad de Ingeniería (Colombia) Num.59 Vol.31 |
| format | Artículo científico |
| id | redalyc_413971146005 |
| institution | Redalyc |
| language | en |
| publishDate | 2022 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| spellingShingle | Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks Cesar-Augusto García-Ubaque Ingeniería White Darcy Weisbach Colebrook Marquardt Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks Cesar-Augusto García-Ubaque Edgar-Orlando Ladino-Moreno María-Camila García-Vaca Ingeniería White Darcy Weisbach Colebrook Marquardt 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. 2022 artículo científico 0121-1129 https://www.redalyc.org/articulo.oa?id=413971146005 https://www.redalyc.org/journal/4139/413971146005/ https://www.redalyc.org/journal/4139/413971146005/html/ https://www.redalyc.org/journal/4139/413971146005/413971146005.epub https://www.redalyc.org/journal/4139/413971146005/movil 10.19053/01211129.v31.n59.2022.14037 en http://www.redalyc.org/revista.oa?id=4139 Facultad de Ingeniería application/pdf Universidad Pedagógica y Tecnológica de Colombia Facultad de Ingeniería (Colombia) Num.59 Vol.31 |
| title | Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks |
| topic | Ingeniería White Darcy Weisbach Colebrook Marquardt |
| url | https://www.redalyc.org/articulo.oa?id=413971146005 https://www.redalyc.org/journal/4139/413971146005/ https://www.redalyc.org/journal/4139/413971146005/html/ https://www.redalyc.org/journal/4139/413971146005/413971146005.epub https://www.redalyc.org/journal/4139/413971146005/movil |