Services on Demand
Journal
Article
Indicators
Cited by SciELO
Access statistics
Related links
Cited by Google
Similars in SciELO
Similars in Google
Share
Revista Facultad de Ingeniería
Print version ISSN 0121-1129On-line version ISSN 2357-5328
Abstract
GARCIA-UBAQUE, Cesar-Augusto; LADINO-MORENO, Edgar-Orlando and GARCIA-VACA, María-Camila. Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks. Rev. Fac. ing. [online]. 2022, vol.31, n.59, e204. Epub May 04, 2022. ISSN 0121-1129. https://doi.org/10.19053/01211129.v31.n59.2022.14037.
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.
Keywords : Artificial Neural Network; Colebrook-White; Darcy-Weisbach; Levenberg-Marquardt; pipeline hydraulics.