Modeling of the friction factor in pressure pipes using Bayesian Learning Neural Networks (2022)
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.