Modeling Friction Factor in Pipeline Flow Using a GMDH-type Neural Network

The standard methods of calculating the fluid friction factor, the Colebrook–White and Haaland equations, require iterative solution of an implicit, transcendental function which entails high computational costs for large-scale piping networks while introducing as much as 15% error. This study applies the group method of data handling to the development of an artificial neural network optimized by multi-objective genetic algorithms to find an explicit polynomial model for friction factor. We developed a relatively simple and explicit model for friction factor that performs well over the entire range of applicability of the Colebrook–White equation: Reynolds number from 4,000 to 108 with relative roughness ranging from 5 × 10−6 to 0.05. For a network with only two hidden layers and a total of five neurons, this model was found to have a mean relative error of only 3.4% in comparison with the Colebrook–White equation; a determination coefficient (R2) over the range of input data was calculated to be 0.9954. The accuracy and simplicity of this model may make it preferable to traditional, transcendental representations of fluid friction factor. Further, this method of model development can be applied to any pertinent data-set—that is to say, the model can be tuned to the physical situation and input data range of interest