The feasibility of Levenberg-Marquardt algorithm combined with imperialist competitive computational method predicting drag reduction in crude oil pipelines

Adding small amounts of drag-reducing agents (DRA) to the crude oil can effectively reduce energy losses and its associated pressure drop in transportation pipelines. They do their roles by reducing the turbulent friction factor of the flowing liquids in the pipeline. In this study, the artificial neural networks (ANN) are utilized for estimation of drag reduction (DR) in crude oil pipelines as a function of Reynolds number, concentration, and type of drag-reducing agents, temperature, and type of pipe. Two different training algorithms, i.e. Levenberg-Marquardt (LM) and imperialist competition algorithm (ICA) are used for adjustment of parameters of multilayer perceptron (MLP) networks. Predictive accuracies of trained MLP by Levenberg-Marquardt (LM-MLP) and imperialist competition algorithm (ICA-MLP) for estimating drag reduction in crude oil pipelines were compared. The comparisons were done by three statistical criteria, i.e. root mean square error (RMSE), the coefficient of determination (R-2), and mean absolute error (MAE). The obtained results show that replacing LM by ICA evolutionary algorithm for adjustment of parameters of MLP leads to increasing R-2 from 0.9585 to 0.9791 in the training phase, and from 0.9310 to 0.9698 in the testing phase. Furthermore, ICA has reduced the RMSE and MAE of testing group from 3.0396 to 2.2616 to the 2.0080 and 1.5579, respectively. Finally, a simple ANN-based formulation is provided for using our developed ICA-MLP model to estimate DR in the crude oil pipelines.