Application of random forest-based decision tree approach for modeling fully developed turbulent flow in rough pipes

Abstract

A random forest (RF) -based decision tree programming methodology was aimed for modeling fully developed turbulent flow conditions in rough pipes. In the present computational study, a flexible RF-based soft-computing strategy was applied for the estimation of the required pipe diameter (D) and Darcy–Weisbach friction factor (λ or f) obtained from the iterative solution of the implicit Colebrook–White equation for five basic pipeline design variables considered in sizing problems (Type 3) of pipe distribution systems. The prediction performance of the implemented RF-based model was assessed more than 15 different statistical goodness-of-fit parameters and useful mathematical diagrams such as box-and-whisker-plots and spread plots. The statistical metrics corroborated the superiority of the RF-based approach in predicting both the required pipe diameter (R2 = 0.9793, MAE = 0.0287 m, RMSE = 0.03833 m, SEE = 0.0326 m, IA or WI = 0.9933, CV(RMSE) or SI = 0.0595, NSE = 0.9753, LMI = 0.8482, and AIC = -1954.6438 for the testing dataset) and friction factor (R2 = 0.9576, MAE = 0.0011, RMSE = 0.0023, SEE = 0.0018, IA or WI = 0.9851, CV(RMSE) or SI = 0.0660, NSE = 0.9478, LMI = 0.8500, and AIC = -3646.7124 for the testing dataset). The descriptive statics suggested that the 25% percentile values (Q1), median values (Q2), and 75% percentile values (Q3) of RF-predicted values of D and λ and the corresponding actual values of these responses were found to be very close. The proposed RF-based model was also tested against additional some dataset obtained from the relevant literature. The validation results indicated that the applied decision tree-based method produced realistic estimations and acceptable statistics (i.e., R2 = 0.9624, MAE = 0.0598 m, and RMSE = 0.0708 m for D values, and R2 = 0.9130, MAE = 0.0043, RMSE = 0.0052 for λ values) even at extreme L values greater than 2000 m. This study demonstrated the importance and ability of the applied soft-computing strategy to accurately predict D and λ values and eliminated error-prone steps of the traditional iterative approach.