Tree-based nonlinear ensemble technique to predict energy dissipation in stepped spillways

In this study, under the skimming flow regime, energy dissipation was investigated with data-driven methods. The data set obtained from the laboratory experiments were modelled by different machine learning (ML) methods, including support vector machine (SVM), K-star (K*) algorithm and artificial neural networks (ANN). Afterwards, for the first time in the literature, linear and nonlinear ensemble models were established in order to improve the accuracy of single models in predicting energy dissipation. Simple average (SA-E) and weighted average (WA-E) were performed as linear ensemble models while M5 Model Tree (M5-MTE) and Random Forest (RF-E) were used to establish non-linear ensemble models. The model results were evaluated according to performance metrics, such as Coefficient of Correlation (CC), Percent Bias (PBIAS), Performance Index (PI), Willmott’s index of agreement (WI) and Nash-Sutcliffe efficiency criteria (NSE). The NSE values are calculated as 0.986, 0.909 and 0.985 for SVM, K* and ANN models, respectively. Moreover, for the ensemble models, higher NSE values were obtained for both linear (NSE_SA-E = 0.9887, NSE_WA-E = 0.9916) and tree-based non-linear (NSE_{M5 MT-E} = 0.9963, NSE_RF-E = 0.9974) models. Overall, it can be stated that tree-based ensemble models make better predictions for energy dissipation calculation in step spilways compared to single ML methods.