Estimating the aeration coefficient and air demand in bottom outlet conduits of dams using GEP and decision tree methods

Abstract

Accurate estimates of air demand are critical when addressing the cavitation phenomenon in bottom outlet conduits of dams. In the present study, this accuracy was evaluated for air demand estimation models using gene expression programming (GEP), classification tree methods [including boosted regression trees (BRT) and random forest (RF) algorithms], and empirical relationships. Using k-fold cross validation and drawing on data from 6 dams, two different air-demand-related parameters were estimated (aerator air discharge demand and aeration coefficient) and the estimation accuracy was assessed using the Nash-Sutcliffe (NS) efficiency and other statistics. Outperforming the other models, the GEP model performed well in estimating aerator air demand (NS =0.674) and the aeration coefficient (NS =0.489). Moreover, on average, the GEP model showed 45% and 12% improvements in aeration coefficient estimation accuracy over empirical relationships and decision tree methods, respectively. Finally, in the function finding phase, the derived mathematical models were presented as non-linear equations to estimate the air demand of aerator and aeration coefficients using a non-linear relation derived from the GEP model.