A new integrated model of the group method of data handling and the firefly algorithm (GMDH-FA): application to aeration modelling on spillways

Due to the high flow velocity over dam spillways and outlets, severe cavitation damage might occur to the structures. Aeration (introducing air into the passing flow) is a useful remedy for preventing or decreasing cavitation, however, proper estimation of aerators air demand is a complex problem. On that account, the standard GMDH model, integrated GMDH-HS (with the harmony search algorithm) model and a novel integrated GMDH-FA model (with the firefly algorithm), were developed and applied to estimate air demand on spillway aerators in dams. Input parameters including flow rate (Q(w)), flow depth (d(0)), relative pressure under the jet (h(s)), ramp angle (alpha), step height (s), and spillway slope (theta) were applied as the effective factors for estimating the amount of air flow of the aerators (Q(a)). General results based on several statistical measures (NRMSE, PCC, NMAE, NSE) and the test of ANOVA for models' residuals, showed that the standard GMDH improved the accuracy of estimating air flow in comparison to empirical equations (an average enhanced efficiency of 59.86% in terms of NRMSE) and multiple linear regression method (an enhanced efficiency of 37.15% in terms of NRMSE). Moreover, findings of the research revealed that the FA and HS algorithms improved the performance of the standard GMDH equal to 17% and 13%, respectively.