Estimating discharge coefficient of triangular free overfall using the GMDH technique

Abstract

Free overfalls are hydraulic structures used in flood control, water supply, irrigation, and flow measurements. The hydraulic systems of free overfall depend on rectangular end shape. The studies that dealt with triangular crest are few and almost non-existent. In this study, a triangular end-shape design uses multiple linear regression (MLR) and group method of data handling (GMDH) methods for four models with six sub-models. Then, 24 scenarios were chosen and compared. The discharge coefficient (Cd) of a free overfall with a triangular terminal was predicted using experimental data. The triangular end edge shape increased crest length, the discharge coefficient, and discharge passing over free overfall. To this goal, 180 triangular free fall tests were performed. Data were collected for two triangular free overfalls with an opposite flow direction with three angles 600, 750, and 900. Results of Cd acquired using the two ways discussed above show that the algorithm GMDH outperforms the other method. Values for the GMDH approach mod46 testing variables: RMSE, MARE, SI, R2, and NSE are 6.08E-17, 2.65E-17, 6.00E-17, 100.00%, and 1.00, respectively, while these values for MLR are 0.06332, 0.05970, 0.06624, 15.431%, and −3.0419, respectively. The GMDH technique shows the best results concerning MLR and then chooses the best four scenarios from 24 with a Cd percentage error not exceeding ±2%.