Prediction of the discharge capacity of piano key weirs using artificial neural networks

Abstract

Abstract The discharge capacity of the piano key weir (PKW) is an important flow feature which ultimately decides the type and geometric design of PKWs. In the present research work, the different architecture of artificial neural networks (ANNs) was employed to predict the discharge capacity of the trapezoidal piano key weir (TPKW) by varying geometric parameters (Si/So, Wi/Wo, Bi/Bo, L/W and α). Furthermore, adaptive neuro-fuzzy interference system (ANFIS), support vector machines (SVMs) and non-linear regression (RM) techniques were also applied to compare the performance of best ANN models. The performance of each model was evaluated using statistical indices including scatter index (SI); coefficient of determination (R2), and mean square error (MSE). The prediction capability of all the models was found to be satisfactory. However, results predicted by ANN-22(H-15) [R2 = 0.998, MSE = 0.0024, SI = 0.0177] was more accurate than ANFIS (R2 = 0.995, MSE = 0.00039, SI = 0.0256), SVM (R2 = 0.982, MSE = 0.000864, SI = 0.0395) and RM (R2 = 0.978, MSE = 0.001, SI = 0.0411). It was observed that Si/So, Wi/Wo and L/W geometric ratios have the greatest effect on the discharge performance of TPKW. Furthermore, sensitivity analysis confirmed that h/P is the most influencing ratio which may considerably affect the discharge efficiency of the TPKW. It was found that ANN models having a single hidden layer and keeping neurons three times of input parameters in hidden layers generated better results.