A laboratory investigation on the potential of computational intelligence approaches to estimate the discharge coefficient of piano key weir

Abstract

The piano key weir (PKW) is a type of nonlinear control structure that can be used to increase unit discharge over linear overflow weir geometries, particularly when the weir footprint area is restricted To predict the outflow passing over a piano key weir, the discharge coefficient in the general equation of weir needs to be known. This paper presents the results of laboratory model testing of a piano key weir located on the straight open channel flume in the hydraulic laboratory of Bu-Ali Sina University. The discharge coefficient of piano key weir is estimated by using four computational intelligence approaches, namely, feed forward back-propagation neural network (FFBPN), an extension of genetic programming namely gene-expression programming (GEP), least square support vector machine (LSSVM) and extreme learning machine (ELM). For this purpose, 70 laboratory test results were used for determining discharge coefficient of piano key weir for a wide range of discharge values. Coefficient of determination (R2), Nash-Sutcliffe efficiency coefficient (NS), root mean square error (RMSE), mean absolute relative error (MARE), scatter index (SI) and BIAS are used for measuring the models’ performance. Overall performance of the models shows that, all the studied models are able to estimate discharge coefficient of piano key weir satisfactorily. Comparison of results showed that the ELM (R2=0.997 and NS= 0.986) and LSSVM (RMSE=0.016 and MARE=0.027) models were able to produce better results than the other models investigated and could be employed successfully in modeling discharge coefficient from the available experimental data.