GMDH-type neural network approach for modeling the discharge coefficient of rectangular sharp-crested side weirs

Abstract

a b s t r a c tEstimating the discharge coefficient using hydraulic and geometrical specifications is one of the influential factors in predicting the discharge passing over a side weir. Taking into account the fact that existing equations are incapable of estimating the discharge coefficient well, artificial intelligence methods are used to predict it. In this study, Group Method of Data Handling (GMDH) was used for the purpose of predicting the discharge coefficient in a side weir. The Froude number (F 1 ), weir dimensionless length (b/B), ratios of weir length to depth of upstream flow (b/y 1 ) and weir height to its length (p/y 1 ) were taken as input parameters to express a new model for predicting the discharge coefficient. Two different sets of laboratory data were used to train the artificial network and test the new model. Different statistical indexes were used to evaluate the performance of the GMDH model presented for two states, training and testing. The results indicate that the proposed model predicts the discharge coefficient precisely (MAPE ¼ 5.263 & RMSE ¼ 0.038) and this model is more accurate in predicting than the feed-forward neural network model and existing nonlinear regression equations.

Prediction of discharge coefficient of side weir using adaptive neuro-fuzzy inference system

“…5 and 6, the ANFIS model's ability is suitable for predicting the values of the Cd sw in the training and testing stages and also this model has suitable performance to predict the maximum values of the Cd sw . The results of this study uphold the results of Ebtehaj et al (2015a) and Ebtehaj et al (2015b). Ebtehaj et al (2015a) stated that for prediction of discharge coefficient of side weir using the GMDH, Fr and P/h 1 are the most important parameters also reviewing the studies which were conducted by Ebtehaj et al (2015b) and Emiroglu et al (2011a, b) showed that they considered more weight for the both parameters during the model development.…”

“…In the computational hydraulic field, the water surface profile and flow properties were studied (Parsaie and Haghiabi 2015a, b). Side weir discharge coefficient was predicted and modeled by most types of neural network techniques such as multilayer perceptron (MLP) neural network, adaptive neuro-fuzzy inference system (ANFIS), and group method of data handling (GMDH) (Ebtehaj et al 2015a;Emiroglu et al 2011b;Kisi et al 2012). Based on the reports the accuracy of these models are much more than the empirical formulas.…”

Development of group method of data handling based on genetic algorithm to predict incipient motion in rigid rectangular storm water channel

“…To survey the variation trend regarding Fr based on input parameters (d=R and t s =R), the partial derivative sensitivity analysis approach is employed [46][47]. In this method, the sensitivity of goal variable (Fr) on di erent input variables (d=R and t s =R) is investigated by partial derivative (@(Fr)=@x i ; x i is the input variable).…”

“…Afterwards, di erent types of neural networks are generated through the connection formed between the inputs and the neurons of the hidden layers. One of the simplest types of these neural networks is the CS-GMDH (Conventional Structure) which uses only the neurons of the adjacent layer to construct neurons in the new layer, but another type is known as GS-GMDH (Generalized Structure) which is utilized in this study and is not limited to using the nonadjacent neurons [30,44]. The length of the neurons is calculated as 2HL + 1 in GS-GMDH,`HL', indicating the hidden layers.…”

“…Group Method of Data Handling network is one of the self-organized methods amongst soft computing methods based on arti cial intelligence, capable of solving di erent problems in extremely complex nonlinear systems [22][23][24][25]. The GMDH method has been used to recognize behavior of nonlinear systems in di erent subjects in hydraulic such as friction factor in pipeline [26], scour depth [27][28][29], discharge condent [30,31], ow discharge in straight compound channels [32,33], basin sediment yield [34], and longitudinal dispersion in water networks [35].…”