Predicting discharge coefficient of triangular labyrinth weir using extreme learning machine, artificial neural network and genetic programming

Weirs are a type of hydraulic structure used to direct and transfer water flows in the canals and overflows in the dams. The important index in computing flow discharge over the weir is discharge coefficient ( C d ). The aim of this study is accurate determination of the C d in triangular labyrinth...

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Published in:	Neural computing & applications Vol. 29; no. 11; pp. 983 - 989
Main Authors:	Karami, Hojat, Karimi, Sohrab, Bonakdari, Hossein, Shamshirband, Shahabodin
Format:	Journal Article
Language:	English
Published:	London Springer London 01.06.2018 Springer Nature B.V
Subjects:	Artificial Intelligence Artificial neural networks Canals Computational Biology/Bioinformatics Computational Science and Engineering Computer Science Data Mining and Knowledge Discovery Discharge coefficient Genetic algorithms Image Processing and Computer Vision Learning theory Neural networks Predictions Probability and Statistics in Computer Science Review Root-mean-square errors Statistical methods Test procedures Training Weirs Artificial neural network Discharge coefficient Extreme learning machine Genetic programming Weir
ISSN:	0941-0643, 1433-3058
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Abstract	Weirs are a type of hydraulic structure used to direct and transfer water flows in the canals and overflows in the dams. The important index in computing flow discharge over the weir is discharge coefficient ( C d ). The aim of this study is accurate determination of the C d in triangular labyrinth side weirs by applying three intelligence models [i.e., artificial neural network (ANN), genetic programming (GP) and extreme learning machine (ELM)]. The calculated discharge coefficients were then compared with some experimental results. In order to examine the accuracy of C d predictions by ANN, GP and ELM methods, five statistical indices including coefficient of determination ( R 2 ), root-mean-square error (RMSE), mean absolute percentage error (MAPE), SI and δ have been used. Results showed that R 2 values in the ELM, ANN and GP methods were 0.993, 0.886 and 0.884, respectively, at training stage and 0.971, 0.965 and 0.963, respectively, at test stage. The ELM method, having MAPE, RMSE, SI and δ values of 0.81, 0.0059, 0.0082 and 0.81, respectively, at the training stage and 0.89, 0.0063, 0.0089 and 0.88, respectively, at the test stage, was superior to ANN and GP methods. The ANN model ranked next to the ELM model.
AbstractList	Weirs are a type of hydraulic structure used to direct and transfer water flows in the canals and overflows in the dams. The important index in computing flow discharge over the weir is discharge coefficient (Cd). The aim of this study is accurate determination of the Cd in triangular labyrinth side weirs by applying three intelligence models [i.e., artificial neural network (ANN), genetic programming (GP) and extreme learning machine (ELM)]. The calculated discharge coefficients were then compared with some experimental results. In order to examine the accuracy of Cd predictions by ANN, GP and ELM methods, five statistical indices including coefficient of determination (R2), root-mean-square error (RMSE), mean absolute percentage error (MAPE), SI and δ have been used. Results showed that R2 values in the ELM, ANN and GP methods were 0.993, 0.886 and 0.884, respectively, at training stage and 0.971, 0.965 and 0.963, respectively, at test stage. The ELM method, having MAPE, RMSE, SI and δ values of 0.81, 0.0059, 0.0082 and 0.81, respectively, at the training stage and 0.89, 0.0063, 0.0089 and 0.88, respectively, at the test stage, was superior to ANN and GP methods. The ANN model ranked next to the ELM model. Weirs are a type of hydraulic structure used to direct and transfer water flows in the canals and overflows in the dams. The important index in computing flow discharge over the weir is discharge coefficient ( C d ). The aim of this study is accurate determination of the C d in triangular labyrinth side weirs by applying three intelligence models [i.e., artificial neural network (ANN), genetic programming (GP) and extreme learning machine (ELM)]. The calculated discharge coefficients were then compared with some experimental results. In order to examine the accuracy of C d predictions by ANN, GP and ELM methods, five statistical indices including coefficient of determination ( R 2 ), root-mean-square error (RMSE), mean absolute percentage error (MAPE), SI and δ have been used. Results showed that R 2 values in the ELM, ANN and GP methods were 0.993, 0.886 and 0.884, respectively, at training stage and 0.971, 0.965 and 0.963, respectively, at test stage. The ELM method, having MAPE, RMSE, SI and δ values of 0.81, 0.0059, 0.0082 and 0.81, respectively, at the training stage and 0.89, 0.0063, 0.0089 and 0.88, respectively, at the test stage, was superior to ANN and GP methods. The ANN model ranked next to the ELM model.
Author	Bonakdari, Hossein Shamshirband, Shahabodin Karami, Hojat Karimi, Sohrab
Author_xml	– sequence: 1 givenname: Hojat surname: Karami fullname: Karami, Hojat email: hkarami@semnan.ac.ir organization: Department of Civil Engineering, Semnan University – sequence: 2 givenname: Sohrab surname: Karimi fullname: Karimi, Sohrab organization: Department of Civil Engineering, Semnan University – sequence: 3 givenname: Hossein surname: Bonakdari fullname: Bonakdari, Hossein organization: Department of Civil Engineering, Razi University – sequence: 4 givenname: Shahabodin surname: Shamshirband fullname: Shamshirband, Shahabodin organization: Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya
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Keywords	Artificial neural network Discharge coefficient Extreme learning machine Genetic programming Weir
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Snippet	Weirs are a type of hydraulic structure used to direct and transfer water flows in the canals and overflows in the dams. The important index in computing flow...
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SubjectTerms	Artificial Intelligence Artificial neural networks Canals Computational Biology/Bioinformatics Computational Science and Engineering Computer Science Data Mining and Knowledge Discovery Discharge coefficient Genetic algorithms Image Processing and Computer Vision Learning theory Neural networks Predictions Probability and Statistics in Computer Science Review Root-mean-square errors Statistical methods Test procedures Training Weirs
Title	Predicting discharge coefficient of triangular labyrinth weir using extreme learning machine, artificial neural network and genetic programming
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