Prediction of Discharge Capacity of Labyrinth Weir with Gene Expression Programming
This paper proposes a model based on gene expression programming for predicting discharge coefficient of triangular labyrinth weirs. The parameters influencing discharge coefficient prediction were first examined and presented as crest height ratio to the
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[email protected] 2 School of Engineering, University of Guelph, Guelph, ON NIG 2W1, Canada 3 Department of Statistics, Razi University, Kermanshah, Iran 4 Department of Mathematics and Informatics, J. Selye University, 94501 Komarno, Slovakia 5 Kalman Kando Faculty of Electrical Engineering, Obuda University, Budapest 1034, Hungary 6 Institute of Structural Mechanics, Bauhaus-Universität Weimar, 99423 Weimar, Germany
Abstract. This paper proposes a model based on gene expression programming for predicting discharge coefficient of triangular labyrinth weirs. The parameters influencing discharge coefficient prediction were first examined and presented as crest height ratio to the head over the crest of the weir (p/y), crest length of water to channel width (L/W), crest length of water to the head over the crest of the √ weir (L/y), Froude number (F = V/ (gy)) and vertex angle (θ) dimensionless parameters. Different models were then presented using sensitivity analysis in order to examine each of the dimensionless parameters presented in this study. In addition, an equation was presented through the use of nonlinear regression (NLR) for the purpose of comparison with Gene Expression Programming (GEP). The results of the studies conducted by using different statistical indexes indicated that GEP is more capable than NLR. This is to the extent that GEP predicts discharge coefficient with an average relative error of approximately 2.5% in such manner that the predicted values have less than 5% relative error in the worst model. Keywords: Discharge coefficient · Soft computing · Weir · Sensitivity analysis · Nonlinear regression
1 Introduction Conventional weirs are structures used to control, regulate and measure water level and flow volume in irrigation and drainage networks and water and wastewater treatment plants. A conventional weir is usually installed along the flow and perpendicular to channel axis. Conventional weirs include rectangular, V-notch, labyrinth and complex weirs. Many theoretical and experimental studies investigated passing flow from conventional weirs. Taylor [1] presented an experimental study on hydraulic labyrinth weirs. Hay and Taylor [2] described how the head on the labyrinth weir effects the discharge ratio. Tullis et al. [3] investigated trapezoid labyrinth weirs and indicated that their discharge © Springer Nature Switzerland AG 2021 K. Arai et al. (Eds.): IntelliSys 2020, AISC 1250, pp. 202–217, 2021. https://doi.org/10.1007/978-3-030-55180-3_17
Prediction of Discharge Capacity of Labyrinth Weir
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capacity was a function of total head, effective length of weir crest and coefficient of discharge of labyrinth weir. Wormleaton and Soufiani [4] studied hydraulic features and aeration of triangle labyrinth weirs. They found that aeration efficiency of triangle labyrinth weirs is more than linear weirs with equal length. Also, Wormleaton and Tsang [5] studied aeration of rectangular weirs experimentally. Emiroglu and Baylar [6] investigated the effects of weir included an
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