Modeling and Assessment of Discharge Coefficient of Arc Labyrinth Weir Using Experimental and Meta-model Methods

Document Type : Research Paper


1 Assistant Professor, Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh, Iran.

2 Department of Civil Engineering, Ra,hormoz Branch, Islamic Azad University, Ramhormoz., Iran

3 Professor , Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Iran.

4 M.Sc.Student. Water and hydraulic structhures, Univ. of Maragheh, Iran


While having economic advantages, nonlinear labyrinth weirs have more passing flow capacity than linear weirs. Having a high capability of extracting hidden complex relationships among dependent and independent variables besides saving financial and time, intelligent algorithms are economic and time-saving and have dedicated a remarkable role among researchers. In this research, the performance of support vector machine (SVM) and gene expression programming (GEP) algorithms is figured out to predict the discharge coefficient (Cd) of the arched labyrinth weir using 226 experimental data series. Involved geometric and hydraulic parameters are total head (Ht), weir height (P), cycle arc angle (θ), Froud number (Fr), cycle wall length (Lt), the width of a cycle (w), weir nose length (A), an increase of weir height of 15% and change of weir crest shape change to quarter circle (U). Results showed that the maximum values of the Cd belong to arc labyrinth weir of arc angle 40 degrees. Numerical simulation illustrated that combination of (c، u،  ، ، ، ) and (c، u،  Fr، ، ، ) parameters have optimum performance in the SVM and GEP algorithms of assessment indices as (R2=0.9791, RMSE=0.03, DC=0.9776) and (R2=0.9871, RMSE=0.0231, DC=0.9856), respectively; showing highly accurate performance of two algorithms in the prediction of the Cd


Main Subjects

Abbaspour A, and Arovanaghy, (2009). Flow prediction weirs Composite Triangular Regular Using Gene Expression Programming. 10th Iran Hydraulic Conference, November, Iran Hydraulic Association, University of Gilan, Iran.
Aydin I., Sakarya A.B., Sisman Cigdem (2011). Discharge formula for rectangular sharp crested weir. Flow Measurement and Instrumentation, 22(2):144-151.
Crookston, B.M. (2010). Labyrinth weirs. Ph.D. thesis, Utah State University, Logan, UT.
Dabling, M.R. (2014). Nonlinear weir hydraulics. M.Sc. Thesis. Utah State University, Logan, UT.
Darvas, L. A. (1971). Performance and design of labyrinth weirs. Journal of Hydraulic Engineering 97(8): 1246-1251.
Dizabadi, Sh., SeyedHakim, S. and AzimiA A.H. (2020). Discharge characteristics and structure of flow in labyrinth weirs with a downstream pool. Flow Measurement and Instrumentation, 71, 1-16.
Farrokhy, A., Givachy, A,. and Azhdary moghaddam. (2009). Estimating Determining the Discharge Coefficient of lateral weirs with neural network and adaptive neural-inference system. 6th National Congress of Civil Engineering, Semnan University, Iran. (In Farsi)
Fuladipanah, M. and Majedi Asl, M. (2020). Soft Computing Application to Amplify Discharge Coefficient Prediction in the Side Rectangular Weirs. Journal Of Irrigation and Water Engineering, DOI: 10.22125/IWE.2020.255601.1438. (In Farsi)
Fuladipanah, M., Majedi Asl, M. and Haghgooyi, A. (2020). Application of intelligent algorithm to model head-discharge relationship for submerged labyrinth and linear weirs. Journal of Hydraulics, 15(2): 149-164. (In Farsi)
Haghiabi, A.H., Parsaie, A. and  Shamsi Z., 2018. Intelligent Modeling of Discharge Coefficient of Lateral Intakes. AUT Journal of Civil Engineering, 2(1): 3-11.
Hay, N. and G. Taylor. 1970. Performance and design of labyrinth weirs. Journal of Hydraulic Engineering 96(11): 2337–2357
Kabiri-Samani, A.R., Ansari, A., and Borghei, S.M. (2010). Hydraulic behavior of flow over an oblique weir. Journal of Hydraulic Research. 48(5): 669-673.
Kumar, M., Sihag, P., Tiwari, N.K. and Ranjan S. (2020). Experimental study and modelling discharge coefficient of trapezoidal and rectangular piano key weirs. Applied Water Science, 10: 43-52.
Lux, F. and Hinchcliff, D. (1985). Design and construction of labyrinth spillways. Proceeding of the 15th Congress ICOLD, Lausanne, Switzerland.
Majedi Asl, M. and Fuladipanah M. (2018). Application of the Evolutionary Methods in Determining the Discharge Coefficient of Triangular Labyrinth Weirs. Journal of Water and Soil Science (Science and Technology of Agriculture and Natural Resources), 22(4), 279-290 (In Farsi)
Mehri, Y., Esmaeili, S., Soltani, J., Saneie, S. and Rostami, M. (2018). Evaluation of SVM and nonlinear regression models for predicting the discharge coefficient of side piano key weirs in irrigation and drainage networks. Iranian Journal of Irrigation and Drainage, 12(70): 994-1003(in Persian).
Norouzi, R., Daneshfaraz, R. and Ghaderi, A. (2019). Investigation of discharge coefficient of trapezoidal labyrinth weirs using artificial neural networks and support vector machines. Applied Water Science, 9(148): 1-10.
Parsaie, A. and Haghiabi, A.H. (2016).  Prediction of discharge coefficient of side weir using adaptive neuro-fuzzy inference system. Sustainable Water Resources Management, 2: 257-264.
Parsaie, A. and Haghiabi, A.H. (2017). Support Vector Machine to predict the discharge coefficient of Sharp crested w-planform weirs. AUT Journal of Civil Engineering, 1(2): 195-204.
Parsaie, A.,Haghiabi, A.H. and Shamsi Z. (2019). Intelligent mathematical modeling of discharge coefficient of nonlinear weirs with triangular plan. AUT Journal of Civil Engineering, 3(2): 149-156.
Roushangar K., Alami M. T., Shiri J. and Majedi Asl, M. (2018). Determining discharge coefficient of labyrinth and arced labyrinth weirs using support vector machine. Hydrology Research, 49(3): 924-938.
Seo, I.W., Do, K.Y., Park, Y.S. and Song, C.G. (2016). Spillway discharges by modification of weir shapes and overflow surroundings. Environmental Earth Science, 75(6):496-509. 
Tullis J.P., Amanian N. and Waldron D. (1995). Design of Labyrinth Spillways. Journal of Hydraulic
Zerihun, Y.T. and Fenton, J.D. (2007). A Boussinesq-type model for flow over trapezoidal profile weirs. Journal of Hydraulic Research, 45(4), 519-528.