Abstract
The scour below spillways can endanger the stability of the dams. Hence, determining the scour depth downstream of spillways is of vital importance. Recently, soft computing models and, in particular, artificial neural networks (ANNs) have been used for scour depth prediction. However, ANNs are not as comprehensible and easy to use as empirical formulas for the estimation of scour depth. Therefore, in this study, two decision-tree methods based on model trees and classification and regression trees were employed for the prediction of scour depth downstream of free overfall spillways. The advantage of model trees and classification and regression trees compared to ANNs is that these models are able to provide practical prediction equations. A comparison between the results obtained in the present study and those obtained using empirical formulas is made. The statistical measures indicate that the proposed soft computing approaches outperform empirical formulas. Results of the present study indicated that model trees were more accurate than classification and regression trees for the estimation of scour depth.
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References
Veronese A (1937) Erosion de fond en aval d’une decharge. In: IAHR, meeting for hydraulic works, Berlin
Kotlus D (1967) Das kolkproblem unter Breucksichtigung der Faktoren Zeit und Geschiebemischung im Rahmen der Wildbachverbauung. Diss. T U Braunschweig
Wu CM (1973) Scour at downstream end of dams in Taiwan. In: International symposium on river mechanics, Bangkok, pp 1–6
Martins RBF (1975) Scouring of rocky river beds by free jet spillways. Water Power Dam Constr 27(4):152–153
Mason PJ (1984) Erosion of Plung pools downstream of dams due to the action of free trajectory Jets. Proc Inst Civil Eng Water Marit Eng 76(5):523–537
Mason PJ, Arumugam K (1985) Free jet scour below dams and flip buckets. J Hydraul Eng 111(2):220–235
Mahboobi E (1997) The effect of sediment size on maximum scour depth in plunge pool. MS thesis in hydraulic structure engineering, University of science and technology, Tehran
Azar FA (1998) Effect of sediment size distribution on scour downstream of free overfall Spillway. MS thesis, Tarbiat Modares University, Tehran
Ghodsian M, Abbasi AA, Azar FA (1998) Maximum depth of scour below free jet spillway. In 5th National Seminar on River Engineering, Ahvaz, pp 372–378
Afshar A, Jabbari E (2001) Effect of bed materials size on the maximum depth of scour in overflow spillway. International Journal of Engineering Science, Special issue on civil engineering, pp 17–27
Ghodsian M, Azar FA (2002) Scour hole characteristics below free overfall Spillway. Int J Sediment Res 17(4):304–313
Azmathullah HMd, Deo MC, Deolalikar PB (2005) Neural networks for estimation of scour downstream of a ski-jump bucket. J Hydraul Eng 131(10):898–908
Azmathullah HMd, Ghani AA (2011) ANFIS-based approach for predicting the scour depth at culvert outlets. J Pipeline Syst Eng Pract 2(1):35–40
Azmathullah HMd, Ghani AA, Zakaria NA, Lai SH, Chang CK, Leow CS, Abuhasan Z (2008) Genetic programming to predict ski-jump bucket spillway scour. J Hydrodyn 20(4):477–484
Guven A, Gunal M (2008) Genetic programming approach for prediction of local scour downstream hydraulic structures. J Irrig Drain Eng 134(2):241–249
Azamathullah HMd, Zakaria NA (2011) Appraisals of soft-computing techniques in prediction of spillway scour depth. Dam Eng XXI 3:189–202
Guven A, Azamathulla HMd, Zakaria NA (2009) Linear genetic programming for prediction of circular pile scour. J Ocean Eng 36(12–13):985–991
Goel A, Pal M (2009) Application of support vector machines in scour prediction on grade-control structures. Eng Appl Artif Intell 22(2):216–223
Agarwal M, Goyal M, Deo MC (2008) Locally weighted projection regression for predicting hydraulic parameters. Civil Eng Environ Syst 27(1):71–80
Samadi M, Jabbari E (2011) Prediction of scour depth downstream of ski-jump spillways using field data. In 10th hydraulic conference of Iran, Guilan University, Rasht
Alavi AH, Gandomi AH (2011) A robust data mining approach for formulation of geotechnical engineering systems. Eng Comput 28(3):242–274
Guven A, Aytek A, Yuce MI, Aksoy H (2008) Genetic programming based empirical model for daily reference evapotranspiration estimation. CLEAN- Soil Air Water 36(10–11):905–912
Kisi O, Guven A (2010) A machine code-based genetic programming for suspended sediment concentration estimation. Adv Eng Softw 41(7–8):939–945
Azamathulla HMd (2012) Gene-expression programming to predict friction factor for Southern Italian rivers. Neural Computing and Applications, pp 1–6
Azamathulla HMd, Ahmad Z, Ghani AA (2012) An expert system for predicting Manning’s roughness coefficient in open channels by using gene expression programming. Neural Computing and Applications, pp 1–7
Gandomi AH, Alavi AH (2012) A new multi-gene genetic programming approach to non-linear system modeling. Part II: geotechnical and earthquake engineering problems. Neural Comput Appl 21(1):189–201
Gandomi AH, Alavi AH, Sahab M (2010) New formulation for compressive strength of CFRP confined concrete cylinders using linear genetic programming. Mater Struct 43(7):963–983
Zakaria NA, Azamathulla HMd, Chang CK, Ghani A (2010) Gene expression programming for total bed material load estimation—a case study. Sci Total Environ 408(21):5078–5085
Guven A, Aytek A, Azamathulla HMd (2012) A practical approach to formulate stage–discharge relationship in natural rivers. Neural Computing and Applications, pp 1–8
Goyal M, Ojha C (2011) Estimation of scour downstream of a ski-jump bucket using support vector and M5 model Tree. Water Resour Manage 25(9):2177–2195
Etemad-Shahidi A, Yasa R, Kazeminezhad MH (2011) Prediction of wave-induced scour depth under submarine pipelines using machine learning approach. Appl Ocean Res 33(1):54–59
Etemad-Shahidi A, Ghaemi N (2011) Model tree approach for prediction of pile groups scour due to waves. Ocean Eng 38(13):1522–1527
Etemad-Shahidi A, Mahjoobi J (2009) Comparison between M5′ model tree and neural networks for prediction of significant wave height in Lake Superior. Ocean Eng 36(15–16):1175–1181
Etemad-Shahidi A, Bonakdar L (2009) Design of rubble-mound breakwaters using M5′ machine learning method. Appl Ocean Res 31(3):197–201
Etemad-Shahidi A, Bali M (2012) Stability of rubble-mound breakwater using H50 wave height parameter. Coast Eng 59(1):38–45
Ayoubloo MK, Azamathulla HM, Ahmad Z, Ghani A, Mahjoobi J, Rasekh A (2011) Prediction of scour depth in downstream of ski-jump spillways using soft computing techniques. Int J Comput Appl 33(1):92–97
Mahjoobi J, Sabzianpoor A, Jabbari E (2010) Application of meta-heuristic models for local scour evaluation. AIP Conf Proc 1303(1):389–397
Ayoubloo MK, Azamathulla HM, Jabbari E, Zanganeh M (2011) Predictive model-based for the critical submergence of horizontal intakes in open channel flows with different clearance bottoms using CART, ANN and linear regression approaches. Expert Syst Appl 38(8):10114–10123
Ayoubloo MK, Etemad-Shahidi A, Mahjoobi J (2010) Evaluation of regular wave scour around a circular pile using data mining approaches. Appl Ocean Res 32(1):34–39
Mahjoobi J, Etemad-Shahidi A (2008) An alternative approach for the prediction of significant wave heights based on classification and regression trees. Appl Ocean Res 30(3):172–177
Gutiérrez ÁG, Schnabel S, Lavado Contador JF (2009) Using and comparing two nonparametric methods (CART and MARS) to model the potential distribution of gullies. Ecol Model 220(24):3630–3637
Jain P, Deo MC (2008) Artificial intelligence tools to forecast ocean waves in real time. Open Ocean Eng J 1:13–21 (Bentham Science)
Jain P, Deo MC, Latha G, Rajendran V (2011) Real time wave forecasting using wind time history and numerical model. Ocean Model 36(1–2):26–39
Quinlan JR (1992) Learning with continuous classes. In: Adams, Sterling (eds) Proceedings of AI’92, World Scientific, pp 343–348
Wang Y, Witten IH (1997) Induction of model trees for predicting continuous classes. In: Proceedings of the Poster Papers of the European Conference on Machine Learning, University of Economics, Faculty of Informatics and Statistics, Prague
Breiman L, Friedman JH, Olshen RA, Stone CJ (1984) Classification and regression trees. Wadsworth Statistical Press, Belmont
Bonakdar L, Etemad-Shahidi A (2011) Predicting wave run-up on rubble-mound structures using M5 model tree. Ocean Eng 38(1):111–118
Bhattacharya B, Price R, Solomatin DP (2007) Machine learning approach to modeling sedimentationtransport. J Hydraul Eng 133(4):440–450
Acknowledgments
The first author expresses special thanks to Mrs. Touran Amini, Eng. Abbas Amini, and Eng. Amir Razzaghi for their support and would like to thank M. K. Ayoubloo and M. Mojallal for their helpful suggestions. In addition, the two first authors are grateful to the Iran Water Resource management company for funding this work (Grant No. RIV4-89107) and to the Deputy of Research, Iran University of Science Technology (IUST), for partial support of this work.
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Samadi, M., Jabbari, E. & Azamathulla, H.M. Assessment of M5′ model tree and classification and regression trees for prediction of scour depth below free overfall spillways. Neural Comput & Applic 24, 357–366 (2014). https://doi.org/10.1007/s00521-012-1230-9
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DOI: https://doi.org/10.1007/s00521-012-1230-9