MARS for Prediction of Shear Force and Discharge in Two-Stage Meandering Channel
Publication: Journal of Irrigation and Drainage Engineering
Volume 145, Issue 8
Abstract
Accurate prediction of shear stress distribution along the boundary in an open channel is the key to the solution of numerous critical engineering problems. This paper investigated the distribution of boundary shear force at the cross section of meandering compound channels. The research focused on developing a model for predicting shear force using a machine learning (ML) method, the multivariate adaptive regression spline (MARS). A nonparametric regression methodology was adopted in MARS for developing a model of shear force percentage in the floodplain of two-stage meandering channels. The width ratio, relative depth, sinuosity, bed slope, and meander belt width ratio of the channel were input variables to the model. The influence of each parameter on predicting the percentage of shear force in the floodplain was also analyzed by adopting a sensitivity analysis. Performance of the MARS model was evaluated by three different machine learning techniques—the group method of data handling (GMDH), support vector machine (SVM) and -nearest neighbor (KNN)—through different statistical measures. The results indicated that the proposed MARS model predicted the shear force percentage in the floodplain satisfactorily, with a coefficient of determination () of 0.94 and 0.93 and a scatter index (SI) of 0.053 and 0.044 for the training and testing phases, respectively. Moreover, the model was successfully applied for validating the two available overbank discharge values for the Baitarani River at Anandapur (drainage area of ), giving the minimum errors of the evaluated methods in terms of mean absolute scaled error (MASE) of 0.014 and 0.066 for flow depths of 7.5 and 8.63 m, respectively.
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Acknowledgments
The authors acknowledge the support received from the Department of Civil Engineering, National Institute of Technology Rourkela, India.
References
Adamowski, J., H. F. Chan, S. O. Prasher, and V. N. Sharda. 2012. “Comparison of multivariate adaptive regression splines with coupled wavelet transform artificial neural networks for runoff forecasting in Himalayan micro-watersheds with limited data.” J. Hydroinf. 14 (3): 731–744. https://doi.org/10.2166/hydro.2011.044.
Akbari, M., P. J. Van Overloop, and A. Afshar. 2011. “Clustered K nearest neighbor algorithm for daily inflow forecasting.” Water Resour. Manage. 25 (5): 1341–1357. https://doi.org/10.1007/s11269-010-9748-z.
Amanifard, N., N. Nariman-Zadeh, M. H. Farahani, and A. Khalkhali. 2008. “Modeling of multiple short-length-scale stall cells in an axial compressor using evolved GMDH neural networks.” Energy Convers. Manage. 49 (10): 2588–2594. https://doi.org/10.1016/j.enconman.2008.05.025.
Annual Water Year Book. 1975. Government of India, Central Water Commission. Bhubaneswar, India: Eastern Rivers Division.
Annual Water Year Book. 1985. Government of India, Central Water Commission. Bhubaneswar, India: Eastern Rivers Division.
Barati, R. 2013. “Application of Excel solver for parameter estimation of the nonlinear Muskingum models.” KSCE J. Civ. Eng. 17 (5): 1139–1148. https://doi.org/10.1007/s12205-013-0037-2.
Bonakdari, H., S. Baghalian, F. Nazari, and M. Fazli. 2011. “Numerical analysis and prediction of the velocity field in curved open channel using artificial neural network and genetic algorithm.” Eng. Appl. Comput. Fluid Mech. 5 (3): 384–396. https://doi.org/10.1080/19942060.2011.11015380.
Cobaner, M., G. Seckin, N. Seckin, and R. Yurtal. 2010. “Boundary shear stress analysis in smooth rectangular channels and ducts using neural networks.” Water Environ. J. 24 (2): 133–139. https://doi.org/10.1111/j.1747-6593.2009.00165.x.
Craven, P., and G. Wahba. 1978. “Smoothing noisy data with spline functions.” Numer. Math. 31 (4): 377–403. https://doi.org/10.1007/BF01404567.
Das, A. K. 1984. “A study of river flood plain interaction and boundary shear stress distribution in a meander channel with one sided flood plain.” Ph.D. thesis, Dept. of Civil Engineering, Indian Institute of Technology Kharagpur.
Deo, R. C., and M. Sahin. 2015. “Application of the extreme learning machine algorithm for the prediction of monthly effective drought index in eastern Australia.” Atmos. Res. 153 (Feb): 512–525. https://doi.org/10.1016/j.atmosres.2014.10.016.
Deo, R. C., P. Samui, and D. Kim. 2016. “Estimation of monthly evaporative loss using relevance vector machine, extreme learning machine and multivariate adaptive regression spline models.” Stochastic Environ. Res. Risk Assess. 30 (6): 1769–1784. https://doi.org/10.1007/s00477-015-1153-y.
Ebtehaj, I., H. Bonakdari, A. H. Zaji, H. Azimi, and F. Khoshbin. 2015. “GMDH-type neural network approach for modeling the discharge coefficient of rectangular sharp-crested side weirs.” Eng. Sci. Technol. Int. J. 18 (4): 746–757. https://doi.org/10.1016/j.jestch.2015.04.012.
Farlow, S. J. 1984. Self-organizing methods in modeling: GMDH type algorithms. Boca Raton, FL: CRC Press.
Friedman, J. H. 1991. “Multivariate adaptive regression splines.” Ann. Stat. 19 (1): 1–67. https://doi.org/10.1214/aos/1176347963.
Friedman, J. H., and C. B. Roosen. 1995. An introduction to multivariate adaptive regression splines. Thousand Oaks, CA: SAGE.
Gandomi, A. H., G. J. Yun, and A. H. Alavi. 2013. “An evolutionary approach for modeling of shear strength of RC deep beams.” Mater. Struct. 46 (12): 2109–2119. https://doi.org/10.1617/s11527-013-0039-z.
Genc, O., and A. Dag. 2016. “A machine learning-based approach to predict the velocity profiles in small streams.” Water Resour. Manage. 30 (1): 43–61. https://doi.org/10.1007/s11269-015-1123-7.
Ghosh, S., and S. B. Jena. 1971. “Boundary shear distribution in open channel compound.” Proc. Inst. Civ. Eng. 49 (4): 417–430. https://doi.org/10.1680/iicep.1971.6191.
Gunn, S. R. 1998. “Support vector machines for classification and regression.”. Southampton, UK: Univ. of Southampton.
Guo, J., and P. Y. Julien. 2005. “Shear stress in smooth rectangular open-channel flows.” J. Hydraul. Eng. 131 (1): 30–37. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:1(30).
Ivakhnenko, A. G. 1971. “Polynomial theory of complex systems.” IEEE Trans. Syst. Man Cybern. SMC-1 (4): 364–378. https://doi.org/10.1109/TSMC.1971.4308320.
Kar, S. K. 1977. “A study of distribution of boundary shear in meander channel with and without floodplain and river floodplain interaction.” Ph.D. thesis, Dept. of Civil Engineering, Indian Institute of Technology Kharagpur.
Karlsson, M., and S. Yakowitz. 1987. “Nearest neighbor methods for nonparametric rainfall runoff forecasting.” Water Resour. Res. 23 (7): 1300–1308. https://doi.org/10.1029/WR023i007p01300.
Khatua, K. K. 2007. “Interaction of flow and estimation of discharge in two stage meandering compound channels.” Ph. D. thesis, Dept. of Civil Engineering, National Institute of Technology Rourkela.
Khatua, K. K., and K. C. Patra. 2007. “Boundary shear stress distribution in compound open channel flow.” ISH J. Hydraul. Eng. 13 (3): 39–54. https://doi.org/10.1080/09715010.2007.10514882.
Khatua, K. K., K. C. Patra, and P. K. Mohanty. 2012. “Stage-discharge prediction for straight and smooth compound channels with wide floodplains.” J. Hydraul. Eng. 138 (1): 93–99. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000491.
Knight, D. W., and J. D. Demetriou. 1983. “Flood plain and main channel flow interaction.” J. Hydraul. Eng. 109 (8): 1073–1092. https://doi.org/10.1061/(ASCE)0733-9429(1983)109:8(1073).
Knight, D. W., J. D. Demetriou, and M. E. Hamed. 1984. “Boundary shear in smooth rectangular channels.” J. Hydraul. Eng. 110 (4): 405–422. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:4(405).
Knight, D. W., and M. E. Hamed. 1984. “Boundary shear in symmetrical compound channels.” J. Hydraul. Eng. 110 (10): 1412–1430. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:10(1412).
Knight, D. W., and H. S. Patel. 1985. “Boundary shear in smooth rectangular ducts.” J. Hydraul. Eng. 111 (1): 29–47. https://doi.org/10.1061/(ASCE)0733-9429(1985)111:1(29).
Lashkar-Ara, B., and M. Fathi-Moghadam. 2010. “Wall and bed shear forces in open channels.” Res. J. Phys. 4 (1): 1–10. https://doi.org/10.3923/rjp.2010.1.10.
Leathwick, J. R., D. Rowe, J. Richardson, J. Elith, and T. Hastie. 2005. “Using multivariate adaptive regression splines to predict the distributions of New Zealand’s freshwater diadromous fish.” Freshwater Biol. 50 (12): 2034–2052. https://doi.org/10.1111/j.1365-2427.2005.01448.x.
Leutheusser, H. J. 1963. “Turbulent flow in rectangular ducts.” J. Hydraul. Div. 89 (3): 1–19.
Mehdizadeh, S., J. Behmanesh, and K. Khalili. 2017a. “Application of gene expression programming to predict daily dew point temperature.” Appl. Therm. Eng. 112 (Feb): 1097–1107. https://doi.org/10.1016/j.applthermaleng.2016.10.181.
Mehdizadeh, S., J. Behmanesh, and K. Khalili. 2017b. “Using MARS, SVM, GEP and empirical equations for estimation of monthly mean reference evapotranspiration.” Comput. Electron. Agric. 139 (Jun): 103–114. https://doi.org/10.1016/j.compag.2017.05.002.
Milukow, H. A., A. D. Binns, J. Adamowski, H. Bonakdari, and B. Gharabaghi. 2019. “Estimation of the Darcy-Weisbach friction factor for ungauged streams using gene expression programming and extreme learning machines.” J. Hydrol. 568 (Jan): 311–321. https://doi.org/10.1016/j.jhydrol.2018.10.073.
Mohanta, A., K. C. Patra, and B. B. Sahoo. 2018. “Anticipate Manning’s coefficient in meandering compound channels.” Hydrology 5 (3): 47 https://doi.org/10.3390/hydrology5030047.
Mohanty, P. K. 2013. “Flow analysis of compound channels with wide flood plains Prabir.” Ph.D. thesis, Dept. of Civil Engineering, National Institute of Technology Rourkela.
Najafzadeh, M., and H. M. Azamathulla. 2013. “Neuro-fuzzy GMDH to predict the scour pile groups due to waves.” J. Comput. Civ. Eng. 29 (5): 04014068. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000376.
Najafzadeh, M., and S. Y. Lim. 2015. “Application of improved neuro-fuzzy GMDH to predict scour depth at sluice gates.” Earth Sci. Inf. 8 (1): 187–196. https://doi.org/10.1007/s12145-014-0144-8.
Najafzadeh, M., M. Rezaie Balf, and E. Rashedi. 2016. “Prediction of maximum scour depth around piers with debris accumulation using EPR, MT, and GEP models.” J. Hydroinf. 18 (5): 867–884. https://doi.org/10.2166/hydro.2016.212.
Najafzadeh, M., M. Rezaie-Balf, and A. Tafarojnoruz. 2018. “Prediction of riprap stone size under overtopping flow using data-driven models.” Int. J. River Basin Manage. 16 (4): 1–8. https://doi.org/10.1080/15715124.2018.1437738.
Newcombe, R. G. 1998. “Two-sided confidence intervals for the single proportion: Comparison of seven methods.” Stat. Med. 17 (8): 857–872. https://doi.org/10.1002/sim.2164.
Patel, H. S. 1984. “Boundary shear in rectangular and compound ducts.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Birmingham.
Patel, V. C. 1965. “Calibration of the Preston tube and limitations on its use in pressure gradients.” J. Fluid Mech. 23 (1): 185–208. https://doi.org/10.1017/S0022112065001301.
Patra, K. C., and S. K. Kar. 2000. “Flow interaction of meandering river with floodplains.” J. Hydraul. Eng. 126 (8): 593–604. https://doi.org/10.1061/(ASCE)0733-9429(2000)126:8(593).
Pradhan, A., and K. K. Khatua. 2017. “Assessment of roughness coefficient for meandering compound channels.” KSCE J. Civ. Eng. 22 (5): 1–13. https://doi.org/10.1007/s12205-017-1818-9.
Preston, J. 1954. “The determination of turbulent skin friction by means of Pitot tubes.” Aeronaut. J. 58 (518): 109–121. https://doi.org/10.1017/S0368393100097704.
Samui, P. 2013. “Multivariate adaptive regression spline (MARS) for prediction of elastic modulus of jointed rock mass.” Geotech. Geol. Eng. 31 (1): 249–253. https://doi.org/10.1007/s10706-012-9584-4.
Sankalp, S., K. K. Khatua, and A. Pradhan. 2015. “Boundary shear stress analysis in meandering channels at the bend apex.” Aquat. Procedia 4: 812–818. https://doi.org/10.1016/j.aqpro.2015.02.101.
Sattar, A. M. A. 2013. “Gene expression models for the prediction of longitudinal dispersion coefficients in transitional and turbulent pipe flow.” J. Pipeline Syst. Eng. Pract. 5 (1): 04013011. https://doi.org/10.1061/(ASCE)PS.1949-1204.0000153.
Shaghaghi, S., H. Bonakdari, A. Gholami, I. Ebtehaj, and M. Zeinolabedini. 2017. “Comparative analysis of GMDH neural network based on genetic algorithm and particle swarm optimization in stable channel design.” Appl. Math. Comput. 313 (Nov): 271–286. https://doi.org/10.1016/j.amc.2017.06.012.
Shende, S., and K.-W. Chau. 2018. “Forecasting safe distance of a pumping well for effective riverbank filtration.” J. Hazard. Toxic Radioactive Waste 23 (2): 04018040. https://doi.org/10.1061/(ASCE)HZ.2153-5515.0000434.
Sin, K.-S., C. I. Thornton, A. L. Cox, and S. R. Abt. 2012. Methodology for calculating shear stress in a meandering channel. Fort Collins, CO: US Dept. of Interior, Colorado State Univ.
Thissen, U., M. Pepers, B. Ustun, W. J. Melssen, and L. M. C. Buydens. 2004. “Comparing support vector machines to PLS for spectral regression applications.” Chemom. Intell. Lab. Syst. 73 (2): 169–179. https://doi.org/10.1016/j.chemolab.2004.01.002.
Vapnik, V. N. 1995. The nature of statistical learning theory. New York: Springer.
Vapnik, V. N. 1999. “An overview of statistical learning theory.” IEEE Trans. Neural Networks 10 (5): 988–999. https://doi.org/10.1109/72.788640.
Varvani, J., and M. R. Khaleghi. 2018. “A performance evaluation of neuro-fuzzy and regression methods in estimation of sediment load of selective rivers.” Acta Geophys. 67 (1): 205–214. https://doi.org/10.1007/s11600-018-0228-9.
Willetts, B. B., and R. I. Hardwick. 1993. “Stage dependency for overbank flow in meandering channels.” Proc. Inst. Civ. Eng. Water Marit. Energy 101 (1): 45–54. https://doi.org/10.1680/iwtme.1993.22989.
Yuvaraj, P., A. R. Murthy, N. R. Iyer, P. Samui, and S. K. Sekar. 2013. “Multivariate adaptive regression splines model to predict fracture characteristics of high strength and ultra high strength concrete beams.” Comput. Mater. Continua 36 (1): 73–97. https://doi.org/10.3970/cmc.2013.036.073.
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Published In
Journal of Irrigation and Drainage Engineering
Volume 145 • Issue 8 • August 2019
Copyright
©2019 American Society of Civil Engineers.
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Received: Jul 24, 2018
Accepted: Mar 5, 2019
Published online: Jun 11, 2019
Published in print: Aug 1, 2019
Discussion open until: Nov 11, 2019
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