RBF modeling of Incipient Motion of Plane Sand Bed Channels

Authors: Gopu Sreenivasulu, Bimlesh Kumar, Achanta Ramakrishna Rao

Abstract:

To define or predict incipient motion in an alluvial channel, most of the investigators use a standard or modified form of Shields- diagram. Shields- diagram does give a process to determine the incipient motion parameters but an iterative one. To design properly (without iteration), one should have another equation for resistance. Absence of a universal resistance equation also magnifies the difficulties in defining the model. Neural network technique, which is particularly useful in modeling a complex processes, is presented as a tool complimentary to modeling incipient motion. Present work develops a neural network model employing the RBF network to predict the average velocity u and water depth y based on the experimental data on incipient condition. Based on the model, design curves have been presented for the field application.

Keywords: Incipient motion, Prediction error, Radial-Basisfunction, Sediment transport, Shields' diagram.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1077257

References:

[1] Shileds, "Anwendung der Ahnlichkeitsmechanik und Turbulenzforschung auf Geschiebebewegung. Mitteilungen der preuss," Versuchsant. f. asserbau u. schiffbau, Heft 26, Berlin, 1936.
[2] J. Buffington and D. Montgomery, "A systematic analysis of eight decades of incipient motion studies, with special reference to gravel bed rivers,-- Water Resour. Res., 33 (8), 1993-2029, 1997.
[3] Kumar, "Finding Discharge at Incipient Motion in an Alluvial Channels," ME Thesis, Department of Civil Engg. IISc, Bangalore, 2003.
[4] J.W. Lavelle and H.O. Mofjeld, "Do critical Stresses for Incipient Motion and Erosion Really Exist?," Journal of Hydraulic Engg., ASCE,113,370-385, 1987.
[5] N.A. Marsh, Andrew W. Western and Rodger B. Grayson, "Comparison of Methods for Predicting Incipient Motion for Sand Bends," J. Hydraulic Engg. ASCE, 616-621, 2004.
[6] D. Taylor and V.A. Vanoni, 1972. "Temperature effects in lowtransport flat bed flow," J. Hydr.. Div. ASCE, 98 (8), 1427-1445, 1972.
[7] T. Yang, "Unit stream power and sediment transport," J. Hydr. Div., ASCE, 98(10), 1805-1826, 1972.
[8] C. T. Yang, "Incipient motion and Sediment Transport," J. Hydr. Div., ASCE, 99(10), 1679-1704, 1973.
[9] J. P. C. Kleijnen, "Statistical Tools for Simulation Practitioners," New York: Marcel Dekker, 1987.
[10] J. Sztipanovits, "Engineering of Computer-Based Systems: An Emerging Discipline," Proceedings of the IEEE ECBSJ98 Conference, 1998.
[11] S. Lingireddy and L. E. Ormsbee, "Neural networks in optimal calibration of water distribution systems," Artificial neural networks for civil engineers: Advanced features and applications, I. Flood and N. Kartam, eds., ASCE, Reston, Va., 53-76, 1998.
[12] L. Ma, X. Kunlun and L. Suiqing, "Using Radial Basis Function Neural Networks to Calibrate Water Quality Model," International Journal of Intelligent Systems and Technologies, 3, 2, 90-98, 2008.
[13] M. Aqil, I. Kita, A. Yano and N. Soichi, "Decision Support System for Flood Crisis Management using Artificial Neural Network," International Journal of Intelligent Systems and Technologies, 1, 1, 70- 77, 2006.
[14] J. R. Kalagnanam and U. M. Diwekar, "An efficient sampling technique for off-line quality control," Technometrics 39 (3), 308-319, 1997.
[15] M. Meckesheimer, A.J. Booker, R.R. Barton and T.W. Simpson, "Computationally inexpensive metamodel assessment strategies," AIAA J., 40(10): 2053-2060, 2002.
[16] M. Johnson and L. L. Rogers, "Accuracy of neural network approximators in simulation-optimization," J. Water Resour. Plan. Manage. 126(2), 48-56, 2000.
[17] R. S. Govindaraju, "Artificial Neural Networks in Hydrology," Kluver Academic Publishers, 2000.
[18] D. Caama├▒o, P. Goodwin and M. Manic, "Derivation of a bed load sediment transport formula using artificial neural networks," 7th international conference on hydro informatics, Nice, France, 2006
[19] S. M. Yalin, "Mechanics of Sediment Transport," Pergamon: Tarrytown, NY., 1976.
[20] R. K. Rao, "A Digital Micro manometer for Very Low Pressure Measurement," Journal of the Instrument Society of India, 35, 1, 54-64, 2005.
[21] K. Ashida and M. Bayazit, "Initiation of motion and roughness of flows in steep channels," 15th Congress, IAHR Conference, Istanbul, 1973.
[22] P. A. Mantz, "Incipient transport of fine grains and flakes by fluids - Extended Shields- diagram", J. Hydr. Div., ASCE, 103(6), 601-614, 1977.
[23] R. K. Rao and N. Sitaram, "Stability and Mobility of Sand-Bed Channels Affected by Seepage," J. Irri and Drainage, ASCE, 125 (16), 370-379, 1999.
[24] S. M. Yalin and E. Karahan, "Inception of Sediment Transport," J. Hydr. Div., ASCE, 105 (11), 1979.
[25] V. A. Vanoni, "Measurement of Critical Shear Stress for Entraining Fine Sediments in a Boundary Layer," Report No. KH-R-7, California Institute of Technology, 1964.
[26] A.R.K. Rao and G. Sreenivasulu, "Design of Plane Sediment Bed Channels at Critical Condition," ISH Journal of Hydraulic Engineering, 12, 94-117, 2006.
[27] V. Ramana Prasad, "Velocity, Shear and Friction factor studies in rough rectangular open channels for super critical flow," Ph.D. thesis, Indian Institute of Science, Bangalore, 1991.
[28] S. Haykin, "Neural networks: a comprehensive foundation," Macmillan, New York, 1994.
[29] F. M. Ham and I. Kostanic, "Principles of Neurocomputing for Science and Engineering," McGraw-Hill India, 2001.
[30] Feng and Y. Liu, "Status quo and Problems in neural networks control," Control theory and applications (China) 11(1), 103-106, 1994.
[31] Z. Bian, "Pattern recognition," Tsinghua University Press: Beijing, China, 1988.
[32] MATLAB® Version 7 The mathworks.com