Application of a Hybrid Optimization Method in Muskingum Parameter Estimation
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Volume 141, Issue 12
Abstract
Two new mathematical forms of the nonlinear Muskingum model called NL4 and NL5, involving four and five parameters, respectively, can be used in river flood routing. The accuracy of the estimation of the Muskingum model parameters is essential for flood routing. This paper proposes a novel hybrid algorithm, based on the shuffled frog leaping algorithm (SFLA) and Nelder-Mead simplex (NMS), for the estimation of parameters of two new nonlinear Muskingum models. The proposed methodology is applied by considering minimization of the sum of the square deviation (SSD) between observed and routed outflows in (1) experimental, (2) real, and (3) multimodal examples. Results show that the SSD is 0.91, 3.97, and 4.44% smaller (better) than pertinent values obtained by the genetic algorithm-generalized reduced gradient (GA-GRG) method in experimental, real, and multimodal examples, respectively.
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References
Barati, R. (2011). “Parameter estimation of nonlinear Muskingum models using Nelder-Mead simplex algorithm.” J. Hydrol. Eng., 946–954.
Barati, R. (2012). “Discussion of ‘Parameter estimation of the nonlinear Muskingum model using parameter-setting-free harmony search’ by Z. W. Geem.” J. Hydrol. Eng., 1414–1416.
Barati, R. (2013a). “Application of Excel solver for parameter estimation of the nonlinear Muskingum models.” KSCE J. Civ. Eng., 17(5), 1139–1148.
Barati, R. (2013b). “Closure to ‘Parameter estimation of nonlinear Muskingum model using Nelder-Mead simplex algorithm’ by R. Barati.” J. Hydrol. Eng., 367–370.
Barati, R. (2014). “Reply to discussion of ‘Application of Excel solver for parameter estimation of the nonlinear Muskingum models’ by Ali R. Vatankhah.” KSCE J. Civ. Eng., 19(1), 337–339.
Chow, V. T. (1959). Open channel hydraulics, McGraw-Hill, New York.
Chow, V. T., Maidment, D. R., and Mays, L. W. (1988). Applied hydrology, McGraw-Hill, New York.
Chu, H. J., and Chang, L. C. (2009). “Applying particle swarm optimization to parameter estimation of the nonlinear Muskingum model.” J. Hydrol. Eng., 1024–1027.
Das, A. (2004). “Parameter estimation for Muskingum models.” J. Irrig. Drain. Eng., 140–147.
Easa, S. (2013a). “New and improved four parameter nonlinear Muskingum model.” Proc. Inst. Civ. Eng. Water Manage., 167(5), 288–298.
Easa, S. M. (2013b). “Improved nonlinear Muskingum model with variable exponent parameter.” J. Hydrol. Eng., 1790–1794.
Easa, S. M. (2014a). “Multi-criteria optimisation of the Muskingum flood model: A new approach.” Proc. ICE Water Manage., in press.
Easa, S. M. (2014b). “Versatile Muskingum flood model with four variable parameters.” Proc. ICE - Water Manage., 168(3), 139–148.
Easa, S. M., Barati, R., Shahheydari, H., Nodoshan, E. J., and Barati, T. (2014). “Discussion: New and improved four-parameter non- linear Muskingum model.” Proc. ICE - Water Manage., 167(10), 612–615.
Eusuff, M. M., and Lansey, K. E. (2003). “Optimization of water distribution network design using the shuffled frog leaping algorithm.” J. Water Resour. Plann. Manage., 210–225.
Fallah-Mehdipour, E., Bozorg Haddad, O., and Mariño, M. A. (2011). “MOPSO algorithm and its application in multipurpose multireservoir operations.” J. Hydroinf., 13(4), 794–811.
Fallah-Mehdipour, E., Bozorg Haddad, O., and Mariño, M. A. (2012). “Real-time operation of reservoir system by genetic programming.” Water Resour. Manage., 26(14), 4091–4103.
Fallah-Mehdipour, E., Bozorg Haddad, O., and Mariño, M. A. (2013). “Extraction of multicrop planning rules in a reservoir system: Application of evolutionary algorithms.” J. Irrig. Drain. Eng., 490–498.
Gandomi, A. H. (2014). “Interior search algorithm (ISA): A novel approach for global optimization.” ISA Trans., 53(4), 1168–1183.
Gandomi, A. H., and Alavi, A. H. (2012). “Krill herd: A new bio-inspired optimization algorithm.” Commun. Nonlinear Sci. Numer. Simul., 17(12), 4831–4845.
Gavilan, G., and Houck, M. H. (1985). “Optimal Muskingum river routing.” Proc., ASCE WRPMD Specialty Conf. on Computer Applications in Water Resources, H. C. Torno, ed., ASCE, Reston, VA, 1294–1302.
Geem, Z. W. (2006). “Parameter estimation for the nonlinear Muskingum model using BFGS technique.” J. Irrig. Drain. Eng., 474–478.
Geem, Z. W. (2011). “Parameter estimation of the nonlinear Muskingum model using parameter-setting-free harmony search algorithm.” J. Hydrol. Eng., 684–688.
Gill, M. A. (1978). “Flood routing by Muskingum method.” J. Hydrol., 36(3–4), 353–363.
Hamedi, F., Bozorg Haddad, O., and Orouji, H. (2014a). “Discussion of ‘Application of Excel solver for parameter estimation of the nonlinear Muskingum models’ By R. Barati.” KSCE J. Civ. Eng., 19(1), 343–344.
Hamedi, F., Bozorg Haddad, O., Orouji, H., Fallah-Mehdipour, E., and Mariño, M. A. (2014b). “Discussion of ‘Parameter estimation of the nonlinear Muskingum flood-routing model using a hybrid harmony search algorithm’ by H. Karahan, G. Gurarslan, and Z. W. Geem.” J. Hydrol. Eng., 352–360.
Karahan, H., Gurarslan, G., and Geem, Z. W. (2013). “Parameter estimation of the nonlinear Muskingum flood-routing model using a hybrid harmony search algorithm.” J. Hydrol. Eng., 352–360.
Karimi-Hosseini, A., Bozorg Haddad, O., and Mariño, M. A. (2011). “Site selection of rain gauges using entropy methodologies.” Proc. Inst. Civ. Eng. Water Manage., 164(7), 321–333.
Kim, J. H., Geem, Z. W., and Kim, E. S. (2001). “Parameter estimation of the nonlinear Muskingum model using harmony search.” J. Am. Water Resour. Assoc., 37(5), 1131–1138.
Lagarias, J. C., Reeds, J. A., Wright, M. H., and Wright, P. E. (1998). “Convergence properties of the Nelder Mead simplex method in low dimensions.” SIAM J. Optim., 9(1), 112–147.
Luo, J., and Xie, J. (2010). “Parameter estimation for nonlinear Muskingum model based on immune clonal selection algorithm.” J. Hydrol. Eng., 844–851.
MATLAB 9.0 [Computer software]. Natick, MA, MathWorks.
Mohan, S. (1997). “Parameter estimation of nonlinear Muskingum models using genetic algorithm.” J. Hydraul. Eng., 137–142.
Natural Environment Research Council (NERC). (1975). “Flood studies report.” Institute of Hydrology, Wallingford, U.K.
Nelder, J. A., and Mead, R. (1965). “A simplex method for function minimization.” Comput. J., 7(4), 308–313.
Noory, H., Liaghat, A. M., Parsinejad, M., and Bozorg Haddad, O. (2012). “Optimizing irrigation water allocation and multicrop planning using discrete PSO algorithm.” J. Irrig. Drain. Eng., 437–444.
Orouji, H., Bozorg Haddad, O., Fallah-Mehdipour, E., and Mariño, M. A. (2013). “Estimation of Muskingum parameter by meta-heuristic algorithms.” Proc. Inst. Civ. Eng. Water Manage., 166(6), 315–324.
Samani, H. M. V., and Jebelifard, S. (2003). “Design of circular urbanstorm sewer systems using multilinear Muskingum flow routing method.” J. Hydraul. Eng., 832–838.
Seifollahi-Aghmiuni, S., Bozorg Haddad, O., Omid, M. H., and Mariño, M. A. (2011). “Long-term efficiency of water networks with demand uncertainty.” Proc. Inst. Civ. Eng. Water Manage., 164(3), 147–159.
Seifollahi-Aghmiuni, S., Bozorg Haddad, O., Omid, M. H., and Mariño, M. A. (2013). “Effects of pipe roughness uncertainty on water distribution network performance during its operational period.” Water Resour. Manage., 27(5), 1581–1599.
Shokri, A., Bozorg Haddad, O., and Mariño, M. A. (2013). “Algorithm for increasing the speed of evolutionary optimization and its accuracy in multi-objective problems.” Water Resour. Manage., 27(7), 2231–2249.
Tung, Y. K. (1985). “River flood routing by nonlinear Muskingum method.” J. Hydraul. Eng., 111(12), 1147–1460.
Vatankhah, A. R. (2014). “Discussion of ‘Parameter estimation of the nonlinear Muskingum flood-routing model using a hybrid harmony search algorithm.’ by H. Karahan, G. Gurarslan, and Z. W. Geem.” J. Hydrol. Eng., 325–360.
Viessman, W., and Lewis, G. L. (2003). Introduction to hydrology, Pearson Education, Upper Saddle River, NJ.
Wilson, E. M. (1974). Engineering hydrology, MacMillan Education, Hampshire, U.K.
Xu, D., Qiu, L., and Chen, S. (2012). “Estimation of nonlinear Muskingum model parameter using differential evolution.” J. Hydrol. Eng., 348–353.
Yang, W., Cao, W., Chung, T., and Morris, J. (2005). Applied numerical methods using MATLAB, Wiley, Hoboken, NJ.
Yang, X. S., Gandomi, A. H., Talatahari, S., and Alavi, A. H. (2012). Metaheuristis in water, geotechnical and transportation engineering, Elsevier, London.
Yoon, J. W., and Padmanabhan, G. (1993). “Parameter estimation of linear and nonlinear Muskingum models.” J. Water Resour. Plann. Manage., 600–610.
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Journal of Irrigation and Drainage Engineering
Volume 141 • Issue 12 • December 2015
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© 2015 American Society of Civil Engineers.
History
Received: Dec 29, 2014
Accepted: May 7, 2015
Published online: Jun 19, 2015
Discussion open until: Nov 19, 2015
Published in print: Dec 1, 2015
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