Parameter Estimation of Nonlinear Muskingum Models Using Genetic Algorithm
Publication: Journal of Hydraulic Engineering
Volume 123, Issue 2
Abstract
The application of the Muskingum model to river and channel flood routing may have some limitations because of its inherent assumption of a linear relationship between channel storage and weighted flow. Although nonlinear forms of the Muskingum model have been proposed, an efficient method for parameter estimation in the calibration process is still lacking. In this paper, the objective approach of genetic algorithm is proposed for the purpose of estimating the parameters of two nonlinear Muskingum routing models. The performance of this algorithm is compared with other reported parameter estimation techniques. Results of the application of this approach to an example with high nonlinearity between storage and weighted-flow, show that the genetic algorithm approach is efficient in estimating parameters of the nonlinear routing models. A supplementary analysis of the sensitivity of the parameters during the performance of genetic algorithm shows that a unique set of parameters exists that would result in the best performance for a given problem. In addition, genetic algorithm does not demand any initial estimate of values of any of the parameters, and thus avoids the subjectivity and computation time associated with the traditional estimation methods.
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References
1.
Booker, L. (1987). “Improving search in genetic algorithms.”Genetic algorithms and simulated annealing, L. Davis, ed., Morgan Kaufmann Publishers, Inc., Los Altos, Calif., 61–73.
2.
Cieniawski, S. E., Eheart, J. W., and Ranjithan, S.(1995). “Using genetic algorithm to solve a multiobjective ground water monitoring problem.”Water Resour. Res., 31(2), 399–409.
3.
Gavilan, G., and Houck, M. H. (1985). “Optimal Muskingum River routing.”Proc., ASCE WRPMD Spec. Conf. on Comp. Applications in Water Resour., ASCE, New York, N.Y., 1294–1302.
4.
Gill, M. A.(1978). “Flood routing by the Muskingum method.”J. Hydro., Amsterdam, The Netherlands, 36, 353–363.
5.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and learning. Addison-Wesley Publishing Co., Reading, Mass.
6.
Holland, J. H. (1992). Adaptation in natural and artificial systems, 2nd Ed., MIT Press, Cambridge, Mass.
7.
Koumousis, V. K., and Georgiou, P. G.(1994). “Genetic algorithms in discrete optimization of steel truss roofs.”J. Comp. in Civ. Engrg., ASCE, 8(3), 309–325.
8.
Liong, S. K., Chan, W. T., and ShreeRam, J. (1994). “Peak flow forecasting with genetic algorithm and SWMM.”Proc., 9th Congr. of the Asian-Pacific Div. of IAHR, 24–26.
9.
Marquardt, D. W.(1963). “An algorithm for least squares estimation of nonlinear parameters.”SIAM J., 11, 431–442.
10.
McCarthy, G. T. (1938). “The unit hydrograph and flood routing.”Proc., Conf. of North Atlantic Div., U.S. Army Corps of Engrs., U.S. Engrg. Ofc., Providence, R.I.
11.
McKinney, D. C., and Lin, M. D.(1994). “Genetic algorithm solution of groundwater management problems.”Water Resour. Res., 30(6), 1897–1906.
12.
Michalewicz, Z. (1992). Genetic algorithms + data structures = evolution programs. Springer-Verlag Inc., New York, N.Y.
13.
Ritzel, B. J., Eheart, J. W., and Ranjithan, S.(1994). “Using genetic algorithms to solve a multiple objective ground water pollution containment problem.”Water Resour. Res., 30(5), 1589–1603.
14.
Tung, Y. K.(1984). “River flood routing by nonlinear Muskingum method.”J. Hydr. Div., ASCE, 111(12), 1447–1460.
15.
Wang, Q. J.(1991). “The genetic algorithm and its application to calibrating conceptual rainfall-runoff models.”Water Resour. Res., 27(9), 2467–2471.
16.
Wilson, E. M. (1974). Engineering hydrology. MacMillan Education Ltd., Hampshire, U.K.
17.
Yoon, J., and Padmanabhan, G.(1993). “Parameter estimation of linear and nonlinear Muskingum models.”J. Water Resour. Plng. Mgmt. Div., ASCE, 119(5), 600–610.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 123 • Issue 2 • February 1997
Pages: 137 - 142
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Feb 1, 1997
Published in print: Feb 1997
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