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Parameter estimation of shallow wave equation via cuckoo search

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Abstract

In this study, cuckoo search is introduced for performing the parameter estimation of shallow wave equation for the first time. Cuckoo search (CS) is invented based on the inspiration of brood parasitic behavior of some cuckoo species in combination with the Lévy flight behavior. These meta-heuristics have been successfully used for solving some optimization problems with promising results. However, this emerging optimization method has not been applied in parameter inversion problem. This study reports a CS-based parameter estimation method to inverse the roughness coefficient and the coefficient of eddy viscosity under some specific conditions. Simulation results and experimental data show that cuckoo search offers a reliable performance for these parameter estimation problems.

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References

  1. Panchang VG, O’Brien JJ (1989) On the determination of hydraulic model parameters using the strong constraint formulation. Modeling marine systems. Boca Raton: CRC Press, Inc., pp 5–18

  2. Yeh WG (1986) Review of parameter identification procedures in groundwater hydrology: the inverse problem. Water Resour Res 22(2):95–108. doi:10.1029/WR022i002p00095

    Article  Google Scholar 

  3. Das SK, Lardner RW (1991) On the estimation of parameters of hydraulic models by assimilation of periodic tidal data. J Geophys Res 96(c8):15187–15196. doi:10.1029/91JC01318

    Article  Google Scholar 

  4. Lal AMW (1995) Calibration of riverbed roughness. J Hydraul Eng 121(9):664–671. doi:10.1061/(ASCE)0733-9429(1995)121:9(664)

    Article  Google Scholar 

  5. Yen BC, Khatibi RH, Williams JJR, Wormleaton PR (1997) Identification problem of open-channel friction parameters. J Hydraul Eng 123(12):1078–1088. doi:10.1061/(ASCE)0733-9429(1997)123:12(1078)

    Article  Google Scholar 

  6. Atanov GA, Evseeva EG, Meselhe EA (1999) Estimation of roughness profile in trapezoidal open channel. J Hydraul Eng 125(3):309–312. doi:10.1061/(ASCE)0733-9429(1999)125:3(309)

    Article  Google Scholar 

  7. Ishii A (2000) Parameter identification of Manning roughness coefficient using analysis of hydraulic jump with sediment transport. Kawahara Group Research Report, Chuo University, Japan

  8. Ramesh R, Datta B, Bhallamudi SM, Narayana A (2000) Optimal estimation of roughness in open-channel flows. J Hydraul Eng 126(4):299–303. doi:10.1061/(ASCE)0733-9429(2000)126:4(299)

    Article  Google Scholar 

  9. Sulzer S, Rutschmann P, Kinzelbach W (2002) Flood discharge prediction using two-dimensional inverse modeling. J Hydraul Eng 128(1):46–54. doi:10.1061/(ASCE)0733-9429(2002)128:1(46)

    Article  Google Scholar 

  10. Ding Y, Wang SSY (2005) Identification of Manning’s roughness coefficients in channel network using adjoint analysis. Int J Comput Fluid Dyn 19(1):3–13. doi:10.1080/10618560410001710496

    Article  MathSciNet  MATH  Google Scholar 

  11. Calo VM, Collier N, Gehre M, Jin B, Radwand H, Santillana M (2013) Gradient-based estimation of Manning’s friction coefficient from noisy data. J Comput Appl Math 238(1):1–13. doi:10.1016/j.cam.2012.08.004

    Article  MathSciNet  MATH  Google Scholar 

  12. Azamathulla HM, Ahmad Z, Ghani AA (2013) An expert system for predicting Manning’s roughness coefficient in open channels by using gene expression programming. Neural Comput Appl 23(5):1343–1349. doi:10.1007/s00521-012-1078-z

    Article  Google Scholar 

  13. Gandomi AH, Yang X-S, Alavi AH, Talatahari S (2013) Bat algorithm for constrained optimization tasks. Neural Comput Appl 22(6):1239–1255. doi:10.1007/s00521-012-1028-9

    Article  Google Scholar 

  14. Yang Xin-She, Deb Suash, Fong Simon (2014) Bat algorithm is better than intermittent search strategy. J Mult Valued Log S 22(3):223–237

    Google Scholar 

  15. Yang XS, Deb S (2010) Engineering optimization by cuckoo search. Int J Math Model Numer Optim 1(4):330–343. doi:10.1504/IJMMNO.2010.03543

    MATH  Google Scholar 

  16. Gandomi AH, Alavi AH (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17(12):4831–4845. doi:10.1016/j.cnsns.2012.05.010

    Article  MathSciNet  MATH  Google Scholar 

  17. Wang Gai-Ge, Gandomi AmirH, Alavi AmirH, Deb Suash (2015) A hybrid method based on krill herd and quantum-behaved particle swarm optimization. Neural Comput Appl. doi:10.1007/s00521-015-1914-z

    Google Scholar 

  18. Yang XS (2010) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio Inspired Comput 2(2):78–84. doi:10.1504/IJBIC.2010.032124

    Article  Google Scholar 

  19. Wang GG, Guo L, Duan H, Wang H (2014) A new improved firefly algorithm for global numerical optimization. J Comput Theor Nanosci 11(2):477–485. doi:10.1166/jctn.2014.3383

    Article  Google Scholar 

  20. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68. doi:10.1177/003754970107600201

    Article  Google Scholar 

  21. Wang GG, Gandomi AH, Zhao X, Chu HE (2014) Hybridizing harmony search algorithm with cuckoo search for global numerical optimization. Soft Comput. doi:10.1007/s00500-014-1502-7

    Google Scholar 

  22. Wang GG, Deb S, Cui Z (2015) Monarch butterfly optimization. Neural Comput Appl. doi:10.1007/s00521-015-1923-y

    Google Scholar 

  23. YangXS KaramanogluM, He X (2014) Flower pollination algorithm: a novel approach for multiobjective optimization. Eng Optim 46(9):1222–1237. doi:10.1080/0305215X.2013.832237

    Article  MathSciNet  Google Scholar 

  24. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. doi:10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  25. Simon D (2008) Biogeography-based optimization. IEEE Trans Evolut Comput 12(6):702–713. doi:10.1109/TEVC.2008.919004

    Article  Google Scholar 

  26. Wang G, Guo L, Duan H, Wang H, Liu L, Shao M (2013) Hybridizing harmony search with biogeography based optimization for global numerical optimization. J Comput Theor Nanos 10(10):2318–2328. doi:10.1166/jctn.2013.3207

    Google Scholar 

  27. Mirjalili S, Mirjalili SM, Lewis A (2014) Let a biogeography-based optimizer train your multi-layer perceptron. Inf Sci 269:188–209. doi:10.1016/j.ins.2014.01.038

    Article  MathSciNet  Google Scholar 

  28. Feng Y, Wang GG, Feng Q, Zhao XJ (2014) An effective hybrid cuckoo search algorithm with improved shuffled frog leaping algorithm for 0-1 Knapsack problems. Comput Intell Neurosci 2014:857254. doi:10.1155/2014/857254

    Google Scholar 

  29. Wang GG, Deb S, Gandomi AH, Zhang Z, Alavi AH (2015) Chaotic cuckoo search. Soft Comput 2015:1–14. doi:10.1007/s00500-015-1726-1

    Google Scholar 

  30. Long W, Liang X, Huang Y, Chen Y (2014) An effective hybrid cuckoo search algorithm for constrained global optimization. Neural Comput Appl 25(3–4):911–926. doi:10.1007/s00521-014-1577-1

    Article  Google Scholar 

  31. Sheng Z, Wang J, Zhou S, Zhou B (2014) Parameter estimation for chaotic systems using a hybrid adaptive cuckoo search with simulated annealing algorithm. Chaos 24(1):1569–1577. doi:10.1063/1.4867989

    Article  MathSciNet  Google Scholar 

  32. Li X, Wang J, Yin M (2014) Enhancing the performance of cuckoo search algorithm using orthogonal learning method. Neural Comput Appl 24(6):1233–1247. doi:10.1007/s00521-013-1354-6

    Article  Google Scholar 

  33. Yang XS (2012) Cuckoo search for inverse problems and simulated-driven shape optimization. J Comput Methods Sci Eng 12(1, 2): 129–137. doi:10.3233/JCM-2012-0408

  34. Bhargava V, Fateen S, Petriciolet AB (2013) Cuckoo Search: a new nature-inspired optimization method for phase equilibrium calculations. Fluid Phase Equilib 337:191–200. doi:10.1016/j.fluid.2012.09.018

    Article  Google Scholar 

  35. Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35. doi:10.1007/s00366-011-0241-y

    Article  Google Scholar 

  36. Henderson FM (1996) Open channel flow. Macmillan Co. Ltd, London

    MATH  Google Scholar 

  37. Lynch DR, Gray WG (1978) Analytic solutions for computer flow model testing. J Hydrau Divis 104(10):1409–1428

    Google Scholar 

  38. Andre J, Siarry P, Dognon T (2001) An improvement of the standard genetic algorithm fighting premature convergence in continuous optimization. Adv Eng Softw 32(1):49–60. doi:10.1016/S0965-9978(00)00070-3

    Article  MATH  Google Scholar 

  39. Yang X, Yang Z, Yin X, Li J (2008) Chaos gray-coded genetic algorithm and its application for pollution source identifications in convection–diffusion equation. Commun Nonlinear Sci Numer Simul 13(8):1676–1688. doi:10.1016/j.cnsns.2007.03.003

    Article  Google Scholar 

  40. Zhang XM, Song W, Feng WW (2015) Improved ant colony algorithm for parameter estimation on the BISQ model. Inverse Probl Sci En 23(6):997–1010. doi:10.1080/17415977.2014.973872

    Article  Google Scholar 

Download references

Acknowledgments

The work was supported by the National Science Foundation of China, under Grant No. 41004052.

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  1. Harbin Institute of Technology Shenzhen Graduate School, Shenzhen, 518055, Guangdong, People’s Republic of China

    Xin-Ming Zhang

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  1. Xin-Ming Zhang
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Zhang, XM. Parameter estimation of shallow wave equation via cuckoo search. Neural Comput & Applic 28, 4047–4059 (2017). https://doi.org/10.1007/s00521-016-2308-6

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