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Parameters identification of chaotic systems based on artificial bee colony algorithm combined with cuckoo search strategy

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Abstract

Artificial bee colony (ABC) algorithm is motivated by the intelligent behavior of honey bees when seeking a high quality food source. It has a relatively simple structure but good global optimization ability. In order to balance its global search and local search abilities further, some improvements for the standard ABC algorithm are made in this study. Firstly, the local search mechanism of cuckoo search optimization (CS) is introduced into the onlooker bee phase to enhance its dedicated search; secondly, the scout bee phase is also modified by the chaotic search mechanism. The improved ABC algorithm is used to identify the parameters of chaotic systems, the identified results from the present algorithm are compared with those from other algorithms. Numerical simulations, including Lorenz system and a hyper chaotic system, illustrate the present algorithm is a powerful tool for parameter estimation with high accuracy and low deviations. It is not sensitive to artificial measurement noise even using limited input data.

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References

  1. Hou L, Chen Y S. Super-harmonic responses analysis for a cracked rotor system considering inertial excitation. Sci China Tech Sci, 2015, 58: 1924–1934

    Article  Google Scholar 

  2. Zheng H W, Wang R B, Qiao L K, et al. The molecular dynamics of neural metabolism during the action potential. Sci China Tech Sci, 2014, 57: 857–863

    Article  Google Scholar 

  3. Yang D, Li G, Cheng G. On the efficiency of chaos optimization algorithms for global optimization. Chaos Soliton Fract, 2007, 34: 1366–1375

    Article  MathSciNet  Google Scholar 

  4. Li L, Wang L, Liu L. An effective hybrid PSOSA strategy for optimization and its application to parameter estimation. Appl Math Comput, 2006, 179: 135–146

    MathSciNet  MATH  Google Scholar 

  5. Tang Y, Guan X. Parameter estimation for time-delay chaotic system by particle swarm optimization. Chaos Soliton Fract, 2009, 40: 1391–1398

    Article  MATH  Google Scholar 

  6. Chen D, Liu Y, Ma X, et al. Control of a class of fractional-order chaotic systems via sliding mode. Nonlinear Dynam, 2012, 67: 893–901

    Article  MathSciNet  MATH  Google Scholar 

  7. Peng H, Li L, Yang Y, et al. Conditiona of parameter identification from time series. Phys Rev E, 2003, 67: 027024

    Article  Google Scholar 

  8. Wang L, Tang F, Wu H. Hybrid genetic algorithm based on quantum computing for numerical optimization and parameter estimation. Appl Math Comput, 2005, 171: 1141–1156

    MathSciNet  MATH  Google Scholar 

  9. Alfi A, Modares H. System identification and control using adaptive particle swarm optimization. Appl Math Model, 2011, 35: 1210–1221

    Article  MathSciNet  MATH  Google Scholar 

  10. Peng B, Liu B, Zhang F Y, et al. Differential evolution algorithmbased parameter estimation for chaotic systems. Chaos Soliton Fract, 2009, 39: 2110–2118

    Article  Google Scholar 

  11. He Q, Wang L, Liu B. Parameter estimation for chaotic systems by particle swarm optimization. Chaos Soliton Fract, 2007, 34: 654–661

    Article  MATH  Google Scholar 

  12. Gao F, Li Z Q, Tong H Q. Parameters estimation online for Lorenz system by a novel quantum-behaved particle swarm optimization. Chin Phys B, 2008, 17: 1196–1201

    Article  Google Scholar 

  13. Sun J, Zhao J, Wu X, et al. Parameter estimation for chaotic systems with a Drift Particle Swarm Optimization method. Phys Lett A, 2010, 374: 2816–2822

    Article  MATH  Google Scholar 

  14. Modares H, Alfi A, Fateh M M. Parameter identification of chaotic dynamic systems through an improved particle swarm optimization. Expert Syst Appl, 2010, 37: 3714–3720

    Article  Google Scholar 

  15. Li L, Yang Y, Peng H, et al. An optimization method inspired by “chaotic” ant behavior. Int J Bifurcat Chaos, 2006, 16: 2351–2364

    Article  MathSciNet  MATH  Google Scholar 

  16. Peng H, Li L, Yang Y, et al. Parameter estimation of dynamical systems via a chaotic ant swarm. Phys Rev E, 2010, 81: 016207

    Article  Google Scholar 

  17. Wang L, Li L. An effective hybrid quantum-inspired evolutionary algorithm for parameter estimation of chaotic systems. Expert Syst Appl, 2010, 37: 1279–1285

    Article  Google Scholar 

  18. Karaboga D, Basturk B. On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput, 2008, 8: 687–697

    Article  Google Scholar 

  19. Sonmez M. Artificial Bee Colony algorithm for optimization of truss structures. Appl Soft Comput, 2011, 11: 2406–2418

    Article  Google Scholar 

  20. Sonmez M. Discrete optimum design of truss structures using artificial bee colony algorithm. Struct Multidiscip Optim, 2011, 43: 85–97

    Article  Google Scholar 

  21. Sun H, Luş H, Betti R. Identification of structural models using a modified Artificial Bee Colony algorithm. Comp Struct, 2013, 116: 59–74

    Article  Google Scholar 

  22. Ding Z H, Huang M, Lu Z R. Structural damage detection using artificial bee colony algorithm with hybrid search strategy. Swarm Evolary Comput, 2016, 28: 1–13

    Article  Google Scholar 

  23. Kang F, Li J. Artificial bee colony algorithm optimized support vector regression for system reliability analysis of slopes. J Comput Civil Eng, 2016, 30: 04015040

    Article  Google Scholar 

  24. Kang F, Xu Q, Li J. Slope reliability analysis using surrogate models via new support vector machines with swarm intelligence. Appl Math Model, 2016, 40: 6105–6120

    Article  MathSciNet  Google Scholar 

  25. Li X, Yin M. Parameter estimation for chaotic systems by hybrid differential evolution algorithm and artificial bee colony algorithm. Nonlinear Dynam, 2014, 77: 61–71

    Article  MathSciNet  Google Scholar 

  26. Hu W, Yu Y, Zhang S. A hybrid artificial bee colony algorithm for parameter identification of uncertain fractional-order chaotic systems. Nonlinear Dynam, 2015, 82: 1441–1456

    Article  MathSciNet  MATH  Google Scholar 

  27. Lazzús J A, Rivera M, López-Caraballo C H. Parameter estimation of Lorenz chaotic system using a hybrid swarm intelligence algorithm. Phys Lett A, 2016, 380: 1164–1171

    Article  MathSciNet  Google Scholar 

  28. Karaboga D, Gorkemli B. A quick artificial bee colony (qABC) algorithm and its performance on optimization problems. Appl Soft Comput, 2014, 23: 227–238

    Article  Google Scholar 

  29. Sharma H, Bansal J C, Arya K V, et al. Lévy flight artificial bee colony algorithm. Int J Syst Sci, 2016, 47: 2652–2670

    Article  MATH  Google Scholar 

  30. Soneji H, Sanghvi R C. Towards the improvement of cuckoo search algorithm. Int J Comput Inf Syst Ind Manag Appl, 2014, 6: 77–88

    Google Scholar 

  31. Tavazoei M S, Haeri M. Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms. Appl Math Comput, 2007, 187: 1076–1085

    MathSciNet  MATH  Google Scholar 

  32. Gao F, Lee J J, Li Z, et al. Parameter estimation for chaotic system with initial random noises by particle swarm optimization. Chaos Soliton Fract, 2009, 42: 1286–1291

    Article  MATH  Google Scholar 

  33. Yang X S, Deb S. Cuckoo search via Lévy flights. In: Proceedings of World Congress on Nature and Biologically Inspired Computing. Coimbatore: IEEE, 2009. 210–214

    Google Scholar 

  34. Yang D, Liu Z, Zhou J. Chaos optimization algorithms based on chaotic maps with different probability distribution and search speed for global optimization. Commun Nonlinear Sci Numer Sim, 2014, 19: 1229–1246

    Article  MathSciNet  Google Scholar 

  35. Xu H, Liu J, Lu Z. Structural damage identification based on cuckoo search algorithm. Adv Struct Eng, 2016, 19: 849–859

    Article  Google Scholar 

  36. Malekzadeh M, Atia G, Catbas F N. Performance-based structural health monitoring through an innovative hybrid data interpretation framework. J Civil Struct Health Monit, 2015, 5: 287–305

    Article  Google Scholar 

  37. Chang J F, Yang Y S, Liao T L, et al. Parameter identification of chaotic systems using evolutionary programming approach. Expert Syst Appl, 2008, 35: 2074–2079

    Article  Google Scholar 

  38. Li X F, Leung A C S, Liu X J, et al. Adaptive synchronization of identical chaotic and hyper-chaotic systems with uncertain parameters. Nonlinear Anal Real World Appl, 2010, 11: 2215–2223

    Article  MathSciNet  MATH  Google Scholar 

  39. Mohan S C, Yadav A, Kumar Maiti D, et al. A comparative study on crack identification of structures from the changes in natural frequencies using GA and PSO. Eng Computation, 2014, 31: 1514–1531

    Article  Google Scholar 

  40. Kang F, Li J, Xu Q. Damage detection based on improved particle swarm optimization using vibration data. Appl Soft Comput, 2012, 12: 2329–2335

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mechanics, Sun Yat-sen University, Guangzhou, 510006, China

    ZhengHao Ding, ZhongRong Lu & JiKe Liu

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  1. ZhengHao Ding
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  2. ZhongRong Lu
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  3. JiKe Liu
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Correspondence to ZhongRong Lu.

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Ding, Z., Lu, Z. & Liu, J. Parameters identification of chaotic systems based on artificial bee colony algorithm combined with cuckoo search strategy. Sci. China Technol. Sci. 61, 417–426 (2018). https://doi.org/10.1007/s11431-016-9026-4

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  • DOI: https://doi.org/10.1007/s11431-016-9026-4

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