Nonlinear system identification using BBO-based multilayer perceptron network method

  • Wei Lung MaoEmail author
  • Suprapto
  • Chung Wen Hung
  • Teng Wen Chang
Technical Paper


Recently, nonlinear system identification has received increasingly more attention due to its promising applications in engineering fields. It has become a challenging task to truly apply this system due to many complex factors especially the nonlinear and dynamical properties. The objective of this paper is to design a nonlinear system identification method using an appropriate learning method. This paper proposes a biogeography-based optimization (BBO)-based multilayer perceptron (MLP) architecture for nonlinear system identification. The BBO algorithm with its habitats imitates the species migration between them. A good solution is featured by an island with a higher High Suitability Index (HSI), and a poor solution by an island with a lower HSI. Higher HSI solutions resist change more effectively than lower HSI solutions. By combining the two schemes, the proposed MLP architecture with BBO learning provides a promising scheme for nonlinear system identification. Three kinds of nonlinear system are adopted for experimental verification, including Mackey–Glass series, Henon system, and nonlinear plant system. Mean squared error (MSE) index is used to calculate the difference between the measured input and output of the systems. By employing the nonlinear cases, the proposed algorithm presents rapid convergence and excellent MSE in nonlinear system identification.



The authors would like to thank the Ministry of Science and Technology of the Republic of China, Taiwan, for financially supporting this research under Contract No. MOST 107-2221-E-224-040-.


  1. Abiyev RH, Kaynak O, Kayacan E (2013) A type-2 fuzzy wavelet neural network for system identification and control. J Franklin Inst 350:1658–1685MathSciNetCrossRefzbMATHGoogle Scholar
  2. Adeniran AA, El Ferik S (2017) Modeling and identification of nonlinear systems: a review of the multimodel approach—part 1. IEEE Trans Syst, Man, and Cybern: Syst 47(7):1149–1159CrossRefGoogle Scholar
  3. Alfi A, Modares H (2011) System identification and control using adaptive particle swarm optimization. Appl Math Mod 35:1210–1221MathSciNetCrossRefzbMATHGoogle Scholar
  4. Ayala HVH, Coelho LDS (2016) Cascaded evolutionary algorithm for nonlinear system identification based on correlation functions and radial basis functions neural networks, Mechanical Systems and Signal Processing, 378–393Google Scholar
  5. Bansal AK, Kumar R, Gupta RA (2013) Economic analysis and power management of a small autonomous hybrid power system (SAHPS) using biogeography based optimization (BBO) algorithm. IEEE Trans Smart Grid 4(1):638–648CrossRefGoogle Scholar
  6. Coban R (2013) A context layered locally recurrent neural network for dynamic system identification. Eng Appl Soft Artif Intell 26:241–250CrossRefGoogle Scholar
  7. El Ferik Sami, Adeniran Ahmed A (2017) Modeling and identification of nonlinear systems: a review of the multimodel approach—Part 2. IEEE Trans Syst, Man, and Cybern: Syst 47(7):1160–1168CrossRefGoogle Scholar
  8. Han H, Qiao J (2010) Aself-organizing fuzzy neural network based on a growing-and-pruning algorithm. IEEE Trans Fuzzy Syst 18:1129–1143CrossRefGoogle Scholar
  9. Hossain MS, Chao OZ, Ismail Z, Noroozi S, Khooa SY (2017) Artificial neural networks for vibration based inverse parametric identifications: a review. Appl Soft Comput 52:203–219CrossRefGoogle Scholar
  10. Khotanzad A, Chung C (1998) Application of multi-layer perceptron neural networks to vision problems. Neural Comput Appl 7:249–259CrossRefGoogle Scholar
  11. Lee C-H, Teng C-C (2000) Identification and control of dynamic systems using recurrent fuzzy neural networks. IEEE Trans Fuz Syst 8(4)Google Scholar
  12. Lin CJ, Chen CH (2006) A compensation-based recurrent fuzzy neural network for dynamic system identification. Eur J Oper Res 172:696–715MathSciNetCrossRefzbMATHGoogle Scholar
  13. Lin Y-Y, Chang J-Y, Lin C-T (2013) Identification and prediction of dynamic systems using an interactively recurrent self-evolving fuzzy neural network. IEEE Trans Neural Netw Learn Syst 24(2):310–321CrossRefGoogle Scholar
  14. Mackey MC, Glass L (1977) Oscillation and chaos in physiological control systems. Science 197(4300):287–289CrossRefzbMATHGoogle Scholar
  15. Mahdi Mofidian SM, Bardaweel Hamzeh (2018) Theoretical study and experimental identification of elastic-magnetic vibration isolation system. J Intell Mater Syst Struct 29(18):3550–3561CrossRefGoogle Scholar
  16. Mahdi Mofidian SM, Bardaweel Hamzeh (2019) A dual-purpose vibration isolator energy harvester: experiment and model. Mech Syst Signal Process 118:360–376CrossRefGoogle Scholar
  17. Majhi B, Panda G (2011) Robust identification of nonlinear complex systems using low complexity ANN and particle swarm optimization technique. Expert Syst Appl 38:321–333CrossRefGoogle Scholar
  18. Mao W-L, Suprapto Hung C-W (2018) Type-2 fuzzy neural network using grey wolf optimizer learning algorithm for nonlinear system identification. Microsyst Tech 24(10):4075–4088CrossRefGoogle Scholar
  19. Nammari A, Caskey L, Negrete J, Bardaweel H (2018) Fabrication and characterization of non-resonant magneto-mechanical low-frequency vibration energy harvester. Mech Syst Signal Process 102:298–311CrossRefGoogle Scholar
  20. Purwar S, Kar IN, Jha AN (2007) On-line system identification of complex systems using Chebyshev neural networks. Appl Soft Comput 7:364–372CrossRefGoogle Scholar
  21. Qiao J-F, Han H-G (2012) Identification and modeling of nonlinear dynamical systems using a novel self-organizing RBF-based approach. Automatica 48:1729–1734MathSciNetCrossRefzbMATHGoogle Scholar
  22. Rubio JJ (2009) SOFMLS: online self-organizing fuzzy modified least-squares network. IEEE Trans Fuzzy Syst 17:1296–1309CrossRefGoogle Scholar
  23. Sharaqa A, Dib N (2014) Design of linear and elliptical antenna arrays using biogeography based optimization. Arab J Sci Eng 39(4):2929–2939CrossRefGoogle Scholar
  24. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713CrossRefGoogle Scholar
  25. Thomas G, Lozovyy P, Simon D (2011) Fuzzy robot controller tuning with biogeography-based optimization, 2. Springer, BerlinCrossRefGoogle Scholar
  26. Tutunji TA (2016) Parametric system identification using neural networks. Appl Soft Comput 47:251–261CrossRefGoogle Scholar
  27. Wang L, Xu Y (2011) An effective hybrid biogeography-based optimization algorithm for parameter estimation of chaotic systems. Expert Syst Appl 38(12):15103–15109CrossRefGoogle Scholar
  28. Wang X, Duan H, Luo D (2013) Cauchy biogeography-based optimization based on lateral inhibition for image matching. Optik 124(22):5447–5453CrossRefGoogle Scholar
  29. Yazdizadeh K, Khorasani K (2002) Adaptive time delay neural network structures for nonlinear system identication. Neurocom. 47:207–240CrossRefzbMATHGoogle Scholar
  30. Zhao H, Zhang J (2009) Nonlinear dynamic system identification using pipelined functional link artificial recurrent neural network. Neurocom. 72:3046–3054CrossRefGoogle Scholar
  31. Zheng Y-J, Ling H-F, Shi H-H, Chen H-S, Chen S-Y (2014) Emergency railway wagon scheduling by hybrid biogeography based optimization. Comput Oper Res 43:1–8MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Graduate School of Engineering Science and Technology, Department of Electrical EngineeringNational Yunlin University of Science and TechnologyDouliouTaiwan, ROC
  2. 2.Departement of Electronics Engineering EducationYogyakarta State UniversityYogyakartaIndonesia
  3. 3.Department of Digital Media DesignNational Yunlin University of Science and TechnologyDouliouTaiwan, ROC

Personalised recommendations