Table of Contents Author Guidelines Submit a Manuscript
Computational Intelligence and Neuroscience
Volume 2015, Article ID 145874, 10 pages
http://dx.doi.org/10.1155/2015/145874
Research Article

Impact of Noise on a Dynamical System: Prediction and Uncertainties from a Swarm-Optimized Neural Network

Departamento de Física y Astronomía, Universidad de La Serena, Casilla 554, La Serena, Chile

Received 27 April 2015; Revised 15 July 2015; Accepted 27 July 2015

Academic Editor: Saeid Sanei

Copyright © 2015 C. H. López-Caraballo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. C. Mackey and L. Glass, “Oscillation and chaos in physiological control systems,” Science, vol. 197, no. 4300, pp. 287–289, 1977. View at Publisher · View at Google Scholar · View at Scopus
  2. K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Optics Communications, vol. 30, no. 2, pp. 257–261, 1979. View at Publisher · View at Google Scholar · View at Scopus
  3. B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Physical Review E, vol. 64, no. 5, Article ID 056216, 2001. View at Publisher · View at Google Scholar
  4. J. D. Hamilton, Time Series Analysis, Princeton University Press, Princeton, NJ, USA, 1994. View at MathSciNet
  5. D. S. K. Karunasinghe and S.-Y. Liong, “Chaotic time series prediction with a global model: artificial neural network,” Journal of Hydrology, vol. 323, no. 1–4, pp. 92–105, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. E. S. Chng, S. Chen, and B. Mulgrew, “Gradient radial basis function networks for nonlinear and nonstationary time series prediction,” IEEE Transactions on Neural Networks, vol. 7, no. 1, pp. 190–194, 1996. View at Publisher · View at Google Scholar · View at Scopus
  7. J.-S. Zhang and X.-C. Xiao, “Predicting chaotic time series using recurrent neural network,” Chinese Physics Letters, vol. 17, no. 2, pp. 88–90, 2000. View at Publisher · View at Google Scholar · View at Scopus
  8. A. Girard, C. Rasmussen, J. Quinonero-Candela, and R. Murray-Smith, “Gaussian process priors with uncertain inputs—application to multiple-step ahead time series forecasting,” in Advances in Neural Information Processing Systems, MIT Press, 2003. View at Google Scholar
  9. N. Sapankevych and R. Sankar, “Time series prediction using support vector machines: a survey,” IEEE Computational Intelligence Magazine, vol. 4, no. 2, pp. 24–38, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Haykin and J. Principe, “Making sense of a complex world [chaotic events modeling],” IEEE Signal Processing Magazine, vol. 15, no. 3, pp. 66–81, 1998. View at Publisher · View at Google Scholar · View at Scopus
  11. D. Li, M. Han, and J. Wang, “Chaotic time series prediction based on a novel robust echo state network,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 5, pp. 787–799, 2012. View at Publisher · View at Google Scholar · View at Scopus
  12. M. Han and X. Wang, “Robust neural predictor for noisy chaotic time series prediction,” in Proceedings of the International Joint Conference on Neural Networks (IJCNN '13), August 2013. View at Publisher · View at Google Scholar · View at Scopus
  13. H. Leung, T. Lo, and S. Wang, “Prediction of noisy chaotic time series using an optimal radial basis function neural network,” IEEE Transactions on Neural Networks, vol. 12, no. 5, pp. 1163–1172, 2001. View at Publisher · View at Google Scholar · View at Scopus
  14. C. Sheng, J. Zhao, Y. Liu, and W. Wang, “Prediction for noisy nonlinear time series by echo state network based on dual estimation,” Neurocomputing, vol. 82, pp. 186–195, 2012. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Han, J. Fan, and J. Wang, “A dynamic feedforward neural network based on gaussian particle swarm optimization and its application for predictive control,” IEEE Transactions on Neural Networks, vol. 22, no. 9, pp. 1457–1468, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. W.-C. Yeh, “New parameter-free simplified swarm optimization for artificial neural network training and its application in the prediction of time series,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 4, pp. 661–665, 2013. View at Publisher · View at Google Scholar · View at Scopus
  17. C. Zhang, H. Shao, and Y. Li, “Particle swarm optimization for evolving artificial neural network,” in Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, vol. 4, pp. 2487–2490, October 2000. View at Scopus
  18. E. A. Grimaldi, F. Grimaccia, M. Mussetta, and R. E. Zich, “PSO as an effective learning algorithm for neural network applications,” in Proceedings of the International Conference on Computational Electromagnetics and Its Applications, pp. 557–560, November 2004. View at Scopus
  19. C.-F. Juang, “A hybrid of genetic algorithm and particle swarm optimization for recurrent network design,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 34, no. 2, pp. 997–1006, 2004. View at Publisher · View at Google Scholar · View at Scopus
  20. C.-M. Huang and F.-L. Wang, “An RBF network with OLS and EPSO algorithms for real-time power dispatch,” IEEE Transactions on Power Systems, vol. 22, no. 1, pp. 96–104, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. Y. Song, Z. Chen, and Z. Yuan, “New chaotic PSO-based neural network predictive control for nonlinear process,” IEEE Transactions on Neural Networks, vol. 18, no. 2, pp. 595–600, 2007. View at Publisher · View at Google Scholar · View at Scopus
  22. A. Banks, J. Vincent, and C. Anyakoha, “A review of particle swarm optimization. Part I: background and development,” Natural Computing, vol. 6, no. 4, pp. 467–484, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. A. Banks, J. Vincent, and C. Anyakoha, “A review of particle swarm optimization. Part II: hybridisation, combinatorial, multicriteria and constrained optimization, and indicative applications,” Natural Computing, vol. 7, no. 1, pp. 109–124, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. R. Thangaraj, M. Pant, A. Abraham, and P. Bouvry, “Particle swarm optimization: hybridization perspectives and experimental illustrations,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5208–5226, 2011. View at Publisher · View at Google Scholar · View at Scopus
  25. Y. Shi and R. Eberhart, “Modified particle swarm optimizer,” in Proceedings of the IEEE International Conference on Evolutionary Computation, pp. 69–73, May 1998. View at Scopus
  26. R. C. Eberhart and Y. Shi, “Comparing inertia weights and constriction factors in particle swarm optimization,” in Proceedings of the Congress on Evolutionary Computation (CEC '00), vol. 1, pp. 84–88, July 2000. View at Scopus
  27. M. Clerc and J. Kennedy, “The particle swarm-explosion, stability, and convergence in a multidimensional complex space,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 1, pp. 58–73, 2002. View at Publisher · View at Google Scholar · View at Scopus
  28. J. A. Lazzús, “Estimation of solid vapor pressures of pure compounds at different temperatures using a multilayer network with particle swarm algorithm,” Fluid Phase Equilibria, vol. 289, no. 2, pp. 176–184, 2010. View at Publisher · View at Google Scholar · View at Scopus
  29. J. A. Lazzús, “Optimization of activity coefficient models to describe vapor–liquid equilibrium of (alcohol + water) mixtures using a particle swarm algorithm,” Computers and Mathematics with Applications, vol. 60, no. 8, pp. 2260–2269, 2010. View at Publisher · View at Google Scholar · View at Scopus
  30. J. A. Lazzús, “Prediction of solid vapor pressures for organic and inorganic compounds using a neural network,” Thermochimica Acta, vol. 489, no. 1-2, pp. 53–62, 2009. View at Publisher · View at Google Scholar · View at Scopus
  31. A. Ratnaweera, S. K. Halgamuge, and H. C. Watson, “Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients,” IEEE Transactions on Evolutionary Computation, vol. 8, no. 3, pp. 240–255, 2004. View at Publisher · View at Google Scholar · View at Scopus
  32. Y. Shi and R. C. Eberhart, “Parameter selection in particle swarm optimization,” in Evolutionary Programming VII, vol. 1447 of Lecture Notes in Computer Science, pp. 591–600, Springer, Berlin, Germany, 1998. View at Publisher · View at Google Scholar
  33. J. D. Farmer, “Chaotic attractors of an infinite-dimensional dynamical system,” Physica D: Nonlinear Phenomena, vol. 4, no. 3, pp. 366–393, 1981/82. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. H. Mirzaee, “Linear combination rule in genetic algorithm for optimization of finite impulse response neural network to predict natural chaotic time series,” Chaos, Solitons and Fractals, vol. 41, no. 5, pp. 2681–2689, 2009. View at Publisher · View at Google Scholar · View at Scopus
  35. J. A. Lazzús, I. Salfate, and S. Montecinos, “Hybrid neural network-particle swarm algorithm to describe chaotic time series,” Neural Network World, vol. 24, no. 6, pp. 601–617, 2014. View at Publisher · View at Google Scholar · View at Scopus
  36. J. Zhao, Y. Li, X. Yu, and X. Zhang, “Levenberg-Marquardt algorithm for Mackey-Glass chaotic time series prediction,” Discrete Dynamics in Nature and Society, vol. 2014, Article ID 193758, 6 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  37. L. X. Wang and J. M. Mendel, “Generating fuzzy rules by learning from examples,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 22, no. 6, pp. 1414–1427, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. S. H. Lee and I. Kim, “Time series analysis using fuzzy learning,” in Proceedings of the International Conference on Neural Information Processing, vol. 6, pp. 1577–1582, Seoul, Republic of Korea, October 1994.
  39. Y. Chen, B. Yang, J. Dong, and A. Abraham, “Time-series forecasting using flexible neural tree model,” Information Sciences, vol. 174, no. 3-4, pp. 219–235, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  40. D. Kim and C. Kim, “Forecasting time series with genetic fuzzy predictor ensemble,” IEEE Transactions on Fuzzy Systems, vol. 5, no. 4, pp. 523–535, 1997. View at Publisher · View at Google Scholar · View at Scopus
  41. Z. Qin and Y. Tang, Uncertainty Modeling for Data Mining. A Label Semantics Approach, Zhejiang University Press, Hangzhou, China; Springer, Berlin, Germany, 2014.
  42. G. G. Yen, Multi-Objective Machine Learning, Springer, Berlin, Germany, 2006.
  43. R. Brown, P. Bryant, and H. D. I. Abarbanel, “Computing the Lyapunov spectrum of a dynamical system from an observed time series,” Physical Review A, vol. 43, no. 6, pp. 2787–2806, 1991. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  44. J. Kaplan and J. York, Functional Differential Equations and Approximation of Fixed Points, H. O. Peitgen and H. O. Walther, Eds., Springer, New York, NY, USA, 1979.
  45. E. J. Kostelich and H. L. Swinney, “Practical considerations in estimating dimension from time series data,” Physica Scripta, vol. 40, no. 3, pp. 436–441, 1989. View at Publisher · View at Google Scholar