Kybernetika 54 no. 1, 79-95, 2018

A novel algorithm for the modeling of complex processes

José de Jesús Rubio, Edwin Lughofer, Angelov Plamen, Juan Francisco Novoa and Jesús A. Meda-CampañaDOI: 10.14736/kyb-2018-1-0079

Abstract:

In this investigation, a new algorithm is developed for the updating of a neural network. It is concentrated in a fuzzy transition between the recursive least square and extended Kalman filter algorithms with the purpose to get a bounded gain such that a satisfactory modeling could be maintained. The advised algorithm has the advantage compared with the mentioned methods that it eludes the excessive increasing or decreasing of its gain. The gain of the recommended algorithm is uniformly stable and its convergence is found. The new algorithm is employed for the modeling of two synthetic examples.

Keywords:

modeling, Kalman filter, recursive least square, complex processes

Classification:

93A30

References:

  1. A. Y. Alanis, L. J. Ricalde, C. Simetti and F. Odone: Neural model with particle swarm optimization Kalman learning for forecasting in smart grids. Math. Problems Engrg. (2013), 9 pages.   DOI:10.1155/2013/197690
  2. A. Y. Alanis, E. N. Sanchez and A. G. Loukianov: A wind speed neural model with particle swarm optimization Kalman learning. In: International Joint Conference on Neural Networks 2006, pp. 1993-2000.   CrossRef
  3. A. Y. Alanis, C. Simetti, L. J. Ricalde and F. Odone: A wind speed neural model with particle swarm optimization Kalman learning. In: World Automation Congress 2012, pp. 1-5.   CrossRef
  4. K. J. Astrom and B. Wittenmark: Adaptive Control. Second edition. Addison-Wesley Longman Publishing Co., Inc., Boston (1994).   CrossRef
  5. A. Bifet and R. Gavalda: Kalman filters and adaptive windows for learning in data streams. In: Discovery Science (L. Todorovski, N. Lavrac, K. P. Jantke, eds.), Lecture Notes in Computer Science 4265 (2006), pp. 29-40, Springer, Berlin, Heidelberg.   DOI:10.1007/11893318
  6. S. Čelikovský: Topological equivalence and topological linearization of controlled dynamical systems. Kybernetika 31 (1995), 141-150.   CrossRef
  7. M. Cerrada, C. Li, R. V. Sanchez, F. Pacheco, D. Cabrera and J. Valente: A fuzzy transition based approach for fault severity prediction in helical gearboxes. Fuzzy Sets and Systems 337 (2018), 52-73.   DOI:10.1016/j.fss.2016.12.017
  8. G. Chen, Q. Xie and L. S. Shieh: Fuzzy Kalman filtering. J. Inform. Sci. 109 (1998), 197-209.   DOI:10.1016/s0020-0255(98)10002-6
  9. J. K. Coelho, M.\.D. Pena and O. J. Romero: Pore-scale modeling of oil mobilization trapped in a square cavity. IEEE Latin Amer. Trans. 14 (2016), 4, 1800-1807.   DOI:10.1109/tla.2016.7483518
  10. Z. Deng, X. Wang and Y. Hong: Distributed optimisation design with triggers for disturbed continuous-time multi-agent systems. IET Control Theory Appl. 11 (2017), 2, 282-290.   DOI:10.1049/iet-cta.2016.0795
  11. K. Dolinský and S. Čelikovský: Kalman filter under nonlinear system transformations. In: American Control Conference 2012, pp. 4789-4794.   DOI:10.1109/acc.2012.6315366
  12. S. M. Guo, L. S. Shieh, G. Chen and N. P. Coleman: Observer-type Kalman innovation filter for uncertain linear systems. IEEE Trans. Aerospace Eelectron. Systems 37 (2001), 4, 1406-1418.   DOI:10.1109/7.976975
  13. J. E.Guillermo, L. J. Ricalde Castellanos, E. N. Sanchez and A. Y. Alanis: Detection of heart murmurs based on radial wavelet neural network with Kalman learning. Neurocomputing 164 (2015), 307-317.   DOI:10.1016/j.neucom.2014.12.059
  14. E. A. Hernandez-Vargas, P. Colaneri and R. H. Middleton: Switching strategies to mitigate HIV mutation. IEEE Trans. Control Systems Technol. 22 (2014), 4, 1623-1628.   DOI:10.1109/tcst.2013.2280920
  15. E. A. Hernandez-Vargas, P. Colaneri and R. H. Middleton: Optimal therapy scheduling for a simplified HIV infection model. Automatica 49 (2013), 2874-2880.   DOI:10.1016/j.automatica.2013.06.001
  16. R. E. Kalman: A New approach to linear filtering and prediction problems. Trans. ASME, J. Basic Engrg. 82 (1960), 35-45.   DOI:10.1115/1.3662552
  17. R. Khemchandani, A. Pal and S. Chandra: Fuzzy least squares twin support vector clustering. Neural Computing Appl. 29 (2018), 553-563.   DOI:10.1007/s00521-016-2468-4
  18. I. Lizasoain and M. Gomez: Products of lattice-valued fuzzy transition systems and induced fuzzy transformation semigroups. Fuzzy Sets and Systems 317 (2017), 133-150.   DOI:10.1016/j.fss.2017.01.006
  19. F. Liu, R. Zhao, T. Tan and Q. Zhang: Existence and verification for decentralized nondeterministic discrete-event systems under bisimulation equivalence. Asian J. Control 18 (2016), 5, 1679-1687.   DOI:10.1002/asjc.1253
  20. L. Ljung: System Identification: Theory for the User. Prentice Hall PTR, Prentic Hall Inc., Upper Saddle River, New Jersey 1999.   CrossRef
  21. E. Lughofer: Evolving Fuzzy Systems - Methodologies, Advanced Concepts and Applications. Springer, Berlin, Heidelberg 2011.   CrossRef
  22. E. Lughofer: Single-pass active learning with conflict and ignorance. Evolving Systems 3 (2012), 4, 251-271.   DOI:10.1007/s12530-012-9060-7
  23. E. Lughofer, E. Weigl, W. Heidl, C. Eitzinger and T. Radauer: Recognizing input space and target concept drifts in data streams with scarcely labeled and unlabelled instances. Inform. Sci. 355-356 (2016), 127-151.   DOI:10.1016/j.ins.2016.03.034
  24. I. Mansouri, A. Gholampour, O. Kisi and T. Ozbakkaloglu: Evaluation of peak and residual conditions of actively confined concrete using neuro-fuzzy and neural computing techniques. Neural Computing Appl. 29 (2018), 873-888.   DOI:10.1007/s00521-016-2492-4
  25. V. K. Nguyen, F. Klawonn, R. Mikolajczyk and E. A. Hernandez-Vargas: Analysis of practical identifiability of a viral infection model. Plos One (2016), 1-16.   DOI:10.1371/journal.pone.0167568
  26. M. Pratama, J. Lu, S. Anavatti, E. Lughofer and C. P. Lim: An incremental meta-cognitive-based scaffolding fuzzy neural network. Neurocomputing 171 (2016), 89-105.   DOI:10.1016/j.neucom.2015.06.022
  27. B. Rehák and S. Čelikovský: Numerical method for the solution of the regulator equation with application to nonlinear tracking. Automatica 44 (2008), 1358-1365.   DOI:10.1016/j.automatica.2007.10.015
  28. J. J. Rubio: Least square neural network model of the crude oil blending process. Neural Networks 78 (2016), 88-96.   DOI:10.1016/j.neunet.2016.02.006
  29. J. J. Rubio: Stable Kalman filter and neural network for the chaotic systems identification. J. Franklin Inst. 354 (2017), 7444-7462.   DOI:10.1016/j.jfranklin.2017.08.038
  30. J. J. Rubio: SOFMLS: Online self-organizing fuzzy modified least square network. IEEE Trans. Fuzzy Systems 17 (2009), 6, 1296-1309.   DOI:10.1109/tfuzz.2009.2029569
  31. E. N. Sanchez, A. Y. Alanis and J. Rico: Electric load demand prediction using neural networks trained by Kalman filtering. In: IEEE International Conference on Neural Networks 2004, pp. 2111-2775.   DOI:10.1109/ijcnn.2004.1381093
  32. X. M. Sun, X. F. Wang, Y. Hong and W. Xia: Stabilization control design with parallel-triggering mechanism. IEEE Trans. Industr. Electron. 64 (2017), 3260-3267.   DOI:10.1109/tie.2016.2637888
  33. Z. Weng, G. Chen, L. S. Shieh and J. Larsson: Evolutionary programming Kalman filter. Inform. Sci. 129 (2000), 197-210.   DOI:10.1016/s0020-0255(00)00064-5
  34. H. Wu and Y. Deng: Logical characterizations of simulation and bisimulation for fuzzy transition systems. Fuzzy Sets and Systems 301 (2016), 19-36.   DOI:10.1016/j.fss.2015.09.012
  35. H. Wu and Y. Deng: Distribution-based behavioural distance for nondeterministic fuzzy transition systems. IEEE Trans. Fuzzy Systems 99 (2017), 1-1.   DOI:10.1109/tfuzz.2017.2670605
  36. H. Wu, Y. Chen, T. Bu and Y. Deng: Algorithmic and logical characterizations of bisimulations for non-deterministic fuzzy transition systems. Fuzzy Sets and Systems 333 (2017), 106-123.   DOI:10.1016/j.fss.2017.02.008
  37. D. Xu, X. Wang, Y. Hong and Z. P. Jiang: Global robust distributed output consensus of multi-agent nonlinear systems: an internal model approach Systems Control Lett. 87 (2016), 64-69.   DOI:10.1016/j.sysconle.2015.11.002