An unscented Kalman filter in designing dynamic GMDH neural networks for robust fault detection

Marcin Mrugalski

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 1, page 157-169
  • ISSN: 1641-876X

Abstract

top
This paper presents an identification method of dynamic systems based on a group method of data handling approach. In particular, a new structure of the dynamic multi-input multi-output neuron in a state-space representation is proposed. Moreover, a new training algorithm of the neural network based on the unscented Kalman filter is presented. The final part of the work contains an illustrative example regarding the application of the proposed approach to robust fault detection of a tunnel furnace.

How to cite

top

Marcin Mrugalski. "An unscented Kalman filter in designing dynamic GMDH neural networks for robust fault detection." International Journal of Applied Mathematics and Computer Science 23.1 (2013): 157-169. <http://eudml.org/doc/251297>.

@article{MarcinMrugalski2013,
abstract = {This paper presents an identification method of dynamic systems based on a group method of data handling approach. In particular, a new structure of the dynamic multi-input multi-output neuron in a state-space representation is proposed. Moreover, a new training algorithm of the neural network based on the unscented Kalman filter is presented. The final part of the work contains an illustrative example regarding the application of the proposed approach to robust fault detection of a tunnel furnace.},
author = {Marcin Mrugalski},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {robust fault detection; non-linear system identification; dynamic GMDH neural network; unscented Kalman filter; nonlinear system identification},
language = {eng},
number = {1},
pages = {157-169},
title = {An unscented Kalman filter in designing dynamic GMDH neural networks for robust fault detection},
url = {http://eudml.org/doc/251297},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Marcin Mrugalski
TI - An unscented Kalman filter in designing dynamic GMDH neural networks for robust fault detection
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 1
SP - 157
EP - 169
AB - This paper presents an identification method of dynamic systems based on a group method of data handling approach. In particular, a new structure of the dynamic multi-input multi-output neuron in a state-space representation is proposed. Moreover, a new training algorithm of the neural network based on the unscented Kalman filter is presented. The final part of the work contains an illustrative example regarding the application of the proposed approach to robust fault detection of a tunnel furnace.
LA - eng
KW - robust fault detection; non-linear system identification; dynamic GMDH neural network; unscented Kalman filter; nonlinear system identification
UR - http://eudml.org/doc/251297
ER -

References

top
  1. Back, A. and Tsoi, A. (1991). FIR and IIR synapses. A new neural network architectures for time series modelling, Neural Computation 3(3): 375-385. 
  2. Bernstein, D. (2005). Matrix Mathematics, Princeton University Press, Princeton, NJ. 
  3. Ding, S. (2008). Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools, Springer-Verlag, Berlin/Heidelberg. 
  4. Elman, J. (1990). Finding structure in time, Cognitive Science 14(2): 179-211. 
  5. Fasconi, P., Gori, M. and Soda, G. (1992). Local feedback multilayered networks, Neural Computation 4(1): 120-130. 
  6. Gori, M., Bengio, Y. and De Mori, R. (1989). BPS: A learning algorithm for capturing the dynamic nature of speech, International Joint Conference on Neural Networks, Washington, DC, USA, pp. 417-423. 
  7. Gupta, M., Liang, J. and Homma, N. (2003). Static and Dynamic Neural Networks, John Wiley & Sons, Hoboken, NJ. 
  8. Haykin, S. (2001). Kalman Filtering and Neural Networks, John Wiley & Sons, New York, NY. 
  9. Haykin, S. (2009). Neural Networks and Learning Machines, Prentice Hall, New York, NY. 
  10. Ichalal, D., Marx, B., Ragot, J. and Maquin, D. (2012). New fault tolerant control strategies for nonlinear Takagi-Sugeno systems, International Journal of Applied Mathematics and Computer Science 22(1): 197-210, DOI: 10.2478/v10006-012-0015-8. Zbl1273.93102
  11. Isermann, R. (2005). Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance, Springer-Verlag, Heidelberg/Berlin. 
  12. Ivakhnenko, A. and Mueller, J. (1995). Self-organization of nets of active neurons, System Analysis Modelling Simulation 20(1-2): 93-106. 
  13. Jordan, M. and Bishop, C. (1997). Neural networks, in A. Tucker (Ed.), CRC Handbook of Computer Science, CRC Press, Boca Raton, FL, pp. 536-556. 
  14. Julier, S. and Uhlmann, J. (2004). Unscented filtering and nonlinear estimation, Proceedings of the IEEE 92(3): 401-422. 
  15. Korbicz, J. and Kościelny, J. (Eds.) (2010). Modeling, Diagnostics and Process Control: Implementation in the DiaSter System, Springer-Verlag, Berlin. 
  16. Korbicz, J., Kościelny, J., Kowalczuk, Z. and Cholewa, W. (Eds.) (2004). Fault Diagnosis. Models, Artificial Intelligence, Applications, Springer-Verlag, Berlin. Zbl1074.93004
  17. Korbicz, J. and Mrugalski, M. (2008). Confidence estimation of GMDH neural networks and its application in fault detection system, International Journal of System Science 39(8): 783-800. Zbl1283.93268
  18. Lee, T. and Jiang, Z. (2006). On uniform global asymptotic stability of nonlinear discrete-time systems with applications, IEEE Transactions on Automatic Control 51(10): 1644-1660. 
  19. Ljung, L. (1999). System Identification: Theory for the User, Prentice Hall PTR, Upper Saddle River, NJ. Zbl0615.93004
  20. Montes de Oca, S., Puig, V., Witczak, M. and Dziekan, Ł. (2012). Fault-tolerant control strategy for actuator faults using LPV techniques: Application to a two degree of freedom helicopter, International Journal of Applied Mathematics and Computer Science 22(1): 161-171, DOI: 10.2478/v10006-012-0012-y. Zbl1273.93049
  21. Mrugalski, M. and Korbicz, J. (2007). Least mean square vs. outer bounding ellipsoid algorithm in confidence estimation of the GMDH neural networks, in B. Beliczynski, A. Dzielinski, M. Iwanowski, and B. Ribeiro (Eds.), Adaptive and Natural Computing Algorithms, Part 2, Lecture Notes in Computer Science, Vol. 4432, Physica-Verlag, Heidelberg, pp. 19-26. 
  22. Mrugalski, M. and Korbicz, J. (2011). GMDH neural networks, in B. Wilamowski and J. Irwin (Eds.), The Industrial Electronics Handbook, 2nd Edn., Vol. 5, CRC Press, Taylor Francis Group, Boca Raton, FL, pp. 8-1-8-21. 
  23. Mrugalski, M. and Witczak, M. (2012). State-space GMDH neural networks for actuator robust fault diagnosis, Advances in Electrical and Computer Engineering 12(3): 65-72. 
  24. Mrugalski, M., Arinton, E. and Korbicz, J. (2003). Dynamic GMDH type neural networks, in L. Rutkowski and J. Kacprzyk (Eds.), Neural Networks and Soft Computing, Heidelberg, Physica-Verlag, pp. 698-703. 
  25. Mrugalski, M., Witczak, M. and Korbicz, J. (2008). Confidence estimation of the multi-layer perceptron and its application in fault detection systems, Engineering Applications of Artificial Intelligence 21(6): 895-906. 
  26. Niemann, H.H. (2012). A model-based approach to fault-tolerant control, International Journal of Applied Mathematics and Computer Science 22(1): 67-86, DOI: 10.2478/v10006-012-0005-x. Zbl1273.93053
  27. Noura, H., Theilliol, D., Ponsart, J. and Chamseddine, A. (2009). Fault-tolerant Control Systems: Design and Practical Applications, Springer-Verlag, London. Zbl1215.93052
  28. Palade, V., Bocaniala, C. and Jain, L. (2006). Computational Intelligence in Fault Diagnosis, Springer-Verlag, London. 
  29. Pan, Y., Sung, S. and Lee, J. (2001). Data-based construction of feedback-corrected nonlinear prediction model using feedback neural networks, Control Engineering Practice 9(8): 859-867. 
  30. Patan, K., Witczak, M. and Korbicz, J. (2008). Towards robustness in neural network based fault diagnosis, International Journal of Applied Mathematics and Computer Science 18(4): 443-454, DOI: 10.2478/v10006-008-0039-2. Zbl1155.93344
  31. Patton, R., Frank, P. and Clark, R. (2000). Non-linear Systems Identification. From Classical Approaches to Neural Networks and Fuzzy Models, Springer-Verlag, Berlin. 
  32. Teixeira, B., Torres, L., Aguirre, L. and Bernstein, D. (2010). On unscented Kalman filtering with state interval constraints, Journal of Process Control 20(1): 45-57. 
  33. Williams, R. and Zipser, D. (1989). A learning algorithm for continually running fully recurrent neural networks, Neural Computation 1(2): 270-280. 
  34. Witczak, M. (2007). Modelling and Estimation Strategies for Fault Diagnosis of Non-Linear Systems. From Analytical to Soft Computing Approaches, Springer-Verlag, Berlin. Zbl1192.93003
  35. Witczak, M., Korbicz, J., Mrugalski, M. and Patton, R. (2006). A GMDH neural network based approach to robust fault detection and its application to solve the Damadics benchmark problem, Control Engineering Practice 14(6): 671-683. 
  36. Witczak, M. and Prętki, P. (2007). Design of an extended unknown input observer with stochastic robustness techniques and evolutionary algorithms, International Journal of Control 80(5): 749-762. Zbl1162.93323
  37. Zamarreño, J. M. and Vega, P. (1998). State space neural network. Properties and application, Neural Networks 11(6): 1099-1112. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.