Least Mean Square vs. Outer Bounding Ellipsoid Algorithm in Confidence Estimation of the GMDH Neural Networks

  • Marcin Mrugalski
  • Józef Korbicz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4432)

Abstract

The paper deals with the problem of determination of the model uncertainty during the system identification with the application of the Group Method of Data Handling (GMDH) neural network. The main objective is to show how to employ the Least Mean Square (LMS) and the Outer Bounding Ellipsoid (OBE) algorithm to obtain the corresponding model uncertainty.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Delaleau, E., Louis, J.P., Ortega, R.: Modeling and Control of Induction Motors. Int. Journal of Applied Mathematics and Computer Science 11, 105–129 (2001)MATHMathSciNetGoogle Scholar
  2. 2.
    Etien, E., Cauet, S., Rambault, L., Champenois, G.: Control of an Induction Motor Using Sliding Mode Linearization. Int. Journal of Applied Mathematics and Computer Science 12, 523–531 (2001)MathSciNetGoogle Scholar
  3. 3.
    Gupta, M.M., Liang, J., Homma, N.: Static and Dynamic Neural Networks. John Wiley & Sons, Hoboken (2003)Google Scholar
  4. 4.
    Ivakhnenko, A.G., Mueller, J.A.: Self-organizing of Nets of Active Neurons. System Analysis Modelling Simulation 20, 93–106 (1996)Google Scholar
  5. 5.
    Korbicz, J., Kościelny, J.M., Kowalczuk, Z., Cholewa, W. (eds.): Fault Diagnosis: Models, Artificial Intelligence, Applications. Springer, Berlin (2004)MATHGoogle Scholar
  6. 6.
    Milanese, M., Norton, J., Piet-Lahanier, H., Walter, E. (eds.): Bounding Approaches to System Identification. Plenum Press, New York (1996)MATHGoogle Scholar
  7. 7.
    Mrugalski, M.: Neural Network Based Modelling of Non-linear Systems in Fault Detection Schemes. Ph.D. Thesis (In Polish), University of Zielona Góra, Zielona Góra (2004)Google Scholar
  8. 8.
    Witczak, M.: Advances in Model-based Fault Diagnosis with Evolutionary Algorithms and Neural Networks. Int. Journal of Applied Mathematics and Computer Science 16, 85–99 (2006)MathSciNetGoogle Scholar
  9. 9.
    Witczak, M., Korbicz, J., Mrugalski, M., Patton, R.J.: A GMDH neural network based approach to robust fault detection and its application to solve the DAMADICS benchmark problem. Control Engineering Practice 14, 671–683 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Marcin Mrugalski
    • 1
  • Józef Korbicz
    • 1
  1. 1.Institute of Control and Computation Engineering, University of Zielona Góra, ul. Podgórna 50, 65–246 Zielona GóraPoland

Personalised recommendations