Analysis of Stochastic Systems Via Maximum Entropy Principle

  • K. Sobczyk
  • J. Trebicki
Conference paper
Part of the IUTAM Symposia book series (IUTAM)

Summary

The principle of maximum entropy introduced first in statistical physics and successfully applied in other fields (statistics, reliability theory, simulation etc.) has recently been developed to analyze the systems governed by stochastic differential equations (cf.[2],[3]). In this paper we extend the maximum entropy methodology to stochastic vibratory nonlinear systems.

Starting from general formulation of the system dynamics and assuming that an information about the response (solution) is available in the form of the equations for moments, the probability distribution of the stationary response is derived as a result of maximization of the entropy functional. Along with the basic scheme of the method the comparisons of the results with prediction of other known procedures is given.

Keywords

Entropy Geophysics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Jeynes E. T., Information theory and statistical mechanics, Physical Rev., 1957, 106(4), 620–630.CrossRefADSGoogle Scholar
  2. 2.
    Sobczyk K., Stochastic Differential Equations with Applications to Physics and Engineering, Kluwer Acad. Publ., Dordrecht, 1991.MATHGoogle Scholar
  3. 3.
    Sobczyk K., Trebicki J., Maximum entropy principle in stochastic dynamics, Probability Eng. Mech., 1990, vol.5, No.3.Google Scholar
  4. 4.
    de Beauregard O. C., Tribus M., Information theory and thermodynamics, Helvetica Physica Acta, vol.47 238–247, 1974.MathSciNetGoogle Scholar
  5. 5.
    Kullback S., Information Theory and Statistics, Chapman and Hall, N. York, 1959.MATHGoogle Scholar
  6. 6.
    Tribus M., Rational Descriptions, Decision and Designs, N. York, Pergamon Press, 1969.Google Scholar
  7. 7.
    Spencer B. F., Bergman L.A., On the estimation of failure probability having prescribed statistical moments of first passage time, Probabilistic Eng. Mech., vol.1, No.3, 1986.Google Scholar
  8. 8.
    Chan M., System simulation and maximum entropy, Operations Research, vol.19, 1751–1753, 1971.CrossRefGoogle Scholar
  9. 9.
    Ulrych T.J., Bishop T.N., Maximum entropy spectral analysis and autoregressive decomposition, Rev. Geophysics and Space Physics, vol.43, No.1, pp. 183–200, 1975.Google Scholar
  10. 10.
    Dimentberg M.F., An exact solution to a certain non-linear random vibration problem, Intern. J. Non-linear Mech. vol.17, 231–236, 1982.CrossRefMATHADSMathSciNetGoogle Scholar
  11. 11.
    Wu W.F., Lin Y.K., Cumulant-neglect closure for nonlinear oscillators under random parametric and external excitations, Int. J. Nonlinear Mech. vol.17, No.4, 349–362, 1984.CrossRefMathSciNetGoogle Scholar
  12. 12.
    Hampl N. C., Schüeller G. I., Probability densities of the response of structures under stochastic dynamics excitation, Prob. Eng. Mech. 1989, Vol. 4, No.1.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • K. Sobczyk
    • 1
  • J. Trebicki
    • 1
  1. 1.Institute of Fundamental Technological ResearchPolish Academy of ScienceWarsawPoland

Personalised recommendations