Analysis of Stochastic Systems Via Maximum Entropy Principle
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.,). 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.
KeywordsLagrange Multiplier Maximum Entropy Moment Equation Maximum Entropy Method Maximum Entropy Principle
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- 3.Sobczyk K., Trebicki J., Maximum entropy principle in stochastic dynamics, Probability Eng. Mech., 1990, vol.5, No.3.Google Scholar
- 6.Tribus M., Rational Descriptions, Decision and Designs, N. York, Pergamon Press, 1969.Google Scholar
- 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
- 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
- 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