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TECHNICAL PAPERS

Information Closure Method for Dynamic Analysis of Nonlinear Stochastic Systems

[+] Author and Article Information
R. J. Chang, S. J. Lin

Department of Mechanical Engineering, National Cheng Kung University, 701 Tainan, Taiwan, R.O.C.

J. Dyn. Sys., Meas., Control 124(3), 353-363 (Jul 23, 2002) (11 pages) doi:10.1115/1.1485746 History: Received December 01, 1999; Online July 23, 2002
Copyright © 2002 by ASME
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References

Maybeck, P. S., 1982, Stochastic Models, Estimation, and Control, Vol. 2, Academic Press, New York.
Sobczyk, K., 1991, Stochastic Differential Equations with Applications to Physics and Engineering, Kluwer Academic Publishers, Boston.
Chang,  R. J., 1993, “Extension in Techniques for Stochastic Dynamic Systems,” Control and Dynamic Systems, 55, pp. 429–470.
Dashevskii,  M. L., and Liptser,  R. S., 1967, “Application of Conditional Semi-Invariants in Problems of Non-Linear Filtering of Markov Process,” Autom. Remote Control (Engl. Transl.), 28, pp. 912–921.
Haken, H., 1988, Information and Self-Organization, Springer-Verlag, Berlin.
Chang,  R. J., 1991, “Maximum Entropy Approach for Stationary Response of Non-linear Stochastic Oscillators,” ASME J. Appl. Mech., 58, pp. 266–271.
Jumarie,  G., 1990, “Solution of the Multivariate Fokker-Planck Equation by Using a Maximum Path Entropy Principle,” J. Math. Phys., 31, pp. 2389–2392.
Phillis,  Y. A., 1982, “Entropy Stability of Continuous Dynamic Systems,” Int. J. Control, 35, pp. 323–340.
Sobczyk,  K., and Trebicki,  J., 1990, “Maximum Entropy Principle in Stochastic Dynamics,” Probab. Eng. Mech., 5, pp. 102–110.
Sobczyk,  K., and Trebicki,  J., 1993, “Maximum Entropy Principle and Non-Linear Stochastic Oscillators,” Physica A, 193, pp. 448–468.
Sobczyk, K., and Trebicki, J., 1995, “Maximum Entropy Closure for Non-Linear Stochastic Systems,” ASME Proc. 1995 Design Engineering Technical Conference, United Engineering Center, New York, Vol. 3A , pp. 1025–1028.
Trebicki,  J., and Sobczyk,  K., 1996, “Maximum Entropy Principle and Non-Stationary Distributions of Stochastic Systems,” Probab. Eng. Mech., 11, pp. 169–178.
Jumarie,  G., 1986, “A Practical Approach to Non-linear Estimation by Using the Maximum Entropy Principle,” ASME J. Dyn. Syst., Meas., Control, 108, pp. 49–55.
Jaynes,  E. T., 1957, “Information Theory and Statistical Mechanics,” Physical Review, 106, pp. 620–630.
Tribus, M., 1969, Rational Descriptions, Decisions and Designs, Pergamon Press, New York.
Young,  G. E., and Chang,  R. J., 1987, “Prediction of the Response of Non-Linear Oscillators under Stochastic Parametric and External Excitations,” Int. J. Non-Linear Mech., 28, pp. 151–160.
Dimentberg,  M. F., 1982, “An Exact Solution to a Certain Non-linear Random Vibration Problem,” Int. J. Non-Linear Mech., 17, pp. 231–236.
Kozin,  F., 1986, “Some Results on Stability of Stochastic Dynamical Systems,” Probab. Eng. Mech., 1, pp. 13–22.
Benaroya,  H., and Rehak,  M., 1989, “Response and Stability of a Random Differential Equation: Part I-Moment Equation Method,” ASME J. Appl. Mech., 56, pp. 192–195.
Benaroya,  H., and Rehak,  M., 1989, “Response and Stability of a Random Differential Equation: Part II-Expansion Method,” ASME J. Appl. Mech., 56, pp. 196–200.
Chang,  R. J., 1991, “A Practical Technique for Spectral Analysis of Non-linear Systems under Stochastic Parametric and External Excitations,” ASME J. Vibr. Acoust., 113, pp. 516–522.

Figures

Grahic Jump Location
Entropy evolution (Hi(x)) and second moment propagation (m2,i) estimated by different entropy modes (i=1∼3), and Monte Carlo simulation (ooo); i=1-mode of exp(−λ1,1(t)x2),i=2-mode of exp(−λ1,2(t)x4), and i=3-mode of exp(−λ1,3(t)x6)
Grahic Jump Location
Nonstationary density (pi(x)) at time instant t=0.5 estimated by different entropy modes (i=1∼3) and Monte Carlo simulation (ooo)
Grahic Jump Location
Entropy evolution (H(xi)), second moment propagation (mij) and associated stationary exact solution (⋯)
Grahic Jump Location
Density evolution p(x1,t) at time instant t=0, 0.7, 1.5, 12, and exact density in stationary
Grahic Jump Location
Stability boundaries under q110q22 and μ0=1 given by different definitions: 1 -almost sure stability, 2 -first moment or density stability, and 3 -second moment, spectral or entropy stability
Grahic Jump Location
Parametric analysis of entropy stability by different modes (i=1∼3) with q33 as a parameter for qualitative root-locus plot; (q33)S,1-mode of exp(−λ1,1x12),(q33)S,2-mode of exp(−λ1,2x14),(q33)S,3-mode of exp(−λ1,3x16)
Grahic Jump Location
Boundaries of entropy stability under ξ0≥2q22 estimated by different modes: 1−q33=(4/225) (μ030−2q22)3/q112),2−q33=(Γ(0.25)2/432Γ(1.75)2) (μ030−2q22)3/q112), and 3−q33=(16Γ(5/6)3/3Γ(1/6)3) (μ030−2q22)3/q112).

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