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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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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