Explicit expression of stationary response probability density for nonlinear stochastic systems
2021
Identifying the exactly or approximately explicit expression of the stationary response
probability density for general nonlinear stochastic dynamical systems is of great
significance in the fields of stochastic dynamics and control. Almost all the existing
methods are devoted to determine the exact or approximate solution for specific values of
system and excitation parameters. Herein, aimed at stochastic systems with
polynomial nonlinearity and excited by Gaussian white noises, a novel method is
proposed to identify the stationary response probability density which explicitly includes
system and excitation parameters. The stationary probability density is first written as
an exponential function according to the maximum entropy principle, the power of the
exponential function is then expressed as a linear combination of prescribed nondimensional
parameter clusters constituted by system and excitation parameters, and
state variables, with the coefficients to be determined. The undetermined coefficients
are derived by minimizing the residual of the associated Fokker-Planck- Kolmogorov
equation. The application and efficacy of the proposed method are illustrated by a
typical numerical example.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
33
References
1
Citations
NaN
KQI