Nonstationary probability densities of a class of nonlinear system excited by external colored noise

作者：Qi LuYuan^*; Xu Wei; Gu XuDong

来源：Science China Physics,Mechanics & Astronomy, 2012, 55(3): 477-482.

DOI：10.1007/s11433-012-4632-x

• colored noise
• nonstationary probability density
• Galerkin method
• stochastic averaging method

This paper deals with the approximate nonstationary probability density of a class of nonlinear vibrating system excited by colored noise. First, the stochastic averaging method is adopted to obtain the averaged Ito equation for the amplitude of the system. The corresponding Fokker-Planck-Kolmogorov equation governing the evolutionary probability density function is deduced. Then, the approximate solution of the Fokker-Planck-Kolmogorov equation is derived by applying the Galerkin method. The solution is expressed as a sum of a series of expansion in terms of a set of proper basis functions with time-depended coefficients. Finally, an example is given to illustrate the proposed procedure. The validity of the proposed method is confirmed by Monte Carlo Simulation.

• 出版日期2012-3
• 单位西北工业大学