高斯白噪声激励下拟可积哈密顿系统的可靠性  

STUDY ON RELIABILITY OF QUASI-INTEGRABLE-HAMILTONIAN SYSTEMS UNDER GAUSSIAN WHITE NOISES

作　　者：甘春标[1] 

机构地区：[1]浙江大学机械与能源工程力学系,杭州310027

出　　处：《振动与冲击》2006年第2期145-146,151,共3页Journal of Vibration and Shock

基　　金：国家自然科学青年基金资助项目(10302025)

摘　　要：研究非共振的拟可积哈密顿系统在受高斯白噪声外激励下的可靠性。利用由随机平均法导出的关于系统的独立运动积分或作用变量的随机平均方程,通过拟可积哈密顿系统的特性以及对漂移与扩散系数作出的一些假定,给出了系统的可靠性函数以及首次穿越损坏的条件转移概率密度函数所满足的后向柯尔莫哥洛夫方程和福克-普朗克方程,并进一步详细地讨论了其边界与可解性条件。通过一个实例的分析以及有限差分方法得出的数值结果表明,关于系统的可靠性函数以及首次穿越损坏的条件转移概率密度函数方面的结果是比较合理的,这也表明此分析方法是正确的。In the present paper, the reliability of quasi-integrable-Hamiltonian systems under Gaussian white noises is investigated. The averaged Ito equations about the system's energies or actions are given based on the stochastic averaging method. The system's safe region is defined, on which the boundary conditions are studied in detail under some suppositions on the drift and diffusion coefficients, and then, the corresponding BK and FPK equations are established to study the system's conditional reliability functions and conditional transitional probability density functions. A simple example is used to illustrate the above processes, and the numerical results about the conditional reliability functions and conditional transitional probability density functions are also given by use of the finite difference method. It is shown that these results are reasonable, and the boundary conditions given in the present paper for the study on high dimensional BK equations are instructive.

关 键 词：拟可积哈密顿系统 高斯白噪声 随机平均 BK方程 可靠性 

分 类 号：O324[理学—一般力学与力学基础] O175[理学—力学]