Gauss白噪声参激下悬挂轮对系统的随机稳定性研究

Stochastic stability of a suspended wheelset system under gauss white noise

在非线性悬挂轮对系统中加入了Gauss白噪声参激,通过Hamilton系统理论和随机微分方程理论,将系统转化为拟不可积Hamilton系统伊藤随机微分方程组,根据拟不可积Hamilton系统的随机平均法,把该方程组降维为一维扩散的平均伊藤随机微分方程,使原系统的解依概率收敛到一维伊藤扩散过程。通过分析一维扩散奇异边界的性态得到了随机全局稳定性的条件。最后对系统的D分叉和P分叉行为进行了研究,并画出了随机P分叉图和随机极限环图。结果表明,随机项的作用使系统的临界速度发生漂移,随着噪声项强度增大,临界速度显著降低。P分叉后系统表现为最大可能意义上的随机极限环振荡,而D分叉后统表现为概率1意义下不稳定的非极限环随机振荡。

Here,Gauss-White-noise parametric random excitation was input in a nonlinear suspended wheelset system.According to Hamilton system and the stochastic differential equation theory,the system could be expressed as a quasi-nonintegrable Hamiltonian system in form of Ito stochastic differential equation. The equation was reduced to one dimensional diffusion Ito average stochastic differential equations with the stochastic averaging method. So,the solution to the original system converged in probability an one-dimensional Ito diffusion process. The global stochastic stability conditions were obtained by analyzing the modality of the singular boundary of the one-dimensional diffusion. At last,the stochastic P-bifurcation and Dbifurcation behaviors of the system were studied. The stochastic P-bifurcation diagram and the stochastic limit cycle one were plotted. The results showed that the random excitation can drift forward the system critical speed and the system critical speed significantly decreases when the intensity of random excitation increases; the P-bifurcation leads to the most possible limit cycle of the system,while the D-bifurcation leads to an unstable non-limit cycle of the system in the sense of probability 1.