随机最优控制下矩形薄板受面内随机参数激励的首次穿越研究

PDF(1044 KB)

振动与冲击 ›› 2012, Vol. 31 ›› Issue (4) : 179-183.

论文

随机最优控制下矩形薄板受面内随机参数激励的首次穿越研究

葛根1; 王洪礼2; 许佳2

作者信息 +

Stochastic stability and first passage failure for a thin rectangular plate subject to stochastic parametrical excitation

Ge Gen1; Wang Hong-li2 ; Xu jia2

Author information +

文章历史 +

摘要

根据建立了四边简支受控矩形薄板受面内高斯白噪声激励的振动模型，并用Galerkin变分法将其化简为二自由度常微分非线性动力学方程。又利用拟不可积Hamilton系统平均理论将方程等价为一个一维的Ito随机过程，随后结合随机动态规划方法，得到了使系统可靠性最大的随机最优控制策略。最后建立了受控系统的条件可靠性函数所满足的Backward Kolmogorov(BK)方程，根据初始条件和边界条件得出数值结果。数值结果表明，随机最优控制对系统的可靠性提升有明显作用

Abstract

One stochastic two dimensional dynamical model of a thin rectangular plate subject to in-plate stochastic parametrical excitation with control is proposed based on Galerkin’s approach. At first the model is simplified applying the stochastic average theory of quasi-integral Hamilton system. Secondly, the optimal control law is derived from the dynamical programming equations and the control constraints.
Finally, the Backward Kolmogorov equation for reliability function had been established. The dynamical programming equations for maximum reliability problem are finalized and their relationships to the backward Kolmogorov equation for the reliability function are pointed out. The numerical results show that the procedure is effective and efficiency.

导出引用

葛根;王洪礼; 许佳. 随机最优控制下矩形薄板受面内随机参数激励的首次穿越研究[J]. 振动与冲击, 2012, 31(4): 179-183

Ge Gen; Wang Hong-li;Xu jia. Stochastic stability and first passage failure for a thin rectangular plate subject to stochastic parametrical excitation[J]. Journal of Vibration and Shock, 2012, 31(4): 179-183