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

Stochastic stability and first passage failure of thin rectangular plate subjected to stochastic parametrical excitation

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。

A stochastic two dimensional dynamical model of controlled thin rectangular plate subjected to in-plate stochastic parametrical excitation was proposed based on Galerkin＇s approach.The model was further simplified applying the stochastic average theory of quasi-integral Hamilton system.The optimal control strategy was derived from the dynamical programming equations and the control constraints.The backward Kolmogorov equation for reliability function of the controlled system was established.The dynamical programming equations for maximum reliability problem were finalized and their relationships to the backward Kolmogorov equation for reliability function were pointed out.The numerical results show that the procedure is effective and efficient.