约束轮对首次穿越失效的随机非线性最优控制

Stochastic Nonlinear Optimal Control for First-passage Failure of Constrained Wheelset

为分析约束轮对首次穿越失效后的最优控制,并改善系统的稳定性性能,建立受控动力学模型中考虑轨道不平顺激励和自身结构参激的动力学模型。基于随机动态规划原理控制策略,运用拟不可积Hamilton系统随机平均法,以可靠度最大化为控制目标,建立可靠性函数和首次穿越时间概率密度函数的动态规划方程。分析表明,通过控制作用,可使原本不稳定的系统在受控后变为概率意义上的稳定系统,在选取适当控制力条件下,可使原本不稳定的系统成为绝对意义上的稳定系统。另外,如果系统运行时失稳,在振动能量较小的失稳初期,提供较小的外界控制约束力,也能达到较好效果;而如果系统运行一段时间后具有较大振动能量,即使此时提供较大的控制约束力,已较难改善系统性能。

In order to analyze nonlinear stochastic optimal control of first-passage failure of elastic constraint wheel system and improve the stability performance of the system,a dynamic model considering track random irregularity and their structure random parameters was established.Based on the control strategy with stochastic dynamic programming principle,the stochastic averaging method of quasi integrable Hamilton system was used to maximize the reliability as the control target.The dynamic programming equations of the reliability function and the probability density function for the first-passage time were established.The results show that under the control function,the unstable system can be changed into a stable system in the sense of probability,and the original unstable system can even become a stable system in the absolute sense,under the condition of selection of appropriate control force.In addition,in the event of unstable operation of the system,in the initial period of instability with less vibration energy,provision of a smaller external control constrained force can also achieve better results.If the system has a large vibration energy after a period of operation,the system performance can hardly be improved even if the control constraint is increased at this time.