非线性时变结构随机地震响应最优多项式控制

Optimal polynomial control for random seismic response of non-linear time-varying structures

以随机地震动作用下具有Bouc-Wen滞回特性的非线性结构系统为受控对象,开展了最优多项式控制算法研究:包括系统矩阵中Maclaurin展开取初始零值衍生的具有时不变增益矩阵的控制律,和系统矩阵中Maclaurin一阶展开衍生的具有时变增益矩阵的控制律。研究表明,受控结构层间位移响应的变异性明显降低,结构的安全性显著提高。同时,基于时不变增益矩阵的控制律的控制效果在一定程度上受制于控制力施加的大小与系统稳定性之间的平衡关系,而考虑了每一个时间步位移和速度对增益矩阵影响、基于时变增益矩阵的控制律则能以较小的控制出力获得较好的控制效果。

The physically-motivated stochastic optimal control is proved to be efficient in performance improvement and risk mitigation of engineering structures. Here, the polynomial control method considering time-variant gain parameters for physical scheme ruling nonlinear stochastic systems was presented. The exceedance probability of structural states and control force served as the critical argument of probabilistic criterion, whereby the parameter optimization of control policy could be readily achieved. A randomly base-excited shear frame structure with Bouc-Wen behaviors was used as the object for control test. Numerical results indicated that using the proposed stochastic optimal control schemes, the variation of inter-storey drift of the structure decreases significantly, and the structural safety is enhanced obviously; the benefit of optimal polynomial control with time-invariant gain parameters is enslaved to the balance relation between system stability and control force, while the optimal polynomial control with time-variant gain parameters involves the contributions of structural velocity and displacement to the gain matrix at each time step, it results in a better structural performance with a smaller control force.