Stochastic Optimal Control of MR Damped Structures with Uncertain Parameters

Abstract

Magneto-rheological (MR) damper has proved its value in vibration mitigation of engineering structures subjected to dynamic excitations such as seismic ground motion and strong wind. The accurate operation, however, of MR damper still remains a challenge due to incomplete knowledge on the randomness inherent in the dynamical behaviors of the damper. While the classical models of MR damper are most of phenomenal formulation lacking of the in-depth analysis of working mechanism at material scale. The stochastic modeling of MR damper is carried out in this paper of which the variability definition of critical parameters renders to the dynamic yield analysis of Magneto-rheological fluids. A randomly base-excited structure controlled by the MR damper is investigated. Numerical results indicate that the MR damping control can reduce the seismic response significantly, where the distribution range of probability density function becomes narrower comparing with that without control. It is thus remarked that the appropriately designed semi-active controller can achieve almost the same effect as the active controller in probabilistic sense. The randomness, meanwhile, of damper parameters could be neglected safely. Magneto-rheological (MR) damper is regarded as one of the most promising control devices due to its perfect dynamic damping behaviors. While the accurate operation of the damper still remains a challenge due to the statistical incompleteness on the classical phenomenal models. The authors explored the variability of dynamic yield behavior of MR fluids using a micro-scale method referring to molecular dynamics simulations (Peng and Li, 2011). The previous work provides a path for the stochastic modeling of MR damper through updating the fluctuation of dynamic yield at MR fluid level. This paper firstly addresses the stochastic modeling of MR dampers, and then investigates the optimal semi-active control of structures using the random-parameterized MR dampers in the context of physically based stochastic optimal control. The physically based stochastic optimal control of structures, hinged on the generalized density evolution equation (GDEE), is proved to be highly efficient for linear and nonlinear structural systems subjected to engineering excitations with non-stationary and non-Gaussian behaviors (Li et al, 2010). In order to reach a good agreement with the dynamic behavior of MR damper, a bounded Hrovat semi-active control strategy is addressed. For illustrative purpose, a randomly base-excited structure controlled by MR damper is investigated, of which viscous damping coefficient is viewed as random variable. Numerical results indicate that the MR damping control can reduce the seismic response