Due to the inherent nonlinear nature of magnetorheological (MR) dampers, one of the challenging aspects for developing and utilizing these devices to achieve high performance is the development of models that can accurately describe their unique characteristics. In this review, the characteristics of MR dampers are summarized according to the measured responses under different conditions. On these bases, the considerations and methods of the parametric dynamic modelling for MR dampers are given and the state-of-the-art parametric dynamic modelling, identification and validation techniques for MR dampers are reviewed. In the past two decades, the models for MR dampers have been focused on how to improve the modelling accuracy. Although the force-displacement behaviour is well represented by most of the proposed dynamic models for MR dampers, no simple parametric models with high accuracy for MR dampers can be found. In addition, the parametric dynamic models for MR dampers with on-line updating ability and the inverse parametric models for MR dampers are scarcely explored. Moreover, whether one dynamic model for MR dampers can portray the force-displacement and force-velocity behaviour is not only determined by the dynamic model itself but also determined by the identification method.

Due to the inherent nonlinear nature of magnetorheological (MR) fluid dampers, one of the challenging aspects for utilizing these devices to achieve high system performance is the development of accurate models and control algorithms that can take advantage of their unique characteristics. In this paper, the direct identification and inverse dynamic modeling for MR fluid dampers using feedforward and recurrent neural networks are studied. The trained direct identification neural network model can be used to predict the damping force of the MR fluid damper on line, on the basis of the dynamic responses across the MR fluid damper and the command voltage, and the inverse dynamic neural network model can be used to generate the command voltage according to the desired damping force through supervised learning. The architectures and the learning methods of the dynamic neural network models and inverse neural network models for MR fluid dampers are presented, and some simulation results are discussed. Finally, the trained neural network models are applied to predict and control the damping force of the MR fluid damper. Moreover, validation methods for the neural network models developed are proposed and used to evaluate their performance. Validation results with different data sets indicate that the proposed direct identification dynamic model using the recurrent neural network can be used to predict the damping force accurately and the inverse identification dynamic model using the recurrent neural network can act as a damper controller to generate the command voltage when the MR fluid damper is used in a semi-active mode.