Nonparametric identification of nonlinear hysteretic systems

A nonparametric identification method for nonlinear hysteretic systems is presented. Making use of the Duhem hysteresis operator, the multivalued relationship of hysteretic restoring force with respect to displacement and velocity of the phase plane is mapped onto two single-valued surfaces in an appropriate subspace in terms of the state variables of displacement and hysteretic restoring force. The functions describing the surfaces need not be specified in specific expressions, so that both the form and parameters of the functions can be fine-tuned to match experimental results. They are identified by fitting the surfaces with the generalized orthogonal polynomials in terms of displacement and hysteretic restoring force. The proposed method is applied to the modeling of hysteretic behavior of a wire-cable vibration isolator from experimental data. Excellent agreement between the predicted and experimental hysteresis loops is obtained. Based on the established hysteretic model, the dynamic response characteristics of a wire-cable isolation system are evaluated.