Parametric identification of nonlinear hysteretic systems

The hysteretic behaviour is an essential feature of many physical systems. Such a feature is conveniently accounted for in hysteretic systems modelling through the well known nonlinear Bouc-Wen equations. But these involve several unknown parameters and internal signals that are not all accessible to measurements. These difficulties make the identification of hysteretic systems a challenging problem. To cope with these issues, previous works are generally based on simplifying assumptions that amount to supposing, among others, that the Bouc-Wen equations describe an isolated physical element in which ‘hysteretis’ is the only dynamic feature. The point is that, even such a case, the control input should be an external driving force and no the displacement. In this paper, the hysteretic equations are let to be what they really are in most practical situations: just a part of the system dynamics. A multi-stage parametric identification scheme is designed and shown to recover consistently the system unknown parameters. The proposed solution is suitable for systems not tolerating large displacements (e.g. like buildings) as well as for situations where force sensors are not available.