Parametric identification of nonlinear hysteretic systems

The hysteretic behavior is an essential feature of many physical systems (e.g. mechanical structures, buildings dampers). Such a feature is conveniently accounted for in hysteretic systems’ modeling through the well-known Bouc–Wen equations. But these involve several unknown parameters and internal signals that are not all accessible to measurements. Furthermore, not all parameters come in linearly. All these difficulties make the identification of hysteretic systems a challenging problem. To cope with these issues, previous works have simplified the problem by supposing that the system displacements are large, the restoring force (and other internal signals) are accessible to measurements, the displacement is the actual control signal, the unknown parameter entering nonlinearly is known or is an integer, etc. In fact, these restrictive assumptions 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 the control input should be an external driving force and not 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. Such a more realistic problem statement has a cost, which is in additional unknown parameters. A multi-stage parametric identification scheme is designed in this paper and shown to recover consistently the unknown system parameters. The proposed solution is suitable for systems not tolerating large displacements (e.g. buildings) as well as for situations where force, velocity and acceleration sensors are not available.