Full Program »

An adaptive online identification scheme for a phenomenological hysteretic law

Several engineering systems are characterized by material nonlinearities. The theory of classical plasticity, i.e. a plasticity theory defined on the basis of a yield surface, a flow rule and a hardening law is widely used to account for the effect of material nonlinearities in structural response. Furthermore, design codes that allow for a ductile behaviour of the structure as part of the Limit State design, are based on classical plasticity derivations in order to define corresponding limit states either in the stress or the stress-resultant space. As with the rest of the structural properties however, the parameters of the underlying plasticity model are often unknown. This in turn leads to the need for identifying the parameters relating to material properties as well as the associated plasticity model.
System identification (Sys-Id) algorithms provide a robust mathematical framework for the evaluation of such unknown model parameters. The identification problem is nonlinear not only due to the insertion of the unknown parameters in the vector of the system’s states but also due to the nonlinearities stemming from the plasticity model. In terms of the relevant mathematical framework, classical plasticity relates to a constrained optimization problem, with the yield surface being the actual constraint.
When assuming that the parameters of the model are known, this yield surface constraint is imposed either by introducing a Lagrangian multiplier or through return mapping plasticity schemes. Neither of these options however can be directly implemented in the case of the identification problem, since the yield surface itself is to be identified. Additionally, from the Sys-Id point of view, this results in a highly nonlinear problem, involving the determination of both the dynamic states and structural parameters but also additional variables whose time evolution is not known, such as the Lagrangian multipliers. In this study, the identification of a system involving material nonlinearities in the form of a yield surface rule will be examined via time-domain identification schemes and finally a scheme for completing this task in an online manner will be proposed.

Author(s):

Eleni Chatzi    
ETH Zürich
Switzerland

Manolis Chatzis    
University of Oxford
United Kingdom

Savvas Triantafyllou    
The University of Nottingham
United Kingdom