A Recursive Model Updating Algorithm for Multi-element Hybrid Simulation of Structures

Abstract

Hybrid simulation is a cost-effective method of testing structures under seismic loading that combines numerical and experimental methods through partitioning the structure into; 1) numerical substructure simulating the well-understood components of the structure, and 2) physical substructure representing the critical components of the structure. The hybrid simulation results can become biased and uncertain when only one or a limited number of potential critical components, e.g., seismic fuses, are physically tested due to laboratory or cost constraints. Furthermore, the critical components modelled in the numerical substructure are often calibrated using experimental test results of similar prototype specimens under a predefined loading protocol, which fails to consider the effects of dynamic loading characteristics to which it will be subjected in hybrid simulation. This paper proposes a new recursive model updating algorithm incorporated into the conventional seismic hybrid simulation framework to leverage the data collected in real-time from the physical specimen of one of the critical elements and integrate a new data-driven model into the numerical substructure. The data-driven model, which is being progressively updated owing to the proposed model updating algorithm, is responsible for predicting the nonlinear cyclic response of the other critical components of the system that are not physically tested. To develop the data-driven model, the parameters of the Prandtl-Ishlinskii model are first estimated using a sparse regression algorithm and then updated during the hybrid simulation using the recursive least-squares algorithm. The simulation accuracy of the model updating algorithm is assessed through nonlinear response history analysis of a two-storey steel buckling-restrained braced frame, which consists of a virtual experimental specimen (first-storey brace) and the model