Real-time hybrid simulation (RTHS) provides an efficient and effective experimental technique for rate-dependent energy-dissipation devices in seismic hazard mitigation. The structure under investigation is generally divided into analytical and physical substructures to enable large-scale experiments for system behavior. Accurate modeling of analytical substructures is critical for truthful structural response replication through RTHS. This presents challenges to laboratory practice of RHTS such as capability of specialized finite-element software to replicate complex nonlinear behavior, and the equipment capacity to accommodate large-scale finite-element modeling to be executed in a real-time manner. This study explores the use of a polynomial chaos nonlinear autoregressive with exogenous input (PC-NARX) model to conduct RTHS in laboratories using existing equipment and general-purpose finite-element analysis (FEA) software readily available in earthquake engineering research. The NARX model can be trained using any existing FEA software for a good representation of structural dynamics. Polynomial chaos expansion (PCE) is then introduced to surrogate NARX model coefficients to account for ground motion uncertainties. Laboratory tests of a self-centering viscous damper were conducted as proof of concept to experimentally demonstrate the effectiveness of RTHS with PC-NARX metamodeling approach. The results were further compared with the kriging surrogate technique for NARX model coefficients to explore a better technique to account for uncertainties in RTHS.

Complex dynamic behavior of nonlinear structures makes it challenging for uncertainty analysis through Monte Carlo simulations (MCS). Surrogate modeling presents an efficient and accurate computational alternative for a large number of MCS. The previous study has demonstrated that the multi-input multi-output nonlinear autoregressive with exogenous input (MIMO-NARX) model provides good discrete-time representations of deterministic nonlinear multi-degree-of-freedom (MDOF) structural dynamic systems. Model order reduction (MOR) is executed to eliminate insignificant modes to reduce the computational burden due to too many degrees of freedom. In this study, the MIMO-NARX strategy is integrated with different meta-modeling techniques for uncertainty analysis. Different meta-models including Kriging, polynomial chaos expansion (PCE), and arbitrary polynomial chaos (APC) are used to surrogate the NARX coefficients for system uncertainties. A nine-DOF structure is used as an MDOF dynamic system to evaluate different meta-models for the MIMO-NARX. Good fitness of statistical responses is observed between the MCS results of the original system and all surrogated MIMO-NARX predictions. It is demonstrated that the APC-NARX model with the advantage of being data-driven is the most efficient and accurate tool for uncertainty quantification of nonlinear structural dynamics.