Solving large numerical substructures in real-time hybrid simulations using proper orthogonal decomposition

Real-time hybrid simulation (RTHS) technique significantly streamlines experimental procedures by allowing researchers to study a substantial portion of the structure through numerical analysis. For effective real-time interconnectivity between the investigated substructures, the numerical component must be solved within an extremely tight time frame. However, achieving a real-time solution for large numerical substructures presents a major challenge. Hence, this paper proposes the Proper Orthogonal Decomposition (POD) method to reduce computational burden in RTHS and shows its implementation. The merits of the approach are shown by comparisons between the full-order and reduced-order numerical substructures, including nonlinearities. A shear frame retrofitted with superelastic shape memory alloy dampers is investigated as a numerical model. The soil-structure interaction is also included using a finite element half-space model with an artificial viscous-spring boundary. Furthermore, the numerical substructure is coupled with shaking table experiments of a tuned liquid column damper to prove the feasibility of the method. With POD, the studied nonlinear numerical substructure can simulate up to 2655 degrees-of-freedom (DOFs) with a given hardware setup, while the full-order model is limited to 135 DOF, underscoring the significance of the POD method in RTHS.