Green’s Function-Based Analysis of Convergence for Offline Iterative Real-Time Hybrid Simulation

Compared to online real-time hybrid simulation (RTHS), offline RTHS transforms the closed-loop interaction into an open-loop iterative process, substantially reducing the computational and communication demands while simplifying the overall testing procedure. Despite its practical advantages, a critical challenge persists that iteration errors in offline RTHS are not guaranteed to decrease monotonically. In fact, errors may initially increase, creating a serious risk of uncontrolled loading when commands exceed the physical limits of specimens or actuators. To date, this phenomenon has lacked a rigorous theoretical explanation. This study pioneers a Green’s function-based analysis to elucidate the convergence behavior of offline RTHS. Practical criterion is derived for ensuring monotonic convergence of iteration errors, providing-for the first time-a theoretical safeguard against divergence in offline testing. Importantly, the analysis establishes that while monotonic convergence is not necessary for ultimate convergence, it is a sufficient condition to prevent loss of loading control. Parametric studies on damping ratio, natural frequency, experimental substructure proportion, test time, and external excitation further reveal their distinct roles in convergence behavior, offering systematic design insights for safe and robust offline RTHS implementation. Although conservative by nature, the proposed criterion represents the first theoretical foundation for analyzing error convergence in offline RTHS. Supported by both numerical simulations and experimental validation, it provides a pioneering step toward improving the reliability, safety, and theoretical understanding of structural hybrid simulation systems.