AbstractReal‐time hybrid testing (RTHT) is an efficient method to simulate the dynamic behavior of complex engineering systems. A novel offline RTHT method has been developed in recent years, wherein the computation of the numerical substructure and the loading of the experimental substructure are independent. Offline RTHT has obvious advantages in terms of accuracy, stability, and cost compared with conventional online RTHT. However, due to the excessive number of iterations, the application range of the existing offline RTHT methods is limited. This paper proposes an accelerated time history iteration (ATHI) method based on system identification and virtual iteration. A two‐loop parameter optimization (TLPO) method is developed to obtain an accurate discrete transfer function. Virtual iterations are performed by replacing the real system with an identified transfer function, which can reduce the number of real iterations. Physical tests were performed on structures equipped with a tuned mass damper or active mass damper, where resonance, nonlinearity, closed‐loop control, and measurement noise exist. The test results suggest that the real system can be accurately represented by the identified transfer function when adopting the TLPO method. The proposed ATHI successfully accelerates the convergence process while ensuring stability and accuracy.

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