AbstractReal‐time hybrid testing (RTHT) is a reliable and efficient method for large‐scale dynamic testing. Unlike online RTHT, offline RTHT allows the computation of the numerical substructure independent of the loading of the experimental substructure, which has obvious advantages in terms of accuracy, stability, and cost. The existing offline RTHT method is difficult to converge in many cases and has a limited range of applications. This paper proposes a new time history iteration (THI) algorithm based on cumulative increments. The increment of the next iteration signal is determined based on the increments of all previous iteration signals. The proposed algorithm can improve the system stability and convergence speed of offline RTHT. The stabilization mechanism and effect of the key parameter were investigated by conducting a series of simulations. Physical tests were performed on structures equipped with a tuned mass damper and an active mass damper. The test results suggest that the proposed THI algorithm can simultaneously consider iterations at all time steps and solve the coupling problem in offline RTHT. The time history iteration is stable and always converges in tests when facing complex situations such as resonance, nonlinearity, closed‐loop control, and measurement noise.

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