Recursive DeepONet for surrogate modelling of nonlinear dynamics and its application in real-time hybrid simulation

This study introduces a recursive DeepONet method for predicting nonlinear dynamic response in real-time hybrid simulation (RTHS). RTHS is an essential technique for dynamic analysis of complex structures, involving experimental substructure and numerical substructure (NS). A key challenge in RTHS is the real-time NS computation, particularly when dealing with complex nonlinear dynamics. The proposed recursive DeepONet predicts the nonlinear response step by step, making it a suitable surrogate model for NS. This study first validated the applicability of DeepONet based on the NS state transition equation. Then, the basic architecture and recursive calculation format of DeepONet were presented, and the recursive cumulative error bound was evaluated. A case study of a 3-story nonlinear benchmark building was conducted. The trained DeepONet’s recursive performance was evaluated and compared with that of LSTM, showing superior prediction accuracy and computation efficiency. The proposed method was further validated on a 20-story benchmark structure. Finally, virtual RTHS was performed, and the effects of signal noise and time delay on DeepONet prediction accuracy were discussed. The overall RTHS performance with advanced control methods to compensate for time delay was analyzed, highlighting the potential of DeepONet in enhancing RTHS applications.