Development and verification of real-time hybrid simulation with deep learning-based nonlinear numerical substructure

Real-time hybrid simulation (RTHS) provides an effective approach for assessing structural responses under dynamic excitation. However, performing RTHS with a complex nonlinear numerical substructure is challenging, as computations must be completed within predefined time steps. In this study, a RTHS framework which contains a rate-dependent experimental substructure and a nonlinear numerical substructure has been proposed and verified. An OpenSees model was constructed to simulate a three-story, one-bay steel building with viscous dampers at each floor and was used to generate the training dataset through a large number of nonlinear time-history analyses. A Recursive Long Short–Term Memory (LSTM) neural network model was trained to predict the nonlinear structural responses using ground acceleration and time-delayed damper force located at the first story. Hence, the Recursive-LSTM model served as a surrogate model for the numerical substructure, implicitly incorporating delay compensation for the experimental substructure. After the training was completed, offline testing was performed to realize the stability of the RTHS framework. Then, online RTHS with a virtual damper taken as the experimental substructure was conducted to further confirm the feasibility and accuracy. Afterwards, a nonlinear rotary fluid viscous damper (RFVD) was fabricated as the actual experimental substructure, whose dynamic response was not considered in training the Recursive-LSTM model. Finally, RTHS with the RFVD was completed successfully and stably, demonstrating the capability of a well-trained Recursive-LSTM model to serve as a nonlinear numerical substructure incorporating constant delay compensation for RTHS. The potential of the proposed RTHS framework is worth further studies in the future.