Structural dynamic equation informed LSTM to predict structural dynamic responses under wind load

For models with a small time step and long simulation duration, the wind-induced structural response of the finite element model by the numerical estimation method is often computationally expensive. With the rapid development of machine learning technology, the Long Short-term Memory (LSTM) has become an effective method to estimate structural response. In this paper, pure data-driven LSTM (P-LSTM) and the structural dynamic equation informed LSTM (SDE-LSTM) are proposed to predict multidimensional dynamic response (displacement, velocity and acceleration) of a single-degree-of-freedom (SDOF) system and multi-degree-of-freedom (MDOF) system. The predicted fittings of response of SDOF and MDOF are above 0.99. Combining multiple indicators including the coefficient of determination R², the mean absolute error (MAE), and the mean absolute percentage error (MAPE), the predictive models can be evaluated comprehensively and is beneficial to the optimization of models parameters. With setting different signal-to-noise ratio (SNR), the robustness is still good. The results of this study show that the SDE-LSTM and P-LSTM have high prediction accuracy, good generalization ability and robustness for predicting SDOF and MDOF system under wind excitation. Additionally, compared with the P-LSTM, SDE-LSTM can improve prediction accuracy, generalization ability and robustness.