Seismic response prediction of RC bridge piers through stacked long short-term memory network

Abstract

This paper aims at addressing the prediction of the displacement time histories and subsequently hysteresis curves of reinforced concrete bridge piers using a real-time hybrid simulation. A deep recursive long short-term memory (LSTM) network combined with a bidirectional LSTM, as a powerful deep learning algorithm, is utilized to achieve this goal. The designed stacked LSTM network includes multiple uncertain input variables, horizontal and vertical ground motions, horizontal and vertical actuator loads, the effective height of the bridge pier, the moment of inertia, and the mass assumed for hybrid simulation. The functional application programming interface in the Keras Python library is utilized to develop a complex model with these multiple inputs. Considering all these variables helps to predict the hysteresis curves of reinforced concrete bridge piers more accurately. The database for the training, validation, and unseen dataset of the proposed LSTM network during the prediction process comprises 12 experimental hybrid simulation tests on the bridge piers considering various aforementioned characteristics. The results reveal that the mean square error, as a loss function, is monotonically decreased to zero for both the training and validation datasets after 5000 epochs, and a high level of correlation is observed between the predicted and the reference values of the displacement time series for all the datasets. The Box-Whisker plot and Gaussian distribution of normalized error are also investigated for all the predictions to have more confidence in the estimations. It can be concluded that the maximum mean of the normalized error is about 0.05 for unseen data. Finally, it brings to an end that the LSTM method implemented in this study can successfully reduce the time and experimental costs to conduct new experimental hybrid simulation tests in the future.