LSTM, WaveNet, and 2D CNN for nonlinear time history prediction of seismic responses

Predicting the nonlinear time-history responses of civil engineering structures under seismic loading remains an essential task in earthquake engineering. This paper explores the promise of developing three deep learning (DL) models, i.e., long short-term memory (LSTM), WaveNet, and 2D convolution neural network (CNN), to predict seismic response time histories of three benchmark structures, including a single degree-of-freedom (SDOF) system, a steel building frame, and a multi-component bridge structure. LSTM has been previously developed and is utilized to serve as a reference model, while WaveNet and 2D CNN (i.e., it deals with the data in coupled time–frequency dimensions) are newly developed in the current study. One other novel contribution is to replace the final layer of the WaveNet with an LSTM layer, which significantly improves the model performance. Methodological backgrounds of these DL models are introduced, followed by discussions on model architectures and hyperparameters, the list of evaluation metrics, and the ground motion (GM) suite selected for data generation. High-fidelity numerical models are developed for conducting nonlinear time history analyses that generate numerous motion-response pairs for training, validating, and testing the DL models. The LSTM and WaveNet directly use time series GM inputs and seismic response outputs to train the models, whereas the CNN makes inferences on time–frequency spectrogram images converted through the short-time Fourier transform (STFT). These three DL models are investigated by comparing deterministic predictions under one testing GM and probabilistic distributions of six evaluation metrics. The models' accuracy, efficiency, and robustness are further examined using a sensitivity study under different training samples and model architectures. Research findings from this study provide a sound reference for the community to leverage these three DL models to achieve reliable and efficient time history response predictions, which are crucial for fulfilling cutting-edge research/practical tasks such as regional seismic risk assessment and performance-based seismic design.