Deep learning frequency loss functions for predicting the seismic responses of structures

Novel loss functions for seismic response prediction, such as physics-informed loss functions, have attracted considerable attention. However, existing loss functions are based on the time domain and do not consider the frequency domain differences contained in structure response signals. This study accordingly designed three loss functions based on frequency domain information — one pure frequency domain loss function and two combined frequency- and time-domain loss functions — using Fourier transforms. The proposed loss functions were applied using a trusted publicly available dataset for a frame structure, and their performances were compared with those obtained using the conventional mean squared error (MSE) loss function. The proposed frequency domain loss function exhibited superior performance, accelerating the convergence of learning curves for long-period signals while simultaneously enhancing their frequency domain accuracy and facilitating the prediction of high-sampling-rate response signals. In addition, the designed loss functions exhibited more stable performances and superior accuracy than the MSE when random dataset partitioning was employed. Finally, the combined time- and frequency-domain loss functions were shown to predict the seismic displacement time-history of tall, long-span bridges more accurately than the MSE by training the model to predict structural acceleration responses, then integrating them to predict displacement responses.