Deep Learning‐Based Response Spectrum Analysis Method for Bridges Subjected to Bi‐Directional Ground Motions

ABSTRACT The response spectrum analysis method is one of the most widely used approaches developed to estimate the seismic demands of structural systems with minimal computational expense while maintaining high accuracy. The authors recently proposed a deep learning‐based combination (DC) rule to enhance the prediction accuracy of the response spectrum analysis method without compromising computational efficiency. The DC rule employs a deep neural network (DNN) model to estimate the contributions of individual modal responses. The DC rule, primarily developed for building structural systems, has limitations in its applications to bridge structures, particularly those subjected to bi‐directional ground motions. Moreover, the inherent “black box” nature of deep learning models restricts the interpretability and practicality of the method. To address these challenges, this research further develops the DC rule in three aspects. First, we construct a seismic demand database for bridge structures subjected to bi‐directional ground motions. Second, the DC rule is extended to accommodate structural systems under bi‐directional ground motion excitations. Third, we develop a simplified regression‐based model to replace the DNN model, thereby enhancing the practicality and interpretability of the DC rule approach. Extensive numerical investigations are conducted to validate the performance of the proposed framework, demonstrating its efficiency and accuracy in predicting the seismic demands of bridge structures. The source codes, data, and trained DNN models are available for download at https://github.com/TyongKim/ERD2 .