Time-frequency gated transformer for structural dynamic response reconstruction

Structural dynamic response reconstruction is of significant importance because data incompleteness critically undermines the reliability of structural health monitoring. Existing deep-learning reconstruction methods focus solely on the time-domain features of structural dynamic responses and neglect their frequency-domain counterpart. This reduces their reconstruction accuracy because the frequency-domain features directly reflect the inherent dynamic characteristics of structures. To address this problem, we propose a time-frequency gated transformer (TFGFormer) leveraging both the time-domain and frequency-domain features. Specifically, multi-scale dilated transformers and dense blocks are respectively used to extract the time-domain global and local features because the former sparsely encode long-range dependencies and the latter aggregate multi-layer representations. Concurrently, frequency modules are used to extract the frequency-domain features because they are able to adaptively learn the spectral complex-valued weights. Finally, gate modules and a joint time-frequency loss function are used to adaptively fuse these features because the former balance dynamically their contributions and the latter simultaneously penalizes their residuals. Validated on full-scale field data from the Canton Tower and the Hardanger Bridge, TFGFormer outperforms representative baseline methods across various data-missing scenarios and enjoys zero-shot robustness and lightweight design. This reconstruction-oriented time-frequency framework may support more reliable downstream SHM tasks.