Self-supervised deep learning digital twin modeling for joint load-response estimation in structural dynamics

Constructing a high-fidelity digital twin model for accurate structural response estimation can facilitate reliable condition assessment of engineering structures. However, the accuracy of structural response estimation is often compromised by the lack of load information. To overcome this limitation, a graph-based autoencoder (GAE) framework is proposed for joint load-response estimation. In this framework, self-supervised load estimation is performed through the encoder, while structural responses are estimated by inputting the estimated loads into the decoder. The novelty lies in its capability to represent the spatial correlations of structural responses at different locations through predefined adjacency matrices, thereby enabling satisfactory load estimation and accurate response reconstruction. The effectiveness of the proposed framework is validated through numerical and experimental case studies, and further demonstrated through a real three-span continuous beam bridge. The estimated loads from the encoder of the GAE model showed good agreement with the measured loads in the frequency domain, with the normalized mean square error (NMSE) of the power spectral density below 0.59. By inputting the estimated loads into the decoder of the GAE model, the accuracy of the estimated responses at unobserved nodes was effectively improved. For the real bridge case, the estimated responses achieved nearly perfect match with the measured responses, with NMSE as low as 6.39×10⁻⁴. Further, the proposed method exhibits a computational efficiency gain exceeding two orders of magnitude over functionally equivalent finite element model, highlighting its great potential for practical deployment in real engineering structures.