Real-time estimation of bridge displacements under vehicle loads using physical mechanism-based attention-LSTM network with partial strain measurements

Dynamic displacement of bridges under moving vehicle loads is a critical safety indicator for bridges, yet directly measuring these displacements poses practical challenges. Although computer vision-based techniques for measuring displacements have gained application, they are influenced by environmental conditions. Alternatively, indirect estimation of bridge displacements has attracted great attention. Currently, some deep learning methods have been developed to estimate displacements at positions deployed with accelerometers or strain sensors. In this paper, a method for real-time estimation of moving vehicle load-induced bridge displacements in interested regions is proposed utilizing an attention-Long Short-Term Memory (LSTM) network with partial strain measurements. It is based on the physical mechanisms of strain-displacement relationship of beam-type structures and bridge modal responses can be estimated from partial strain measurements to reconstruct structural displacements through the superposition of modal responses. For network training, the physical mapping between partial strains and the displacements in interested regions is learned by an attention-based LSTM network. Then, bridge displacements in interested regions can be estimated by the trained network using only partial strain measurements. Numerical examples of estimating the displacements of a simply supported beam bridge and the Hainan Haiwen bridge under random moving loads validate that the proposed method can estimate bridge displacements in any interested regions in real-time using only partial strain measurements.