A physics-informed auto-encoder based cable force identification framework for long-span bridges

Cable force identification is crucial for ensuring the safety and operational performance of in-service long-span bridge structures. Besides the commonly-used frequency measurements for calculating cable forces using frequency-cable force relationship formulas, more efficient and straightforward identification could be achieved by directly utilizing frequency response functions (FRFs). This study presents a novel approach that employs neural networks to model the relationship between the FRFs and cable forces, resulting in a more streamlined method for identifying cable forces on long-span bridges. Firstly, the working mechanism of an auto-encoder is merged with the unique characteristics of the FRFs, giving the cross signature assurance criterion. This criterion is then integrated into the loss function as a constraint to account for the poor interpretability of pure data-driven methodology in solving engineering problems, leading to a grey-box data-driven paradigm. Following this paradigm, a physics-informed auto-encoder (PIAE) network is employed to reduce the dimensionality of the FRF data during extracting key features. The reduced FRF data are paired with the cable forces to form training samples. The PIAE network is then trained directly on these samples for the purpose of cable force identification. Finally, the validation of the proposed method was conducted on the actual monitoring data from a cable-stayed bridge and a concrete-filled steel tubular arch bridge. Results indicate that the proposed method achieves not only high prediction accuracy, but also a good fit between the predicted and actual developmental trends of cable forces, and is well-suited for the different types of bridges.