A Universal Shape Sensing Strategy Based on Distributed Fiber-Optic Sensing: Extended Inverse Finite Element Method Using Solid Elements

This study proposes a universal shape sensing strategy to reconstruct the shape of structures with complex geometries by introducing solid elements into the inverse finite element method (iFEM). By introducing energy-based regularization, i.e., assuming that the true deformation state is close to the state with the minimum deformation energy under the strain constraint, distributed fiber-optic sensing (DFOS) is able to meet the huge demand for strain measurement imposed by spatially arranged inverse solid elements. Compared to standard iFEM, the proposed method involves not only the priori deformation model described by the shape function but also extends to the relationship between energy and displacement contained in the forward finite element, which is the reason why it is named the extended iFEM (EiFEM). The numerical simulations demonstrate that the proposed shape sensing strategy can effectively model structures with complex geometries and adapt to high strain gradients due to local discontinuities. The DFOS-based experiment validates the effectiveness of EiFEM with real-world data.