Sparse strain-based inverse finite element method for deformation reconstruction of beam-like structures: Theoretical study and experimental validation

Shape sensing is a critical process in structural health monitoring, and the inverse finite element method (iFEM) is a promising tool for deformation reconstruction. However, iFEM still suffers from several limitations. Because the continuous strain fields are difficult to obtain, the functional must be discretized, which makes the system matrix highly sensitive to sensor placement when solving the linear equations. Improper placement can easily lead to severe ill-posedness. Furthermore, to ensure reconstruction accuracy, iFEM requires strain sensors within each element, causing the required number of sensors to grow significantly as the mesh is refined. To address these issues, this paper proposes a deformation reconstruction method for beam-like structures based on sparse strain. Rather than a straightforward extension of existing methods that couple modal expansion with iFEM for plate structures, the proposed method establishes a novel functional formulation and avoids dependence on a high-fidelity finite element model and prior modal analysis. In the first stage, modal parameters are identified from measured responses, and the continuous generalized strain distribution function is obtained from discrete measured strains. In the second stage, the local generalized strain distribution function is used to construct a functional, from which the deformation is then obtained through simple linear operations. Numerical and experimental validation cases, which confirm the strong predictive performance of the proposed method, have been conducted.