Strain pre-extrapolation methods for shape sensing: A comparative study between modal virtual sensor expansion and smoothing element analysis

Reconstructing displacement fields from sparse strain measurements, commonly referred to as shape sensing, has become a key component in developing effective Structural Health Monitoring (SHM) systems and for enabling accurate digital twin representations of engineering structures. Among available techniques, the inverse Finite Element Method (iFEM) is widely used but typically requires a dense sensor network. To reduce this dependency, strain pre-extrapolation methods are employed. The most established approach is Smoothing Element Analysis (SEA), which performs well for simple geometries but struggles with complex built-up structures. A recently proposed alternative, the Modal Virtual Sensor Expansion (Modal VSE), leverages modal strain shapes to virtually expand the strain field and has shown promising results, though it has not yet been benchmarked against existing methods. This study provides the first direct comparison between Modal VSE and SEA for strain pre-extrapolation and subsequent iFEM-based shape sensing of a composite stiffened panel. Results demonstrate that Modal VSE achieves higher accuracy and better adaptability across the examined configurations. Its superior performance persists even when sensor signals are corrupted by noise representative of experimental conditions. These findings highlight Modal VSE as a robust and effective tool for enhancing shape sensing in complex structural domains, thereby supporting more practical implementations of iFEM-based SHM and digital twin frameworks.