Shape sensing techniques enable the real-time reconstruction of wing displacements based on measured strain. As wing designs become more flexible, they may at some point exhibit geometric non-linear deformation. This eventually leads to erroneous displacement estimates if applied methods rely on the assumption of linear deformation. In this research, the Incremental Modal Method (IMM) is presented which accounts for the change of the employed mode shapes due to structural deformation. The method is applied on the finite element model of a high aspect ratio wing undergoing geometric non-linear deflections in flap-wise bending. In the process, a setup of virtual strain sensors is presumed which is representative as instrumentation in experiments. Along a reference line of the wing, the displacement estimates of IMM are compared to results obtained using the Modal Rotation Method (MRM), another shape sensing scheme recently developed for the non-linear regime. For the chosen segmentation and virtual instrumentation of the investigated wing, IMM proves to be a promising candidate for realtime displacement reconstruction in experiments, provided that mode shapes in intermediate deflected states can be determined. @en

The reconstruction of the deformations from strain measurements is usually called shape sensing and is of interest in the field of structural health monitoring. In this paper the problem is studied with a limited amount of strain data since for real applications and an on-line monitoring it might be unfeasible to employ a large amount of sensors. In this context the deformations are computed with the inverse Finite Element Method (iFEM) taking advantage from a preliminary strain pre-extrapolation done with the Smoothing Element Analysis (SEA). The results are then compared with another common shape sensing method, the so-called Modal Method (MM), using as study case a composite wing-like structure. Noise and uncertainties and their influences on the results are also assessed. The outcome obtained points out that iFEM is largely improved after the preliminary strain pre-extrapolation. However, for this study case, the Modal Method performs better despite the intrinsic disadvantage in requiring the material properties of the structure (compared to iFEM, where no constitutive relation is needed), which affects the results in case uncertainties are present in the system.@en