Uncertainty Quantification of the Modal Rotation Shape Sensing Method for Geometrically Non-Linear Deformation

Abstract

There are technical applications where structures undergo deformation in the geometrically non-linear domain. This is the case for high-aspect-ratio wings, which may play a more important role in the future aircraft designs. Shape sensing methods can estimate the deflection of these structures during operation, if a direct measurement of the displacements is inconvenient or not possible. For the geometrically nonlinear range, the modal rotation method has been proposed as a candidate suitable for slender structures. The method superposes modal rotation increments of segments along the length of the structure, typically obtained from a finite element model. If the method is applied model-free, based on modal rotations identified from test data, the variability of the modal rotations leads to uncertainty in the displacement estimates. The present study illustrates how displacement output uncertainty can be expressed using linearised propagation formulae, relying on the prerequisite that the modal rotations exhibit a normally distributed and independent scatter around their mean. This uncertainty propagation is investigated in the shape sensing of a high-aspect-ratio wing model, and verification through Monte Carlo simulations demonstrates that the derived expressions accurately propagate the uncertainty from variable modal rotations. Consequently, these expressions can be applied to specific shape sensing tasks in experiments where this variability can be recorded.