21. A Material Basis Frame Approach for Global Deflection Reconstruction of Rod-Like Structures from Strain Measurements

This paper presents an approach for determining three-dimensional global displacement (for arbitrarily-sized deformations) of thin rod- or tether-like structures from a limited set of scalar strain measurements. The approach is rooted in exploiting a reference frame that is materially adapted, i.e., it moves with the cross section. Local linearization of the frame evolution equations is shown to yield local solutions that may be assimilated into a global solution via continuity relationships. The solution is shown to be robust to potential singularities from vanishing bending and twisting angle derivatives and from vanishing measured strain, and the approach includes strain resulting from pure neutral axis extension (such as due to thermal loads). Validation of the approach is performed through comparison with finite element simulations. The average root mean square reconstruction error of 0.01–1 % of the total length, for reasonable sensor counts. Analysis of error due to extraneous noise sources and boundary condition uncertainty shows how error scales with those effects.