A displacement reconstruction strategy for long, slender structures from limited strain measurements and its application to underground pipeline monitoring

Abstract

In this paper, we discuss about reconstructing the global deformed shape of slender structures such as pipelines, tethers, or cables from a limited set of scalar surface strain measurements. We present a comprehensive approach that captures the effect of curvature, shear, torsion, and axial deformation. Our primary focus is to demonstrate the applicability of the approach to aid in damage detection algorithms. This theory utilizes Cosserat rod theory and exploit localized linearization approach that helps to obtain local basis function set for the displacement solution in director frame. The uniaxial strain vector and the surface strain for the Cosserat beam incorporating the above-mentioned effects are obtained and used to develop the reverse algorithm to reconstruct global shape of the structure. Error analysis due to noise in measured strain values is performed and results are discussed.