A single-sided inverse absolute nodal coordinate formulation for large-deformation shape sensing of slender structures

Shape sensing reconstructs structural displacement fields from discrete strain measurements and is important for monitoring flexible slender structures. For large-deformation cases, existing inverse strain-based methods often require back-to-back measurements and prescribed sensor locations, limiting their use when only one surface is accessible or installation conditions are constrained. This paper proposes a single-sided strain-to-shape reconstruction framework for slender structures, termed SS-iANCF, based on inverse absolute nodal coordinate kinematics. Unilateral surface strain is converted into curvature information and embedded in a nonlinear least-squares inverse problem. An inextensibility penalty and an inter-element curvature-continuity constraint are introduced to stabilize reconstruction without opposite-side strain data. The influence of intra-element sampling location on accuracy and Hessian conditioning is also examined. Numerical simulations and experiments using a weak-FBG/OFDR sensing system confirm that SS-iANCF achieves high-fidelity reconstruction for both unidirectional large-deformation and reverse-bending configurations. Across the experimental cases, the mean absolute reconstruction error remains below 5 mm, with a maximum mean normalized displacement error of 1.22 × 10 −2 occurring in the reverse-bending case with curvature reversal.