Unified inverse isogeometric analysis and distributed fiber optic strain sensing for monitoring structure deformation and stress

Inverse analysis is an efficient and reliable approach to the estimation of structural state such as deformation and stress distribution from measured real-world data and numerical algorithms. In this work, a new method of inverse analysis is proposed which integrates Isogeometric Analysis (IGA) and distributed fiber optic sensing (DFOS) using a framework based on non-uniform rational B-spline (NURBS) functions. This formulation expands on the existing inverse Finite Element Methods (iFEM) by developing a new approach to use the exact geometry of strain-sensing optical fibers. The constraint equations of theoreti-cal and measured strains are derived using a discrete least-squares functional and then coupled with isogeometric finite element equations to provide regularization for ill-posed inverse problems. The explicit strain fiber model not only separates the structure mesh and strain sensing locations but also can adapt to the sensing parameters such as spa-tial resolution of DFOS instrument, which is not yet possible with the current models. The proposed method is validated with four numerical examples using plate, hemisphere and cylindrical geometries under prescribed force or displacement boundary conditions. Fur-thermore, the sensitivity of the inverse solution to the sampling interval and measurement noise is studied. The unified inverse IGA and DFOS is tested under simulated measurement noise up to 30 micro-strains with strain sampling intervals ranging from 10 mm to 1 m, and validated with the comparisons of reference and inverse solutions.(c) 2023 Elsevier Inc. All rights reserved.