Improved Modal Rotation Method for Geometrically Nonlinear Shape Sensing

Abstract

Accurate reconstruction of large, geometrically nonlinear structural deformations is essential for assessing deformation-dependent aeroelastic behavior in experimental test scenarios with limited sensor availability. This work presents an improved modal-rotation-based shape-sensing framework that enhances displacement reconstruction from strain and rotational measurements. The classical modal rotation method (MRM) is revisited, and its key limitations are identified, including integration inaccuracies and approximation errors associated with incremental rotation formulations in three-dimensional finite-rotation kinematics. To address these limitations, the proposed improved MRM (IMRM) introduces two principal advances: consistent evaluation of finite rotations using exact rotation matrices via the Rodrigues formulation and higher-order numerical integration of the beam reference line from discrete rotation data. The resulting framework enables geometrically consistent deformation reconstruction without requiring loading information. Numerical investigations on two- and three-dimensional beam problems demonstrate that the classical MRM systematically overestimates deflections under sparse instrumentation, whereas the proposed method significantly improves accuracy. Application to a swept high-aspect-ratio wing undergoing geometrically nonlinear deformations further confirms the performance of the method for structural configurations and sensor densities representative of wind-tunnel and flight testing.