An inverse finite element method for full-field deformation reconstruction of wind turbine towers using one-sided uniaxial strain

With the expansion of offshore wind farms into deeper and more remote seas, the operational environment for offshore wind turbine structures is becoming increasingly harsh. Consequently, ensuring the long-term safety of the tower structure—which supports the entire unit—under complex marine conditions is of critical importance. The Inverse Finite Element Method (iFEM) can reconstruct the full-field deformation of the tower structure in real time, thereby providing a crucial guarantee for real-time structural health monitoring. However, the classical iFEM requires the back-to-back installation of triaxial strain sensors on both sides of the element. This significantly increases the complexity and economic cost of sensor deployment. To address this limitation, this paper proposes a One-Sided Uniaxial Strain-based iFEM (OSUS-iFEM). Then, an optimization method for the weighting coefficients utilizing the Multi-Island Genetic Algorithm has been developed to enhance the reconstruction performance. The proposed method significantly reduces the requirements for sensor configuration by reformulating the error functional. Numerical results demonstrate that the OSUS-iFEM supports flexible selection of in-plane strain measurement schemes (uniaxial, biaxial, or triaxial). Compared to the classical iFEM, this approach significantly reduces the number of sensors required (by up to 83.3%) and simplifies installation complexity. Furthermore, the method demonstrates good robustness even with sparse sensor configurations and a coarse mesh. Even in an extremely sparse configuration (using only 24 sensors), the MAE and RMSE remain within 8.5 mm and 9.5 mm, respectively. After optimization, the MAE and RMSE values are consistently maintained below 2.4 mm and 4.1 mm, respectively.