An optimized single-side inverse finite element method for displacement field reconstruction of wind turbine tower

Wind turbines are subjected to complex dynamic loads during actual operation, which are difficult to predict accurately in advance, which may lead to inaccurate structural strength assessment in the structural design stage, and thus bring safety risks to wind power towers. Inverse Finite Element Method (iFEM) is a reconstruction method of structural displacement distribution, which can estimate the full-field displacement distribution of tower, and used for structural on-line health monitoring. However, conventional iFEM require sensors to be placed on both sides of the structure, which greatly limits its engineering practicality. For this reason, a single- side inverse finite element (iFEM_S) was developed in this study to enhance the engineering applicability of iFEM. Both iFEM and iFEM_S are based on the principle of least squares variation, and the solution equations can be established when the measured strain is known. The core idea of iFEM_S is to find the optimal node displacement s to minimize the sum of mean square errors between the theoretical and measured strains on one side of the structure, thereby generating a set of algebraic equations. Solving these linear equations can achieve the structural displacement field. Additionally, A cyclic optimization algorithm (COA) was developed in this study to improve the robustness of reconstruction results through optimizing strain gauge locations, in which the condition number of pseudo stiffness matrix was used as the objective function, and the condition number is minimized, named iFEM_S_O. Finally, the reconstruction accuracy and robustness and of iFEM, iFEM_S and iFEM_S_O were verified through several numerical examples. The simulated reconstruction results indicated that iFEM_S_O is more accurate and stable than iFEM_S, and iFEM_S is more accurate and stable than iFEM.