Real-time shape sensing of large-scale honeycomb antennas with a displacement-gradient-based variable-size inverse finite element method

Abstract

Real-time thermal deformation monitoring plays a crucial role in calibrating phase signals and maintaining satellite performance for large spaceborne antennas. The inverse finite element method (iFEM) represents a promising shape-sensing methodology applicable to monitor the three-dimensional displacement of structures through surface-measured strain. However, the high-accuracy reconstruction of large-scale structures involves a large number of inverse elements, which leads to the low level of computational efficiency. To address this issue, a displacement-gradient-based variable-size iFEM is proposed in this paper. According to the characteristics of deformation, this method optimizes the size of each inverse element to reduce the number of inverse elements required, which improves real-time performance and maintains the high accuracy of reconstruction. The real-time performance of the proposed method is verified by conducting a simulation test on a large-scale honeycomb antenna. According to the simulation results, the variable-size iFEM is applicable to achieve the same accuracy of reconstruction using fewer inverse elements than conventional iFEM. An experimental test is performed and the optimal variable-size discretization that balances accuracy and efficiency is determined. The results show that the maximum error of reconstructed displacement is less than 7.3 % and the reconstruction time is in no excess of 0.1 s.