## 1 Introduction
Then, the elevation angle of the reflector surface can be adjusted via the position change of the gravity center based on the moving mass inside the FCRA. The moving mass control has been studied on the roll control of flexible aircraft and the deformation control of flexible wings [29; 30]. Hence, a moving mass gear drive method was adopted here to control the elevation angle adjustment for the reflector. There are several advantages of FCRAs. The vast ocean space can be utilized to expand the sites of this movable reflector antenna. It can be combined with existing radio telescopes on land to form a very long baseline interferometry (VLBI) network. Furthermore, the size of a VLBI network can be extended to the scale of the Earth's diameter with the good mobility of an FCRA. Thus, a better observation performance can be obtained, and more signal sources can be tracked. Further, in consideration of the effect of structural deformation on reflector accuracy, it is necessary to perform structural health monitoring (SHM) for the back frame structure of an FCRA. Known as shape sensing, the reconstruction of full-field structural deformation is a key component of SHM by utilizing discrete in situ strain measurements. [PERSON] and [PERSON] [31] developed a computationally efficient methodology called the inverse finite element method (iFEM) for the purpose of performing accurate shape sensing of plate and shell structures by using a three-node triangular inverse-shell element (iMIN3). The proposed method is based on a least-squares variational principle to reconstruct the full-field deformation from measured surface strains. Subsequently, more types of elements have been developed based on the work of [PERSON], such as the four-node inverse-shell element (iQS4) [32] and the inverse beam-frame element [33]. Regarding the application of iFEM, it has been utilized in an offshore structure [34], a cantilever plate [35], a wing frame [36], a wind turbine tower [37], and so on. Numerous investigations have demonstrated the unique suitability of iFEM in terms of structural deformation monitoring. However, regarding the SHM of the back frame structure during the angle adjustment process, there is little research on the deformation reconstruction for the complex structure with over-constraints under a mechanism motion process. In this paper, a new FCRA driven by a moving mass is developed using parametric design. The mechanism behaviors of this FCRA are analyzed via the mutual verification of the theoretical model, software simulation, and a prototype test. The shape sensing of the back frame is carried out via iFEM methodology to reconstruct the three-dimensional displacement of the over-constrained structure during the angle adjustment process by using several quasi-static sampling moments. The paper is organized as follows. The structural design of the FCRA is introduced in Section 2. Then, the non-dimensional design parameters, kinematic relationship, water surface constraint, and structural stability are analyzed in Section 3. The elevation angle adjustment process is studied by using a prototype model test and software simulation in Section 4. Further, the iFEM algorithm based on the iQS4 element is briefly reviewed, and the deformation analysis and shape sensing for the back frame of the FCRA are carried out in Section 5. The conclusions are provided at the end of Section 6.