An Online Measurement and Calibration Method for a Radio Telescope Sub-Reflector Support Structure Using Fiber Bragg Grating  
[PERSON]  
1 Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi 830011, China 12 Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, Urumqi 830011, China 23 Xinjiang Key Laboratory of Radio Astrophysics, Urumqi 830011, China 34 Key Laboratory of Electronic Equipment Structure Design, Ministry of Education, Xidian University, Xi'an710071, China; [EMAIL_ADDRESS]  
Hong Bao  
4 Correspondence: [EMAIL_ADDRESS]; Tel. : +86-(0991-36894534  
Adjusting the sub-reflector position by an active surface control system is the main method to improve electrical performance [2; 3; 4]. In this approach, the position and altitude of a deformed sub-reflector support structure must be accurately obtained first in order to provide an accurate input to the active surface control system. Currently, photogrammetry is generally used in engineering for such measurements. However, this method can only be used offline and at night, which means that it only compensates for the deformation caused by gravity. The Sardinian Radio Telescope (SRT) measurement team developed a non-contact measurement scheme based on a position sensing device (PSD) [5], which is composed of a laser diode and a complementary metal oxide semiconductor (CMOS) camera. In this scheme, the accuracy of the PSD can reach about 0.1 mm for a 40 mm measurement range. Owing to the laser capturing capability of the CMOS cameras being easily influenced by the incident angle of the sunlight, this measurement scheme is limited to daytime operation. In order to overcome the above limitations, a contact measurement technique was proposed and applied to large structures [6; 7; 8]. Compared with traditional strain sensors, Fiber Bragg Grating (FBG) has been widely studied and applied in the field of shape perception because of its lightness, high accuracy, anti-electromagnetic interference, and anti-radiation [9; 10]. [PERSON] [11] presented important advances in the sensing design and principle of FBG-based displacement sensors. [PERSON] et al. discussed the reliability of the traditional temperature compensation method and proposed a novel temperature compensation method specifically for structures under different loading conditions [12]. The support structure of an antenna sub-reflector is a typical truss structure, which is composed of beam elements. In order to measure the deformation of the beam elements, [PERSON] et al. proposed a load-independent method based on piece-wise continuous polynomials and classical beam theory [13]. The disadvantage of this method is that it only reconstructs structure deformation in one dimension. In practice, it is necessary to measure the deformation of the support structure for the sub-reflector in three dimensions. [PERSON] et al. analyzed and verified the effectiveness of the modal conversion method by reconstructing structural deformation [14]. Although this method has many advantages, it requires an accurate finite element model. In addition, this method requires a substantial amount of eigenvalue analysis and a detailed description of the properties of the elastic and inertial materials. To address the problem of inadaptability in the Ko and the modal methods when applying to complex topological structures and boundary conditions during reconstruction, [PERSON] proposed the inverse finite element method (iFEM) based on the variational prin  
Figure 1: Radio telescope and the sub-reflector. ciple [15; 16]. From the kinematic assumptions of the iFEM frame and Timoshenko beam theory, [PERSON] et al. proposed an inverse finite element method for sensing the deformation of a beam or frame structure [17; 18]. [PERSON] et al. [19] developed the single variable iFEM model to reduce the number of strain sensors required in multi-node load. [PERSON] et al.