## 5 Conclusions  
We have proposed an online measurement and calibration method for deformation estimation for the support structure of a sub-reflector in order to provide accurate adjustment data for the sub-reflector control system of a radio telescope. Firstly, the fiber \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Strain** & **Time** & \(\epsilon_{1}\)/\(\mu\epsilon\) & \(\epsilon_{2}\)/\(\mu\epsilon\) & \(\epsilon_{3}\)/\(\mu\epsilon\) & \(\epsilon_{4}\)/\(\mu\epsilon\) & \(\epsilon_{5}\)/\(\mu\epsilon\) & \(\epsilon_{6}\)/\(\mu\epsilon\) \\ \hline \multirow{4}{*}{\(\epsilon\)} & Midnight & \(-20.48\) & \(-484.92\) & \(-111.42\) & \(-345.13\) & \(417.76\) & \(-79.67\) \\  & Noon & \(-327.20\) & \(-601.49\) & \(-118.92\) & \(-354.49\) & \(45.15\) & \(-125.02\) \\ \cline{1-1}  & Midnight & \(353.65\) & \(-315.15\) & \(48.26\) & \(-152.23\) & \(616.02\) & \(86.15\) \\ \cline{1-1}  & Noon & \(52.94\) & \(-442.72\) & \(38.77\) & \(-150.58\) & \(246.41\) & \(45.80\) \\ \cline{1-1}  & Midnight & \(-374.14\) & \(-169.77\) & \(-159.69\) & \(-192.91\) & \(-198.26\) & \(-165.83\) \\ \cline{1-1}  & Noon & \(-380.14\) & \(-158.77\) & \(-157.69\) & \(-203.91\) & \(-201.26\) & \(-170.83\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Two strain measurements for No. 1 support leg at \(55^{\circ}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Acons** & \(\mathbf{55^{\circ}}\) & \(\mathbf{40^{\circ}}\) & \(\mathbf{30^{\circ}}\) & \(\mathbf{15^{\circ}}\) \\ \hline \multirow{4}{*}{**FBG strain**} & \(\epsilon_{1}\) & \(13\) & \(-9\) & \(-30\) & \(-73\) \\  & \(\epsilon_{2}\) & \(-369\) & \(-338\) & \(-299\) & \(-220\) \\ \cline{1-1}  & \(\epsilon_{3}\) & \(26\) & \(-1\) & \(-21\) & \(-61\) \\ \cline{1-1}  & \(\epsilon_{4}\) & \(-191\) & \(-176\) & \(-165\) & \(-140\) \\ \cline{1-1}  & \(\epsilon_{5}\) & \(-288\) & \(-272\) & \(-239\) & \(-184\) \\ \cline{1-1}  & \(\epsilon_{6}\) & \(421\) & \(337\) & \(258\) & \(100\) \\ \cline{1-1}  & \(\epsilon_{1}\) & \(11\) & \(10\) & \(18\) & \(28\) \\ \cline{1-1}  & \(\epsilon_{2}\) & \(21\) & \(21\) & \(27\) & \(30\) \\ \cline{1-1}  & \(\epsilon_{3}\) & \(35\) & \(36\) & \(37\) & \(36\) \\ \cline{1-1}  & **compensation** & \(\epsilon_{4}\) & \(5\) & \(8\) & \(15\) & \(23\) \\ \cline{1-1}  & \(\epsilon_{5}\) & \(37\) & \(39\) & \(42\) & \(34\) \\ \cline{1-1}  & \(\epsilon_{6}\) & \(18\) & \(24\) & \(27\) & \(27\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: FBG strains and temperature compensation for No. 4 support leg. grating sensors are used to measure the surface strain of the support leg. It is then followed by deformation reconstruction for the end of the support leg of the sub-reflector using the inverse finite element method. Finally, the proposed calibration method is used to calibrate the reconstruction displacement to improve the precision. The results show that the percentage error for each support leg is less than 4%, with the minimum error reaching 0%. Comparing the calibration results along the three directions, we demonstrate that our calibration method is accurate along the main deformation direction. For problems relating to small sample data, this paper proposes the use of the cubic B-spline to expand the initial working condition data so as to provide a data guarantee for the training of a high-precision calibration network. In addition, a temperature compensation device is designed to compensate the measured strains in order to reduce the influence of ambient temperature on reconstruction accuracy. The experimental results show that the device can effectively reduce the influence of service temperature on the reconstruction. Furthermore, the demonstrated calibration method can be applied to other structures, such as large reflectors, for deformation measurement. However, our experimental period was short, and further exploration is required for the long-term application of the temperature compensation device over wide temperature ranges. Conceptualization, Q.X. ; Methodology, Q.X. ; Validation, H.B. ; Formal analysis, Q.X.