## 4 Experimental Examples
According to Equation (3), the reconstruction errors can be obtained in the form of \(\left\{\Delta u_{x},\ \Delta u_{y},\ \Delta u_{z}\right\}\). From the 12 working conditions, the data at the elevation angles of \(15^{\circ},30^{\circ},\ 40^{\circ}\), and \(55^{\circ}\) were used to test the precision of the calibration network, and the data of the remaining eight working conditions were used to train the self-architected fuzzy calibration network. For each support leg, the strain \(\varepsilon^{*}\) that shows the greatest reaction to changes of the elevation angle in the model is selected and combined with the reconstruction error to form three control points of deformation direction, designated by \(\left\{\varepsilon^{*},\ \Delta u_{x}(x_{k},y_{k},z_{k})\right\}\), \(\left\{\varepsilon^{*},\ \Delta u_{y}(x_{k},y_{k},z_{k})\right\}\) and \(\left\{\varepsilon^{*},\Delta u_{z}(x_{k},y_{k},z_{k})\right\}\), with \(\left(k=1,2\cdots 8\right)\). Consider \(\left\{\varepsilon^{*},\Delta u_{x}(x_{k},y_{k},z_{k})\right\}\), the eight working conditions form eight vertices. According to Section 3.1, the cubic B-spline curve can be  
Figure 10: Test antenna model at two different elevation angles. Figure 9: Global and local coordinate systems. obtained. The data from the eight groups of working conditions can be expanded based on the value in the parameter \(\upmu\) from 0 to 1, in step of 0.002, thereby forming 501 sets of data. Similarly, for \(\left\{\varepsilon^{*},\ \Delta u_{y}(x_{k},y_{k},z_{k})\right\}\) and \(\left\{\varepsilon^{*},\Delta u_{z}(x_{k},y_{k},z_{k})\right\}\), which are also expanded into 501 sets of data. Using the extended data from a single direction of the support leg for training, three sets of fuzzy calibration networks, \(SSFN_{x}\), \(SSFN_{y}\), and \(SSFN_{z}\), can be obtained. This is then followed by inputting the measured strains, obtained at the elevation angles of \(15^{\circ}\), \(30^{\circ}\), \(40^{\circ}\), and \(55^{\circ}\), into each \(SSFN_{x}\), \(SSFN_{y}\), and \(SSFN_{z}\) to determine the calibrated displacement error. Finally, the calibration displacement value is obtained by adding the calibration error to the initial reconstruction displacement. When the fuzzy calibration network is completed, the real-time input strain and output deformation calibration can be realized. In this paper, four elevation angles taken at midnight were used as a case study to validate the calibration network. For the support 1, the displacement and calibration error as shown in Table 2, and corresponding FBG strains and temperature compensation as shown in Table 3. Meanwhile, the estimated index of the fuzzy calibration network's ability defined as  
\[\delta(\%)=\frac{\left|u^{act}-u^{cal}\right|}{u^{act}}\times 100\% \tag{18}\]  
the actual, reconstructed, and calibrated displacements are denoted as \(u^{act}\), \(u^{FEM}\) and \(u^{cal}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Angles** & & **x Direction** & **y Direction** & **z Direction** \\ \hline \multirow{5}{*}{\(55^{\circ}\)} & \(u^{act}\) & 1.86 mm & 19.01 mm & 4.76 mm \\  & \(u^{FEM}\) & 1.53 mm & 17.48 mm & 4.56 mm \\  & \(u^{cal}\) & 1.83 mm & 18.79 mm & 4.71 mm \\  & \(\delta(\%)\) & 1.61\% & 1.16\% & 1.05\% \\  & \(u^{act}\) & 1.56 mm & 15.85 mm & 3.99 mm \\  & \(u^{FEM}\) & 1.26 mm & 14.18 mm & 3.71 mm \\  & \(u^{cal}\) & 1.54 mm & 15.85 mm & 3.98 mm \\  & \(\delta(\%)\) & 1.28\% & 0\% & 0.25\% \\  & \(u^{act}\) & 1.29 mm & 12.70 mm & 3.25 mm \\
30\({}^{\circ}\) & \(u^{FEM}\) & 0.97 mm & 10.75 mm & 2.85 mm \\  & \(u^{cal}\) & 1.28 mm & 12.68 mm & 3.22 mm \\  & \(\delta(\%)\) & 0.78\% & 0.16\% & 0.92\% \\  & \(u^{act}\) & 0.75 mm & 6.66 mm & 1.77 mm \\
15\({}^{\circ}\) & \(u^{FEM}\) & 0.48 mm & 5.15 mm & 1.41 mm \\  & \(u^{cal}\) & 0.74 mm & 6.49 mm & 1.73 mm \\  & \(\delta(\%)\) & 1.33\% & 2.55\% & 2.26\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Displacement and calibration error for No. 1 support leg.