# A Refined Shape Sensing Method for Skin Antenna Structure Based on Inverse Finite Element Method
## 3 Numerical and Experimental Examples
In comparison, the deformation values of nodes are listed in Table 2. Based on these dates, the profile of structure can be reconstructed again by iFEM(b), as shown in Figure 4.  
Table 2 displays the results from two approaches. The maximum deflection of the nodes is 2.5 mm, and the maximum deviation is 0.1 mm. The reconstruction \(ME\) is 0.3 mm, and the RMS of reconstruction accuracy is 0.3 mm. However, adopting the refined method, the RMS value of the deformation reconstruction accuracy decreases 0.1 mm. Figures 3 and 4 depict the total deformed shapes of the plate employing different interpolation technologies iFEM(a) and iFEM(b) separately. For a view of profiles approaching FEM, the improved approximating skill raises the reconstruction accuracy dramatically. In this section, one part of the antenna plate is considered. For the purpose of demonstrating the effectiveness put forward above, the panel has a length of 0.560 m, a height of 0.200 m, and a uniform thickness of 3.2 mm. For the aim of according with the simulated condition, 11 holes were arranged on the board, which was connected to fixed base by way of a bolt and screw. Meanwhile, the magnitude of the load is controlled by adjusting the nut up and down. The fixed device is shown (Figure 5a). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Node**} & \multicolumn{2}{c}{**Z Directional Deformation (mm)**} \\ \cline{2-4}  & **Fem** & **iFEM** & **Error** \\ \hline
3 & 2.27 & 2.01 & 0.26 \\
4 & 2.49 & 2.11 & 0.38 \\
5 & 1.31 & 1.10 & 0.15 \\
8 & 1.83 & 1.35 & 0.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the nodes deformation. Figure 4: Deformation of the plate structure. According to the location sensors configuration from the simulation model, the fiber grating sensors are pasted at the corresponding positions of the experimental board one by one, and the markers with functions of photosensization are pasted on the surface of the plate (Figure 5d). The variation of three-dimensional coordinates can be tracked by a 3D measurement system supplied by NDI (Waterloo, Ontario, Canada) (Figure 5c), and the surface strain date of structure can be read by the Fiber Bragg Grating (FBG) demodulator (Figure 5b). Under the constraint conditions of the cantilever for the test article, the structure subjected to concentrated force is applied in the positive z direction. The inverse element is produced simplistically by these markers defined as element nodes at the edge. The markers number is the same as in Figure 2. The markers' initial and final position coordinates can be captured by NDI in real time, and the difference of the two sets of coordinates is the deformation of markers. Based on the measured strains and markers' variation, the results from the iFEM analysis and the NDI measurements are shown as Table 3, and the outline of the whole structure can be viewed in Figure 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Marker**} & \multicolumn{2}{c}{**Z Directional Deformation (mm)**} \\ \cline{2-4}  & **NDI** & **iFEM** & **Error** \\ \hline
3 & 6.71 & 6.00 & 0.71 \\
4 & 6.92 & 6.16 & 0.76 \\
5 & 2.70 & 1.85 & 0.85 \\
6 & 19.6 & 16.9 & 2.70 \\
7 & 19.7 & 17.0 & 2.70 \\
8 & 12.5 & 11.6 & 0.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The results of markers deformation. Figure 5: The measurement system; (**a**) fixed device; (**b**) Fiber Bragg Grating (FBG) demodulator; (**c**) Northern Digital Incorporation (NDI); (**d**) marker; (**e**) Measurement process. Table 3 lists the results generated from NDI measurements and iFEM, regarding the former as the benchmark. The maximum deformation of the structure in the Z direction is 19.7 mm. The reconstruction _ME_ is 1.6 mm, and the RMS of reconstruction accuracy is 1.5 mm. Furthermore, on the basis of the proposed interpolation technology, the RMS value is 0.9 mm, and the reconstruction accuracy increased to 0.6 mm.