## 2 Materials and Methods
### Third Test: Vertical Inclinometer Equipped with GG and CG Transducer  
One of the most critical aspects regarding the evaluation of the experimental results is structural identification. That means determining a numerical model suitable for providing accurate predictions of the behavior of the structural element subjected to specific stresses. The identification of the structural model consists of applying inverse calculation techniques to correlate the test results to the actual stresses or displacements. This approach consists of the identification of mechanical properties, modifying their values appropriately, and minimizing a suitable functional norm of the difference between the experimental results and the expected theoretical ones. Therefore, based on experimental data and reliable information on geometry and materials, it is possible to define a predictive model that represents the behavior of the tested elements.  
The third experiment has been designed to apply structural identification techniques to the measured data. To the scope, the inclinometer has been disposed vertically and fixed to support using flexible collars; the structure was subjected to prescribed displacements at some of the supports whilst the remainder was kept fixed. The inclinometer pipe was instrumented with the proposed transducer and with its traditional displacement acquisition system.  
Figure 7 represents the structural model of the third experiment. Prescribed displacements acted on the structure. In particular, the displacements \(\delta_{1}\) and \(\delta_{2}\) are the prescribed displacements of magnitude 2.5 cm that were applied to the pipe. The displacements \(\delta_{3}\)\(\delta_{4}\) are unknown, due to the flexibility of the supporting devices. The displacement depended on the fastening devices that evidenced rewardable mobility. The structural identification consisted of finding the minimal difference norm between the measured and calculated strain along the beam. As design variables, we chose, besides the constraint displacements \(\delta_{i},\ i\in\{1,\ldots,4\}\), the span measures \(L_{1},\ L_{2},\ L_{3},\ L_{4},\ L_{5}\) (Figure 7).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Type** & **Structural Glue** & **Fiber** & **Length [mm]** & **Optical Fiber** & **Resin** & **Control Unit** & **Resolution [mm]** \\ \hline \multirow{4}{*}{GG} & ADEKIT 140 by & Glass-Glass & & & & & \\  & Axon & (mat22) fiberglass & & & & & \\  & (bi-component & polyester & & & & \\  & epoxy resin & composite) & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Second test: transducer parameters.  
Figure 6: Second test: Structural scheme.  
The tested specimen was equipped with two kinds of transducers, as shown in Table 5.  
The test set-up is represented in Figure 8, where the inclinometer cylinder has been schematically represented as a one-dimensional beam subjected to prescribed boundary displacements.  
Like in the previous example, the procedure consists of comparing the strain obtained from displacement measurements via space derivation to the strain measured with the NSHT.  
The measured strain using the CG and the GG transducers was acquired according to two different set-ups. The first set-up concerned a CG transducer that was fastened to the cylinder starting at a  
Figure 8: Layouts of vertical inclinometer: (**a**) GG transducer side, (**b**) CG transducer side.  
Figure 7: Third test: structural identification.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Length [mm]** & **Radius [mm]** & **Thickness [mm]** & **Inertia [cm4]** \\ \hline
7600 & 80 & 3 & 56.4871 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Third test–geometrical parameters.  
The difference shown in the graph between the measured values and the theoretical model could undoubtedly be attributed to the fact that the theoretical values refer to the axis of the pipe, while the measured ones refer to the fiber positioned at the boundary of the cross-section.