## 4 Discussion: AoA Identification  
Loads were identified by solving the mechanical problems as in Equations (1)-(6). At the same time, the lift load distribution, \(\mathbf{L}\), is in an aerodynamic problem as  
\[\mathbf{L}=q\mathbf{C_{L}}(\mathbf{\delta},\mathbf{\alpha})\mathbf{A}, \tag{7}\]  
where \(q\) is the dynamic pressure, \(\mathbf{\alpha}\) is the AoA, \(\mathbf{C_{L}}\) is the lift coefficients, and \(\mathbf{A}\) is the areas of the wing segments. In the experiment, we could assume that the dynamic pressure \(q\) and the wing areas \(\mathbf{A}\) were constant, and the \(\mathbf{C_{L}}\) was a function of the flap angles \(\mathbf{\delta}\) and the AoA \(\mathbf{\alpha}\). The variables in the aerodynamic problem were the lift loads \(\mathbf{L}\), the flap angles \(\mathbf{\delta}\), and the AoA \(\mathbf{\alpha}\). Considering that the flap angles are observable and the lift loads are now identified, it was anticipated that the AoA could be theoretically and practically solved by setting \(\mathbf{L}\) and \(\mathbf{\delta}\) as inputs as  
\[\mathbf{\alpha}=NN(\mathbf{L},\mathbf{\delta}). \tag{8}\]  
In this case again, the regression nature of the neural network approach would enhance the stability of solutions. Furthermore, the non-linear transformation is beneficial specifically because the aerodynamic problems show non-linearity.  
We designed a neural-network-based identification process for the AoA as shown in Figure 12. In this design, we identify load distributions by using the 60 FBGs (strain) and flap angle data through the neural network for the load identification as discussed above, and thereafter we identify the AoA by using the identified load distribution and the flap angles through another neural network for the AoA identification. This process requires only the FBG and flap angle data to be observed, which is a feasible assumption.  
The neural network for the AoA identification had one hidden layer with 10 neurons, which was determined experimentally. We set other properties and training parameters in the same way as the load identification. In order to train the neural network for the AoA identification, we prepared a dataset of flap angles and estimated loads, which were the output from the neural network for the load identification for the training test cases (\"aligned,\" \"random,\" and \"single\"). The other cases (\"controlled\") were used to check the performance from the new conditions.  
Figure 13 shows the results of the neural network AoA predictions. The good agreement between the applied and estimated AoAs indicated the theoretical validation of the AoA identification approach. The error ranges were from \(-0.78\)-\(0.46^{\circ}\) and from \(-1.03\)-\(0.16^{\circ}\) for the training and other data, respectively. The standard deviations of the errors were \(0.15^{\circ}\) and \(0.38^{\circ}\) for the training and other data, respectively.  
Figure 11: Comparison between applied and estimated loads.  
Because of limitations of the experimental setup, we defined and observed the AoA as the turntable angle. If we could measure the profile of the AoA along the wing span, the neural network approach might be capable of identifying local AoAs, which would contribute to the development of effective wing twist techniques.