# Large Deformation Modeling of Wing-Like Structures Based on Support Vector Regression
## 4 Results and Discussion  
The SVR model was established to predict the static large deformation of the flexible wing model. In this research, 70% (190 samples) of the sample dataset described in Section 3.2 was used to train the proposed method as a training sample, and the remaining 30% (80 samples) was used for testing the performance. After training and testing, correlation coefficient (R) and root mean squared error (RMSE) were used to evaluate the method as statistical performance indices. Each of the indices are calculated as:  
\[\text{R}= \frac{\sum\limits_{i=1}^{NT}{(x_{i}-\overline{x})(y_{i}-\overline{y})}}{ \sqrt{\sum\limits_{i=1}^{NT}{(x_{i}-\overline{x})^{2}\sum\limits_{i=1}^{NT}{(y_ {i}-\overline{y})^{2}}}}} \tag{22}\] \[\text{RMSE}=\sqrt{\frac{1}{NT}{\sum\limits_{i=1}^{NT}{(x_{i}-y_{i}) ^{2}}}} \tag{23}\]  
where \(x_{i},y_{i}\) represent the actual sample value and predicted value. \(\overline{x},\overline{y}\) represent the mean of actual values and predicted values. Based on the correlation coefficient, R, SVR parameter \(c\) is chosen as 32, \(\gamma\) is chosen as 1/16 and \(\varepsilon\) is given as 0.05. Figures 13-16 present the prediction results with the test dataset. The order of test data samples has been rearranged based on the prediction value, from smallest to largest. The prediction results show the excellent correlation coefficient between actual values with a black solid line and predicted values with a red circle symbol. With this SVR model, the generalized coordinates can be predicted accurately for excited load input. Translating the coordinates from modal space to physical space by Equation (4), the actual and predicted values in test datasets of wingtip vertical deformation are shown in Figure 17. Predicted values reached good agreement with actual values. The SVR model proposed in this research has good performance in large deformation calculation of the flexible wing model. Figure 11: Fiber grating (FBG) sensor on the wing model. Figure 12: Arrangement of FBG sensors (wavelength in bracket). Figure 14: Prediction results of second generalized coordinate. Figure 13: Prediction results of first generalized coordinate. Figure 15: Prediction results of third generalized coordinate. Although the training and test datasets were generated via FEM calculation, it is notable that the proposed methods are applicable to the real-world datasets. That is also an important practical application of efficient large deformation calculation with a real wing model. The ground test of the real wing model [37] was completed to validate the accuracy of the SVR model proposed. In the first test, the test model is deformed under self-weight. The wingtip vertical deformation is up to 0.253 m, which is 25.3% of the span length. The deformation results of measurement and SVR model prediction are listed in Table 4. The position, s denotes the location coordinate of measurement on the wing model. Two results reached excellent agreement with deviation up to 1.2% in the wingtip. Figure 18 shows the deformed beam configuration of this test. The black and red solid lines represent the measurement results and predicted results, respectively. In the second test, the test model is loaded by a 200 g weight at the tip. That is equivalent to loading a 1.96 N tip force on the basis of the first test. The wingtip vertical deformation is up to 0.459 m, which is 45.9% of the span length. It is much bigger that all sample datasets in the training procedure of the SVR model. The deformation results of measurement and SVR model prediction are listed in Table 5. Figure 19 shows the deformed beam configuration of this test. Deviation up to 4.02% in the wingtip is larger than the first test. The results are acceptable considering the deformation is far beyond the sample datasets in this test. The generalization capability of the SVR model proposed is excellent and it is very suitable for large deformation prediction of the flexible wing model.