Nonparametric Fitting of Aerodynamic Data Using Smoothing Thin-Plate Splines

Helicopter fuselage aerodynamic data fitting using multivariate smoothing thin plate splines

“…The identification of the optimal smoothing parameter value for an assigned observation set can be devolved to automatic procedures, the most common of them being based on a generalized cross-validation (GCV) approach, which privileges the predictive capabilities of the model over unsampled input vectors rather than data fitting. 9 The main result of the roughness penalty approach is that natural thin plate splines can be demonstrated to be the unique solutions to the two-objective data fitting problem described above, and this makes the identification of the response surface a fully deterministic problem, where nothing needs to be imposed by the analyst except for the smoothing parameter, which on the other hand may be automatically determined.…”

“…Finally, the plots at the bottom left of Figure 7 illustrate the GCV() score behavior as a function of the equivalent degrees of freedom of the model, which is directly correlated to the value of the smoothing parameter . 9 Actually, the minimum of GCV() identifies the effective value of the smoothing parameter used in the statistical model.…”

“…Among the numerous data fitting techniques available today, smoothing thin plate splines (STPS) is one of the most promising. In a previous paper, 9 the authors proposed an application to aerodynamic data fitting based on a STPS technique, which proved to be robust and reliable for a bivariate problem, i.e. the fitting of aerodynamic data of a sample 3D-shaped body over a wide range of two attitude angles (pitch and yaw).…”

“…It is worth noting that the extension to a multivariate fitting problem for a 3D shape, where not only attitude angles, but also geometric variables are treated as input variables (in fact, in Benini and Ponza 9 the independent variables were only the attitude angles, while in Ponza and Benini 10 only the geometric variables and flow regime), equips the STPS methodology with fundamental skills enabling STPS to become an useful design tool. Finally, the prediction capability, which is indeed one of the major concerns for almost all fitting techniques dealing with complex multivariate data, seems to be one of the strength of the STPS methodology, as will be shown hereafter.…”

Surrogate-Based Shape Optimization of Stall Margin and Efficiency of a Centrifugal Compressor

“…Zhang et al [12] investigated the characterization of the uncertainty in the prediction of surrogate models and the effectiveness of the leave-one-out-crossvalidation (LOOCV) technique in providing a local error measure of the metamodels approximations. Also Benini and Ponza [13] discussed the importance of using RBF in the construction of response surfaces over aerodynamic data sets, and they compared several concurrent methods in a two-dimensional problem, namely, a linear model, a bivariate spline, a radial basis function network, a support vector regression technique, a regression Kriging, and a moving-least-squares approach, to this purpose. Their conclusion, supported by rigorous k-fold cross-validation tests, was that RBFs are indeed robust and accurate even when a scarcely populated data set is available.…”