ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

The ability to identify accurate global models of complex nonlinear systems is highly desired in many fields of science and engineering. We present a powerful new method for global nonlinear model identification based on a recent type of multivariate spline, the multivariate simplex spline. Multivariate simplex splines are defined on non-rectangular domains and can be used to accurately fit scattered nonlinear datasets in any number of dimensions. The simplex splines consist of piecewise defined, ordinary multivariate polynomials with a predefined continuity between neighboring polynomial pieces. A new linear regression model for the simplex splines was developed. This regression scheme allows for the use of standard parameter estimators, like generalized least squares and maximum likelihood estimators, for the estimation of the polynomial coefficients of the splines. The new identification method was used to estimate a global 5-dimensional aerodynamic model for the aerodynamic force and moment coefficients of the F-16 fighter aircraft based on a NASA wind tunnel dataset. The multivariate simplex spline based aerodynamic model was validated and integrated in a non-linear F-16 simulator.