Improving Flexibility of Multivariate Spline Model Structures for Aerodynamic Modeling

Recently, multivariate simplex B-splines (MVSB) function approximators have been investigated with the aim of providing accurate global aerodynamic models for use in adaptive flight control systems. In this paper, a new approach for constructing multivariate spline models is presented in the form of the tensor-product MVSB (TP-MVSB) that consists of tensor products of ordinary MVSB. The key advantage of this new approach is that it provides more flexibility in the definition of the spline model structure than the standard multivariate spline approach. This flexibility allows the user to include a priori (expert) knowledge of the system in the definition of the spline model structure leading to more efficient and physically meaningful models. The TP-MVSB maintains the desirable properties of the MVSB in the sense that the global B-form regression vector is normalized, each basis polynomial is guaranteed to be well-conditioned numerically, and differentiability is maintained along each input dimension. The new approach is validated using data obtained from a nonlinear F-16 model. Simulation results show that the new approach can achieve a higher level of approximation accuracy using fewer parameters when modeling the aerodynamic moment coefficients, and in addition can provide accurate estimations of the control effectiveness matrix in cases where the system is affine in the inputs.