Full Flight Envelope Aerodynamic Modelling of the Cessna Citation II using Physical Splines

Abstract

A new aviation legislation makes it mandatory for air-carrier pilots to go through stall recovery training on simulators. As a result, new aerodynamic modeling techniques are required to model complex non-linear behavior of the aircraft flight envelope. In 2005, the Multivariate Simplex B-Splines method was developed. MSBS are a true general function approximator and are easily integrated in standard identification routines. Their downside is that the basis functions and B-coefficients, forming the B-net, do not have a straightforward physical interpretation. Also creating the triangulation is not a trivial process. Parts of the triangulation domain can require higher approximation power and continuity. The consequence is an overall dense triangulation and high order basis functions. This introduces problems such as over fitting the model and divergent behavior on triangulation boundaries. Physical-Splines make use of a linear transformation that transforms from the barycentric coordinate space to the Cartesian coordinate space, giving the MSBS a physical interpretation. The physical transformation is introduced to the optimization process in the form of equality and inequality constraints. This way a-priori aerodynamic information can form a bound on the stability derivatives. Promising results show that they are robust, prevent over-fitting, prevent propagation of erroneous data, remove divergent behavior on triangulation boundaries, and that they can be used for extrapolation of sparse datasets. Also a stepwise orthonormalization can create physical model structure constraints and set unimportant physical model terms to zero. Overall, the physical constraints make it possible to adjust model approximation power locally and alter the B-net via the physical parameters without breaking them.