Approximation of unsteady aerodynamic forces Q(k, M) by use of fuzzy techniques

The unsteady aerodynamic forces acting on an F/A-18 aircraft are calculated in the frequency domain using a doublet-lattice method (subsonic regime) or a constant-pressure method (supersonic regime). To study the effects of the control laws on a flexible fly-by-wire aircraft structure and calculate the flutter velocities and frequencies, these aerodynamic forces must be approximated in the Laplace domain. We show here that in the case where the aerodynamic forces data are calculated for a range of unevenly spaced reduced frequencies, a combination of fuzzy clustering and shape-preserving techniques can be used to obtain a very good approximation of these unsteady aerodynamic forces. Because the approximation of these forces by this new method remains actually in the frequency domain, we could easily further use for their conversion from the frequency domain into Laplace domain, classical methods such as least squares or minimum state. Finally, care must be used in the choice of reduced frequencies range, to determine the method to be deployed.