Uncertainty importance measure by fast fourier transform for wing transonic flutter

Considering the natural frequency, parameters of gravity center, and mass ratio of aircraft wing as random parameters, the global sensitivity, also named as uncertainty importance measure, is analyzed on the fast Fourier transform. The most crucial and difficult problem of importance measure is how to obtain the unconditional and conditional probability density function or failure probability of the model rapidly and properly. The fast Fourier transform technique can estimate the probability density function and cumulative distribution function of the structural response efficiently and robustly, so two moment-independent importance measure indexes (including the importance measure of basic random variable on the probability distribution of response and the importance measure of basic random variable on the failure probability) are solved by use of the fast Fourier transform technique. For the two-dimensional aircraft wing transonic flutter problem, reduced order modeling method on computational fluid dynamics is used to construct the aerodynamic state equations. Coupling structural state equations with aerodynamic state equations, the state equations of aeroelasticity system can be obtained, on which the limit state function of flutter is founded by considering the critical velocity, which is solved by the eigenvalue of the state matrix, satisfying the requirement. For the aeroelastic flutter response models of a two-dimensional wing without flap and with a flap, two importance measure indexes can quantificationally reflect the influence of the random variables on the structural response. Comparing with the importance measure results of Monte-Carlo simulation, those of fast Fourier transform are higher in efficiency with acceptable precision.