Aeroelastic responses, such as accelerations measured in flight, are non-stationary signals in which the frequency content varies with flight speed and, therefore, in time. Aeroelastic responses might also be nonlinear due to large structural deformations (in very flexible configurations), structural free-play (e.g., in control surfaces), nonlinear aerodynamic forces (e.g., in transonic flight), or due to a very large excitation (e.g., in-store ejection). The objective of aeroelastic data analysis is to obtain an accurate representation of the dynamics of the non-stationary nonlinear system. The current research study explores and compares several time-frequency methods for non-stationary nonlinear data analysis, including the Short-time Fourier transform (STFT), Wavelets, and the Hilbert-Huang Transform (HHT), with emphasis on the latter.
In the current research study, the various time-frequency analysis methods were applied to aeroelastic response data of a wing obtained from computation and a wind-tunnel test. The computational data included accelerations due to gust excitation in multiple velocities. The wind tunnel data included accelerations measured at various speeds, all the way to flutter. The data were analyzed using the above-mentioned signal processing techniques. Time-frequency responses are presented as Energy spectrum’s namely, Spectrogram, Scalogram, and HHT Spectrum (for the STFT, Wavelets, and HHT, respectively). These time-frequency graphs provide insight into system identification and change in frequency content with time, as the airspeed is increased. All three techniques yielded similar results when the data was analyzed for multiple velocities. However, precise details were obtained with Scalogram and HHT spectrum when the data were analyzed for individual speeds. Additionally, damping ratios were calculated using HHT amplitude energies and power spectral densities, which provided the damping ratio of the stable and unstable modes for multiple velocities until flutter. The advantages and shortcomings of different techniques are discussed in the test cases.
