Frequency and damping identification in flutter flight testing using singular value decomposition and QR factorization

Abstract

14A new method, based on Singular Value Decomposition (SVD) and QR factorization, has been 15 developed and applied to the analysis of F-18 flutter flight-test data. The method is capable of 16 identifying the frequency and damping of the critical aircraft modes, those responsible for the flutter 17 phenomenon. The procedure relies on the capability of SVD for the analysis, modelling and 18 prediction of data series with periodic features and also on its power to identify matrix rank. The 19 analysis of simulated and real flutter flight test data demonstrates the effectiveness, robustness, 20 noise-immunity and the capability for automation of the method proposed under specific conditions. 21 22

Multimodal Estimation of Sine Dwell Vibrational Responses from Aeroelastic Flutter Flight Tests

“…Matrix Pencil is a variant of the Prony Method, and a description of the technique can be found in [19][20][21][22]. It is based on the same principle as the Prony Method, a decomposition of the signal in sums of exponentially damped sinusoids, with the particularity that instead of decomposing in as many modes as possible considering the number of samples in the signal (as for the Prony Method), it is possible to select a number of signals so that the fit is the best possible with that number of elements.…”

“…Once the flight tests end and data are gathered, it is necessary to post-process data to characterize the aeroelastic behavior of the aircraft and validate the aeroelastic simulation model. In a general case there are many techniques described to process these data, like wavelet [12,13], non-linear techniques [14,15], Rational Fractional Polynomials [16][17][18], Prony and variants, like Matrix Pencil and Eigenvalue Realization Algorithm (ERA) [19][20][21][22], etc. Once the different frequencies and damping factors for the critical modes have been identified it is necessary to predict the flutter point (the corresponding envelope boundary) from extrapolation.…”

“…For the particular case of Sine Dwell excitations, characterized by being very short time series (3 s to 5 s) as related to the frequencies of interest (2 Hz to 10 Hz), not all the postprocessing techniques described above are suitable. Several require long times to get accurate results, usually requiring Frequency Sweeps lasting around 30 s to 60 s. For short time techniques, the most accurate identified are variants of Prony method [19][20][21][22], wavelet techniques [12,13], a bandwidth based estimation (Peak-Amplitude technique) proposed by [29] and the classical logarithmic decrements technique ( [30], citing a generic text for the sake of completeness), although this last technique is limited to signals where only one single mode is present with close to zero phase angle. Note that the outcome of these techniques sometimes is not suitable for the estimation of multiple modes with close natural frequencies, as will be demonstrated in upcoming sections.…”