Aircraft Flutter Modal Parameter Identification Using a Numerically Robust Least-squares Estimator in Frequency Domain

Recently, frequency-based least-squares （LS） estimators have found wide application in identifying aircraft flutter parameters. However, the frequency methods are often known to suffer from numerical difficulties when identifying a continuous-time model, especially, of broader frequency or higher order. In this article, a numerically robust LS estimator based on vector orthogonal polynomial is proposed to solve the numerical problem of multivariable systems and applied to the flutter testing. The key idea of this method is to represent the frequency response function （FRF） matrix by a right matrix fraction description （RMFD） model, and expand the numerator and denominator polynomial matrices on a vector orthogonal basis. As a result, a perfect numerical condition （numerical condition equals 1） can be obtained for linear LS estimator. Finally, this method is verified by flutter test of a wing model in a wind tunnel and real flight flutter test of an aircraft. The results are compared to those with notably LMS PolyMAX, which is not troubled by the numerical problem as it is established in z domain （e.g. derived from a discrete-time model）. The verification has evidenced that this method, apart from overcoming the numerical problem, yields the results comparable to those acquired with LMS PolyMAX, or even considerably better at some frequency bands.

Efficient WENOCU4 scheme with three different adaptive switches

Although classical WENOCU schemes can achieve high-order accuracy by introducing a moderate constant parameter C to increase the contribution of optimal weights,they exhibit distinct numerical dissipation in smooth regions.This study presents an extension of our previous research which confirmed that adaptively adjusting parameter C can indeed overcome the inadequacy of the usage of a constant small value.Cmin is applied near a discontinuity while Cmax is used elsewhere and they are switched according to the variation of the local flow-field property.This study provides the reference values of the adaptive parameter C of WENOCU4 and systematically evaluates the comprehensive performance of three different switches(labeled as the binary,continuous,and hyperbolic tangent switches,respectively)based on an optimized efficient WENOCU4 scheme(labeled as EWENOCU4).Varieties of 1D scalar equations,empirical dispersion relation analysis,and multi-dimensional benchmark cases of Euler equations are analyzed.Generally,the dissipation and dispersion properties of these three switches are similar.Especially,employing the binary switch,EWENOCU4 achieves the best comprehensive properties.Specifically,the binary switch can efficiently filter more misidentifications in smooth regions than others do,particularly for the cases of 1 D scalar equations and Euler equations.Also,the computational efficiency of the binary switch is superior to that of the hyperbolic tangent switch.Moreover,the optimized scheme exhibits high-resolution spectral properties in the wavenumber space.Therefore,employing the binary switch is a more cost-effective improvement for schemes and is particularly suitable for the simulation of complex shock/turbulence interaction.This study provides useful guidance for the reference values of parameter C and the evaluation of adaptive switches.