Identification of Nonlinear Aeroelastic Systems Based on the Volterra Theory: Progress and Opportunities

Abstract

The identification of nonlinear aeroelastic systems based on the Volterra theory of nonlinear systems is presented. Recent applications of the theory to problems in computational and experimental aeroelasticity are reviewed. Computational results include the development of computationally efficient reduced-order models (ROMs) using an Euler/Navier-Stokes flow solver and the analytical derivation of Volterra kernels for a nonlinear aeroelastic system. Experimental results include the identification of aerodynamic impulse responses, the application of higher-order spectra (HOS) to wind-tunnel flutter data, and the identification of nonlinear aeroelastic phenomena from flight flutter test data of the active aeroelastic wing (AAW) aircraft.

Improving the approximation ability of Volterra series identified with a cross-correlation method

“…A comparison between the FOA and LeeSchetzen methods can be found in [13]. Other identification methods and a survey of possible applications of Volterra series ranging from signal processing to identification of mechanical and physiological systems can be found in [9,10,17].…”

“…A potential disadvantages of the Volterra theory, as explicitly stated in [17], includes input amplitude limitations related to convergence issues and the need for higher-order kernels. The effect of input amplitude on convergence was investigated in [12], where it has been shown that identification input non-idealities makes the output MSE a function of the input variance.…”

Multivariance nonlinear system identification using Wiener basis functions and perfect sequences

“…Given the multivariance Wiener kernels {k (0) 0 , k (1) 1,. , k (2) 2,.,. , ...}, we want to estimate the corresponding Volterra kernels, which are independent of the input variance. Equating (3) and (5), it can be noticed that the two largest order kernels of the WN filter are always equal to the corresponding kernels of the Volterra filter for any input variance σ 2 x , i.e., for r = 0, .., N − 2, s = r, .., N − 1, t = 0, .., N − 1 − s: h 3,t,t+r,t+s = k (3) 3,t,t+r,t+s (6) and for r = 0, .., N − 1, t = 0, .., N − 1 − r:…”

“…A known drawback of Volterra and Wiener theory [6] is the input amplitude limitations related to convergence issues when higher-order kernels are needed. The non-idealities of input noise make the output mean square error (MSE) a function of the input variance [4].…”

Prediction of Transonic Limit-Cycle Oscillations Using an Aeroelastic Harmonic Balance Method

“…For several years, the research community has developed Reduced Order Models (ROM) to avoid the penalty of full order time domain analysis. Several methods have been proposed and used, for example: Proper Orthogonal Decomposition (POD) [8,9], Volterra Series [10][11][12], Neural Networks [13]. Typically, ROMs lack generality as their application is dependent on the original parameters used in building the ROM.…”