Reduced-Order Models Based on Linear and Nonlinear Aerodynamic Impulse Responses

This paper discusses a method for the identification and application of reduced-order models based on linear and nonlinear aerodynamic impulse responses. The Volterra theory of nonlinear systems and an appropriate kernel identification technique are described. Insight into the nature of kernels is provided by applying the method to the nonlinear Riccati equation in a non-aerodynamic application. The method is then applied to a nonlinear aerodynamic model of an RAE 2822 supercritical airfoil undergoing plunge motions using the CFL3D Navier-Stokes flow solver with the Spalart-Allmaras turbulence model. Results demonstrate the computational efficiency of the technique.

[1]  Y. H. Ku,et al.  Volterra functional analysis of nonlinear time-varying systems , 1967 .

[2]  Leon O. Chua,et al.  Fading memory and the problem of approximating nonlinear operators with volterra series , 1985 .

[3]  Patrick Reisenthel,et al.  Development of a nonlinear indicial model for maneuvering fighter aircraft , 1996 .

[4]  Walter A. Silva,et al.  Application of nonlinear systems theory to transonic unsteady aerodynamic responses , 1993 .

[5]  Leon O. Chua,et al.  Measuring Volterra kernels , 1983 .

[6]  William T. Baumann,et al.  Accurate Modeling of Nonlinear Systems using Volterra Series Submodels , 1987, 1987 American Control Conference.

[7]  Y. W. Lee,et al.  Measurement of the Wiener Kernels of a Non-linear System by Cross-correlation† , 1965 .

[8]  J. B. Roberts Nonlinear Analysis of Slow Drift Oscillations of Moored Vessels in Random Seas , 1981 .

[9]  W. Silva,et al.  Discrete-time linear and nonlinear aerodynamic impulse responses for efficient cfd analyses , 1997 .

[10]  R. Flake Volterra series representation of nonlinear systems , 1963, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[11]  J. G. Leishman,et al.  A state-space model of unsteady aerodynamics in a compressible flow for flutter analyses , 1989 .

[12]  Eduardo Alves Rodrigues Linear and nonlinear discrete-time state-space modeling of dynamic systems for control applications , 1993 .

[13]  Walter A. Silva,et al.  Extension of a nonlinear systems theory to general-frequency unsteady transonic aerodynamic responses , 1993 .

[14]  E. Bedrosian,et al.  The output properties of Volterra systems (nonlinear systems with memory) driven by harmonic and Gaussian inputs , 1971 .

[15]  Earl H. Dowell,et al.  Eigenmode Analysis in Unsteady Aerodynamics: Reduced Order Models , 1997 .

[16]  Martin B. Brilliant,et al.  Theory of the analysis of nonlinear systems , 1958 .

[17]  E. Powers,et al.  Estimation of nonlinear transfer functions for fully developed turbulence , 1986 .

[18]  Walter A. Silva,et al.  IDENTIFICATION OF LINEAR AND NONLINEAR AERODYNAMIC IMPULSE RESPONSES USING DIGITAL FILTER TECHNIQUES , 1997 .

[19]  I. W. Sandberg Nonlinear input-output maps and approximate representations , 1985, AT&T Technical Journal.

[20]  Stephen P. Boyd,et al.  Analytical Foundations of Volterra Series , 1984 .