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Abstract
This paper discusses a simple technique to identify global models for nonlinear aerodynamic force and moment coefficients of aircraft using multivariate orthogonal functions. Classical Gram-Schmidt procedure and Predicted Squared Error metric are used to generate the orthogonal functions. Global models for the F-16 aircraft are identified from a simplified subsonic (Mach < 0.6) wind tunnel database available in open literature. The identified models are compared with those found in literature for the same wind tunnel database and conclusions are drawn.
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References
- Klien, V. and Batterson, J.G., "Determination of Airplane Model Structure from Flight Data by Using Modified Stepwise Regression", NASA TP 1916, March 1981.
- Hall, W.E. Jr., Gupta, N.K. and Tyler, J.S., "Model Structure Determination and Parameter Estimation for Nonlinear Aerodynamic Flight Regimes", Methods for Aircraft State and parameter Estimation, AGARD-CP-172, Paper 21, November 1974.
- Mehra, R.K. and Corrol, J.V., "Global Stability and Control Analysis of Aircraft at High Angles-of-Attack", Vol.2, Office of the Naval Research, Report ONR-CR215-248-2, Arlington, VA, August 1979.
- Trankle, T.L. and Bachner, S.D., "Identification of a Full Subsonic Envelope Nonlinear Aerodynamic Model of the F-14 Aircraft", AIAA Paper 93-3634, Atmospheric Flight Mechanics Conference, Monterey, CA, 1993.
- Klein, V. and Batterson, J.G., "Determination of Airplane Model Structure from Flight Data Using Splines and Stepwise Regression", NASA TA 2126, March 1983.
- Lo, C.F., Zaho, J.L. and DeLoach, R., "Application of Neural Networks to Wind Tunnel Data Response Surface Methods", AIAA 2000-2639, 21st AIAA AMT and GT Conference, Denver, CO, June 2000.
- Morelli, E.A., "Nonlinear Aerodynamic Modeling Using Multivariate Orthogonal Functions", AIAA93-3636-CP, 1993.
- Morelli, E.A., "Global Nonlinear Aerodynamic Modeling Using Multivariate Orthogonal Functions", Journal of Aircraft, Vol.32, No.2, March-April 1995, pp. 270-277.
- Morelli, E.A., "Global Nonlinear Modeling with Application to F-16 Aerodynamics", ACC Paper WP042, Paper ID I-98010-2, American Control Conference, Philadelphia, Pennsylvania, June 24-28, 1998.
- Morelli, E.A., "Response Surface Modeling using Multivariate Orthogonal Functions", AIAA Paper 2001-0168, 39th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 2001.
- Weisfeld, W., "Orthogonal Polynomials in Several Variables", Numerishe Mathematik, Vol.1, 1959, pp.38-40.
- Barron, A.R., "Predicted Squared Error : A Criterion for Automatic Model Selection", Self-Organizing Methods in Modelling, Edited by S.J. Farlow and Marcel Dekker, New York, 1984, pp.87-104.
- Morelli, E.A. and DeLoach, R., "Wind Tunnel Database Development Using Modern Experiment Design and Multivariate Orthogonal Functions", AIAA Paper 2003-653, 41st Aerospace Sciences Meeting and Exhibit, 2003.
- Stevens, B.L. and Lewis, F.L., Aircraft Control and Simulation, New York, John Wiley and Sons Inc., 1992, Appendix A, pp.584-592.
- Hayes, J.G., "Numerical Approximation to Functions and Data", The Institute of Mathematics and its Applications, University of London, 1970.
- Nguyen, L.T., "Simulator Study of Stall/Post-Stall Characteristics of a Fighter Airplane with Relaxed Longitudinal Static Stability", NASA TP 1538, December 1979.
References
Klien, V. and Batterson, J.G., "Determination of Airplane Model Structure from Flight Data by Using Modified Stepwise Regression", NASA TP 1916, March 1981.
Hall, W.E. Jr., Gupta, N.K. and Tyler, J.S., "Model Structure Determination and Parameter Estimation for Nonlinear Aerodynamic Flight Regimes", Methods for Aircraft State and parameter Estimation, AGARD-CP-172, Paper 21, November 1974.
Mehra, R.K. and Corrol, J.V., "Global Stability and Control Analysis of Aircraft at High Angles-of-Attack", Vol.2, Office of the Naval Research, Report ONR-CR215-248-2, Arlington, VA, August 1979.
Trankle, T.L. and Bachner, S.D., "Identification of a Full Subsonic Envelope Nonlinear Aerodynamic Model of the F-14 Aircraft", AIAA Paper 93-3634, Atmospheric Flight Mechanics Conference, Monterey, CA, 1993.
Klein, V. and Batterson, J.G., "Determination of Airplane Model Structure from Flight Data Using Splines and Stepwise Regression", NASA TA 2126, March 1983.
Lo, C.F., Zaho, J.L. and DeLoach, R., "Application of Neural Networks to Wind Tunnel Data Response Surface Methods", AIAA 2000-2639, 21st AIAA AMT and GT Conference, Denver, CO, June 2000.
Morelli, E.A., "Nonlinear Aerodynamic Modeling Using Multivariate Orthogonal Functions", AIAA93-3636-CP, 1993.
Morelli, E.A., "Global Nonlinear Aerodynamic Modeling Using Multivariate Orthogonal Functions", Journal of Aircraft, Vol.32, No.2, March-April 1995, pp. 270-277.
Morelli, E.A., "Global Nonlinear Modeling with Application to F-16 Aerodynamics", ACC Paper WP042, Paper ID I-98010-2, American Control Conference, Philadelphia, Pennsylvania, June 24-28, 1998.
Morelli, E.A., "Response Surface Modeling using Multivariate Orthogonal Functions", AIAA Paper 2001-0168, 39th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 2001.
Weisfeld, W., "Orthogonal Polynomials in Several Variables", Numerishe Mathematik, Vol.1, 1959, pp.38-40.
Barron, A.R., "Predicted Squared Error : A Criterion for Automatic Model Selection", Self-Organizing Methods in Modelling, Edited by S.J. Farlow and Marcel Dekker, New York, 1984, pp.87-104.
Morelli, E.A. and DeLoach, R., "Wind Tunnel Database Development Using Modern Experiment Design and Multivariate Orthogonal Functions", AIAA Paper 2003-653, 41st Aerospace Sciences Meeting and Exhibit, 2003.
Stevens, B.L. and Lewis, F.L., Aircraft Control and Simulation, New York, John Wiley and Sons Inc., 1992, Appendix A, pp.584-592.
Hayes, J.G., "Numerical Approximation to Functions and Data", The Institute of Mathematics and its Applications, University of London, 1970.
Nguyen, L.T., "Simulator Study of Stall/Post-Stall Characteristics of a Fighter Airplane with Relaxed Longitudinal Static Stability", NASA TP 1538, December 1979.