Abstract
Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations and experimental conditions. Identification of parametric nonlinear models involves estimating unknown parameters and detecting its underlying structure. Structure computation is concerned with selecting a subset of parameters to give a parsimonious description of the system that may afford greater insight into the functionality of the system or a simpler controller design. Structure-detection methods applicable to NARMAX modeling are applied to aeroelastic dynamics. Among other methods, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of nonlinear systems. Simulation results from a nonlinear dynamic aircraft model demonstrate that methods developed for NARMAX structure computation provide good accuracy for selection of the exact model structure from an over-parameterized model description. Applicability of the method to more complex systems such as those encountered in aerospace applications is shown by identifying parsimonious system descriptions of the F/A-18 active aeroelastic wing (AAW) using flight-test data.
This work was prepared as part of the second author’s official duties as an employee of the U. S. Government and in accordance with 17 U.S.C. 105, is not available for copyright protection in the United States. NASA is the owner of any foreign copyright that can be asserted for the work. Copyright@2006 by NASA.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Åström, K. and Wittenmark, B. (1996). Computer-Controlled Systems: Theory and Design. Prentice Hall, Englewood Cliffs NJ, 3rd edition.
Baldelli, D., Chen, P. C., Liu, D. D., Lind, R., and Brenner, M. (2004). Nonlinear aeroelastic modeling by block-oriented identification. 45th AIAA/ASME/ASCE/AHS/ Structures, Structural Dynamics & Materials Conference, pp. AIAA-2004-1938. Palm Springs, CA.
Baldelli, D., Mazzaro, M., and Sánchez Peña, R. (2001). Robust identification of lightly damped flexible structures by means of orthonormal bases. IEEE Transactions on Control Systems Technology 9(5), 696–707.
Beck, J. and Arnold, K. (1977). Parameter Estimation in Engineering and Science. Wiley series in probability and mathematical statistics. John Wiley & Sons, New York.
Billings, S. and Chen, S. (1989). Extended model set, global data and threshold model identification of severely non-linear systems. International Journal of Control 50(5), 1897–1923.
Billings, S. and Jones, G. (1992). Orthogonal least-squares parameter estimation algorithms for non-linear stochastic systems. International Journal of Systems Science 23(7), 1019–1032.
Billings, S. and Voon, W. (1983). Structure detection and model validation tests in the identification of nonlinear systems. IEE Proceedings, Part D. 130, 193–199.
Billings, S. and Voon, W. (1984). Least squares parameter estimation algorithms for non-linear systems. International Journal of Systems Science 15(6), 601–615.
Billings, S. and Voon, W. (1986). Correlation based model validity tests for non-linear models. International Journal of Control 44(1), 235–244.
Boyd, S. and Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press, Cambridge, U.K., 1st edition.
Bunton, R. and Denegri, C. (2000). Limit cycle oscillation characteristics of fighter aircraft. AIAA Journal of Aircraft 37(5), 916–918.
Chen, P., Sarhaddi, D., and Liu, D. (1998). Limit cycle oscillation characteristics of fighter aircraft with external stores. AIAA-98, p. 1727.
Chen, S. and Billings, S. (1989). Representations of non-linear systems: the NARMAX model. International Journal of Control 49(3), 1013–1032.
Chen, S., Billings, S., Cowan, C., and Grant, P. (1990). Practical identification of NARMAX models using radial basis functions. International Journal of Control 52, 1327–1350.
Chen, S., Donoho, D., and Saunders, M. (2001). Atomic decomposition by basis pursuit. SIAM Journal on Scientific Compututing 43(1), 129–159.
Copas, J. (1983). Regression, prediction and shrinkage. Journal of the Royal Statistical Society B 45(2), 311–354.
Denegri, C. (2000). Limit cycle oscillation flight test results of a fighter with external stores. AIAA Journal of Aircraft 37(5), 761–769.
Dowell, E., Edwards, J., and Strganac, T. (2003). Nonlinear aeroelasticity. AIAA Journal of Aircraft 40(1), 857–874.
Draper, N. and Smith, H. (1981). Applied Regression Analysis. JohnWiley & Sons, New York, 2nd edition.
Efron, B. (1979). Computer and the theory of statistics: Thinking the unthinkable. SIAM Review 21(4), 460–480.
Efroymson, M. (1960). Multiple Regression and Correlation. in Mathematical Methods for Digital Computers. John Wiley & Sons, New York, 1st edition.
Eykhoff, P. (1974). System Identification. John Wiley & Sons, New York, 1st edition.
Franklin, G., Powell, J., and Emami-Naeini, A. (2002). Feedback Control of Dynamic Systems. Addison-Wesley, New York, 4th edition.
Freund, J. (1962). Mathematical Statistics. Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1st edition.
Gawronski, W. (1996). Balanced Control of Flexible Structures. Springer-Verlag, London, 1st edition.
Goodwin, G. and Payne, R. (1977). Dynamic System Identification: Experiment Design and Data Analysis, volume 136 of Mathematics in Science and Engineering. Academic Press, New York.
Greblicki, W. and Pawlak, M. (1991). Nonparametric identification of a cascade nonlinear time series system. Signal Processing 22, 61–75.
Grigoriadis, M. and Ritter, K. (1969). A parametric method for semidefinite quadratic programs. SIAM J. Control 7(4), 559–577.
Haber, R. and Unbehauen, H. (1990). Structure identification of nonlinear dynamic systems-a survey on input/output approaches. Automatica 26, 651–677.
Harris, C. and Billings, S. (1985). Self Tuning and Adaptive Control: Theory and Applications. Peter Peregrinus, London, 2nd edition.
Hurvich, C. and Tsai, C. L. (1990). The impact of model selection on inference in linear regression. The American Statistician 44, 214–217.
Korenberg, M. and Hunter, I. (1990). The identification of nonlinear biological systems: Wiener kernel approaches. Annals of Biomedical Engineering 18, 629–654.
Kosut, R., Lau, M., and Boyd, S. (1992). Set-membership identification of systems with parameteric and nonparametric uncertainty. IEEE Transactions on Automatic Control 37(7), 929–942.
Kukreja, S. (2003). A suboptimal bootstrap method for structure detection of nonlinear output-error models. Proc. 13th IFAC Symp. System Identification, volume 13, pp. 1566–1571. Rotterdam, The Netherlands.
Kukreja, S., Galiana, H., and Kearney, R. (2003). NARMAX representation and identification of ankle dynamics. IEEE-TBME 50(1), 70–81.
Kukreja, S., Galiana, H., and Kearney, R. (2004). A bootstrap method for structure detection of NARMAX models. International Journal of Control 77(2), 132–143.
Kvasnica, M., Grieder, P., Baotić, M., and Morari, M. (2004). Multi Parametric Toolbox (MPT). Hybrid Systems: Computation and Control, volume 2993 of Lecture Notes in Computer Science, pp. 448–462. Springer Verlag, Philadelphia.
Lee, B., Pricei, S., and Wong, Y. (1999). Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos. Progress in Aerospace Sciences 35, 205–334.
Leontaritis, I. and Billings, S. (1985). Input-output parametric models for non-linear systems part I: deterministic non-linear systems. International Journal of Control 41(2), 303–328.
Leontaritis, I. and Billings, S. (1985). Input-output parametric models for non-linear systems part II: stochastic non-linear systems. International Journal of Control 41(2), 329–344.
Lind, R. and Brenner, M. (1999). Robust Aeroservoelastic Stability Analysis: Flight Test Applications. Springer-Verlag, New York, 1st edition.
Lind, R., Prazenica, R., and Brenner, M. (2003). Estimating nonlinearity using volterra kernals in feedback with linear models. AIAA-03, volume 44, pp. 1406–1416. Norfolk, Virginia.
Ljung, L. (1999). System Identification: Theory for the User. Prentice Hall, Inc., Englewood Cliffs, New Jersey, 2nd edition.
Mantel, M. (1970). Why stepdown procedures in variable selection. Technometrics 12, 621–625.
Masri, S. and Caughey, T. (1979). A nonparametric identification technique for nonlinear dynamic problems. Journal of Applied Mechanics 46(2), 433–447.
Mészáros, C. (1998). The BPMPD interior point solver for convex quadratic problems. Technical Report 98-8, Hungarian Academy of Science, Budapest.
Miller, A. (1996). The convergence of Efroymson’s stepwise regression algorithm. The American Statistician 50(2), 180–181.
Mukhopadhyay, V. (1995). Flutter suppression control low design and testing for the acting flexible wing. AIAA Journal of Aircraft (Special Adaptive Flexible Wing Issue) 32(1), 45–51.
Mukhopadhyay, V. (2003). Historical perspective on analysis and control of aeroelastic responses. AIAA Journal of Guidance, Control, and Dynamics 26(5), 673–684.
Osborne, M., Presnell, B., and Turlach, B. (2000). On the LASSO and its dual. Journal of Computational and Graphical Statistics 9(2), 319–337.
Ostrom, C. (1990). Time Series Analysis: Regression Techniques. Sage Publications, Newberry Park, Calif., 2nd edition.
Palanthandalam-Madapusi, H., Hoagg, J., and Berstein, D. (2004). Basis-function optimization for subspace-based nonlinear identification of systems with measured-input nonlinearities. Proc. IEEE American Control Conference, volume 5, pp. 4788–4793. Boston, Massachusetts.
Panuska, V. (1968). A stochastic approximation method for identification of linear systems using adaptive filtering. Proceedings 9th Joint Automatic Control Conference, pp. 1014–1021. IEEE, Ann Arbor, MI, USA.
Panuska, V. (1969). An adaptive recursive least squares identification algorithm. Proceedings 8th IEEE Symp. on Adaptive Processes, p. paper 6e. University Park, PA, USA.
Pearson, R. (1995). Nonlinear input/output modelling. Journal of Process Control 5(4), 197–211.
Pendleton, E., Bessette, D., Field, P., Miller, G., and Griffin, K. (2000). Active aeroelastic wing flight research program: Technical program and model analytical development. AIAA J. Aircraft 37(4), 554–561.
Pottmann, M. and Pearson, R. (1998). Block-oriented NARMAX models with output multiplicities. AIChE Journal 44(1), 131–140.
Seber, G. (1977). Linear Regression Analysis. John Wiley & Sons, New York, 1st edition.
Shao, J. (1993). Linear model selection by cross-validation. Journal of the American Statistical Association 88, 486–494.
Sjöberg, J., et al. (1995). Nonlinear black-box modeling in system identification: a unified overview. Automatica 31(12), 1691–1724.
Smillie, K. (1966). An Introduction to Regression and Correlation. Academic Press Inc., London, 1st edition.
Smith, R. (1995). Eigenvalue perturbation models for robust control. IEEE Automatic Control 40(6), 10631–1066.
Smith, R. S. (1995). Model validation for robust control: An experimental process control application. Automatica 31(11), 1637–1647.
Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society B 58(1), 267–288.
Unbehauen, H. (1996). Some new trends in identification and modeling of nonlinear dynamical systems. Applied Mathematics and Computation 78, 279–297.
Young, P. (1968). The use of linear regression and relaxed procedures for the identification of dynamic processes. Proceedings 7th IEEE Symp. on Adaptive Processes, pp. 501–505. Los Angeles, CA, USA.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag London Limited
About this chapter
Cite this chapter
Kukreja, S.L., Brenner, M.J. (2007). Nonlinear System Identification of Aeroelastic Systems: A Structure-detection Approach. In: Sánchez Peña, R.S., Cayuela, V.P., CasÃn, J.Q. (eds) Identification and Control. Springer, London. https://doi.org/10.1007/978-1-84628-899-9_5
Download citation
DOI: https://doi.org/10.1007/978-1-84628-899-9_5
Publisher Name: Springer, London
Print ISBN: 978-1-84628-898-2
Online ISBN: 978-1-84628-899-9
eBook Packages: EngineeringEngineering (R0)