Abstract
A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both digital simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in contrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.
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References
Thompson J. M. T. and H. B. Stewart,Nonlinear Dynamics and Chaos, John Wiley and Sons, Great Britain, 1986.
Nayfeh A. H. and D. T. Mook,Nonlinear Oscillations, Wiley, New York, 1979.
Natke, H. G., J.-N. Juang, and W. Gawronski,Identification of Nonlinear Mechanical Systems: A Brief Review, NASA Langley Research Center, Hampton, VA, U.S.A.
Jedner, U. and H. Unbehauen, ‘Identification of a class of nonlinear systems by parameter estimation of a linear multi-model’, inIMACS, Modeling and Simulation for Control of Lumped and Distributed Parameter Systems, June 3–6, 1986, pp. 11–15.
Ibanez P., ‘Identification of dynamic parameters of linear and non-linear structural models from experimental data’,Nuclear Engineering and Design 25, 1973, 32–41.
Yasuda K., S. Kawamura, and K. Watanabe, ‘Identification of nonlinear multi-degree-of-freedom systems (identification under noisy measurements)’,JSME International Journal 3, 1988, 502–509.
Yasuda K., S. Kawamura, and K. Watanabe, ‘Identification of nonlinear multi-degree-of-freedom systems (presentation of an identification technique)’,JSME International Journal 3, 1988, 8–14.
Billings S. A. and W. S. F. Voon, ‘A prediction-error and stepwise regression estimation algorithm for nonlinear systems’,Int. J. Control 44, 1986, 803–822.
Greblick W. and M. Pawlak, ‘Hammerstein system identification by non-parametric regression estimation’,Int. J. Control 45, 1987, 343–354.
Kortmann, M. and H. Unbehauen, ‘Application of a recursive prediction error method to the identification of nonlinear systems using the Wiener model’,IMACS, Modeling and Simulation for Control of Lumped and Distributed Parameter Systems, June 3–6, 1986, pp. 3–9.
Distefano N. and A. Rath, ‘System identification in nonlinear seismic dynamics’,Computer Methods in Applied Mechanics and Engineering 5, 1975, 353–372.
Broersen P. M. T., ‘Estimation of parameters of non-linear dynamical systems’,Int. J. Non-Linear Mechanics 9, 1974, 355–361.
Hanagud S. V., M. Meyyappa, and J. I. Craig, ‘Method of multiple scales and identification of nonlinear dynamical systems’,AAIA J. 23, 1985, 802–807.
Marmarelis P. Z. and F. E. Udwadia, ‘The identification of building structural systems—Part II: The nonlinear case’,Bulletin of the Seismological Society of America 66, 1979, 153–171.
Chen H., N. Ishii, and N. Suzumura, ‘Structural classification of non-linear systems by input and output’,Int. J. Systems Sci. 17, 1986, 741–774.
Wang M. L. and R. Y. Chang, ‘Model reduction and control system design by shifted Legendre polynomial functions’,ASME J. Dynam. Sys. Meas. Control 105, 1983, 52–55.
Horn I.-R. and J.-H. Chou, ‘Analysis and identification of non-linear systems via shifted Jacobi series’,Int. J. Control 45, 1987, 279–290.
Yun C.-B. and M. Shinozuka, ‘Identification of nonlinear structural dynamic systems’,J. Struct. Mech. 8, 1980, 187–203.
Hammond, J. K., H. R. Lo, and E. J. Seager-Smith, ‘Identification of nonlinearities in vibrating systems using optimal control techniques’,IMAC, 1987, 1467–1473.
Mook D. J. and J. L. Junkins, ‘Minimum model error estimation for poorly modeled dynamic systems’,AIAA J.G.N.C. 11, 1988, 256–261.
Mook D. J., ‘Estimation and identification of nonlinear dynamic systems’,AIAA J. 27, 1989, 968–974.
Geering H. P., ‘Continuous time optimal control theory for cost functionals including discrete state penalty terms’,IEEE Trans. A.C. AC-21, 1976, 860–869.
Mook D. J. and J.-H. Lew, ‘Multiple shooting algorithms for jump-discontinuous problems in optimal control and estimation’,IEEE Trans. A.C. 36 (8), 1990, 979–983.
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Stry, G.I., Mook, D.J. An experimental study of nonlinear dynamic system identification. Nonlinear Dyn 3, 1–11 (1992). https://doi.org/10.1007/BF00045467
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DOI: https://doi.org/10.1007/BF00045467