Estimation of generalized frequency response functions for quadratically and cubically nonlinear systems

Journal of Sound and Vibration

Volumn 330, Issue 3, 2011, Pages 461-470

  Li, L M ^a   Billings, S A ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

FREQUENCY DOMAINS; GENERALIZED FREQUENCY RESPONSE FUNCTIONS; NEW APPROACHES; NON-PARAMETRIC ALGORITHM; NONPARAMETRIC METHODS; RESPONSE FUNCTIONS; TIME DOMAIN MEASUREMENT; VOLTERRA KERNELS;

DISCRETE FOURIER TRANSFORMS; FREQUENCY ESTIMATION; FREQUENCY RESPONSE; METADATA;

TIME DOMAIN ANALYSIS;

EID: 78049465361     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2010.08.018     Document Type: Article

References (22)

1. V. Volterra Theory of Functionals 1930 Blackie and Sons
2. M. Schetzen The Volterra and Wiener Theories of Non-linear System 1980 Wiley New York
3. W.J. Rugh Nonlinear System TheoryThe Volterra/Wiener Approach 1981 The John Hopkins University Press
4. W. Sandberg A perspective on system theory IEEE Transactions on Circuits and Systems CAS-31 1984 88 103
5. F.J. Doyle III, R.K. Pearson, and B.A. Ogunnaike Identification and Control Using Volterra Models 2002 Springer-Verlag London
6. E.J. Ewen, and D.D. Weiner Identification of weakly nonlinear systems using input and output measurements IEEE Transactions on Circuits and Systems CAS-27 1980 1255 1261
7. A.Y. Kibangou, and G. Favier WienerHammerstein systems modeling using diagonal Volterra kernels coefficients IEEE Signal Processing Letters 13 2006 381 384
8. S.A. Billings, and K.M. Tsang Spectral analysis for nonlinear systems, part IIinterpretation of nonlinear frequency response functions Mechanical Systems and Signal Processing 3 1989 341 359
9. J.C. Peyton Jones, and S.A. Billings A recursive algorithm for computing the frequency response of a class of non-linear difference equation models International Journal of Control 50 1989 1925 1940
10. L.J. Tick The estimation of transfer functions of quadratic systems Technometrics 3 1961 563 567
11. K.I. Kim, and E.J. Powers A digital method of modelling quadratically non-linear systems with a general random input IEEE Transactions on Acoustics, Speech, and Signal Processing 36 1988 1758 1769
12. S.W. Nam, and E.J. Powers Application of higher-order spectral analysis to cubically nonlinear system identification IEEE Transactions on Signal Processing 42 1994 1746 1765
13. Y.S. Cho, and E.J. Powers Quadratic system identification using higher order spectra of i.i.d signals IEEE Transactions on Signal Processing 42 1994 1268 1271
14. H.J. Rice, and K.Q. Xu Linear path identification of general nonlinear systems Mechanical Systems and Signal Processing 10 1996 55 63
15. S. Boyd, Y.S. Tang, and L.O. Chua Measuring Volterra Kernels IEEE Transactions on Circuits and Systems CAS-30 1983 571 577
16. S.A. Billings, and J.C. Peyton Jones Mapping non-linear integro-differential equations into the frequency domain International Journal of Control 52 1990 863 879
17. L.A. Aguirre, and S.A. Billings Dynamical effects of overparameterization in nonlinear models Physica D 80 1995 26 40
18. S.A. Billings, and Q.M. Zhu Model validation tests for multivariable nonlinear models including neural networks International Journal of Control 62 1995 749 766
19. L.A. Aguirre, and S.A. Billings Validating identified nonlinear models with chaotic dynamics International Journal of Bifurcation and Chaos 4 1994 109 125
20. I.J. Leontaritis, and S.A. Billings Experimental-design and identifiability for nonlinear systems International Journal of Systems Science 18 1987 189 202
21. S.A. Billings, M.J. Korenberg, and S. Chen Identification of non-linear output-affine systems using an orthogonal least-squares algorithm International Journal of Systems Science 19 1988 1559 1568
22. L.M. Li, and S.A. Billings Continuous time non-linear system identification in the frequency domain International Journal of Control 74 2001 1052 1061