SPECTRAL IDENTIFICATION OF NONLINEAR STRUCTURAL SYSTEMS

The paper discusses a spectral method for identification of nonlinear systems encountered in structural applications. The nonlinearity is accounted for by a combination of linear subsystems and known zero-memory nonlinear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a “Gram-Schmidt” type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of a Duffing oscillator with nonlinear damping elucidates the applicability of the proposed method.

[1]  J. R. Morison,et al.  The Force Exerted by Surface Waves on Piles , 1950 .

[2]  P. Welch.  The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms , 1967 .

[3]  H. Saunders.  Literature Review : RANDOM DATA: ANALYSIS AND MEASUREMENT PROCEDURES J. S. Bendat and A.G. Piersol Wiley-Interscience, New York, N. Y. (1971) , 1974 .

[4]  S. Masri,et al.  Nonparametric Identification of Nearly Arbitrary Nonlinear Systems , 1982 .

[5]  J H Vugts,et al.  A NON-LINEAR, FREQUENCY DOMAIN DESCRIPTION OF WAVE FORCES ON AN ELEMENT OF A VERTICAL FILE IN RANDOM SEAS , 1985 .

[6]  R. W. Miksad,et al.  Application of digital cross-bispectral analysis techniques to model the non-linear response of a moored vessel system in random seas , 1985 .

[7]  H. G. Natke,et al.  System identification techniques , 1986 .

[8]  J. Bendat,et al.  DECOMPOSITION OF WAVE FORCES INTO LINEAR AND NON-LINEAR COMPONENTS , 1986 .

[9]  H. Rice,et al.  Simplified partial coherence functions for multiple input/output analysis , 1988 .

[10]  G. Tomlinson,et al.  Recent advances in the application of functional series to non-linear structures , 1989 .

[11]  Henry J. Rice,et al.  A procedure for the identification of linear and non-linear multi-degree-of-freedom systems , 1991 .

[12]  G. Tomlinson,et al.  Direct parameter estimation for linear and non-linear structures , 1992 .

[13]  Robert N. Coppolino,et al.  A General Identification Technique for Nonlinear Differential Equations of Motion , 1992 .

[14]  David R. Brillinger,et al.  Some basic aspects and uses of higher-order spectra , 1994, Signal Process..

[15]  Pol D. Spanos,et al.  Nonlinear System Identification in Offshore Structural Reliability , 1995 .

[16]  P. Spanos,et al.  Identification of Nonlinear Systems under Random Excitation , 1996 .