Identification of a Duffing oscillator under different types of excitation

In many engineering applications the dynamics may significantly be affected by nonlinear effects, which must be accounted for in order to accurately understand and robustly model the dynamics. From a practical point of view, it is very important to solve the inverse problem related to system identification and output prediction. In this paper the recently developed Nonlinear Subspace Identification (NSI) method is presented and applied to an oscillator described by the Duffing equation, with different types of excitation including random forces, which are demonstrated to be very suitable for the identification process. The estimates of system parameters are excellent and, as a consequence, the behaviour of the system, including the jump phenomena, is reconstructed to a high level of fidelity. In addition, the possible memory limitations affecting the method are overcome by the development of a novel algorithm, based on a specific computation of the QR factorisation.

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

[2]  Keith Worden.  On jump frequencies in the response of the Duffing oscillator , 1996 .

[3]  Anita C. Faul,et al.  Non-linear systems , 2006 .

[4]  A. H. Nayfeh,et al.  Calculation of the jump frequencies in the response of s.d.o.f. non-linear systems , 2002 .

[5]  Keith Worden,et al.  Nonlinear system identification of automotive dampers: A time and frequency-domain analysis , 2009 .

[6]  Rajendra Singh,et al.  FEASIBILITY OF IDENTIFYING NON-LINEAR VIBRATORY SYSTEMS CONSISTING OF UNKNOWN POLYNOMIAL FORMS , 1999 .

[7]  Gaëtan Kerschen,et al.  A Frequency Domain Versus a Time Domain Identification Technique for Nonlinear Parameters Applied to Wire Rope Isolators , 2001 .

[8]  John E. T. Penny,et al.  The Accuracy of Jump Frequencies in Series Solutions of the Response of a Duffing Oscillator , 1994 .

[9]  Sami F. Masri,et al.  A Nonparametric Identification Technique for Nonlinear Dynamic Problems , 1979 .

[10]  K. Worden,et al.  Past, present and future of nonlinear system identification in structural dynamics , 2006 .

[11]  Luigi Garibaldi,et al.  Performances Analysis of Frequency Domain Nonlinear Identification Techniques , 2004 .

[12]  Luigi Garibaldi,et al.  A time domain approach for identifying nonlinear vibrating structures by subspace methods , 2008 .

[13]  Bart De Moor,et al.  Subspace Identification for Linear Systems: Theory ― Implementation ― Applications , 2011 .

[14]  M. Soliman.  Jump phenomena resulting in unpredictable dynamics in the driven damped pendulum , 1996 .

[15]  Randall J. Allemang,et al.  A FREQUENCY DOMAIN METHOD FOR ESTIMATING THE PARAMETERS OF A NON-LINEAR STRUCTURAL DYNAMIC MODEL THROUGH FEEDBACK , 2000 .

[16]  Rajendra Singh,et al.  IDENTIFICATION OF MULTI-DEGREE-OF-FREEDOM NON-LINEAR SYSTEMS UNDER RANDOM EXCITATIONS BY THE “REVERSE PATH” SPECTRAL METHOD , 1998 .

[17]  Guido De Roeck,et al.  Reference-based combined deterministic–stochastic subspace identification for experimental and operational modal analysis , 2006 .

[18]  I. Kovacic,et al.  On the jump-up and jump-down frequencies of the duffing oscillator , 2008 .

[19]  Gene H. Golub,et al.  Matrix computations , 1983 .