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This paper shows that time-frequency analysis is most appropriate for nonlinearity identification, and presents advanced
signal processing techniques that combine time-frequency decomposition and perturbation methods for parametric and
non-parametric identification of thin-walled structures and other dynamical systems. Hilbert-Huang transform (HHT) is
a recent data-driven adaptive time-frequency analysis technique that combines the use of empirical mode decomposition
(EMD) and Hilbert transform (HT). Because EMD does not use predetermined basis functions and function
orthogonality for component extraction, HHT provides more concise component decomposition and more accurate timefrequency
analysis than the short-time Fourier transform and wavelet transform for extraction of system characteristics
and nonlinearities. However, HHT's accuracy seriously suffers from the end effect caused by the discontinuity-induced
Gibbs' phenomenon. Moreover, because HHT requires a long set of data obtained by high-frequency sampling, it is not
appropriate for online frequency tracking. This paper presents a conjugate-pair decomposition (CPD) method that
requires only a few recent data points sampled at a low frequency for sliding-window point-by-point adaptive timefrequency
analysis and can be used for online frequency tracking. To improve adaptive time-frequency analysis, a
methodology is developed by combining HHT and CPD for noise filtering in the time domain, reducing the end effect,
and dissolving other mathematical and numerical problems in time-frequency analysis. For parametric identification of a
nonlinear system, the methodology processes one steady-state response and/or one free damped transient response and
uses amplitude-dependent dynamic characteristics derived from perturbation analysis to determine the type and order of
nonlinearity and system parameters. For non-parametric identification, the methodology uses the maximum
displacement states to determine the displacement-stiffness curve and the maximum velocity states to determine the
velocity-damping curve. Numerical simulations and experimental verifications of several nonlinear discrete and
continuous systems show that the proposed methodology can provide accurate parametric and non-parametric
identifications of different nonlinear dynamical systems.
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