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Presented here is an amplitude and frequency modulation method (AFMM) for extracting damage-induced nonlinear
characteristics and intermittent transient responses by processing steady-state/transient responses using the empirical
mode decomposition, Hilbert-Huang transform (HHT), and nonlinear dynamic characteristics derived from perturbation
analysis. A sliding-window fitting (SWF) method is derived to show the physical implication of the proposed method
and other methods for time-frequency signal decomposition. Similar to the short-time Fourier transform and wavelet
transform the SWF uses windowed regular harmonics and function orthogonality to extract time-localized regular and/or
distorted harmonics. On the other hand the HHT uses the apparent time scales revealed by the signal's local maxima and
minima to sequentially sift components of different time scales, starting from high-frequency to low-frequency ones.
Because HHT does not use predetermined basis functions and function orthogonality for component extraction, it
provides more accurate instant amplitudes and frequencies of extracted components for accurate estimation of system
characteristics and nonlinearities. Moreover, because the first component extracted from HHT contains all original
discontinuities, its time-varying amplitude and frequency are excellent indicators for pinpointing times and locations of
impulsive external loads and damages that cause intermittent responses. However, the discontinuity-induced Gibbs'
effect makes HHT analysis inaccurate around the two data ends. On the other hand, the SWF analysis is not affected by
Gibbs' effect, but it cannot extract accurate time-varying frequencies and amplitudes. Numerical results show that the
proposed AFMM can provide accurate estimations of softening and hardening effects, different orders of nonlinearity,
linear and nonlinear system parameters, and time instants of intermittent transient responses for damage detection and
estimation.
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