Structural damage detection and estimation by amplitude and frequency modulation analysis

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.