Nonlinear Structural Dynamics Characterization by Decomposing Time Signals Using Hilbert-Huang Transform

Abstract

Presented are methods for extracting nonlinearities and localized transient vibration effects caused by external impact loading and/or internal damage by processing stationary/transient responses using the Hilbert-Huang transform (HHT) and a sliding-window fitting (SWF) technique. Similar to the wavelet transform the SWF uses windowed regular harmonics and function orthogonality to extract local harmonic components. However, the SWF decomposes a signal into just a few regular and/or distorted harmonics, and the time-varying amplitudes and frequencies of the harmonics can reveal nonlinearities contained in the signal. To extract components from a signal HHT uses the apparent time scales shown by the local maxima and minima of the signal and cubic splines of extrema to sequentially sift components of different time scales, starting from high-frequency to low-frequency ones. Because HHT does not use any chosen basic functions and their orthogonality for component extraction, it provides more accurate instantaneous amplitudes and frequencies of extracted components for accurate estimation of system characteristics and nonlinearities. Moreover, because the first extracted component contains all original discontinuities, its time-varying amplitude and frequency are excellent indicators of sudden transient disturbances. However, the discontinuity-induced Gibbs’ phenomenon makes HHT analysis inaccurate around the two data ends. On the other hand, the SWF analysis has no Gibbs’ phenomenon at the two data ends, but it cannot extract accurate modulation frequencies due to the use of the sliding-window fitting technique and non-orthogonal basic functions. Numerical and experimental results show that HHT can provide accurate extraction of intrawave amplitude- and phase-modulation, distorted harmonic response under a single-frequency harmonic excitation, softening and hardening effects, different orders of nonlinearity, interwave amplitude- and phase-modulation, multiple-mode vibrations caused by internal/external resonances, and instants of impact loading on a structure. These phenomena are keys for performing dynamics-based system identification and structural health monitoring.