Analytical Mode Decomposition of Time Series with Decaying Amplitudes and Overlapping Instantaneous Frequencies


In this study, the recently developed analytical mode decomposition with Hilbert transform was extended to the decomposition of a non-stationary and nonlinear signal with two or more amplitude-decaying and frequency-changing components. The bisecting frequency in the analytical mode decomposition became time-varying, and could be selected between any two adjacent instantaneous frequencies estimated from a preliminary wavelet analysis. The mathematical foundation for this new extension was integration of the bisecting frequency over time so that the original time series is actually decomposed in the phase domain. Parametric studies indicated that the analytically derived components are insensitive to the selection of bisecting frequency and the presence of up to 20% noise, sufficiently accurate when the sampling rate meets the Nyquist-Shannon sampling criterion, and applicable to both narrowband and wideband frequency modulations even when the signal amplitude decays over time. The proposed analytical mode decomposition is superior to the empirical mode decomposition and wavelet analysis in the preservation of signal amplitude, frequency and phase relations. It can be directly applied for system identification of buildings with time-varying stiffness.


Civil, Architectural and Environmental Engineering

Keywords and Phrases

Analytical Mode Decompositions; Empirical Mode Decomposition; Hilbert Transform; Instantaneous Frequency; Mathematical Foundations; Nonlinear Signals; Sampling Criterions; Time-Varying Stiffness; Wavelet Analysis; Time Series

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Article - Journal

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