| Hilbert Huang Transform faces several challenges in dealing with closely-spaced frequency components, short-time and weak disturbances, and interrelationships between two time-varying modes of nonlinear vibration due to its mixed mode problem associated with empirical mode decomposition (EMD). To address these challenges, analytical mode decomposition (AMD) based on Hilbert Transform is proposed and developed for an adaptive data analysis of both stationary and non-stationary responses. With a suite of predetermined bisecting frequencies, AMD can analytically extract the individual components of a structural response between any two bisecting frequencies and function like an adaptive bandpass filter that can deal with frequency-modulated responses with significant frequency overlapping. It is simple in concept, rigorous in mathematics, and reliable in signal processing.;In this dissertation, AMD is studied for various effects of bisecting frequency selection, response sampling rate, and noise. Its robustness, accuracy, efficiency, and adaptability in signal analysis and system identification of structures are compared with other time-frequency analysis techniques such as EMD and wavelet analysis. Numerical examples and experimental validations are extensively conducted for structures under impulsive, harmonic, and earthquake loads, respectively. They consistently demonstrate AMD's superiority to other time-frequency analysis techniques. In addition, to identify time-varying structural properties with a narrow band excitation, a recursive Hilbert Huang Transform method is also developed. Its effectiveness and accuracy are illustrated by both numerical examples and shake table tests of a power station structure. |
