A combined method for instantaneous frequency identification in low frequency structures

Civil engineering structures such as high-rise buildings and long-span cable-supported bridges usually exhibit low-frequency characteristics and the resultant response signals may be non-asymptotic (the amplitude change rate is higher than its phase change rate) and even have closely-spaced frequency components. The identification of satisfactory instantaneous frequencies of such response signals is a challenge faced by standard synchrosqueezing wavelet transform. The paper aims to propose a combined method to address this challenge. The proposed method combines an extended analytical mode decomposition (AMD) method, a recursive Hilbert transform and a zoom synchrosqueezing wavelet transform (consisting of frequency-shift operation and partial zoom synchrosqueezing operation). In the method, a multi-component signal, which may consist of closely spaced frequency components, is firstly decomposed into several mono-component signals by the extended AMD, and the extracted mono-components are then demodulated into asymptotic signals by recursively using the Hilbert transform. After that, a frequency-shift operation is employed to improve time resolution and a partial zoom synchrosqueezing operation is then applied to improve the frequency resolution in the narrow low frequency range of interest. Two numerical examples, an experiment on an aluminum cantilever beam with abrupt mass reduction and an experiment on a cable with time-varying tension forces are provided to illustrate the effectiveness, accuracy and robustness of the method.