Instantaneous frequency identification of time-varying structures by continuous wavelet transform

Frequency variation and sensor contribution assessment: Application to an offshore platform in the South China Sea

“…Xu et al [10] proposed a time-varying modal parameter identification method based on a linear timefrequency representation and a Hilbert transform. Wang et al [11] proposed a method based on the wavelet ridges of a continuous wavelet transform for the instantaneous frequency identification of time-varying structures; their results further verified that the proposed method could effectively identify the instantaneous frequencies of time-varying structures with high accuracy. However, Kijewski and Kareem [12] argued that civil engineering structures usually possess long-period motions and thus require finer frequency resolution in the parent wavelets.…”

“…(23), then the corresponding λ n ¼ lnðz n Þ=Δt can be computed by implementing Eqs. (9)- (11). From Eq.…”

A Generalized Demodulation and Hilbert Transform Based Signal Decomposition Method

“…This provides evidence that the Fourier transform is not suitable for nonstationary signal processing. Thus a continuous wavelet transform is performed to trace the time-frequency energy distribution of the signal, in which the complex Morlet wavelet is used [2]. The WT scalogram of the signal ( ) is shown in Figure 5(b), from which the fluctuations of the instantaneous frequency of the signal can be observed.…”

“…With the aid of the WT, Ruzzene et al identified natural frequencies and damping with real world data from a bridge, and Wang et al identified instantaneous frequency (IF) of time-varying structures [1,2]. Although the WT method has many successful engineering applications, it is difficult to achieve high resolutions in time and frequency domains simultaneously due to the Heisenberg-Gabor uncertainty principle [3].…”

Identification of sudden stiffness changes in the acceleration response of a bridge to moving loads using ensemble empirical mode decomposition

“…The first question that arises is how to characterize a non-linear response. This has been addressed in a wide range of mechanical and civil engineering applications via methods such as the Continuous Wavelet Transform (CWT) [4,5], Unscented Kalman Filter (UKF) [6,7], Hilbert-Huang Transform (HHT) [2,[8][9][10] and others. The HHT utilises Empirical Mode Decomposition (EMD) to estimate the Instantaneous Frequency (IF) and the Instantaneous Phase (IP).…”