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SIMULATION OF NONSTATIONARY RANDOM PROCESSES BASED ON HILBERT-HUANG TRANSFORM
Published in W. Q. Zhu, G.Q. Cai, R.C. Zhang, Advances in Stochastic Structural Dynamics, 2003
Recently, Huang et al (1998) introduced a new method of spcctral analysis of nonstationary processes based on Hilbert transform and the concept of instantaneous frequency. Unlike Fourier transform, Hilbert transform emphasizes local behavior and docs not decompose the process into sine and cosinc waves of fixed frcqucncics. The Hilbert energy or amplitude spectrum as function of time and frequency can be then described in terms of the amplitude functions and instantaneous frequency. No assumption of slowly time-varying behavior of the processes is required and no sine or cosine waves of fixed frequencies are used. The Hilbert spectrum gives a much sharper description of the frequency content of the physical phenomena as function of time. It has been proved superior to the Fourier or wavelet spectrum in its resolution power and truthful description of a number of nonstationary and nonlinear theoretical and geophysical problems. It is a new approach to the challenging problem of frequency domain analy sis of nonstationary processes.
A new DFT-based dynamic detection framework for polygonal wear state of railway wheel
Published in Vehicle System Dynamics, 2023
Qiushi Wang, Zhongmin Xiao, Jinsong Zhou, Dao Gong, Zegen Wang, Zhanfei Zhang, Tengfei Wang, Yanling He
Generally, the vehicle-mounted detection method is to install the acceleration sensor on the axle box, and the acceleration time-domain signal is obtained to detect the wheel polygon wear state. Ding, et al. detected the wheel irregularity by performing the wavelet transform analysis of frequency slices [35]. However, this method can not quantitatively evaluate the wheel polygonal wear state. Zhou, Li, et al. applied the empirical mode decomposition (EMD) theory and Hilbert transform theory to obtain the Hilbert spectrum and finally detected wheel polygon fault by observing the Hilbert spectrum [36,37]. Song et al. applied the improved EMD theory and Wingner Ville theory to identify the wheel fault by using the simulated axle box vibration acceleration signal [38]. However, EMD is an empirical method that lacks strict theoretical proof, and it is prone to problems such as mode aliasing and endpoint effect in the application process [39]. Sun, et al. proposed a wheel polygon detection method based on angle domain synchronous average technology [40]. Although this method solves the problem of signals non-stationary caused by running speed change, it can not rule out the influence of track irregularity or random defects on the detection results.
Non-modal vibration-based methods for bridge damage identification
Published in Structure and Infrastructure Engineering, 2020
Rick M. Delgadillo, Joan R. Casas
In this section, an exhaustive analysis of IVI parameter is developed. IVI utilises the time–frequency–energy representation of the well-known Hilbert Spectrum in a novel manner that provides more quantifiable measure of signal variations. In this study, the IVIs obtained for each vehicle crossing are analysed across a 10 s duration that captures the forced vibration response of the bridge under the vehicle load (see case study number 2). For the undamaged condition, Figure 9 shows an example of Hilbert–Huang Spectrum that is obtained for the first three IMFs of sensor 1 in the steel truss bridge described in the case of study. The time–frequency variation shows energy concentration around 3 Hz, 6.8 Hz and 13.3 Hz, which represent the first, second and fifth vibrational modes as per Kim et al. (2014). However, considering only this information is difficult to ascertain changes in structural behaviour. For this reason, a more quantitative representation known as IVI is presented in Figure 10. This relation obtained from Equation (10) considers both instantaneous frequencies and amplitudes.
Failure modes of slope stabilized by frame beam with prestressed anchors
Published in European Journal of Environmental and Civil Engineering, 2022
J. J. Zhang, J. Y. Niu, X. Fu, L. C. Cao, S. J. Yan
The marginal spectrum is the integral of Hilbert spectrum on the time axis, which can characterize the contribution of any frequency in the signal to the energy amplitude. The physical meaning of the marginal spectrum of the Hilbert spectrum can be understood as that the signal energy distribution varies with the frequency, namely the energy generated by a certain frequency in all the time of the original signal is accumulated. The change in the peak value of the marginal spectrum means the change in the maximum total energy of a certain instantaneous frequency. The damage of slope under earthquake is a concerned problem. Although there are some ways to identify damage, such as wavelet analysis and intrinsic mode analysis (Onsay & Haddow, 1994), there are different defects in these methods. The main reason is that their analysis results depend on the selected basis functions. The researches of Fan, Zhang, Zhang, and Ouyang (2017) show that the HHT transform and marginal spectral method can be better applied to seismic damage identification of slope. If a part of the slope is damaged by seismic waves, this part will affect the upward propagation of seismic energy, and the lost energy will cause fluctuations or mutations in the amplitude of the marginal spectrum. If the peak value of the marginal spectrum at the vertical cross section increases linearly with increasing elevation, it indicates that the rock mass inside the slope is not damaged. The damage development process of the slope can be evaluated by analyzing the change trend of the peak amplitude of the marginal spectrum of different measuring points under different earthquake excitation conditions.