, 28:4

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

قابلیت تبدیل ارتقاء یافته در مقایسه با تبدیل کلاسیک هیلبرت‌-هوانگ

  • S. RamezaniAffiliated withInternational Institute of Earthquake Engineering and Seismology
  • , O. BaharAffiliated withInternational Institute of Earthquake Engineering and Seismology Email author 



The Hilbert-Huang transform (HHT) consists of empirical mode decomposition (EMD) and Hilbert spectral analysis. EMD, as the key part, decomposes a signal to a set of intrinsic mode functions (IMFs), which satisfy the necessary condition to apply Hilbert spectral analysis. Then, Hilbert spectral analysis, by use of the Hilbert transform, presents time-frequency-amplitude characteristics of the signal in a Hilbert spectrum. The latter part of HHT has some mathematical limitations, which may strongly affect the accuracy and efficacy of the results obtained from the HHT method. Also, noise effects inherently existing in wideband signals result in large scattering on recognition of instantaneous frequencies of the IMFs determined by the Hilbert transform. In addition, the large variation of instantaneous frequencies of the first few IMFs leads to the deteriorated readability of the Hilbert spectrum, especially at higher frequency ranges.

In the present paper, in order to bypass the above mentioned limitations in Hilbert spectral analysis, a new enhanced Hilbert-Huang transform (EHHT), in which the mathematical limitations of the Hilbert spectral analysis are avoided by use of an additional parameter, is employed to reduce noise effects on the instantaneous frequency of IMFs. Four numerical examples are presented in order to demonstrate the efficacy of the enhanced method. In the first case, a two-component, nonstationary signal, with known frequency modulation, is analyzed by the EHHT method to investigate the ability of the method in accurate estimation of frequency in the time domain. In the second case, to examine the accuracy of the enhanced method in estimation of the envelope of frequency, the ambient response of a typical 3- DOF system with known modal frequencies is considered through the EHHT method. To show the effectiveness of EHHT to improve the readability of the time-frequencyamplitude of the wideband signals, the ground motion record of the El Centro earthquake (1940, N—S) is studied, as a third case. Finally, in the fourth case, the ability of EHHT to make an exact 90 degree shift in the phase functions of IMFs is demonstrated. In each case, results of HHT and EHHT are compared together. The case studies indicate that the proposed EHHT method provides more accurate and physically meaningful results than HHT and is able to be applied as an efficient tool for the time-frequency analysis of signals.

Key words

HHT EHHT hilbert spectrum instantaneous frequency T-F-A spectrum phase function