Comparative study of Hilbert–Huang transform, Fourier transform and wavelet transform in pavement profile analysis

Abstract

This study employs the Hilbert–Huang transform (HHT), the wavelet transform and the Fourier transform to analyse the road surface profiles of three pavement profiles. The wavelet and Fourier transforms have been the traditional spectral analysis methods, but they are predicated on a priori selection of basis functions that are either of infinite length or have fixed finite widths. The central idea of HHT is the empirical mode decomposition, which decomposes a signal into basis functions called the intrinsic mode functions (IMFs). The Hilbert transform can then be applied to the IMFs to generate an energy–time–frequency spectrum called the Hilbert spectrum. The strength of HHT is the ability to process non-stationary and non-linear data. Unlike the Fourier transform, which transforms information from the time domain into the frequency domain, the HHT does not lose temporal information after transformation, i.e. energy–frequency information is maintained in the time domain. This paper attempts to reveal the frequency and energy content of the road profile data with the three methods mentioned as a means to establishing the most suitable way of characterising the pavement profiles in terms of ride quality. In performing the analyses, the nature and behaviour of the road profiles as indicated by the literature are taken into account, that road profiles are non-stationary and are inherently non-Gaussian. It is demonstrated that HHT offers more flexibility in terms of detailed profile analysis and description, which can be beneficial to pavement profile analysts in understanding the effects on vehicle vibrations and ride quality.

Keywords:

• Hilbert-Huang transform
• pavement profiles
• international roughness index