Crack evaluation is essential for effective classification of pavement cracks. Digital images of pavement cracks have been analyzed using techniques such as fuzzy set theory and neural networks. Bidimensional empirical mode decomposition (BEMD), a new image analysis method recently developed, can potentially be used for pavement crack evaluation. BEMD is an extension of the empirical mode decomposition (EMD), which can decompose nonlinear and nonstationary signals into basis functions called intrinsic mode functions (IMFs). IMFs are monocomponent functions that have well-defined instantaneous frequencies. EMD is a sifting process that is nonparametric and data driven; it does not depend on an a priori basis set. It is able to remove noise from signals without complicated convolution processes. BEMD decomposes an image into two-dimensional IMFs. The present paper explores pavement crack detection using BEMD together with the Sobel edge detector. A number of images are filtered with BEMD to remove noise, and the residual image analyzed with the Sobel edge detector for crack detection. The results are compared with results from the Canny edge detector, which uses a Gaussian filter for image smoothing before performing edge detection. The objective is to qualitatively explore how well BEMD is able to smooth an image for more effective edge detection with the Sobel method.
Information extraction from time series has traditionally been done with Fourier analysis, which use stationary sines and cosines as basis functions. However, data that come from most natural phenomena are mostly nonstationary. A totally adaptive alternative method has been developed called the Hilbert–Huang transform (HHT), which involves generating basis functions called the intrinsic mode functions (IMFs) via the empirical mode decomposition (EMD). The EMD is a numerical procedure that is prone to numerical errors that may persist in the decomposition as extra IMFs. In this study, results of numerical experiments are presented, which would establish a stringent threshold by which relevant IMFs are distinguished from IMFs that may have been generated by numerical errors. The threshold is dependent on the correlation coefficient between the IMFs and the original signal. Finally, the threshold is applied to IMFs of earthquake signals from five accelerometers located in a building.
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 energytime-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.
Scattered data interpolation is an essential part of bidimensional empirical mode decomposition (BEMD) of an image. In the decomposition process, local maxima and minima of the image are extracted at each iteration and then interpolated to form the upper and the lower envelopes, respectively. The number of two-dimensional intrinsic mode functions resulting from the decomposition and their properties are highly dependent on the method of interpolation. Though a few methods of interpolation have been tested and/or applied to the BEMD process, many others remain to be tested. This paper evaluates the performance of some of the widely used surface interpolation techniques to identify one or more good choices of such methods for envelope estimation in BEMD. The interpolation techniques studied in this paper include various radial basis function interpolators and Delaunay triangulation based interpolators. The analysis is done first using a synthetic texture image and then using two different real texture images. Simulations are made to focus mainly on the effect of interpolation methods by providing less or negligible control on the other parameters or factors of the BEMD process.
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