Discrete Wavelet Transform Decomposition Research Articles

Wavelet-Based Multiresolution Analysis of Pavement Profiles as a Diagnostic Tool

Discrete wavelet transform (DWT) was proposed as a new diagnostic tool for locating various frequency-related features of profiles, such as repeated waves and short-lived surface distress, that affect ride quality. The shortcomings of power spectrum density (PSD) analysis in evaluating the distribution of energy of a profile between various frequency bandwidths were pointed out. The theoretical background and the basics of the DWT decomposition algorithm are discussed. Advantages of DWT analysis over PSD analysis in detection of short-lived features of the profile are illustrated by an example. The results of both the PSD and DWT analyses of three profile data, taken from data collected as a part of an ongoing research project sponsored by New Jersey Department of Transportation, are presented. The results indicate that DWT analysis can capture both short-lived high-frequency and long-lived low-frequency features of the profile and, consequently, provides a better representation of the profile characteristics. The application of DWT in the development of new ride indices is also discussed.

Wavelet-Based Multiresolution Analysis of Pavement Profiles as a Diagnostic Tool

Discrete wavelet transform (DWT) was proposed as a new diagnostic tool for locating various frequency-related features of profiles, such as repeated waves and short-lived surface distress, that affect ride quality. The shortcomings of power spectrum density (PSD) analysis in evaluating the distribution of energy of a profile between various frequency band-widths were pointed out. The theoretical background and the basics of the DWT decomposition algorithm are discussed. Advantages of DWT analysis over PSD analysis in detection of short-lived features of the profile are illustrated by an example. The results of both the PSD and DWT analyses of three profile data, taken from data collected as a part of an ongoing research project sponsored by New Jersey Department of Transportation, are presented. The results indicate that DWT analysis can capture both short-lived high-frequency and long-lived low-frequency features of the profile and, consequently, provides a better representation of the profile characteristics. The application of DWT in the development of new ride indices is also discussed.

GEARBOX FAULT DIAGNOSIS USING ADAPTIVE WAVELET FILTER

Vibration signals from a gearbox are usually noisy. As a result, it is difficult to find early symptoms of a potential failure in a gearbox. Wavelet transform is a powerful tool to disclose transient information in signals. An adaptive wavelet filter based on Morlet wavelet is introduced in this paper. The parameters in the Morlet wavelet function are optimised based on the kurtosis maximisation principle. The wavelet used is adaptive because the parameters are not fixed. The adaptive wavelet filter is found to be very effective in detection of symptoms from vibration signals of a gearbox with early fatigue tooth crack. Two types of discrete wavelet transform (DWT), the decimated with DB4 wavelet and the undecimated with harmonic wavelet, are also used to analyse the same signals for comparison. No periodic impulses appear on any scale in either DWT decomposition.

Discrete wavelet transform: data dependence analysis and synthesis of distributed memory and control array architectures

We perform a thorough data dependence and localization analysis for the discrete wavelet transform algorithm and then use it to synthesize distributed memory and control architectures for its parallel computation. The discrete wavelet transform (DWT) is characterized by a nonuniform data dependence structure owing to the decimation operation it is neither a uniform recurrence equation (URE) nor an affine recurrence equation (ARE) and consequently cannot be transformed directly using linear space-time mapping methods into efficient array architectures. Our approach is to apply first appropriate nonlinear transformations operating on the algorithm's index space, leading to a new DWT formulation on which application of linear space-time mapping can become effective. The first transformation of the algorithm achieves regularization of interoctave dependencies but alone does not lead to efficient array solutions after the mapping due to limitations associated with transforming the three-dimensional (3-D) algorithm onto one-dimensional (1-D) arrays, which is also known as multiprojection. The second transformation is introduced to remove the need for multiprojection by formulating the regularized DWT algorithm in a two-dimensional (2-D) index space. Using this DWT formulation, we have synthesized two VLSI-amenable linear arrays of LPEs computing a 6-octave DWT decomposition with latencies of M and 2M-1, respectively, where L is the wavelet filter length, and M is the number of samples in the data sequence. The arrays are modular, regular, use simple control, and can be easily extended to larger L and J. The latency of both arrays is independent of the highest octave J, and the efficiency is nearly 100% for any M with one design achieving the lowest possible latency of M.