Fatigue Data Analysis Using Continuous Wavelet Transform and Discrete Wavelet Transform

2011 ◽  
Vol 462-463 ◽  
pp. 461-466 ◽  
Author(s):  
Shahrum Abdullah ◽  
S.N. Sahadan ◽  
Mohd Zaki Nuawi ◽  
Zulkifli Mohd Nopiah
Keyword(s):  
Wavelet Transform ◽  
Data Analysis ◽  
Discrete Wavelet Transform ◽  
Wavelet Transforms ◽  
Data Extraction ◽  
Morlet Wavelet ◽  
Analysis Time ◽  
Discrete Wavelet ◽  
Continuous Wavelet ◽  
Fatigue Data

The wavelet transform is well known for its ability in vibration analysis in fault detection. This paper presents the ability of wavelet transform in fatigue data analysis starts from high amplitude events detection and it is then followed by fatigue data extraction based on wavelet coefficients. Since the wavelet transform has two main categories, i.e. the continuous wavelet transforms (CWT) and the discrete wavelet transform (DWT), the comparison study were carried out in order to investigate performance of both wavelet for fatigue data analysis. CWT represents by the Morlet wavelet while DWT with the form of the 4th Order Daubechies wavelet (Db4) was also used for the analysis. An analysis begins with coefficients plot using the time-scale representation that associated to energy coefficients plot for the input value in fatigue data extraction. Ten extraction levels were used and all levels gave the damage difference, (%∆D) less than 10% with respect to original signal. From the study, both wavelet transforms gave almost similar ability in editing fatigue data but the Morlet wavelet provided faster analysis time compared to the Db4 wavelet. In comparison to have the value of different at 5%, the Morlet wavelet achieved at L= 5 while the Db4 wavelet at L=7. Even though it gave slower analysis time, both wavelets can be used in fatigue data editing but at different time consuming.

scholarly journals The Improvement of Discrete Wavelet Transform

2021 ◽  
Author(s):  
Zhihua Zhang
Keyword(s):  
Wavelet Transform ◽  
Decay Rate ◽  
Discrete Wavelet Transform ◽  
Wavelet Transforms ◽  
Polynomial Interpolation ◽  
Discrete Wavelet ◽  
Two Dimensional ◽  
Wavelet Coefficients ◽  
Periodic Wavelet ◽  
Improved Algorithm

Discrete wavelet transform and discrete periodic wavelet transform have been widely used in image compression and data approximation. Due to discontinuity on the boundary of original data, the decay rate of the obtained wavelet coefficients is slow. In this study, we use the combination of polynomial interpolation and one-dimensional/two-dimensional discrete periodic wavelet transforms to mitigate boundary effects. The decay rate of the obtained wavelet coefficients in our improved algorithm is faster than that of traditional two-dimensional discrete wavelet transform. Moreover, our improved algorithm can be extended naturally to the higher-dimensional case.

ON-LINE HEALTH MONITORING AND DAMAGE DETECTION OF STRUCTURES BASED ON THE WAVELET TRANSFORM

2008 ◽  
Vol 08 (03) ◽  
pp. 367-387 ◽  
Author(s):  
B. ZHU ◽  
A. Y. T. LEUNG ◽  
C. K. WONG ◽  
W. Z. LU
Keyword(s):  
Wavelet Transform ◽  
Damage Detection ◽  
Discrete Wavelet Transform ◽  
Health Monitoring ◽  
Continuous Wavelet Transform ◽  
Abrupt Change ◽  
Discrete Wavelet ◽  
Continuous Wavelet ◽  
Random Decrement Technique ◽  
On Line

Presented herein is an experiment that aims to investigate the applicability of the wavelet transform to damage detection of a beam–spring structure. By burning out the string that is connected to the cantilever beam, high-frequency oscillations are excited in the beam–spring system, and there results an abrupt change or impulse in the discrete-wavelet-transformed signal. In this way, the discrete wavelet transform can be used to recognize the damage at the moment it occurs. In the second stage of damage detection, the shift of frequencies and damping ratios is identified by the continuous wavelet transform so as to ensure that the abrupt change or impulse in the signal from the discrete wavelet transform is a result of the damage and not the noise. For the random forced vibration, the random decrement technique is used on the original signal to obtain the free decaying responses, and then the continuous wavelet transform is applied to identify the system parameters. Some developed p version elements are used for the parametric studies on the first stage of health monitoring and to find the damage location. The results show that the two-stage method is successful in damage detection. Since the method is simple and computationally efficient, it is a good candidate for on-line health monitoring and damage detection of structures.

PERFECT-TRANSLATION-INVARIANT CUSTOMIZABLE COMPLEX DISCRETE WAVELET TRANSFORM

2013 ◽  
Vol 11 (04) ◽  
pp. 1360003 ◽  
Author(s):  
HIROSHI TODA ◽  
ZHONG ZHANG ◽  
TAKASHI IMAMURA
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Frequency Domain ◽  
Wavelet Transforms ◽  
Wavelet Packet ◽  
Variable Density ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Translation Invariant ◽  
High Degree

The theorems, giving the condition of perfect translation invariance for discrete wavelet transforms, have already been proven. Based on these theorems, the dual-tree complex discrete wavelet transform, the 2-dimensional discrete wavelet transform, the complex wavelet packet transform, the variable-density complex discrete wavelet transform and the real-valued discrete wavelet transform, having perfect translation invariance, were proposed. However, their customizability of wavelets in the frequency domain is limited. In this paper, also based on these theorems, a new type of complex discrete wavelet transform is proposed, which achieves perfect translation invariance with high degree of customizability of wavelets in the frequency domain.

scholarly journals Development of an Efficient Indoor Optical System using Different Wavelet Transforms

2021 ◽  
Author(s):  
Ankita Aggarwal ◽  
Gurmeet Kaur
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Communication System ◽  
Wavelet Transforms ◽  
Low Frequency ◽  
Digital Signal ◽  
Fluorescent Light ◽  
Discrete Wavelet ◽  
Stationary Wavelet Transform ◽  
Light Interference

For an effective communication system whether indoor or outdoor, the most important concern is minimum noise. In this paper, an efficient noise reduction technique is presented using various wavelet transform techniques for indoor optical wireless communication system (IOWC). In IOWC system, Fluorescent Light Interference (FLI) is main source of noise. Here, in this paper three methods are used to reduce the effect of noise from a digital signal. These are Discrete Wavelet Transform (DWT), Stationary Wavelet transform (SWT) and Discrete Wavelet transform-Stationary Wavelet Transform (DWT-SWT). Through sub band coding in DWT the signal is decomposed into lower sub bands of high and low frequency respectively of unequal size; while in SWT the decomposed signal have sub bands of equal size. In DWT-SWT the high frequency components of both DWT and SWT are added. Using Pulse Position Modulation, the comparison between these three techniques is described here to enhance the overall performance of the IOWC system.

Visualization of Shear Stress With Micro Imaging Chip and Discrete Wavelet Transform

2002 ◽  
Vol 124 (4) ◽  
pp. 1018-1024 ◽  
Author(s):  
Motoaki Kimura ◽  
Masahiro Takei ◽  
Chih-Ming Ho ◽  
Yoshifuru Saito ◽  
Kiyoshi Horii
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Wavelet Transforms ◽  
Wave Number ◽  
Discrete Wavelet ◽  
Two Dimensional ◽  
Micro Electro Mechanical Systems ◽  
Low Speed

The two-dimensional low-speed structure of a turbulent boundary layer has been clearly visualized by a combination of a shear stress sensor using micro electro mechanical systems and the discrete wavelet transform. The application of two-dimensional discrete wavelet transforms to the visualization of wall shear stress data obtained using the micro shear stress imaging chip is described. The experiment was carried out under various Reynolds number conditions. It is shown that it is possible to visualize the low-speed streak structure as contours of two-dimensional wavelet level corresponding to spanwise wave number as a function of Reynolds number.

Image Denoising Using Wavelet Transform and Wavelet Transform with Enhanced Diversity

2011 ◽  
Vol 403-408 ◽  
pp. 866-870
Author(s):  
Vaibhav Nigam ◽  
Smriti Bhatnagar ◽  
Sajal Luthra
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Image Denoising ◽  
Wavelet Transforms ◽  
Signal To Noise Ratio ◽  
Practical Implementation ◽  
Discrete Wavelet ◽  
Maximum Output ◽  
Denoising Method ◽  
Detail Coefficient

This paper is a comparative study of image denoising using previously known wavelet transform and new type of wavelet transform, namely, Diversity enhanced discrete wavelet transform. The Discrete Wavelet Transform (DWT) has two parameters: the mother wavelet and the number of iterations. For every noisy image, there is a best pair of parameters for which we get maximum output Peak Signal to Noise Ratio, PSNR. As the denoising algorithms are sensitive to the parameters of the wavelet transform used, in this paper comparison of DEDWT to DWT has been presented. The diversity is enhanced by computing wavelet transforms with different parameters. After the filtering of each detail coefficient, the corresponding wavelet transforms are inverted and the estimated image, having a higher PSNR, is extracted. To benchmark against the best possible denoising method three thresholding techniques have been compared. In this paper we have presented a more practical, implementation oriented work.

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