Variational Mode Decomposition-Informed Empirical Wavelet Transform for Electric Vibrator Noise Analysis

Electric vibrators find wide applications in reliability testing, waveform generation, and vibration simulation, making their noise characteristics a topic of significant interest. While Variational Mode Decomposition (VMD) and Empirical Wavelet Transform (EWT) offer valuable support for studying signal components, they also present certain limitations. This article integrates the strengths of both methods and proposes an enhanced approach that integrates VMD into the frequency band division principle of EWT. Initially, the method decomposes the signal using VMD, determining the mode count based on residuals, and subsequently employs EWT decomposition based on this information. This addresses mode aliasing issues in the original method while capitalizing on VMD’s adaptability. Feasibility was confirmed through simulation signals and ultimately applied to noise signals from vibrators. Experimental results demonstrate that the improved method not only resolves EWT frequency band division challenges but also effectively decomposes signal components compared to the VMD method.

Study on Rhizome Crops by Fourier Transform Infrared Spectroscopy Combined with Wavelet Analysis

In order to distinguish 8 kinds of rhizome crops, the 40 samples were studied by Fourier transform infrared spectroscopy （FTIR） combined with wavelet transform （WT）, principal component analysis （PCA） and hieramhical cluster analysis （HCA）. The results showed that the infrared spectra were similar on the whole, but there were differences in peak position, peak shape and peak absorption intensity in the range of 1 800-700 cm-1. The infrared spectra in the range of 1 800-700 cm-1 were selected to perform continuous wavelet transform （CWT） and discrete wavelet transform （DWT）. The 15th-Ievel decomposition coefficients of CWT and the 5=-level detail coefficients of DWT were classified by PCA and HCA. The cumulative contri- bution rates of the first three principal components of CWT and DWT were 93.12% and 89.78%, respectively. The accurate recognition rates of PCA and HCA were all 100%. It is proved that FTIR combined with WT can be used to distinguish different kinds of rhizome crops.

ELECTROCHEMICAL NOISE ANALYSIS OF PURE ALUMINUM IN SODIUM CHLORIDE SOLUTION WITH WAVELET TRANSFORM TECHNIQUE

Wavelet transforms (WT) are proposed as an alternative tool to overcome the limitations of Fourier transforms (FFT) in the analysis of electrochemical noise (EN) data. The most relevant feature of this method of analysis is its capability of decomposing electrochemical noise records into different sets of wavelet coefficients, which contain information about the time scale characteristic of the associated corrosion event. In this context, the potential noise fluctuations during the free corrosion of pure aluminum in sodium chloride solution was recorded and analyzed with wavelet transform technique. The typical results showed that the EN signal is composed of distinct type of events, which can be classified according to their scales, i.e. their time constants. Meanwhile, the energy distribution plot (EDP) can be used as 'fingerprints' of EN signals and can be very useful for analyzing EN data in the future.

SIGNAL FEATURE EXTRACTION BASED UPON INDEPENDENT COMPONENT ANALYSIS AND WAVELET TRANSFORM

It is an important precondition for machine fault diagnosis that vibrationsignal can be extracted effectively. Based on the characteristic of noise interfused during thecourse of sampling vibration signal, independent component analysis (ICA) method is combined withwavelet to de-noise. Firstly, The sampled signal can be separated with ICA, then the function offrequency band chosen with multi-resolution wavelet transform can be used to judge whether thestochastic disturbance singular signal is interfused. By these ways, the vibration signals can beextracted effectively, which provides favorable condition for subsequent feature detection ofvibration signal and fault diagnosis.

RESEARCH OF WAVELET TRANSFORM INSTRUMENT SYSTEM FOR SIGNAL ANALYSIS

After brief describing the Principle of wavelet transform (WT) of signals, a new signals analysis system based on wavelet transform is introduced. The design and development of the instryment of wavelet transform are described. A number of practical uses of this system demonstrate that wavelet transform system is specially functional in identifying and processing impulse, singular and non-smooth signals, so that it should be evaluated the most advanced signal analyzing system.

Blind Separation of Speech Signals Based on Wavelet Transform and Independent Component Analysis

Speech signals in frequency domain were separated based on discrete wavelet transform (DWT) and independent component analysis (ICA). First, mixed speech signals were decomposed into different frequency domains by DWT and the subbands of speech signals were separated using ICA in each wavelet domain; then, the permutation and scaling problems of frequency domain blind source separation (BSS) were solved by utilizing the correlation between adjacent bins in speech signals; at last, source signals were reconstructed from single branches. Experiments were carried out with 2 sources and 6 microphones using speech signals at sampling rate of 40 kHz. The microphones were aligned with 2 sources in front of them, on the left and right. The separation of one male and one female speeches lasted 2.5 s. It is proved that the new method is better than single ICA method and the signal to noise ratio is improved by 1 dB approximately.

Hilbert-Huang transform and wavelet analysis of time history signal

The brief theories of wavelet analysis and Hilbert-Huang transform (HHT) are introduced firstly in the present paper. Then several signal data were analyzed by using wavelet and HHT methods, respectively. The comparison shows that HHT is not only an effective method for analyzing non-stationary data, but also is a useful tool for examining detailed characters of time history signal.

Numerical solution of Poisson equation with wavelet bases of Hermite cubic splines on the interval

A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite element analysis. The lifting scheme of the wavelet-based finite element method is discussed in detail. For the orthogonal characteristics of the wavelet bases with respect to the given inner product, the corresponding multi-scale finite element equation can be decoupled across scales, totally or partially, and suited for nesting approximation. Numerical examples indicate that the proposed method has the higher efficiency and precision in solving the Poisson equation.

Rolling Element Bearing Diagnostics by Combination of Envelope Analysis and Wavelet Transform

Rolling element-bearing diagnostics has been studied over the last thirty years, and envelope analysis is widely recognized as being the best approach for detection and diagnosis of rolling element bearing incipient failure. But one of the on-going difficulties with envelope technique is to determine the best frequency band to envelop. Here, wavelet transform technique is introduced into envelope analysis to solve the problem by capturing bearing defects-sensory scales (i.e. frequency bands). A modulated Gaussian function is chosen to be the analytical wavelet because it coincides well with bearing defect-induced vibration signal patterns. Vibration signals measured from railway bearing tests were studied by the proposed method. Cases of bearings with single and multiple defects on inner and outer race under different testing conditions are presented. Experimental results showed that the proposed method allowed a more accurate local description and separation of transient signal part, which were caused by impacts between defects and the mating surfaces in the bearing. The combination method provides an effective signal detection technique for rolling element-bearing diagnostics.

Fault Feature Extraction of Rotating Machinery Based on Wavelet Transformation and Multi-resolution Analysis

This paper expounded in detail the principle of energy spectrum analysis based on discrete wavelet transformation and multiresolution analysis. In the aspect of feature extraction method study, with investigating the feature of impact factor in vibration signals and considering the non-placidity and non-linear of vibration diagnosis signals, the authors import wavelet analysis and fractal theory as the tools of faulty signal feature description. Experimental results proved the validity of this method. To some extent, this method provides a good approach of resolving the wholesome problem of fault feature symptom description.

Wavelet analysis and its application to signal processing

The construction of basic wavelet was discussed and many basic analyzing wavelets was compared. Acomplex analyzing wavelet which is continuous, smoothing, orthogonal and exponential decreasing was presented, andit was used to decompose two blasting seismic signals with the continuous wavelet transforms (CWT). The resultshows that wavelet analysis is the better method to help us determine the essential factors which create damage effectsthan Fourier analysis.

Analysis of corrosion behavior of LY12 in sodium chloride solution with wavelet transform technique

Wavelet transforms(WT) are proposed as an alternative tool to overcome the limitations of fast Fourier transforms(FFT) in the analysis of electrochemical noise(EN) data. The most relevant feature of this method of analysis is its capability of decomposing electrochemical noise records into different sets of wavelet coefficients(distinct type of events), which contains information about the time scale characteristic of the associated corrosion event. In this context, the potential noise fluctuations during the free corrosion of commercial aluminum alloy LY12 in sodium chloride solution was recorded and analyzed with wavelet transform technique. The typical results show that the EN signal is composed of distinct type of events, which can be classified according to their scales, i.e. their time constants. Meanwhile, the energy distribution plot(EDP) can be used as "fingerprints" of EN signals and can be very useful for analyzing EN data in the future.

GAP STRUCTURE ANALYSIS OF FOREST TRANSECT USINGTHE 1-D DISCRETE WAVELET TRANSFORM

Wavelets is a very effective technique for time-frequency analysis with the ability of preserving loeal information, applied to many areas such as nonlinear science, information processing.quantum physics etc.. In this paper. from the view of ecology spatial pattern, the authors try to process the sample data of Larix forest transects to identify the canopy gap structures by wavelet analysis. The caleulation of wavelet variance, derived from the transtform facilitates comparison based on dominant scale of pattern between multiple datasets such as the stands described.

Application and Analysis of Wavelet Transform in Image Edge Detection

For the image processing technology, technicians have been looking for a convenient and simple detection method for a long time, especially for the innovation research on image edge detection technology. Because there are a lot of original information at the edge during image processing, thus, we can get the real image data in terms of the data acquisition. The usage of edge is often in the case of some irregular geometric objects, and we determine the contour of the image by combining with signal transmitted data. At the present stage, there are different algorithms in image edge detection, however, different types of algorithms have divergent disadvantages so It is diffi cult to detect the image changes in a reasonable range. We try to use wavelet transformation in image edge detection, making full use of the wave with the high resolution characteristics, and combining multiple images, in order to improve the accuracy of image edge detection.

Multi-Focus Image Fusion Based on Wavelet Transformation

In the fusion of image,how to measure the local character and clarity is called activity measurement. According to the problem,the traditional measurement is decided only by the high-frequency detail coefficients, which will make the energy expression insufficient to reflect the local clarity. Therefore,in this paper,a novel construction method for activity measurement is proposed. Firstly,it uses the wavelet decomposition for the fusion resource image, and then utilizes the high and low frequency wavelet coefficients synthetically. Meantime,it takes the normalized variance as the weight of high-frequency energy. Secondly,it calculates the measurement by the weighted energy,which can be used to measure the local character. Finally,the fusion coefficients can be got. In order to illustrate the superiority of this new method,three kinds of assessing indicators are provided. The experiment results show that,comparing with the traditional methods,this new method weakens the fuzzy and promotes the indicator value. Therefore,it has much more advantages for practical application.

Local Extrema of Periodic Function’s Wavelet Transform

The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wavelet, and research the local extreme point and extrema of the wavelet transform on periodic function for the collection of signal＇ s instantaneous amplitude and period.

Determination of micro yttrium in an ytterbium matrix by inductively coupled plasma atomic emission spectrometry and wavelet transform

In the determination of trace yttrium (Y) in an ytterbium (Yb) matrix byinductively coupled plasma atomic emission spectrometry (ICP-AES), the most prominent line ofyttrium, Y 371.030 nm line, suffers from strong interference due to an emission line of ytterbium.In mis work, a method based on wavelet transform was proposed for the spectral interferencecorrection. Haar wavelet was selected as the mother wavelet. The discrete detail after the thirddecomposition, D3, was chosen for quantitative analysis based on the consideration of bothseparation degree and peak height. The linear correlation coefficient between the height of the leftpositive peak in D3 and the concentration of Y was calculated to be 0.9926. Six synthetic sampleswere analyzed, and the recovery for yttrium varied from 96.3 percent to 110.0 percent. The amountsof yttrium in three ytterbium metal samples were determined by the proposed approach with an averagerelative standard deviation (RSD) of 2.5 percent, and the detection limit for yttrium was 0.016percent. This novel correction technique is fast and convenient, since neither complicated modelassumption nor time-consuming iteration is required. Furthermore, it is not affected by thewavelength drift inherent in monochromators that will severely reduce the accuracy of resultsobtained by some chemometric methods.

Transient-Spatial Pattern Mining of Eddy Current Pulsed Thermography Using Wavelet Transform

Eddy current pulsed thermography（ECPT） is an emerging Non-destructive testing and evaluation（NDT E） technique, which uses hybrid eddy current and thermography NDT E techniques that enhances the detectability from their compensation. Currently, this technique is limited by the manual selection of proper contrast frames and the issue of improving the efficiency of defect detection of complex structure samples remains a challenge. In order to select a specific frame from transient thermal image sequences to maximize the contrast of thermal variation and defect pattern from complex structure samples, an energy driven approach to compute the coefficient energy of wavelet transform is proposed which has the potential of automatically selecting both optimal transient frame and spatial scale for defect detection using ECPT. According to analysis of the variation of different frequency component and the comparison study of the detection performance of different scale and wavelets, the frame at the end of heating phase is automatically selected as an optimal transient frame for defect detection. In addition, the detection capabilities of the complex structure samples can be enhanced through proper spatial scale and wavelet selection. The proposed method has successfully been applied to low speed impact damage detection of carbon fibre reinforced polymer（CFRP） composite as well as providing the guidance to improve the detectability of ECPT technique.

Study of the Functions of Wavelet Packet Transform （WPT） and Continues Wavelet Transform （CWT） in Recognizing the Damage Specification

Modem and efficient methods focus on signal analysis and have drawn researchers＇ attention to it in recent years. These methods mainly include Continuous Wavelet and Wavelet Packet transforms. The main advantage of the application of these Wavelets is their capacity to analyze the signal position in different occasions and places. However, in sites with high frequencies its resolution becomes much more difficult. Wavelet packet transform is a more advanced form of continuous wavelets and can make a perfect level by level resolution for each signal. Although very few studies have been done in the field. In order to do this, in the present study, f^st there was an attempt to do a modal analysis on the structure by the ANSYS finite elements software, then using MATLAB, the wavelet was investigated through a continuous wavelet analysis. Finally the results were displayed in 2-D location-coefficient figures. In the second form, transient-dynamic analysis was done on the structure to find out the characteristics of the damage and the wavelet packet energy rate index was suggested. The results indicate that suggested index in the second form is both practical and applicable, and also this index is sensitive to the intensity of the damage.

Blind source separation of multichannel electroencephalogram based on wavelet transform and ICA

Combination of the wavelet transform and independent component analysis （ICA） was employed for blind source separation （BSS） of multichannel electroencephalogram （EEG）. After denoising the original signals by discrete wavelet transform, high frequency components of some noises and artifacts were removed from the original signals. The denoised signals were reconstructed again for the purpose of ICA, such that the drawback that ICA cannot distinguish noises from source signals can be overcome effectively. The practical processing results showed that this method is an effective way to BSS of multichannel EEG. The method is actually a combination of wavelet transform with adaptive neural network, so it is also useful for BBS of other complex signals.