Performance of Continuous Wavelet Transform over Fourier Transform in Features Resolutions

This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic data obtained from the Tano Basin in West Africa, Ghana. The research focuses on a comparative analysis of image clarity in seismic attribute analysis to facilitate the identification of reservoir features within the subsurface structures. The findings of the study indicate that CWT has a significant advantage over FFT in terms of image quality and identifying subsurface structures. The results demonstrate the superior performance of CWT in providing a better representation, making it more effective for seismic attribute analysis. The study highlights the importance of choosing the appropriate image enhancement technique based on the specific application needs and the broader context of the study. While CWT provides high-quality images and superior performance in identifying subsurface structures, the selection between these methods should be made judiciously, taking into account the objectives of the study and the characteristics of the signals being analyzed. The research provides valuable insights into the decision-making process for selecting image enhancement techniques in seismic data analysis, helping researchers and practitioners make informed choices that cater to the unique requirements of their studies. Ultimately, this study contributes to the advancement of the field of subsurface imaging and geological feature identification.

DETECTION OF INCIPIENT LOCALIZED GEAR FAULTS IN GEARBOX BY COMPLEX CONTINUOUS WAVELET TRANSFORM

As far as the vibration signal processing is concerned, composition ofvibration signal resulting from incipient localized faults in gearbox is too weak to be detected bytraditional detecting technology available now. The method, which includes two steps: vibrationsignal from gearbox is first processed by synchronous average sampling technique and then it isanalyzed by complex continuous wavelet transform to diagnose gear fault, is introduced. Twodifferent kinds of faults in the gearbox, i.e. shaft eccentricity and initial crack in tooth fillet,are detected and distinguished from each other successfully.

PARAMETERS OPTIMIZATION OF CONTINUOUS WAVELET TRANSFORM AND ITS APPLICATION IN ACOUSTIC EMISSION SIGNAL ANALYSIS OF ROLLING BEARING

Morlet wavelet is suitable to extract the impulse components of mechanical fault signals. And thus its continuous wavelet transform （CWT） has been successfully used in the field of fault diagnosis. The principle of scale selection in CWT is discussed. Based on genetic algorithm, an optimization strategy for the waveform parameters of the mother wavelet is proposed with wavelet entropy as the optimization target. Based on the optimized waveform parameters, the wavelet scalogram is used to analyze the simulated acoustic emission （AE） signal and real AE signal of rolling bearing. The results indicate that the proposed method is useful and efficient to improve the quality of CWT.

Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding letter （2007 Opt. Lett. 32 554） we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.

COMPUTATION OF CONTINUOUS WAVELET TRANSFORM AT DYADIC SCALES BY SUBDIVISION SCHEME

A new algorithm to compute continuous wavelet transforms at dyadic scales is proposed here. Our approach has a similar implementation with the standard algorithme a trous and can coincide with it in the one dimensional lower order spline case.Our algorithm can have arbitrary order of approximation and is applicable to the multidimensional case.We present this algorithm in a general case with emphasis on splines anti quast in terpolations.Numerical examples are included to justify our theorerical discussion.

Natural frequencies and damping estimation based on continuous wavelet transform

The continuous wavelet transform(CWT)based method was improved for estimating the natural frequencies and damping ratios of a structural system in this paper.The appropriate scale of CWT was selected by means of the least squares method to identify the systems with closely spaced modes.The important issues related to estimation accuracy such as mode separation and end effect,were also investigated.These issues were associated with the parameter selection of wavelet function based on the fitting error of least squares.The efficiency of the method was confirmed by applying it to a simulated 3dof damped system with two close modes.

The Time-Frequency Energy Attenuation Factor and Its Application on the Basis of Gauss Linear Frequency-Modulated Continuous Wavelet Transform

Based on the Gauss linear frequency modulated wavelet transform, a new characteristic index is presented, namely time frequency energy attenuation factor which can reflect the difference features of waveform in earthquake focus mechanism, wave traveling path and its attenuation characteristics in focal area or near field. In order to test its validity, we select the natural earthquakes and explosion or collapse events whose focus mechanisms vary obviously,and some natural earthquakes located at the same site or in a very small area. The study indicates that the time frequency energy attenuation factors of the natural earthquakes are obviously different with that of explosion or collapse events, and the change of the time frequency energy attenuation factors is relatively stable for the earthquakes under the normal seismicity background. Using the above mentioned method, it is expected to offer a useful criterion for strong earthquake prediction by continuous earthquake observation.

Estimating inter-area dominant oscillation mode in bulk power grid using multi-channel continuous wavelet transform

This paper proposes a novel continuous wavelet transform(CWT) based approach to holistically estimate the dominant oscillation using measurement data from multiple channels. CWT has been demonstrated to be effective in estimating power system oscillation modes.Using singular value decomposition(SVD) technique, the original huge phasor measurement unit(PMU) datasets are compressed to finite useful measurement data which contain critical dominant oscillation information. Further,CWT is performed on the constructed measurement signals to form wavelet coefficient matrix(WCM) at the same dilation. Then, SVD is employed to decompose the WCMs to obtain the maximum singular value and its right eigenvector. A singular value vector with the entire dilation is constructed through the maximum singular values. The right eigenvector corresponding to the maximum singular value in the singular-value vector is adopted as the input of CWT to estimate the dominant modes. Finally, the proposed approach is evaluated using the simulation data from China Southern Power Grid(CSG) as well as the actual field-measurement data retrieved from the PMUs of CSG.The simulation results demonstrate that the proposed approach performs well to holistically estimate the dominant oscillation modes in bulk power systems.

CONTINUOUS WAVELET TRANSFORM OF TURBULENT BOUNDARY LAYER FLOW

The spatio-temporal characteristics of the velocity fluctuations in a fully-developed turbulent boundary layer flow was investigated using hotwire. A low-speed wind tunnel was established. The experimental data was extensively analyzed in terms of continuous wavelet transform coefficients and their auto-correlation. The results yielded a potential wealth of information on inherent characteristics of coherent structures embedded in turbulent boundary layer flow. Spatial and temporal variations of the low- and high- frequency motions were revealed.

Cylindrical Guided Wave Signals for Underground Pipe Inspection using Different Continuous Wavelet Mother Functions

Over the past decade, wavelets provided a powerful and flexible set of tools for handling fundamental problems in science and engineering. Wavelet analyses are being used for solving problems in different engineering areas like audio de-noising, signal compression, object detection, image decomposition, speech recognition etc. Wavelet analysis employs orthonormal as well as non-orthonornal functions. This research investigates the effectiveness of wavelet analysis in detecting defects in underground steel pipe networks. Continuous Wavelet Transforms （CWT） has been performed on the received signals of cylindrical guided waves. Cylindrical Guided waves are generated and propagated through the pipe wall boundaries in a pitch-catch system. Piezo-electric transducers are used to generate as well as receive guided waves. Several mother wavelet functions such as Daubechies, Symlet, Coiflet and Meyer have been used for the Continuous Wavelet Transform to investigate the most suitable function for defect detection. This research also investigates the effect of surrounding soil on wavelet transforms for different mother wavelet functions.

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.

Low-power Analog VLSI Implementation of Wavelet Transform

For applications requiring low-power,low-voltage and real-time,a novel analog VLSI implementation of continuous Marr wavelet transform based on CMOS log-domain integrator is proposed. Marr wavelet is approximated by a parameterized class of function and with Levenbery-Marquardt nonlinear least square method,the optimum parameters of this function are obtained. The circuits of implementating Marr wavelet transform are composed of analog filter whose impulse response is the required wavelet. The filter design is based on IFLF structure with CMOS log-domain integrators as the main building blocks. SPICE simulations indicate an excellent approximations of ideal wavelet.

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.

An ensemble learning method to retrieve sea ice roughness from Sentinel-1 SAR images

Sea ice surface roughness(SIR)affects the energy transfer between the atmosphere and the ocean,and it is also an important indicator for sea ice characteristics.To obtain a small-scale SIR with high spatial resolution,a novel method is proposed to retrieve SIR from Sentinel-1 synthetic aperture radar(SAR)images,utilizing an ensemble learning method.Firstly,the two-dimensional continuous wavelet transform is applied to obtain the spatial information of sea ice,including the scale and direction of ice patterns.Secondly,a model is developed using the Adaboost Regression model to establish a relationship among SIR,radar backscatter and the spatial information of sea ice.The proposed method is validated by using the SIR retrieved from SAR images and comparing it to the measurements obtained by the Airborne Topographic Mapper(ATM)in the summer Beaufort Sea.The determination of coefficient,mean absolute error,root-mean-square error and mean absolute percentage error of the testing data are 0.91,1.71 cm,2.82 cm,and 36.37%,respectively,which are reasonable.Moreover,K-fold cross-validation and learning curves are analyzed,which also demonstrate the method’s applicability in retrieving SIR from SAR images.

Phase-unwrapping algorithm combined with wavelet transform and Hilbert transform in self-mixing interference for individual microscale particle detection

The self-mixing interferometry(SMI)technique is an emerging sensing technology in microscale particle classification.However,due to the nature of the SMI effect raised by a microscattering particle,the signal analysis suffers from many problems compared with a macro target,such as lower signal-to-noise ratio(SNR),short transit time,and time-varying modulation strength.Therefore,the particle sizing measurement resolution is much lower than the one in typical displacement measurements.To solve these problems,in this paper,first,a theoretical model of the phase variation of a singleparticle SMI signal burst is demonstrated in detail.The relationship between the phase variation and the particle size is investigated,which predicts that phase observation could be another alternative for particle detection.Second,combined with continuous wavelet transform and Hilbert transform,a novel phase-unwrapping algorithm is proposed.This algorithm can implement not only efficient individual burst extraction from the noisy raw signal,but also precise phase calculation for particle sizing.The measurement shows good accuracy over a range from 100 nm to 6μm with our algorithm,proving that our algorithm enables a simple and reliable quantitative particle characteristics retrieval and analysis methodology for microscale particle detection in biomedical or laser manufacturing fields.

A novel method for gamma spectrum analysis of low-level and intermediate-level radioactive waste

The uncertainty of nuclide libraries in the analysis of the gamma spectra of low-and intermediate-level radioactive waste(LILW)using existing methods produces unstable results.To address this problem,a novel spectral analysis method is proposed in this study.In this method,overlapping peaks are located using a continuous wavelet transform.An improved quadratic convolution method is proposed to calculate the widths of the peaks and establish a fourth-order filter model to estimate the Compton edge baseline with the overlapping peaks.Combined with the adaptive sensitive nonlinear iterative peak,this method can effectively subtracts the background.Finally,a function describing the peak shape as a filter is used to deconvolve the energy spectrum to achieve accurate qualitative and quantitative analyses of the nuclide without the aid of a nuclide library.Gamma spectrum acquisition experiments for standard point sources of Cs-137 and Eu-152,a segmented gamma scanning experiment for a 200 L standard drum,and a Monte Carlo simulation experiment for triple overlapping peaks using the closest energy of three typical LILW nuclides(Sb-125,Sb-124,and Cs-134)are conducted.The results of the experiments indicate that(1)the novel method and gamma vision(GV)with an accurate nuclide library have the same spectral analysis capability,and the peak area calculation error is less than 4%;(2)compared with the GV,the analysis results of the novel method are more stable;(3)the novel method can be applied to the activity measurement of LILW,and the error of the activity reconstruction at the equivalent radius is 2.4%;and(4)The proposed novel method can quantitatively analyze all nuclides in LILW without a nuclide library.This novel method can improve the accuracy and precision of LILW measurements,provide key technical support for the reasonable disposal of LILW,and ensure the safety of humans and the environment.

Revealing True and False Brain States Based on Wavelet Analysis of Electroencephalogram

Statement of the Problem: As you know, there exist two different states in the brain’s mental activity: true and false. In recent years, a progressive method of wavelet transformation of the electroencephalogram (EEG) has been developed, which enabled us to establish the fundamental possibility of direct objective registration of the human brain’s mental activity. Earlier, we created an experimental model and software for recognizing true and false mental responses of a person based on the EEG wavelet transformation and described it in the article. The developed experimental model and information software made it possible to compare the two mental states of brain activity by electroencephalographic indicators, one of which is false and the other is true. The goal is to develop a fundamentally new information technology for recognizing true and false states in the brain’s mental activity based on the wavelet transformation of the electroencephalogram. Results: It was revealed that the true and false states of the brain can be distinguished using the method of continuous wavelet transformation and calculation of the EEG wavelet energy. It is shown that the main differences between true and false mental responses are observed in the delta and alpha ranges of the EEG. In the EEG delta rhythm, the wavelet energy is reliably higher in case of a false answer compared to a true one. In the EEG alpha rhythm, the wavelet energy is significantly higher with a true answer than a false one. Practical significance of the research: The data obtained open up the fundamental possibility of identifying true and false mental states of the brain on the basis of continuous wavelet transformation and calculation of the EEG wavelet energy.

Characteristics of Surface Water Quality Affected by Agricultural Non-point Sources in Guigang City

[Objectives]To analyze the influence characteristics of surface water quality by agricultural non-point sources in Guigang City of Guangxi.[Methods]The daily concentration series of water quality indicators at three state-controlled monitoring stations in Guigang City from^(2)019 to 2021 was analyzed by using Daubechies(db)wavelet,and Morlet wavelet was used to analyze the daily average concentration of water quality indicators.Continuous wavelet transform(CWT)was used to analyze the monthly concentration series of water quality indicators at three state-controlled monitoring stations in Guigang City from^(2)014 to 2021.[Results]The Daubechies(db)wavelet analysis showed that the concentrations of COD_(Mn),TP,and TN had the maximum values during June-July and October-November,and there were spatial differences among monitoring stations(COD_(Mn) concentration exceeding the standard was the most serious in Shizui,and DO concentration not up to standard was the most in Thermal Power Plant,and NH_(3)-N,TP and TN exceeding the standard was the most in Wulin Ferry).Morlet results showed that principal period of wavelet variance graphs of COD_(Mn),NH_(3)-N,and TP was 340 d,and there was the same sub-period of 140 d,and principal period of wavelet variance graph of DO was 260 d.CWT results showed that COD_(Cr) had similar resonance periods of about 1-2 and 5-7 months;BOD 5 and COD_(Mn) was dominant by the resonance period of 1-4 months(2014-2017);DO had a similar resonance period of about 1-3 months;NH_(3)-N was dominant by the resonance period of 1-5 months.[Conclusions]The surface water quality of Guigang City was mainly affected by the residual nitrogen and phosphorus nutrients and pesticide residues from agricultural production activities.

A Monitoring Method for Transmission Tower Foots Displacement Based on Wind-Induced Vibration Response

The displacement of transmission tower feet can seriously affect the safe operation of the tower,and the accuracy of structural health monitoring methods is limited at the present stage.The application of deep learning method provides new ideas for structural health monitoring of towers,but the current amount of tower vibration fault data is restricted to provide adequate training data for Deep Learning(DL).In this paper,we propose a DT-DL based tower foot displacement monitoring method,which firstly simulates the wind-induced vibration response data of the tower under each fault condition by finite element method.Then the vibration signal visualization and Data Transfer(DT)are used to add tower fault data samples to solve the problem of insufficient actual data quantity.Subsequently,the dynamic response test is carried out under different tower fault states,and the tower fault monitoring is carried out by the DL method.Finally,the proposed method is compared with the traditional online monitoring method,and it is found that this method can significantly improve the rate of convergence and recognition accuracy in the recognition process.The results show that the method can effectively identify the tower foot displacement state,which can greatly reduce the accidents that occurred due to the tower foot displacement.

Rolling Bearing Fault Diagnosis Based On Convolutional Capsule Network

Fault diagnosis technology has been widely applied and is an important part of ensuring the safe operation of mechanical equipment.In response to the problem of frequent faults in rolling bearings,this paper designs a rolling bearing fault diagnosis method based on convolutional capsule network(CCN).More specifically,the original vibration signal is converted into a two-dimensional time–frequency image using continuous wavelet transform(CWT),and the feature extraction is performed on the two-dimensional time–frequency image using the convolution layer at the front end of the network,and the extracted features are input into the capsule network.The capsule network converts the extracted features into vector neurons,and the dynamic routing algorithm is used to achieve feature transfer and output the results of fault diagnosis.Two different datasets are used to compare with other traditional deep learning models to verify the fault diagnosis capability of the method.The results show that the CCN has good diagnostic capability under different working conditions,even in the presence of noise and insufficient samples,compared to other models.This method contributes to the safe and reliable operation of mechanical equipment and is suitable for other rotating scenarios.