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.

Spectroscopic Leaf Level Detection of Powdery Mildew for Winter Wheat Using Continuous Wavelet Analysis

Powdery mildew （Blumeria graminis） is one of the most destructive crop diseases infecting winter wheat plants, and has devastated millions of hectares of farmlands in China. The objective of this study is to detect the disease damage of powdery mildew on leaf level by means of the hyperspectral measurements, particularly using the continuous wavelet analysis. In May 2010, the reflectance spectra and the biochemical properties were measured for 114 leaf samples with various disease severity degrees. A hyperspectral imaging system was also employed for obtaining detailed hyperspectral information of the normal and the pustule areas within one diseased leaf. Based on these spectra data, a continuous wavelet analysis （CWA） was carried out in conjunction with a correlation analysis, which generated a so-called correlation scalogram that summarizes the correlations between disease severity and the wavelet power at different wavelengths and decomposition scales. By using a thresholding approach, seven wavelet features were isolated for developing models in determining disease severity. In addition, 22 conventional spectral features （SFs） were also tested and compared with wavelet features for their efficiency in estimating disease severity. The multivariate linear regression （MLR） analysis and the partial least square regression （PLSR） analysis were adopted as training methods in model mildew on leaf level were found to be closely related with the development. The spectral characteristics of the powdery spectral characteristics of the pustule area and the content of chlorophyll. The wavelet features performed better than the conventional SFs in capturing this spectral change. Moreover, the regression model composed by seven wavelet features outperformed （R2=0.77, relative root mean square error RRMSE=0.28） the model composed by 14 optimal conventional SFs （R2---0.69, RRMSE--0.32） in estimating the disease severity. The PLSR method yielded a higher accuracy than the MLR method. A combination of CWA and PLSR was found to be promising in providing relatively accurate estimates of disease severity of powdery mildew on leaf level.

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.

The continuous wavelet projections algorithm: A practical spectral-feature-mining approach for crop detection

Spectroscopy can be used for detecting crop characteristics. A goal of crop spectrum analysis is to extract effective features from spectral data for establishing a detection model. An ideal spectral feature set should have high sensitivity to target parameters but low information redundancy among features.However, feature-selection methods that satisfy both requirements are lacking. To address this issue,in this study, a novel method, the continuous wavelet projections algorithm(CWPA), was developed,which has advantages of both continuous wavelet analysis(CWA) and the successive projections algorithm(SPA) for generating optimal spectral feature set for crop detection. Three datasets collected for crop stress detection and retrieval of biochemical properties were used to validate the CWPA under both classification and regression scenarios. The CWPA generated a feature set with fewer features yet achieving accuracy comparable to or even higher than those of CWA and SPA. With only two to three features identified by CWPA, an overall accuracy of 98% in classifying tea plant stresses was achieved, and high coefficients of determination were obtained in retrieving corn leaf chlorophyll content(R^(2)= 0.8521)and equivalent water thickness(R^(2)= 0.9508). The mechanism of the CWPA ensures that the novel algorithm discovers the most sensitive features while retaining complementarity among features. Its ability to reduce the data dimension suggests its potential for crop monitoring and phenotyping with hyperspectral data.

Analysis of realistic rough surface for its globally dominant parameters using continuous wavelets

Continuous Morlet and Mexican hat wavelets are used to analyze a highly irregular rough surface replicated from real turbine blades which are roughened by deposi-tion of foreign materials. The globally dominant aspect ratio, length scale, and orientation of the roughness elements are determined. These parameters extracted from this highly irregular rough surface are important for the future studies of their effects on turbulent flows over this kind of rough surfaces encountered in Washington aerospace and power generating industries.

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.

Quantitative identification of crop disease and nitrogen-water stress in winter wheat using continuous wavelet analysis

It is necessary to quantitatively identify different diseases and nitrogen-water stress for the guidance in spraying specific fungicides and fertilizer applications.The winter wheat diseases,in combination with nitrogen-water stress,are therefore common causes of yield loss in winter wheat in China.Powdery mildew(Blumeria graminis)and stripe rust(Puccinia striiformis f.sp.Tritici)are two of the most prevalent winter wheat diseases in China.This study investigated the potential of continuous wavelet analysis to identify the powdery mildew,stripe rust and nitrogen-water stress using canopy hyperspectral data.The spectral normalization process was applied prior to the analysis.Independent t-tests were used to determine the sensitivity of the spectral bands and vegetation index.In order to reduce the number of wavelet regions,correlation analysis and the independent t-test were used in conjunction to select the features of greatest importance.Based on the selected spectral bands,vegetation indices and wavelet features,the discriminate models were established using Fisher’s linear discrimination analysis(FLDA)and support vector machine(SVM).The results indicated that wavelet features were superior to spectral bands and vegetation indices in classifying different stresses,with overall accuracies of 0.91,0.72,and 0.72 respectively for powdery mildew,stripe rust and nitrogen-water by using FLDA,and 0.79,0.67 and 0.65 respectively by using SVM.FLDA was more suitable for differentiating stresses in winter wheat,with respective accuracies of 78.1%,95.6%and 95.7%for powdery mildew,stripe rust,and nitrogen-water stress.Further analysis was performed whereby the wavelet features were then split into high-scale and low-scale feature subsets for identification.The accuracies of high-scale and low-scale features with an overall accuracy(OA)of 0.61 and 0.73 respectively were lower than those of all wavelet features with an OA of 0.88.The detection of the severity of stripe rust using this method showed an enhanced reliability(R^(2)=0.828).

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.

Comparative Analysis of Wavelet Transform for Time-Frequency Analysis and Transient Localization in Structural Health Monitoring

A critical problem facing data collection in structural health monitoring,for instance via sensor networks,is how to extract the main components and useful features for damage detection.A structural dynamic measurement is more often a complex time-varying process and therefore,is prone to dynamic changes in time-frequency contents.To extract the signal components and capture the useful features associated with damage from such nonstationary signals,a technique that combines the time and frequency analysis and shows the signal evolution in both time and frequency is required.Wavelet analyses have proven to be a viable and effective tool in this regard.Wavelet transform(WT)can analyze different signal components and then comparing the characteristics of each signal with a resolution matched to its scale.However,the challenge is the selection of a proper wavelet since various wavelets with varied properties that are to analyze the same data may result in different results.This article presents a study on how to carry out a comparative analysis based on analytic wavelet scalograms,using structural dynamic acceleration responses,to evaluate the effectiveness of various wavelets for damage detection in civil structures.The scalogram’s informative time-frequency regions are examined to analyze the variation of wavelet coefficients and show how the frequency content of a signal changes over time to detect transient events due to damage.Subsequently,damage-induced changes are tracked with time-frequency representations.Towards this aim,energy distribution and sharing information are investigated.The undamaged and damaged simulated comparative results of a structure reveal that the damaged structure were shifted from the undamaged structure.Also,the Bump wavelet shows the best results than the others.

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.

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.

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.

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.

Changing features of extreme precipitation in the Yangtze River basin during 1961-2002

The total precipitation of the highest 1 day, 3 day, 5 day and 7 day precipitation amount （R1 D, R3D, R5D and R7D） in the Yangtze River basin was analyzed with the help of linear trend analysis and continuous wavelet transform method. The research results indicated that： 1） Spatial distribution of RID is similar in comparison with that of R3D, R5D and R7D. The Jialingjiang and Hanjiang river basins are dominated by decreasing trend, which is significant at 〉95% confidence level in Jialingjiang River basin and insignificant at 〉95% confidence level in Hanjiang River basin. The southern part of the Yangtze River basin and the western part of the upper Yangtze River basin are dominated by significant increasing trend of RID extreme precipitation at 〉95% confidence level. 2） As for the R3D, R5D and R7D, the western part of the upper Yangtze River basin is dominated by significant increasing trend at 〉95% confidence level. The eastern part of the upper Yangtze River basin is dominated by decreasing trend, but is insignificant at 〉95% confidence level. The middle and lower Yangtze River basin is dominated by increasing trend, but insignificant at 〉95% confidence level. 3） The frequency and intensity of extreme precipitation events are intensified over time. Precipitation anomalies indicated that the southeastern part, southern part and southwestern part of the Yangtze River basin are dominated by positive extreme precipitation anomalies between 1993-2002 and 1961-1992. The research results of this text indicate that the occurrence probability of flash flood is higher in the western part of the upper Yangtze River basin and the middle and lower Yangtze River basin, esp. in the southwestern and southeastern parts of the Yangtze River basin.

Deep Spatiotemporal Convolutional-Neural-Network-Based Remaining Useful Life Estimation of Bearings

The remaining useful life(RUL)estimation of bearings is critical for ensuring the reliability of mechanical systems.Owing to the rapid development of deep learning methods,a multitude of data-driven RUL estimation approaches have been proposed recently.However,the following problems remain in existing methods:1)Most network models use raw data or statistical features as input,which renders it difficult to extract complex fault-related information hidden in signals;2)for current observations,the dependence between current states is emphasized,but their complex dependence on previous states is often disregarded;3)the output of neural networks is directly used as the estimated RUL in most studies,resulting in extremely volatile prediction results that lack robustness.Hence,a novel prognostics approach is proposed based on a time-frequency representation(TFR)subsequence,three-dimensional convolutional neural network(3DCNN),and Gaussian process regression(GPR).The approach primarily comprises two aspects:construction of a health indicator(HI)using the TFR-subsequence-3DCNN model,and RUL estimation based on the GPR model.The raw signals of the bearings are converted into TFR-subsequences by continuous wavelet transform and a dislocated overlapping strategy.Subsequently,the 3DCNN is applied to extract the hidden spatiotemporal features from the TFR-subsequences and construct HIs.Finally,the RUL of the bearings is estimated using the GPR model,which can also define the probability distribution of the potential function and prediction confidence.Experiments on the PRONOSTIA platform demonstrate the superiority of the proposed TFR-subsequence-3DCNN-GPR approach.The use of degradation-related spatiotemporal features in signals is proposed herein to achieve a highly accurate bearing RUL prediction with uncertainty quantification.