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.

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.

Implementing Classical Hadamard Transform Algorithm by Continuous Variable Cluster State

Measurement-based one-way quantum computation, which uses cluster states as resources, provides an efficient model to perforrn computation. However, few of the continuous variable （CV） quantum algorithms and classical algorithms based on one-way quantum computation were proposed. In this work, we propose a method to implement the classical Hadamard transform algorithm utilizing the CV cluster state. Compared with classical computation, only half operations are required when it is operated in the one-way CV quantum computer. As an example, we present a concrete scheme of four-mode classical Hadamard transform algorithm with a four-partite CV cluster state. This method connects the quantum computer and the classical algorithms, which shows the feasibility of running classical algorithms in a quantum computer efficiently.

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.

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.

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.

Microstructural Transformation and Precipitation of an Ultra-high Strength Steel under Continuous Cooling

We investigated phase transition and precipitation of ultra-high strength steel（UHSS）in a new ＂short process＂ with controlled rolling and controlled cooling.Thermalexpansion test combined with metallographic observation was used to research the continuous cooling transformation（CCT）curve.Moreover,the microstructuraltransformation and precipitation law was revealed by morphologicalobservation and alloying elements by electron probe micro-analyzer（EPMA）.Transmission electron microscopy（TEM）was utilized to analyze the composition and grain orientation of microstructure.The study showed that the measured criticaltransformation temperatures of Ac1 and Ac3 were 746 and 868 ℃,respectively.The CCT curve indicated that the undercooled austenite was transformed into proeutectoid ferrite and bainite with HV 520 in a broad range of cooling rate 0.1^（-1） ℃·s^（-1）.When subjected to a cooling rate of 1 ℃·s^（-1）,the undercooled austenite was divided into small-sized blocks by formed martensite.With further increase of cooling rate,micro-hardness increased dramatically,the microstructure of specimen was mainly lathe bainite（LB）,granular bainite（GB）,lath martensite（LM）and residualaustenite.By diffraction test analysis,it was identified that there was K-S orientation relationship between martensite and austenite for {110}_α//{111}_γ,{111}_α//{101}_γ.EPMA clearly showed that carbon diffused adequately due to staying for a long time at high temperature with a lower cooling rate of 2 ℃·s-1.Phase transition drive force was lower and the residualaustenite existed in the block form of Martensite austenite island（M-A）.With the increase of cooling rate to 10 ℃·s^（-1）,the block residualaustenite reduced,the carbon content of residualaustenite increased and α phase around the residualaustenite formed into a low carbon bainite form.

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.

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.

A Two-step Inverse Method for Quantitative Damage Evaluation of Plate-like Structures Using Vibration Approach

This study presents a novel two-step approach to assess plate-like structural laminar damages,particularly for delamination damage detection of composite structures.Firstly,a 2-D continuous wavelet transform is employed to identify the damage location and sizes from vibration curvature data.An inverse method is subsequently then used to determine the bending stiffness reduction ratio along a specified direction,enabling the quantification of the delamination severity.The method employed in this study is an extension of the one-dimensional inverse method developed in a previous work of the authors.The applicability of the two-step inverse approach is demonstrated in a simulation analysis and by an experimental study on a cantilever composite plate containing a single delamination.The inverse method is shown to have the capacity to reveal the detailed damage information of delamination within a constrained searching space and can be used to determine the effective flexural stiffness of composite plate structures,even in cases of complex delamination damage.

Precipitation kinetics of NZ30K-Mg alloys based on electrical resistivity measurement

The electrical resistivity of NZ30K-Mg alloy was measured at different heating rates during continuous heating to stud the precipitation kinetics.Two kinds of metastable phases,β＂ and β＇,formed during the heating.Kissinger method and differentia isoconversional method were employed to assess the precipitation kinetic parameters of NZ30K-Mg alloy,activation energy Eα an pre-exponential factor A＇α.The fraction of transformation（α） and the precipitation sequence in NZ30K-Mg alloy were determinec Continuous heating transformation（CHT） and isothermal heating transformation（IHT） diagrams were further obtained for guidin the aging of NZ30K-Mg alloy.The analysis shows that the precipitation kinetic parameters of NZ30K-Mg alloy can be obtaine accurately using isoconversional method.

Continuous Cooling Transformation Behavior and Kinetic Models of Transformations for an Ultra-Low Carbon Bainitic Steel

The aim was to investigate transformation behavior and transformation kinetics of an ultra-low carbon bai- nitic steel during continuous cooling. Continuous cooling transformation （CCT） curves of tested steel were measured by thermal dilatometer and metallographic structures at room temperature were observed by optical microscope. Then transformation kinetic equation of austenite to ferrite as well as austenite to bainite was established by analyzing the relationship of lnln]-l/（1--f）] and lnt in the kinetic equation on the basis of processed experimental data. Finally, the measured and calculated kinetic behaviors of the steel during continuous cooling were compared and growth pat- terns of transformed ferrite and bainite were analyzed. Results showed that calculated result was in reasonable agree- ment with the experimental data. It could be concluded that the growth modes of transformed ferrite and bainite were mainly one dimension as the Avrami exponents were between 1 and 2.

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.

Neutron-gamma discrimination method based on blind source separation and machine learning

The discrimination of neutrons from gamma rays in a mixed radiation field is crucial in neutron detection tasks.Several approaches have been proposed to enhance the performance and accuracy of neutron-gamma discrimination.However,their performances are often associated with certain factors,such as experimental requirements and resulting mixed signals.The main purpose of this study is to achieve fast and accurate neutron-gamma discrimination without a priori information on the signal to be analyzed,as well as the experimental setup.Here,a novel method is proposed based on two concepts.The first method exploits the power of nonnegative tensor factorization(NTF)as a blind source separation method to extract the original components from the mixture signals recorded at the output of the stilbene scintillator detector.The second one is based on the principles of support vector machine(SVM)to identify and discriminate these components.In addition to these two main methods,we adopted the Mexican-hat function as a continuous wavelet transform to characterize the components extracted using the NTF model.The resulting scalograms are processed as colored images,which are segmented into two distinct classes using the Otsu thresholding method to extract the features of interest of the neutrons and gamma-ray components from the background noise.We subsequently used principal component analysis to select the most significant of these features wich are used in the training and testing datasets for SVM.Bias-variance analysis is used to optimize the SVM model by finding the optimal level of model complexity with the highest possible generalization performance.In this framework,the obtained results have verified a suitable bias–variance trade-off value.We achieved an operational SVM prediction model for neutron-gamma classification with a high true-positive rate.The accuracy and performance of the SVM based on the NTF was evaluated and validated by comparing it to the charge comparison method via figure of merit.The results indicate that the proposed approach has a superior discrimination quality(figure of merit of 2.20).

Recognition of Milankovitch cycles in the stratigraphic record: application of the CWT and the FFT to well-log data

The authors applied a the combination of Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT) methods to gamma ray well-log data from the Q3, G1 and D2 wells. This high-resolution stratigraphic study was based on Milankovitch's orbital cycle theory. It was found that the CWT scale factors, ‘a,’ of 12, 24 and 60 match the ratios of the periodicities of precession, obliquity and eccentricity very well. Nine intervals of the Permo-carboniferous strata were recognized to have Milankovitch cycles in them. For example, section A of well Q3 has 29 precession cycles, 15 obliquity cycles and 7 short eccentricity cycles. The wavelengths are 2.7, 4.4 and 7.8 m for precession, obliquity and eccentricity, respectively. Important geological parameters such as the stratigraphic completeness and the accumulation rate were also estimated. These results provide basic information for further cyclostratigraphic correlation studies in the area. They are of great significance for the study of ancient and future climate change.

Identifying Scale-location Specific Control on Vegetation Distribution in Mountain-hill Region

vegetation continuous The scale-location specific control on distribution was investigated through wavelet transforms approaches in subtropical mountain-hill region, Fujian, China. The Normalized Difference Vegetation Index （NDVI） was calculated as an indicator of vegetation greenness using Chinese Environmental Disaster Reduction Satellite images along latitudinal and longitudinal transects. Four scales of variations were identified from the local wavelet spectrum of NDVI, with much stronger wavelet variances observed at larger scales. The characteristic scale of vegetation distribution within mountainous and hilly regions in Southeast China was around 20 km. Significantly strong wavelet coherency was generally examined in regions with very diverse topography, typically characterized as small mountains and hills fractured by rivers and residents. The continuous wavelet based approaches provided valuable insight on the hierarchical structure and its corresponding characteristic scales of ecosystems, which might be applied in defining proper levels in multilevel models and optimal bandwidths in Geographically Weighted Regression.

Complexity analysis of precipitation in changing environment in Chien River Basin,China

The hydrological processes influenced by the multiple factors of climate, geography, vegetation, and human activities are becoming more and more complex, which is an important characteristic of hydrological systems. The different complexity distributions of precipitation processes of the Chien River Basin （a sub-basin of the Minjiang Basin） in two periods （from 1952 to 1980, and from 1981 to 2009） are illustrated using the fractal based on the continuous wavelet transform （CWT）. The results show that （1） at the basin scale the precipitation process in the latter period is more complex than in the former period; （2） the maximum value of the complexity distribution moved from the east to the middle; and （3） through analysis of the time-information and space-information concealed in this complexity change, the precipitation characteristics in the changing environment in the basin can be illuminated. This study could provide a reference for research on disaster pre-warning in changing environments and for integrated water resources management in the local basin.