ASTER Data Processing by Discrete Wavelets Transform and Band Ratio Techniques for the Identification of Lineaments and Hydrothermal Alteration Zones in Poli, North Cameroon

The aim of this study is to carry out hydrothermal alteration mapping and structural mapping using ASTER images in order to identify indices that could guide mining exploration work in the Poli area and its surroundings. To achieve this, the ASTER images were first preprocessed to correct atmospheric effects and remove vegetation influence. Secondly, a lineament mapping was conducted by applying Discrete Wavelet Transform (DWT) algorithms to the First Principal Component Analysis (PCA1) of Visible Near-Infrared (VNIR) and Shortwave Infrared (SWIR) bands. Lastly, band ratio methods were applied to the VNIR, SWIR, and Thermal Infrared (TIR) bands to determine indices of iron oxides/hydroxides (hematite and limonite), hydroxyl-bearing minerals (chlorite, epidote, and muscovite), and the quartz index. The results obtained showed that the lineaments were mainly oriented NE-SW, ENE-WSW, and E-W, with NE-SW being the most predominant direction. Concerning hydrothermal alteration, the identified indices covered almost the entire study area and showed a strong correlation with lithological data. Overlaying the obtained lineaments with the hydrothermal alteration indices revealed a significant correlation between existing mining indices and those observed in the field. Mineralized zones generally coincided with areas of high lineament density exhibiting significant hydrothermal alteration. Based on the correlation between existing mining indices and the results of hydrothermal and structural mapping, the results obtained can then be used as a reference document for any mining exploration in the study area.

Application of Wavelets Transform to Fault Detection in Rotorcraft UAV Sensor Failure

This paper describes a novel wavelet-based approach to the detection of abrupt fault of Rotorcrafi Unmanned Aerial Vehicle （RUAV） sensor system. By use of wavelet transforms that accurately localize the characteristics of a signal both in the time and frequency domains, the occurring instants of abnormal status of a sensor in the output signal can be identified by the multi-scale representation of the signal. Once the instants are detected, the distribution differences of the signal energy on all decomposed wavelet scales of the signal before and after the instants are used to claim and classify the sensor faults.

GENERALIZED WAVELETS AND INVERSION OF THE RADON TRANSFORM ON THE LAGUERRE HYPERGROUP

Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.

Wavelet transform for Fresnel-transformed mother wavelets

In this paper, we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation. This motivation can let the mother-wavelet-state itself vary from ｜ψ〉 to Ftr, s ｜ψ〉, except for variation within the family of dilations and translations. The Parseval＇s equality, admissibility condition and inverse transform of this continuous Fresnel-wavelet combinatorial transform are analysed. By taking certain parameters and using the admissibility condition of this continuous Fresnel-wavelet combinatorial transform, we obtain some mother wavelets. A comparison between the newly found mother wavelets is presented.

Research on the longitudinal protection of a through-type cophase traction direct power supply system based on the empirical wavelet transform

This paper proposes a longitudinal protection scheme utilizing empirical wavelet transform(EWT)for a through-type cophase traction direct power supply system,where both sides of a traction network line exhibit a distinctive boundary structure.This approach capitalizes on the boundary’s capacity to attenuate the high-frequency component of fault signals,resulting in a variation in the high-frequency transient energy ratio when faults occur inside or outside the line.During internal line faults,the high-frequency transient energy at the checkpoints located at both ends surpasses that of its neighboring lines.Conversely,for faults external to the line,the energy is lower compared to adjacent lines.EWT is employed to decompose the collected fault current signals,allowing access to the high-frequency transient energy.The longitudinal protection for the traction network line is established based on disparities between both ends of the traction network line and the high-frequency transient energy on either side of the boundary.Moreover,simulation verification through experimental results demonstrates the effectiveness of the proposed protection scheme across various initial fault angles,distances to faults,and fault transition resistances.

Price prediction of power transformer materials based on CEEMD and GRU

The rapid growth of the Chinese economy has fueled the expansion of power grids.Power transformers are key equipment in power grid projects,and their price changes have a significant impact on cost control.However,the prices of power transformer materials manifest as nonsmooth and nonlinear sequences.Hence,estimating the acquisition costs of power grid projects is difficult,hindering the normal operation of power engineering construction.To more accurately predict the price of power transformer materials,this study proposes a method based on complementary ensemble empirical mode decomposition(CEEMD)and gated recurrent unit(GRU)network.First,the CEEMD decomposed the price series into multiple intrinsic mode functions(IMFs).Multiple IMFs were clustered to obtain several aggregated sequences based on the sample entropy of each IMF.Then,an empirical wavelet transform(EWT)was applied to the aggregation sequence with a large sample entropy,and the multiple subsequences obtained from the decomposition were predicted by the GRU model.The GRU model was used to directly predict the aggregation sequences with a small sample entropy.In this study,we used authentic historical pricing data for power transformer materials to validate the proposed approach.The empirical findings demonstrated the efficacy of our method across both datasets,with mean absolute percentage errors(MAPEs)of less than 1%and 3%.This approach holds a significant reference value for future research in the field of power transformer material price prediction.

Adaptive Wavelets Based on Second Generation Wavelet Transform and Their Applications to Trend Analysis and Prediction

In order to make trend analysis and prediction to acquisition data in amechanical equipment condition monitoring system, a new method of trend feature extraction andprediction of acquisition data is proposed which constructs an adaptive wavelet on the acquisitiondata by means of second generation wavelet transform ( SGWT), Firstly, taking the vanishing momentnumber of the predictor as a constraint, the linear predictor and updater are designed according tothe acquisition data by using symmetrical interpolating scheme. Then the trend of the data isobtained through doing SGWT decomposition , threshold processing and SGWT reconstruction. Secondly,under the constraint of the vanishing moment number of the predictor, another predictor based on theacquisition data is devised to predict the future trend of the data using a non-symmetricalinterpolating scheme, A one-step prediction algorithm is presented to predict the future evolutiontrend with historical data. The proposed method obtained a desirable effect in peak-to-peak valuetrend analysis for a machine set in an oil refinery.

Weak Fault Feature Extraction of the Rotating Machinery Using Flexible Analytic Wavelet Transform and Nonlinear Quantum Permutation Entropy

Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform(FAWT)with Nonlinear Quantum Permutation Entropy.FAWT,leveraging fractional orders and arbitrary scaling and translation factors,exhibits superior translational invariance and adjustable fundamental oscillatory characteristics.This flexibility enables FAWT to provide well-suited wavelet shapes,effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults.In our approach,gearbox vibration signals undergo FAWT to obtain sub-bands.Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy,a feature that more accurately characterizes the operational state of vibration simulation signals.The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery.A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method.Comparative assessments with parameters derived from traditional permutation entropy,sample entropy,wavelet transform(WT),and empirical mode decomposition(EMD)underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.

Olive Leaf Disease Detection via Wavelet Transform and Feature Fusion of Pre-Trained Deep Learning Models

Olive trees are susceptible to a variety of diseases that can cause significant crop damage and economic losses.Early detection of these diseases is essential for effective management.We propose a novel transformed wavelet,feature-fused,pre-trained deep learning model for detecting olive leaf diseases.The proposed model combines wavelet transforms with pre-trained deep-learning models to extract discriminative features from olive leaf images.The model has four main phases:preprocessing using data augmentation,three-level wavelet transformation,learning using pre-trained deep learning models,and a fused deep learning model.In the preprocessing phase,the image dataset is augmented using techniques such as resizing,rescaling,flipping,rotation,zooming,and contrasting.In wavelet transformation,the augmented images are decomposed into three frequency levels.Three pre-trained deep learning models,EfficientNet-B7,DenseNet-201,and ResNet-152-V2,are used in the learning phase.The models were trained using the approximate images of the third-level sub-band of the wavelet transform.In the fused phase,the fused model consists of a merge layer,three dense layers,and two dropout layers.The proposed model was evaluated using a dataset of images of healthy and infected olive leaves.It achieved an accuracy of 99.72%in the diagnosis of olive leaf diseases,which exceeds the accuracy of other methods reported in the literature.This finding suggests that our proposed method is a promising tool for the early detection of olive leaf diseases.

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.

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.

The Second-generation Wavelet Transform and its Application in Denoising of Seismic Data

This paper discusses the principle and procedures of the second-generation wavelet transform and its application to the denoising of seismic data. Based on lifting steps, it is a flexible wavelet construction method using linear and nonlinear spatial prediction and operators to implement the wavelet transform and to make it reversible. The lifting scheme transform -includes three steps： split, predict, and update. Deslauriers-Dubuc （4, 2） wavelet transforms are used to process both synthetic and real data in our second-generation wavelet transform. The processing results show that random noise is effectively suppressed and the signal to noise ratio improves remarkably. The lifting wavelet transform is an efficient algorithm.

Application of fast wavelet transformation in signal processing of MEMS gyroscope

Decomposition and reconstruction of Mallat fast wavelet transformation （WT） is described. A fast algorithm, which can greatly decrease the processing burden and can be very easy for hardware implementation in real-time, is analyzed. The algorithm will no longer have the processing of decimation and interpolation of usual WT. The formulae of the decomposition and the reconstruction are given. Simulation results of the MEMS （micro-electro mechanical systems） gyroscope drift signal show that the algorithm spends much less processing time to finish the de-noising process than the usual WT. And the de-noising effect is the same. The fast algorithm has been implemented in a TMS320C6713 digital signal processor. The standard variance of the gyroscope static drift signal decreases from 78. 435 5 （°）/h to 36. 763 5 （°）/h. It takes 0. 014 ms to process all input data and can meet the real-time analysis of signal.

A study of wavelet transforms applied for fracture identification and fracture density evaluation

Combining wavelet transforms with conventional log differential curves is used to identify fractured sections is a new idea.In this paper,we first compute the mother wavelet transform of conventional logs and the wavelet decomposed signals are compared with fractures identified from image logs to determine the fracture-matched mother wavelet.Then the mother wavelet-based decomposed signal combined with the differential curves of conventional well logs create a fracture indicator curve,identifying the fractured zone.Finally the fracture density can be precisely evaluated by the linear relationship of the indicator curve and image log fracture density.This method has been successfully used to evaluate igneous reservoir fractures in the southern Songnan basin and the calculated density from the indicator curve and density from image logs are both basically consistent.

Flight Flutter Modal Parameters Identification with Atmospheric Turbulence Excitation Based on Wavelet Transformation

In view of the feature of flight flutter test data with atmospheric turbulence excitation, a method which combines wavelet transformation with random decrement technique for identifying flight flutter modal parameters is presented. This approach firstly uses random decrement technique to gain free decays corresponding to the acceleration response of the structure to some non-zero initial conditions. Then the continuous Morlet wavelet transformation of the free decays is performed; and the Parseval formula and residue theorem are used to simplify the transformation. The maximal wavelet transformation coefficients in different scales are searched out by means of band-filtering characteristic of Morlet wavelet, and then the modal parameters are identified according to the relationships with maximal modulus and angle of the wavelet transform. In addition, the condition of modal uncoupling is discussed according to variation trend of flight flutter modal parameters in the flight flutter state. The analysis results of simulation and flight flutter test data show that this approach is not only simple, effective and feasible, but also having good noise immunity.

Performance of Wavelet-Transform-Domain Adaptive Equalizers

In this paper performances of wavelet transform domain (WTD) adaptive equalizers based on the least mean￣square (LMS) algorithm are analyzed. The optimum Wiener solution, the condition of convergence, the minimum mean square error (MSE) and the steady state excess MSE of the WTD adaptive equalizer are obtained. Constant and time varying convergence factor adaptive algorithms are studied respectively. Computational complexities of WTD LMS equalizers are given. The equalizer in WTD shows much better convergence performance than that of the conventional in time domain.

Wavelet transform and gradient direction based feature extraction method for off-line handwritten Tibetan letter recognition

To improve the recognition accuracy of off-line handwritten Tibetan characters the local gradient direction histograms based on the wavelet transform are proposed as the recognition features.First for a Tibetan character sample image the first level approximation component of the Haar wavelet transform is calculated.Secondly the approximation component is partitioned into several equal-sized zones. Finally the gradient direction histograms of each zone are calculated and the local direction histograms of the approximation component are considered as the features of the character sample image.The proposed method is tested on the recently developed off-line Tibetan handwritten character sample database.The experimental results demonstrate the effectiveness and efficiency of the proposed feature extraction method.Furthermore compared with the detail components the approximation component contributes more to the recognition accuracy.

Generation of artificial earthquakes for matching target response unsmooth spectrum via wavelet package transform

The seismic records of target response spectrum used in the time-history analysis should be allowed to meet the norms. However, the previous fitting methods of target spectrum are mostly for the situations that the target spectrum is a smooth curve. In many cases, it needs to match unsmooth target spectrum for single determined response spectrum. An adjustment of time history via wavelet packet transform was presented, which is able to fit unsmooth target spectrum. It was found that there is a certain bias between the band center frequency of the component of seismic record after wavelet packet decomposition and the peak frequency of response spectra of wavelet packet components. For this reason, five strategies were presented to select iteration points, and the effects of the five strategies were compared with two calculation examples. It was turned out that the peak frequency of the response spectrum of wavelet packet component can lead to good fitting effect when it is selected as the iteration point. In the iteration process, it shows great promise in fitting non-smooth target spectrum and has a trend of converge.

The Segmentation of FMI Image Based on 2-D Dyadic Wavelet Transform

A key aspect in extracting quantitative information from FMI logs is to segment the FMI image to get images of pores, vugs and fractures. A segmentation method based on the dyadic wavelet transform in 2-D is introduced in this paper. The first step is to find all the edge pixels of the FMI image using the 2-D wavelet transform. The second step is to calculate a segmentation threshold based on the average value of the edge pixels. Field data processing examples show that sub-images of vugs and fractures can be correctly separated from original FMI data continuously and automatically along the depth axis. The image segmentation lays the foundation for in-situ parameter calculation.

Analysis and application of wavelet transform in target imaging and detection of stepped frequency MMW radar

The imaging and target detection methods for stepped frequency signal based on the wavelet transform and its power spectrum are investigated. Not only an imaging and target detection algorithm for stepped frequency signal based on the wavelet transform, but also its respective power spectrum are proposed. The multisampling property of stepped frequency signal is studied and wavelet transform is well suited for analyzing the signal. After multisampling property of stepped frequency signal being studied, it is shown that the wavelet transform is appropriate to analyze the signal. Based on the theory, the wavelet power spectrum analysis is applied to obtain the target range profile and the binary wavelet transform is used to perform target detection. To determine a suitable wavelet scaling for imaging of range profile's MMW radar, the distance resolution ΔR technique is proposed. The effectiveness of this new method is evaluated using simulated noisy radar signal. Results show that the proposed method can bring out the exactness and low computational complexity of this method.