Wavelet Decomposition Coefficients Research Articles

Fault line selection algorithm for single-phase grounding faults in distribution networks based on multi-feature fusion of multi-level wavelet decomposition coefficients

Fault line selection algorithm for single-phase grounding faults in distribution networks based on multi-feature fusion of multi-level wavelet decomposition coefficients

Research on Removing Image Noise and Distortion in Machine Dial Recognition

This study aims to address the issues of image noise and distortion in machine dial recognition via initial denoising. A wavelet local threshold denoising method that combines high-frequency wavelet coefficients with wavelet decomposition coefficients in various directions is proposed. This method shows good results on 102 images of car dashboards, aircraft instrument panels, spacecraft displays, and dial instruments on robots. Although a few denoised images exhibit distortion due to intense lighting or heavy contamination, the denoising accuracy for the remaining images is 98.04%, demonstrating substantial practical value. Future research will concentrate on addressing complex image noise and structures.

A maximum-likelihood-based approach to estimate the long memory parameter using fractional spline wavelets

Fractional spline wavelets act as fractional differentiators for essentially low-pass signals, which is a useful property to analyze time series with fractal behavior. Moreover, under suitable scaling of wavelet coefficients, one can whiten a fractional Gaussian noise inputted in the wavelet channels. In this article, we demonstrate the two former statements and, by employing them, propose a method based on maximum likelihood to estimate the long-memory parameter using fractional spline wavelets. The proposed estimator exhibits competitive behavior in terms of mean squared error in the simulation studies we conducted, dominating all other methods as the sample size increases. In empirical applications, the proposed method outperformed other approaches in 10 of 12 evaluations for three different time series. Moreover, the proposed method allows for estimation in a continuous search grid, even when the Hurst coefficient lies outside of stationarity boundaries, which is a clear advantage over many algorithms: in such cases, the proposed method displays a stable behavior and an increasing outperformance margin. We also propose an identification procedure for the persistence or antipersistence of a given signal, based on the energy concentration of the coefficients of wavelet decomposition and its theoretical properties.

ОПТИМІЗАЦІЯ АЛГОРИТМУ ПАКЕТНОЇ ВЕЙВЛЕТ-ФІЛЬТРАЦІЇ СИГНАЛІВ

A wavelet packet filtering algorithm has been developed, which includes cyclic movement along the branches of the wavelet packet tree with a constraint on each branch of the approximation and detail coefficients until the minimum root-mean-square error is attained, with the optimal parameters of the wavelet threshold and threshold function. To calculate the root-mean-square error of filtering, after each cycle of processing the wavelet decomposition coefficients, the signal is reconstructed in the time domain. In the next cycle, the received signal is decomposed into approximation and detail coefficients until the root-mean-square error reaches a minimum for all possible values of the basic wavelet-threshold and the threshold function. The study was conducted with twenty of the most commonly used signals, including signals with linear and non-linear frequencies. To confirm the efficiency of packet wavelet filtering, a comparative analysis with the known methods based on a common threshold of detail coefficients at all levels of wavelet decomposition is given. Keywords: wavelet analysis, packet wavelet filtering, entropy, threshold function, threshholding.

Legendre Multiwavelet Transform and Its Application in Bearing Fault Detection

Bearing failures often result from compound faults, where the characteristics of these compound faults span across multiple domains. To tackle the challenge of extracting features from compound faults, this paper proposes a novel fault detection method based on the Legendre multiwavelet transform (LMWT) combined with envelope spectrum analysis. Additionally, to address the issue of identifying suitable wavelet decomposition coefficients, this paper introduces the concept of relative energy ratio. This ratio assists in identifying the most sensitive wavelet coefficients associated with fault frequency bands. To assess the performance of the proposed method, the results obtained from the LMWT method are compared with those derived from the empirical wavelet transform (EWT) method using different datasets. Experimental findings demonstrate that the proposed method exhibits more effective frequency spectrum segmentation and superior detection performance across various experimental conditions.

A wavelet analysis method to retrieve thermal conductivity and radiative properties of intense extinction and low conductive medium

The accurate acquisition of the physical properties of strongly extinction materials limits their application development. In order to solve the problem of large errors in the high temperature measurement of these materials, this paper constructs an inversion model for the radiative and conductive coupled heat transfer through wavelet decomposition coefficients, and compares it with traditional methods. The radiative and conductive coupled heat transfer model is solved by finite volume method and Monte Carlo method. Daubechies nine wavelet is used for signal wavelet analysis. It has been discovered that the wavelet decomposition parameters of the temperature field are mainly concentrated in the 4–8 wavelet frequency band of wavelet, it can separate from the random error that is mainly concentrated in the 1–3 frequency band of wavelet. Most of physical properties like the heating power, convective heat transfer coefficient, material thermal conductivity, extinction coefficient has a great impact on the waveform and amplitude of wavelet detail coefficient and approximation coefficient, and the change trend of approximation coefficient and detail coefficient amplitude is consistent with the trend of temperature field. However, the effect of scattering albedo on wavelet parameters is tiny. Through inversion, it is found that the inversion model based on wavelet decomposition parameters of 5–7 frequency band has higher accuracy when random error exists.

Local theory for 2‐microlocal Besov and Triebel–Lizorkin spaces of Jaffard type

AbstractIn this paper, we introduce new 2‐microlocal Besov and Triebel–Lizorkin spaces of Jaffard type, which contain many classical functions. We establish local theory of these function spaces by the φ‐transform and the wavelet decomposition coefficients. Moreover, we give a characterization of these local spaces by a local polynomial approximation.

Starlet higher order statistics for galaxy clustering and weak lensing

We present a first application to photometric galaxy clustering and weak lensing of wavelet-based multi-scale (beyond two points) summary statistics: starlet peak counts and starlet ℓ1-norm. Peak counts are the local maxima in the map, and ℓ1-norm is computed via the sum of the absolute values of the starlet (wavelet) decomposition coefficients of a map, providing a fast multi-scale calculation of the pixel distribution, encoding the information of all pixels in the map. We employ the cosmo-SLICS simulations sources and lens catalogues, and we compute wavelet-based non-Gaussian statistics in the context of combined probes and their potential when applied to the weak-lensing convergence maps and galaxy maps. We obtain forecasts on the matter density parameter Ωm, the reduced Hubble constant h, the matter fluctuation amplitude σ8, and the dark energy equation of state parameter w0. In our setting for this first application, we consider the two probes to be independent. We find that the starlet peaks and the ℓ1-norm represent interesting summary statistics that can improve the constraints with respect to the power spectrum, even in the case of photometric galaxy clustering and when the two probes are combined.

Nested DWT–Based CNN Architecture for Monocular Depth Estimation

Applications such as medical diagnosis, navigation, robotics, etc., require 3D images. Recently, deep learning networks have been extensively applied to estimate depth. Depth prediction from 2D images poses a problem that is both ill-posed and non-linear. Such networks are computationally and time-wise expensive as they have dense configurations. Further, the network performance depends on the trained model configuration, the loss functions used, and the dataset applied for training. We propose a moderately dense encoder-decoder network based on discrete wavelet decomposition and trainable coefficients (LL, LH, HL, HH). Our Nested Wavelet-Net (NDWTN) preserves the high-frequency information that is otherwise lost during the downsampling process in the encoder. Furthermore, we study the effect of activation functions, batch normalization, convolution layers, skip, etc., in our models. The network is trained with NYU datasets. Our network trains faster with good results.

Remote Fault Identification and Analysis in Electrical Distribution Network Using Artificial Intelligence

This research describes a method for wavelet decomposition and machine learning-based fault site classification in a radial power distribution network. The first statistical observation is produced using wavelet decomposition and wavelet-based detailed coefficients in terms of Kurtosis and Skewness parameters. For this objective, six distinct machine learning methods are deployed. They are evaluated and compared using unknown data sets with varying degrees of unpredictability. One approach has been shown to be the most accurate in locating the location of the problem bus.

Improvement of Wheat Growth Information by Fusing UAV Visible and Thermal Infrared Images

To improve and enrich the wheat growth information, visible and thermal infrared (TIR) remote sensing images were simultaneously acquired by an unmanned aerial vehicle (UAV). A novel algorithm was proposed for fusing the visible and TIR images combing the intensity hue saturation (IHS) transform and regional variance matching (RVM). After registering the two images, IHS transform was first conducted to derive the Intensities of two images. Wavelet transform was then applied to the Intensities for obtaining the coefficients of low- and high-frequency sub-bands. The fusion rules of the fused image were developed based on regional correlation of wavelet decomposition coefficients. More specifically, the coefficients of low-frequency sub-bands were calculated by averaging the coefficients of two images. Regional variance was used to generate the coefficients of high-frequency sub-bands using the weighted template of a 3 × 3 pixel window. The inverse wavelet transform was used to create the new Intensity for the fused image using the low- and high-frequency coefficients. Finally, the inverse IHS transform consisting of the new Intensity, the Hue of visible image, and the Saturation of TIR image was adopted to change the IHS space to red–green–blue (RGB) color space. The fusion effects were validated by the visible and TIR images of winter wheat at the jointing stage and the middle and late grain-filling stage. Meanwhile, IHS and RV were also comparatively evaluated for validating our proposed method. The proposed algorithm can fully consider the correlation of wavelet coefficients in local regions. It overcomes the shortcomings (e.g., block phenomenon, color distortion) of traditional image fusion methods to obtain smooth, detailed and high-resolution images.

Reliability and validity analysis of personality assessment model based on gait video.

Personality affects an individual’s academic achievements, occupational tendencies, marriage quality and physical health, so more convenient and objective personality assessment methods are needed. Gait is a natural, stable, and easy-to-observe body movement that is closely related to personality. The purpose of this paper is to propose a personality assessment model based on gait video and evaluate the reliability and validity of the multidimensional model. This study recruited 152 participants and used cameras to record their gait videos. Each participant completed a 44-item Big Five Inventory (BFI-44) assessment. We constructed diverse static and dynamic time-frequency features based on gait skeleton coordinates, interframe differences, distances between joints, angles between joints, and wavelet decomposition coefficient arrays. We established multidimensional personality trait assessment models through machine learning algorithms and evaluated the criterion validity, split-half reliability, convergent validity, and discriminant validity of these models. The results showed that the reliability and validity of the Gaussian process regression (GPR) and linear regression (LR) models were best. The mean values of their criterion validity were 0.478 and 0.508, respectively, and the mean values of their split-half reliability were all greater than 0.8. In the formed multitrait-multimethod matrix, these methods also had higher convergent and discriminative validity. The proposed approach shows that gait video can be effectively used to evaluate personality traits, providing a new idea for the formation of convenient and non-invasive personality assessment methods.

Matrix-based wavelet transformation embedded in recurrent neural networks for wind speed prediction

Accurate wind speed forecasts are essential for wind energy applications. It is challenging to accurately anticipate wind speed because of its high volatility and non-stationarity. Although wavelet transformation-based hybrid models, the most representative hybrid models, are extensively used, the endpoint effect and fixed decomposition parameters limit their prediction accuracy. To enhance the performance of such models, a special end-to-end model architecture combined with wavelet decomposition in matrix form and recurrent neural networks (RNNs) is proposed. In addition, a two-stage training optimization approach is presented to prevent the characteristics of the wavelet decomposition coefficients from vanishing during model training. In this framework, three conventional RNNs, consisting of the standard RNN, the long short-term memory network (LSTM), and the gated recurrent units network (GRU), are utilized to construct three innovative models, referred to as MW-RNN, MW-RNN, and MW-GRU, respectively. Then, using two years of data from a site, the recommended models are contrasted with the standard ones. The results show that the recommended models beat traditional ones in a variety of error indices with just a slight increase in training costs. Additionally, the impacts of wavelet decomposition parameters on forecast accuracy are contrasted, and suggested settings for actual wind speed predictions are offered.

Cumulant analysis in wavelet space for studying effects of aging on electrical activity of the brain

Multiresolution wavelet analysis with thorough processing of decomposition coefficients using a set of cumulants is proposed as a way to improve the characterization of complex dynamics based on experimental data. The application of this approach for quantification the effects of aging in the responses of the electrical activity of the brain to fine motor tasks (clenching the fist) is considered. It is shown that young and elderly adults have significant differences in reactions to this type of movements carried out by the dominant and non-dominant hand. The characterization of inter-group distinctions using the skewness and kurtosis of the probability distribution of the wavelet decomposition coefficients outperforms the diagnostics of age-related differences based on standard deviation of this distribution.

Fault Detection of the Harmonic Reducer Based on CNN-LSTM With a Novel Denoising Algorithm

The harmonic reducer is a key component of the industrial robot. Its reliability has significant influence on the consecutive operation of the industrial robot. However, its failure rate is high due to the complicated internal structure and long-term working conditions of large load and high torque. To identify the fault type of the harmonic reducer under different working conditions, this article proposes the joint wavelet regional correlation threshold denoising (WRCTD) algorithm and convolutional neural network-long short term memory (CNN-LSTM) fault detection method. Firstly, the WRCTD algorithm utilizes the regional correlation of the wavelet decomposition coefficients and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\sigma $ </tex-math></inline-formula> criterion to suppress noise in the raw sensor data. Then, the CNN-LSTM model could mine hidden features of the processed sensor data to identify fault correctly. To evaluate the proposed method, the vibration signals of the harmonic reducer under different working conditions are collected by establishing a test rig. Comparative experimental results show that the proposed WRCTD algorithm can significantly improve the accuracy of the fault detection method. The specific values for the CNN-LSTM method and the LSTM method are 9.5% and 12.2%, respectively. In addition, the proposed CNN-LSTM method has better performance than traditional methods. It achieves the fault detection over 94.0%, which is 1.5%, 2.0%, 2.0%, 1.9%, and, 1.9% higher than the highest accuracy values of CNN, LSTM, and SVM methods in five experiments.

МАРКИРОВКА НЕПОДВИЖНЫХ ИЗОБРАЖЕНИЙ С ИСПОЛЬЗОВАНИЕМ ФРАКТАЛЬНОГО ГАУССОВСКОГО ШУМА И ДВУМЕРНОГО ДИСКРЕТНОГО ВЕЙВЛЕТ ПРЕОБРАЗОВАНИЯ ДЛЯ ЗАЩИТЫ АВТОРСКИХ ПРАВ

Introduction. The relevance of copyright protection for multimedia content is determined by the using digital objects in all areas of life. The number and qualification of malefactors aimed at using someone else's intellectual work is constantly growing. The problem of copyright protection can be solved by using steganography methods. Despite the wide development of the topic, there are a number of problems that limit the use of classical steganography methods. The resistance of many well-known methods to unauthorized access is based on knowledge of the algorithm without the use of additional keys. This leaves the methods vulnerable to modification and removal of the embedded label by an intruder. The aim of the study is to increase the stability of copyright protection algorithms from unauthorized access. It is proposed to embed watermarks in two stages: at the first stage, the digital watermark values are replaced by sequences of fractal Gaussian noise, then the resulting fractal key is embedded in the protected image by replacing the wavelet decomposition coefficients. Methods: The fast Fourier transform algorithm was used to generate fractal Gaussian noise. The Hurst exponent of noise sequences was estimated using R/S analysis. Results: A new algorithm for embedding digital watermarks into images based on fractal Gaussian noise and discrete wavelet transform is proposed. The values of rational parameters of the algorithm, such as the decomposition level, the scaling factor, the length of the noise sequence, the values of the Hurst exponent for a single sequence, and the threshold value, are determined to achieve the best balance between the quality of embedding and extraction.

Minimization of errors in discrete wavelet filtering of signals during ultrasonic measurements and testing

Error minimizing methods for discrete wavelet filtering of ultrasonic meter signals are considered. For this purpose, special model signals containing various measuring pulses are generated. The psi function of the Daubechies 28 wavelet is used to generate the pulses. Noise is added to the generated pulses. A comparative analysis of the two filtering algorithms is performed. The first algorithm is to limit the amount of detail of the wavelet decomposition coefficients in relation to signal interference. The minimum value of the root mean square error of wavelet decomposition signal deviation which is restored at each level from the initial signal without noise is determined. The second algorithm uses a separate threshold for each level of wavelet decomposition to limit the magnitude of the detail coefficients that are proportional to the standard deviation. Like in the first algorithm, the task is to determine the level of wavelet decomposition at which the minimum standard error is achieved. A feature of both algorithms is an expanded base of discrete wavelets ‒ families of Biorthogonal, Coiflet, Daubechies, Discrete Meyer, Haar, Reverse Biorthogonal, Symlets (106 in total) and threshold functions garotte, garrote, greater, hard, less, soft (6 in total). The model function uses random variables in both algorithms, so the averaging base is used to obtain stable results. Given features of algorithm construction allowed to reveal efficiency of ultrasonic signal filtering on the first algorithm presented in the form of oscilloscopic images. The use of a separate threshold for limiting the number of detail coefficients for each level of discrete wavelet decomposition using the given wavelet base and threshold functions has reduced the filtering error.

A new method of vibration signal denoising based on improved wavelet

Noise cancellation is one of the most successful applications of the wavelet transform. Its basic idea is to compare wavelet decomposition coefficients with the given thresholds and only keep those bigger ones and set those smaller ones to zero and then do wavelet reconstruction with those new coefficients. It is most likely for this method to treat some useful weak components as noise and eliminate them. Based on the cyclostationary property of vibration signals of rotating machines, a novel wavelet noise cancellation method is proposed. A numerical signal and an experimental signal of rubbing fault are used to test and compare the performances of the new method and the conventional wavelet based denoising method provided by MATLAB. The results show that the new noise cancellation method can efficaciously suppress the noise component at all frequency bands and has better denoising performance than the conventional one.

Cotton stubble detection based on wavelet decomposition and texture features

BackgroundAt present, the residual film pollution in cotton fields is crucial. The commonly used recycling method is the manual-driven recycling machine, which is heavy and time-consuming. The development of a visual navigation system for the recovery of residual film is conducive, in order to improve the work efficiency. The key technology in the visual navigation system is the cotton stubble detection. A successful cotton stubble detection can ensure the stability and reliability of the visual navigation system.MethodsFirstly, it extracts the three types of texture features of GLCM, GLRLM and LBP, from the three types of images of stubbles, residual films and broken leaves between rows. It then builds three classifiers: Random Forest, Back Propagation Neural Network and Support Vector Machine in order to classify the sample images. Finally, the possibility of improving the classification accuracy using the texture features extracted from the wavelet decomposition coefficients, is discussed.ResultsThe experiment proves that the GLCM texture feature of the original image has the best performance under the Back Propagation Neural Network classifier. As for the different wavelet bases, the vertical coefficient texture feature of coif3 wavelet decomposition, combined with the texture feature of the original image, is the feature having the best classification effect. Compared with the original image texture features, the classification accuracy is increased by 3.8%, the sensitivity is increased by 4.8%, and the specificity is increased by 1.2%.ConclusionsThe algorithm can complete the task of stubble detection in different locations, different periods and abnormal driving conditions, which shows that the wavelet coefficient texture feature combined with the original image texture feature is a useful fusion feature for detecting stubble and can provide a reference for different crop stubble detection.

Characteristic signal based on the combination of empirical mode decomposition method and time series AR model Extraction method

In the process of signal decomposition by wavelet theory, the wavelet basis function is artificially selected based on experience, and the method based on empirical mode decomposition is decomposed according to the time scale of the signal itself. The article uses two methods to decompose a certain segmented frequency conversion signal to obtain the intrinsic modal component matrix and the wavelet decomposition coefficient matrix, then calculates the Hilbert time spectrum of the two decomposition matrices. cThe calculations shows that the false information generated by the empirical mode decomposition signal is obviouly more less. Therefore, the empirical mode decomposition method is used to decompose the bearing vibration signal, and the stationary natural mode function obtained is very suitable for establishing an autoregressive AR model to extract the power spectrum of each component for analysis. Finally, the characteristic frequencies of different states of rolling bearings are extracted, which provides support for data-driven fault diagnosis.