Daubechies Wavelet Research Articles

USE OF DISCRETE WAVELET ANALYSIS OF VIBRO-ACOUSTIC SIGNALS TO DETECT BEARING DEFECTS OF ROTATING ELECTRIC MACHINES

The paper shows that one of the most effective methods for processing the time realization of a vibro-acoustic signal from electrical machines is a discrete wavelet transform. At the same time, due to the lack of built-in tools for separating periodic and aperiodic components in the latter, it significantly complicates the process of identifying periodic disturbing factors, which makes it necessary to develop new approaches to identifying periodic components of vibration based on discrete wavelet transform, which can be caused by a number of defects in rotating electrical machines. A new integral highly informative numerical criterion for the presence of bearing defects, obtained on the basis of a discrete wavelet transform of a vibro-acoustic signal of an electric machine, is proposed. It has been found that upon detection of the indicated defect, it is advisable to analyze the frequency bands, which include the rotor frequency and its first harmonic components. The expediency of using the parent wavelet function of higher orders upon detection of the indicated defect has been theoretically substantiated and experimentally proved. It is shown that, based on considerations of simplifying the mathematical apparatus of calculation and increasing the flexibility of the diagnostic system, it is advisable to use the Daubechies wavelet family, the calculation of the coefficients of which involves the use of a clear mathematical algorithm. The necessary duration of time realizations of vibration is theoretically substantiated and experimentally confirmed, which is advisable to use when determining the proposed highly informative numerical criterion. It is shown that the duration of such realizations should be significantly longer than the period of rotation of the rotor of the electric machine.

Breast Cancer Detection and Classification Using Deep CNN Techniques

Breast cancer is a commonly diagnosed disease in women. Early detection, a personalized treatment approach, and better understanding are necessary for cancer patients to survive. In this work, a deep learning network and traditional convolution network were both employed with the Digital Database for Screening Mammography (DDSM) dataset. Breast cancer images were subjected to background removal followed by Wiener filtering and a contrast limited histogram equalization (CLAHE) filter for image restoration. Wavelet packet decomposition (WPD) using the Daubechies wavelet level 3 (db3) was employed to improve the smoothness of the images. For breast cancer recognition, these preprocessed images were first fed to deep convolution neural networks, namely GoogleNet and AlexNet for Adam. Root mean square propagation (RMSprop) and stochastic gradient descent with momentum (SGDM) optimizers were used for different learning rates, such as 0.01, 0.001, and 0.0001. As medical imaging necessitates the presence of discriminative features for classification, the pretrained GoogleNet architectures extract the complicated features from the image and increase the recognition rate. In the latter part of this study, particle swarm optimization-based multi-layer perceptron (PSO-MLP) and ant colony optimization-based multi-layer perceptron (ACO-MLP) were employed for breast cancer recognition using statistical features, such as skewness, kurtosis, variance, entropy, contrast, correlation, energy, homogeneity, and mean, which were extracted from the preprocessed image. The performance of GoogleNet was compared with AlexNet, PSO-MLP, and ACO-MLP in terms of accuracy, loss rate, and runtime and was found to achieve an accuracy of 99% with a lower loss rate of 0.1547 and the lowest run time of 4.14 minutes.

RFID System for Respiratory Rate Monitoring

In this work, an RFID system was developed to monitor the respiratory rate. This monitoring was based on variations in the Received Signal Strength Indicator (RSSI) by the reader due to respiratory movements. In some breath measurement configurations, the maximum read range was greater than 1 m, which is the distance considered in the measurement configurations described in some scientific papers. The RSSI data, obtained by reading the RFID tag, were processed using the Daubechies wavelet of order 3 (db3) and considering three levels of signal decomposition. Less noisy breathing signals were obtained in the measurements with the participant seated and the RFID tag with the polyethylene foam on the abdomen. The respiratory frequencies acquired from the variations of the RSSI parameter were validated by comparison with the results obtained using a vital signals monitor.

Correlation Between Skin Autofluorescence and Muscle Activities of Lower Limb in Aging Without Disease and Disability.

Skin autofluorescence is a useful index to estimate the accumulation of advanced glycation end-products in human tissues. Elderly persons with higher skin autofluorescence have lower muscle mass, muscle strength and muscle power, however, little is known about the relationship between the skin autofluorescence level and each muscle activity. We measured the values of skin autofluorescence from five places on a lower limb, and the signals of surface electromyogram during isometric contractions from five muscles on that, simultaneously. The waveforms of surface electromyogram were analyzed by Daubechies-4 wavelet transformation. The value of skin autofluorescence was increased in the proximal part of the lower limb compared with the value of the distal part. The principal component of surface electromyogram activity in a time-frequency domain was lower in the proximal part compared with that of the distal part. There was a weak negative correlation between the value of skin autofluorescence on the gluteal region and the value of the mean wavelet coefficient of the surface electromyogram signals within the gluteus maximus muscle. The higher accumulation of advanced glycation end-products on the gluteal region might suggest the lower muscle activity in aging without disease and disability.

Wavelet transforms of the time series of small wholesale prices in the agricultural sector

The article provides a wavelet analysis of small wholesale prices for white cabbage in Rostov-on-Don from 2017 to 2020 year. Approximation coefficients show a steady trend, the detailing coefficients reflect seasonal and insignificant temporary price fluctuations. The constituent scaling approximation coefficients and the detailing components are highlighted in the form of separate graphs. The series was decomposed up to the 6th level using the Haar and Daubechies wavelets.

COVID-19 Chest X-Ray Detection Performance Through Variations of Wavelets Basis Function

Our previous work regarding the X-Ray detection of COVID-19 using Haar wavelet feature extraction and the Support Vector Machines (SVM) classification machine has shown that the combination of the two methods can detect COVID-19 well but then the question arises whether the Haar wavelet is the best wavelet method. So that in this study we conducted experiments on several wavelet methods such as biorthogonal, coiflet, Daubechies, haar, and symlets for chest X-Ray feature extraction with the same dataset. The results of the feature extraction are then classified using SVM and measure the quality of the classification model with parameters of accuracy, error rate, recall, specification, and precision. The results showed that the Daubechies wavelet gave the best performance for all classification quality parameters. The Daubechies wavelet transformation gave 95.47% accuracy, 4.53% error rate, 98.75% recall, 92.19% specificity, and 93.45% precision.

Development of a method for noise suppression of a signal from pressure sensors on main gas pipelines using wavelet transformation

Natural gas produced in the Russian Federation is transported through main gas pipelines united into the Unified Gas Supply System of the Russian Federation. The system of main gas pipelines - the most important link in the unified gas supply system – is a large, complex and continuously developing technological system. Maximum internal pressure is one of the key characteristics for any pipeline. This indicator helps to set the limit for the capacity of the pipeline (maximum volume of pumped gas per unit of time), its level of reliability, as well as the level of hazard and potential risk (the higher the pressure inside the pipeline, the more potential threat it carries). In order to increase the reliability of determining the pressure in the gas pipeline, it is proposed to perform noise suppression using a wavelet transform in the work. Noise reduction in the wavelet transform is carried out due to the fact that the signal is decomposed into approximating and detailing coefficients. After removing the detailing component, the decomposition is restored and the output is a slightly distorted signal. Thus, when you remove an insignificant part of the original signal, the graphs of the change in values become more visual. This paper compares the efficiency of wavelet based thresholding techniques in the presence of noise for various wavelet family. For comparison, the trend processing was performed by two types of wavelets recommended for noise reduction - Symlet and Daubechies wavelets.

An efficient wavelet-based numerical method to solve nonlinear Fredholm integral equation of second kind with smooth kernel

In this paper, a wavelet-based numerical algorithm is described to obtain approximate numerical solution of a class of nonlinear Fredholm integral equations of second kind having smooth kernels. The algorithm involves approximation of the unknown function in terms of Daubechies scale functions. The properties of Daubechies scale and wavelet functions together with one-point quadrature rule for the product of a smooth function and Daubechies scale functions are utilized to transform the integral equation to a system of nonlinear equations. The efficiency of the proposed method is demonstrated through three illustrative examples.

Detection of Tonic-Clonic Seizures using Wavelet Entropy of Scalp EEG.

Epilepsy is the most common chronic neurologic disorder characterized by the recurrence of unprovoked seizures. These seizures are paroxysmal events that result from abnormal neuronal discharges and are categorized into various types based on the clinical manifestations and localization. Tonic-Clonic seizures (TCSZ) may lead to injuries, and constitute the major risk factor for sudden unexpected death in epilepsy (SUDEP), especially in unattended patients. Therapeutic decisions and clinical trials rely on Video EEG which is not practical outside of clinical setting. In this study, wavelet entropy of scalp EEG signals are utilized to discriminate the seizures with and without clinical manifestations. The scalp EEG records from the publically available Temple University Hospital (TUH) dataset are considered for this work. A sevenlevel, fourth order Daubechies (db4) wavelet is utilized for the decomposition of first four seconds of scalp EEG during seizures. The entropy is extracted from the resultant coefficients and are used to develop SVM based models. Most of the extracted features found to have significant differences (p<0.05). The results show that polynomial SVM model achieves an accuracy of 95.5%, positive predictive value (PPV) of 99.4%, negative predictive value (NPV) of 91.57% and F-Score of 95.9%. Therefore, the proposed approach could be a support in detecting life-threatening seizures.

Auto-detection of Spectral Notches of Head-related Transfer Function using Wavelet Multi-resolution Analysis

The spectral features of pressure characterized by the human outer ear, head, and torso are vital for sound localization in humans, especially for sound above 5 kHz. Many studies have shown that spectral notches contribute significantly as cues for this purpose. These spectral notches and their center frequencies depend on the shape and geometry of each individual, so their characteristics are different between individuals. We used wavelet multi-resolution analysis to automatically detect the center frequencies of spectral notches in head-related transfer functions (HRTFs). Auto-detection of these notches at certain locations for an individual helps in using suitable, complete, 3D HRTFs from HRTF datasets that have similar notch characteristics for an individual. Symlet and Daubechies wavelets were successfully used at different decomposition levels for this purpose. Symlet2 gives the best performance in terms of the auto-detection sensitivity.

Multi-resolution wavelet basis for solving steady forced Korteweg\u2013de Vries model

A steady forced Korteweg–de Vries (fKdV) model which includes gravity, capillary, and pressure distributions is solved numerically using the wavelet Galerkin method. The anti-derivatives of Daubechies wavelets are developed as the basis of the solution subspaces for the mixed boundary condition type. Accuracy of numerical solutions can be improved by increasing the number of wavelet levels in the multi-resolution analysis. The theoretical result of convergence rate is also shown. The problem can be viewed as gravity-capillary wave flows over an applied pressure distribution. The flow regime can be characterized by subcritical, supercritical, and critical flows depending on the value of the Froude number. Trapped depression and elevation waves are found over the pressure distribution. For a near-critical flow regime, a generalized solitary wave with ripples is presented. This shows a capillary effect in balance to gravity and the pressure force on the free surface.

Wavelet decomposition and embeddings of generalised Besov–Morrey spaces

We study embeddings between generalised Besov–Morrey spaces Nφ,p,qs(Rd). Both sufficient and necessary conditions for the embeddings are proved. Embeddings of the Besov–Morrey spaces into the Lebesgue spaces Lr(Rd) are also considered. Our approach requires a wavelet characterisation of the spaces which we establish for the system of Daubechies wavelets.

Thermal Imagery Feature Extraction Techniques and the Effects on Machine Learning Models for Smart HVAC Efficiency in Building Energy

The control of thermostats of a heating, ventilation, and air-conditioning (HVAC) system installed in commercial and residential buildings remains a pertinent problem in building energy efficiency and thermal comfort research. The ability to determine the number of people at a particular time in an area is imperative for energy efficiency in order to condition only occupied regions and thermally deficient regions. In this study of the best features comparison for detecting the number of people in an area, feature extraction techniques including wavelet scattering, wavelet decomposition, grey-level co-occurrence matrix (GLCM) and feature maps convolution neural network (CNN) layers were explored using thermal camera imagery. Specifically, the pretrained CNN networks explored are the deep residual (Resnet-50) and visual geometry group (VGG-16) networks. The discriminating potential of Haar, Daubechies and Symlets wavelet statistics on different distributions of data were investigated. The performance of VGG-16 and ResNet-50 in an end-to-end manner utilizing transfer learning approach was investigated. Experimental results showed the classification and regression trees (CART) model trained on only GLCM and Haar wavelet statistic features, individually achieved accuracies of approximately 80% and 84%, respectively, in the detection problem. Moreover, k-nearest neighbors (KNN) trained on the combined features of GLCM and Haar wavelet statistics achieved an accuracy of approximately 86%. In addition, the performance accuracy of the multi classification support vector machine (SVM) trained on deep features obtained from layers of pretrained ResNet-50 and VGG-16 was between 96% and 97%. Furthermore, ResNet-50 transfer learning outperformed the VGG-16 transfer learning model for occupancy detection using thermal imagery. Overall, the SVM model trained on features extracted from wavelet scattering emerged as the best performing classifier with an accuracy of 100%. A principal component analysis (PCA) on the wavelet scattering features proved that the first twenty (20) principal components achieved a similar accuracy level instead of training on the whole feature set to reduce the execution time. The occupancy detection models can be integrated into HVAC control systems for energy efficiency and security systems, and aid in the distribution of resources to people in an area.

Multiresolution Daubechies finite wavelet domain method for transient dynamic wave analysis in elastic solids

AbstractThe multiresolution capability provided by the family of Daubechies wavelets is exploited to develop a new computational approach, termed as multiresolution finite wavelet domain method for the fast and hierarchical prediction of transient dynamic problems with focus on wave propagation in one‐ and two‐dimensional structural configurations. In the developed method, both scaling and wavelet functions are employed as basis functions for the approximation of displacements in the governing dynamic equations. Because of the orthogonal and the multiresolution properties of Daubechies wavelets, a two‐scale system of mass uncoupled dynamic equations, representing the coarse and the fine spatial wave component solutions is derived. Numerical results concerning wave propagation in one‐ and two‐dimensional elastic structures demonstrate substantial computational gains of the method in comparison with other well‐established numerical methods. Moreover, additional benefits of the involved coarse and fine solutions enabling the analysis and characterization of the resultant wave response are revealed and discussed.

Quality evaluation of metal surfaces treatment by wavelet analysis

Purpose. Analyze the effectiveness of using wavelet analysis to assess the quality of metal surfaces. Investigate the possibility of using wavelet analysis in ultrasonic flaw detection. Determine the optimal wavelet families and their criteria for assessing the quality of metal surface processing.&#x0D; Research methods. Orthogonal wavelets are considered: Daubechies wavelet, Simlet wavelet and Coiflet wavelet, which provide the possibility of performing a discrete wavelet transform procedure. The criteria influencing the effectiveness of ultrasonic signal filtering by methods using wavelet analysis are considered. Ultrasonic signals were filtered using wavelet functions.&#x0D; Results. It has been determined that for successful signal filtering, the selected wavelet method must provide a discrete wavelet transformation and have a similarity in the wavelet function shape in the local features of the ultrasonic signals flaw detector. During the work, a rigid threshold for limiting the detail coefficients of wavelet analysis was chosen, as it is the best for filtering tasks. The filtering efficiency is confirmed by the relatively high signal to noise ratio, as well as by the fact that the shape of the pulse extracted from the defect remained almost unchanged.&#x0D; Scientific novelty. When using the Daubechies and Coiflet wavelets as basic functions, as a result of wavelet filtering, it was possible to increase the signal to noise ratio by 20 dB and confidently isolate the useful signal against the background noise, which indicates the prospects of using this kind of transformations in filtering problems.&#x0D; Practical value. The obtained solutions can be used for implementation in signal filtering algorithms in digital processing units of automated non-destructive ultrasonic control systems.

Suicide cases in developed and emerging countries: an analysis using wavelets

ABSTRACT Objective The aim of this study was to use a wavelet technique to determine whether the number of suicides is similar between developed and emerging countries. Methods Annual data were obtained from World Health Organization (WHO) reports from 1986 to 2015. Discrete nondecimated wavelet transform was used for the analysis, and the Daubechies wavelet function was applied with five-level decomposition. Regarding clustering, energy (variance) was used to analyze the clusters and visualize the clustering process. We constructed a dendrogram using the Mahalanobis distance. The number of groups was set using a specific function in the R program. Results The cluster analysis verified the formation of four groups as follows: Japan, the United States and Brazil were distinct and isolated groups, and other countries (Austria, Belgium, Chile, Israel, Mexico, Italy and the Netherlands) constituted a single group. Conclusion The methods utilized in this paper enabled a detailed verification of countries with similar behaviors despite very distinct socioeconomic, geographic and climate characteristics.

Adaptive Weight Fusion Algorithm of Infrared and Visible Image Based on High-Frequency Domain CNN

Aiming at covering the shortage of single source sensor imaging and improving the contrast between the target and the background in image, this paper proposes an adaptive weight fusion algorithm of infrared and visible image based on a High-frequency Domain Convolutional Neural Network (HDCNN). Firstly, the high and low frequency components of the original image are obtained by using the Daubechies wavelet transform, and then a high-frequency domain convolutional neural network which can detect the frequency information ratio of infrared and visible light in the high-frequency subband is trained. Secondly, the network is used to perform adaptive weight fusion for the high frequency components and regional energy is used for fusion of the low frequency components. Finally, the fusion image is obtained by inverse wavelet transform. A large number of experiments have proved that the algorithm in this paper has a greater improvement over similar comparison algorithms in objective evaluation metrics such as standard deviation, spatial frequency and average gradient. The algorithm enhances the contrast between the target and the background in the fusion image, and enriches the characteristic information of the target itself.

No-Reference Retinal Image Sharpness Metric Using Daubechies Wavelet Transform

Retinal fundus images are increasingly used by ophthalmologists both manually and without human intervention for detecting ocular diseases. Poor quality retinal images could lead to misdiagnosis or delayed treatment. Hence, a picture quality index was a crucial measure to ensure that the obtained images from acquisition system were suitable for reliable medical diagnosis. In this paper, a no-reference retinal image quality assessment based on wavelet transform is presented. A multiresolution Daubechies (db2) wavelet at level 4 was employed to decompose an original image into detail, and approximation sub-bands for extracting the sharpness information. The sharpness quality index was calculated from the entropy of the sub-bands. The proposed measure was validated by using images from the High-Resolution Fundus (HRF) dataset. The experimental results show that the proposed index performed more consistent with human visual perception and outperformed the Abdel-Hamid et al method.

The comprehensive analysis of the determination of wavelet function-level pair for the decomposition and reconstruction of artificial S1 heart signals by using multi-resolution analysis

Two major sounds of the normal heart sound like “lub dub”. The “lub” is the first heart sound, commonly termed S1 results from mitral (M1) and tricuspid (T1) valve closure at the start of systole. In this work, the noisy-S1 heart signal was investigated to separate M1 and T1 components of it by making the comprehensive analysis of the determination of wavelet function-level pair for the decomposition and reconstruction of artificial S1 by using multiresolution analysis (MRA) and discrete wavelet transform (DWT). For this purpose, a synthetic S1 and its three different noisy-S1 signals were created by using the linear chirp transient model and then decomposed to their approximations and details at three different decomposition levels (3,4,5). 86 daughter wavelets of Biorthogonal, Coiflet, Daubechies, and Symlet were used to reconstruct noisy-S1 signals using comprehensive MRA&DWT. S1 and reconstructed noisy-S1 were compared qualitatively and quantitatively. For quantitative assessment, signal-to-noise-ratio (SNR), peak-SNR (PSNR), root-mean-square-error (RMSE), and structural-similarity (SSIM(%)) metrics were used for noisy-S1 signals at 3–4-5 decomposition levels. In the final evaluation of 86 daughter wavelets, db5, bior3.3, and bior3.9 performed superior results both qualitatively and quantitatively. The db5 was the superior one qualitatively at level 5, and quantitatively, the SNR values of the reconstructed signal by db5 were 8.620, 8.009, and 6.333 for %5-,%10-, and %20-noisy heart signals, respectively. The study proved that MRA&DWT provides a comprehensive analysis opportunity consisting of 86 daughter wavelets for perfect reconstruction of the S1 heart signals and detecting transients between M1 and T1 components.

Fault analysis on continuous variable transmission using DB-06 wavelet decomposition and fault classification using ANN

This study aims at developing a novel method for condition monitoring technique for detection and classification of developing faults and increase the working life of continuous variable transmission (CVT) using Daubechies Wavelet 06 (DB-06). The vibration data is collected for 4 different types of faults and healthy condition. Using a magnetic accelerometer and signal analyser, vibration data is collected from the system in the time-domain which is then used as input for a MATLAB code producing the plot of the frequency-domain signal. Maximum frequency is determined to diagnose the faults which are induced over three different belts. Collected data for large scale automotive system (CVT) is used to train the network and then it is tested based on random data points. Faults were classified using ANN with a classification rate of 90.8 %.