Wavelet-based Method Research Articles

Sleep’s depth detection using electroencephalogram signal processing and neural network classification

: The sleep related diseases became common nowadays and thus sleep stages detection has an important role in the diagnosis of such kinds of diseases. However, conventional sleep stages detection methods face challenges from the complex mathematical models associated with them and the feature extraction processes. In addition, there may be rapid fluctuations between sleep stages which may affect the accurate features extraction and would possibly lead to an inaccurate evaluation of electroencephalogram (EEG) sleep phases. Hence, we suggest an automatic sleep stages classification approach based totally on a neural community, blended with a wavelet-based function extraction method. In this work 4 sleep ranges will be classified, consisting of Awake, Stage 1 + rapid eye movement (REM), Stage two and Slow Wave Stage primarily based only on the EEG signal. In order to validate the efficiency of our algorithm, we used PhysioNet database EEG signals for in vitro tests. After the sleep stages detection, we target the brain computer interface (BCI) design, in order to control some equipment around the subject of study. Actually, our target is to establish the communication between the brain and the external world. Because the sleep stages detection is useful for other areas, like the tiredness detection and drowsiness detection for drivers as well. But in this work, we aim to detect only the sleep stages in an efficient method.

A variance-based approach for the detection and localization of cracks in a beam

A variance-based method is proposed for the detection and localization of cracks in a beam. A crack in a beam introduces a slope discontinuity in the beam elastic line. The local slope discontinuity due to the crack results in a localized change in the beam deflection variance values. In the present work, the local variance is obtained using a rectangular moving window along the beam length. A significant change in the local variance values is observed at the crack location. A two-time application of moving window variance leads to a clear spike at the crack location. Localization of cracks in cantilever and simply supported beams is presented. The proposed method is compared with the widely used wavelet-based method for crack localization. The present method is more suitable for locating the crack in the high slope region of beam deflection. Finite element analysis is used to obtain the simulated cracked cantilever and simply supported beam responses. White Gaussian noise is added to the simulated beam deflection to test the noise-robustness of the algorithm. A key challenge in the detection of cracks in a beam is to obtain a high-resolution spatial beam deflection measurement. For experimental verification, the high-resolution spatial measurement of the vibrating beam is obtained by photographic measurement. The high spatial resolution gives localized spikes corresponding to the crack location. The proposed algorithm is capable of localizing multiple simultaneous cracks in a beam. Experimental localization of cracks in single and double cracked cantilever beams is presented.

Wavelet Based Filters for Artifact Elimination in Electroencephalography Signal: A Review.

Electroencephalography (EEG) is a diagnostic test that records and measures the electrical activity of the human brain. Research investigating human behaviors and conditions using EEG has increased from year to year. Therefore, an efficient approach is vital to process the EEG dataset to improve the output signal quality. The wavelet is one of the well-known approaches for processing the EEG signal in time-frequency domain analysis. The wavelet is better than the traditional Fourier Transform because it has good time-frequency localized properties and multi-resolution analysis where the transient information of an EEG signal can be extracted efficiently. Thus, this review article aims to comprehensively describe the application of the wavelet method in denoising the EEG signal based on recent research. This review begins with a brief overview of the basic theory and characteristics of EEG and the wavelet transform method. Then, several wavelet-based methods commonly applied in EEG dataset denoising are described and a considerable number of the latest published EEG research works with wavelet applications are reviewed. Besides, the challenges that exist in current EEG-based wavelet method research are discussed. Finally, alternative solutions to mitigate the issues are recommended.

Detection of Slow Slip Events Using Wavelet Analysis of GNSS Recordings

ABSTRACT At many places, tectonic tremor is observed in relation to slow slip and can be used as a proxy to study slow slip events of moderate magnitude in which surface deformation is hidden in Global Navigation Satellite System (GNSS) noise. However, in subduction zones in which no clear relationship between tremor and slow slip occurrence is observed, these methods cannot be applied, and we need other methods to be able to better detect and quantify slow slip. Wavelets methods such as the Discrete Wavelet Transform and the Maximal Overlap Discrete Wavelet Transform (MODWT) are mathematical tools for analyzing time series simultaneously in the time and the frequency domains by observing how weighted differences of a time series vary from one period to the next. In this article, we use wavelet methods to analyze GNSS time series and seismic recordings of slow slip events in Cascadia. We use detrended GNSS data, apply the MODWT transform, and stack the wavelet details over several nearby GNSS stations. As an independent check on the timing of slow slip events, we also compute the cumulative number of tremor in the vicinity of the GNSS stations, detrend this signal, and apply the MODWT transform. In both the time series, we can then see simultaneous waveforms where timing corresponds to the timing of slow slip events. We assume that there is a slow slip event whenever there is a positive peak followed by a negative peak in the wavelet signal. We verify that there is a good agreement between slow slip events detected with only GNSS data and slow slip events detected with only tremor data for northern Cascadia. The wavelet-based detection method effectively detects events of magnitude higher than 6, as determined by independent event catalogs (e.g., Michel et al., 2019). As a demonstration of using the wavelet analysis in a region without significant tremor, we also analyze GNSS data from New Zealand and detect slow slip events that are spatially and temporally close to those detected previously by other studies.

A Novel Gegenbauer Wavelet-Based Approach for Stability and Surface Location Error Analyses of Milling Process

Abstract This paper proposes a novel wavelet-based method for the computation of the milling stability and surface location error (SLE). The governing equation of milling processes considering the self-vibration and forced-vibration is formulated as a delayed differential equation with state space form. The total time period is considered as a whole, sampled by the Chebyshev nodes. Then, the vibration displacement corresponding to each sampling grid point is fitted by a weighted linear sum of Gegenbauer orthogonal polynomials. A new method named direct differentiation based algorithm (DDBA) is proposed to determine these weight coefficients, which gets rid of dependence on the classic differential operator. On the one hand, the Floquet matrix is constructed to calculate the milling stability. On the other hand, the coefficient matrix independent of time is established to predict the SLE. The benchmark and experimentally verified examples are employed to validate the effectiveness of the proposed approach. The optimal combination of orthogonal polynomials is fixed by exploring the effect of the control parameter on the predictive accuracy. At last, the calculation vulnerability that can cause the prediction accuracy to be dropped obviously in some step lengths is revealed and repaired.

Numerical simulation for Tiwari–Das model for Homann flow of nanofluid due to a spiraling disk: A spectral technique

This study extracts heat transfer analysis for the axisymmetric flow of CuO-water nanofluid imposing normal to a spiraling disk uniformly rotating and radially stretching. The combined influence of uniformly rotating and linearly radial stretching surface engenders the logarithmic spirals in motion. The governing system is transformed into a system of the ordinary differential equations that represent the flow. The Tiwari–Das [Int. J. Heat Mass Trans. 50, 2002 (2007)] model is utilized to envisage the heat transfer and other physical properties of the nanofluid. A highly precise numerical technique named as Legendre wavelet-based spectral method is practiced to computing the impacts of the pertinent variables on the flow. The results of physical significance including the wall shear, skin frictions and heat transfer rate are attained for the multiple spiraling parameters and the nanoparticle volume fraction. The asymptotic results for the large spiraling parameter are also presented to analyze the flow behavior for the high spiraling parameter. The influence of the nanoparticles is also investigated and the enhancement in thermal conductivity is measured. The temperature and thermal layer thickness reduce for large spiraling parameter. Also addition of the nanoparticles enhances the heat transfer rate of the nanofluid.

Decision thresholding on fMRI activation maps using the Hilbert–Huang transform

Objective. Functional magnetic resonance imaging (fMRI) requires thresholds by which to identify brain regions with significant activation, particularly for experiments involving real-life paradigms. One conventional non-parametric approach to generating surrogate data involves decomposition of the original fMRI time series using the Fourier transform, after which the phase is randomized without altering the magnitude of individual frequency components. However, it has been reported that spontaneous brain signals could be non-stationary, which, if true, could lead to false-positive results. Approach. This paper introduces a randomization procedure based on the Hilbert–Huang transform by which to account for non-stationarity in fMRI time series derived from two fMRI datasets (stationary or non-stationary). The significance of individual voxels was determined by comparing the distribution of empirical data versus a surrogate distribution. Main results. In a comparison with conventional phase-randomization and wavelet-based permutation methods, the proposed method proved highly effective in generating activation maps indicating essential brain regions, while filtering out noise in the white matter. Significance. This work demonstrated the importance of considering the non-stationary nature of fMRI time series when selecting resampling methods by which to probe brain activity or identify functional networks in real-life fMRI experiments. We propose a statistical testing method to deal with the non-stationarity of continuous brain signals.

Short-Term Load Forecasting with a Novel Wavelet-Based Ensemble Method

“Short-term load forecasting (STLF)” is increasingly significant because of the extensive use of distributed energy resources, the incorporation of intermitted RES, and the implementation of DSM. This paper provides a novel ensemble forecasting model with wavelet transform for the STLF depending on the decomposition principle of load profiles. The model can effectively capture the portion of daily load profiles caused by seasonal variations. The results indicate that it is possible to improve STLF accuracy with the proposed method. The proposed approach is tested with the data taken from Ontario’s electricity market in Canada. The results show that the proposed technique performs well in-terms of prediction when compared to existing traditional and cutting-edge methods. The performance of the model was validated with different datasets. Moreover, this approach can provide accurate load forecasting using ensemble models. Therefore, utilities and smart grid operators can use this approach as an additional decision-making tool to improve their real-time decisions.

Two‐dimensional wavelet based statistical monitoring of image data

AbstractStatistical process monitoring techniques are widely used to monitor process stability. In high volume and highly automated processes, effective methods are required to monitor several quality characteristics of interest. Advances in imaging technology have paved the grounds to capture and analyze product images from different perspectives in real time. Advantages of considering images have led to their increasing role in process monitoring. When images are used for process monitoring, complicated data structures should be analyzed. Various methods including data transformation and dimension reduction have been proposed in the literature to cope with these complexities. In this paper, a two‐dimensional (2D) wavelet based method is proposed to monitor image data. A likelihood ratio test (LRT) is developed to monitor the expected values of wavelet coefficient, and the derived likelihood ratio based statistic is monitored over time to detect out‐of‐control conditions as well as change point estimation. This information can help practitioners to diagnose the process, find the potential assignable cause(s) and return the process to the in‐control state. One of the advantages of the proposed method compared to other competing methods is that the performance of the proposed method does not depend on the fault location. Simulation studies indicate satisfactory performance for the proposed method in detecting out‐of‐control conditions and estimating change points. Moreover, the performance of the proposed method is also compared to two existing approaches. The results reveal that the proposed approach performs superior in detecting either diagonal or square defects.

Wavesdropper

Most existing eavesdropping attacks leverage propagating sound waves for speech retrieval. However, soundproof materials are widely deployed in speech-sensitive scenes (e.g., a meeting room). In this paper, we reveal that human speech protected by an isolated room can be compromised by portable and commercial off-the-shelf mmWave devices. To achieve this goal, we develop Wavesdropper, a word detection system that utilizes a mmWave probe to sense the targeted speaker's throat vibration and recover speech contents in the obstructed condition. We proposed a CEEMD-based method to suppress dynamic clutters (e.g., human movements) in the room and a wavelet-based processing method to extract the delicate vocal vibration information from the hybrid signals. To recover speech contents from mmWave signals related to the vocal vibration, we designed a neural network to infer the speech contents. Moreover, we explored word detection on a conversation with multiple (two) probes and reveal that the adversary can detect words on multiple people simultaneously with only one mmWave device. We performed extensive experiments to evaluate the system performance with over 60,000 pronunciations. The experimental results indicate that Wavesdropper can achieve 91.3% accuracy for 57-word recognition on 23 volunteers.

On a wavelet-based numerical method for linear and nonlinear fractional Volterra integro-differential equations with weakly singular kernels

On a wavelet-based numerical method for linear and nonlinear fractional Volterra integro-differential equations with weakly singular kernels

Super-resolution of very low-resolution face images with a wavelet integrated, identity preserving, adversarial network

Super-resolution of face images, known as Face Hallucination (FH), has been excessively studied in recent years. Modern FH methods use deep Convolution Neural Networks (CNN) with a pixel-wise MSE loss function to infer high-resolution facial images. The MSE-oriented approaches generate over-smooth results, particularly when dealing with very low-resolution images. Recently, Generative Adversarial Networks (GANs) have successfully been exploited to synthesize perceptually more pleasant images. However, the GAN-based models do not guarantee identity preservation during face super-resolution. To address these challenges, we have proposed a novel Wavelet-integrated, Identity Preserving, Adversarial (WIPA) approach. Specifically, we present Wavelet Prediction blocks attached to a Baseline CNN network to predict wavelet missing details of facial images. The extracted wavelet coefficients are concatenated with original feature maps in different scales to recover fine details. Unlike other wavelet-based FH methods, this algorithm exploits the wavelet-enriched feature maps as complementary information to facilitate the hallucination task. We introduce a wavelet prediction loss to push the network to generate wavelet coefficients. In addition to the wavelet-domain cost function, a combination of perceptual, adversarial, and identity loss functions has been utilized to achieve low-distortion and perceptually high-quality images while maintaining identity. The extensive experiments prove the superiority of the proposed approach over the state-of-the-art methods by achieving PSNR of 25.16 dB for CelebA dataset and verification rate of 86.1% for LFW dataset; both conducted on 8X magnification factor.

A wavelet-based method for thrust noise assessment in gravitational wave detection over wide-frequency-range

Electric thrusters are considered to be the most promising propulsion system of choice for space gravitational wave detection. However, the requirement of high accuracy and drag-free control results in significant challenges in thrust measurements. In order to detect gravitational wave signals over a wide frequency range, it is necessary to assess the thrust noise of electric thrusters. This paper demonstrates a wavelet-based method for thrust noise evaluation in a time-frequency domain aspect, and aims to expand thrust noise analysis to a wide frequency range from 10−3Hz–1Hz. Over this frequency range, a frequency-varying metric boundary is proposed for thrust noise evaluation. This metric boundary is established based on the spectral density of gravitational waves and the time-varying spectrum analysis method, which is used to judge whether the thruster exceeds the requirements for the detection of gravitational waves. A Hall Thruster was ignited and measured experimentally to verify the thrust noise assessment method. The metric boundary evaluates the thrust noise limits in the frequency range from 10−3 to 1Hz over the entire operating duration to the thruster's power-off period. This time-frequency-varying thrust noise assessment method allows us to identify the time and frequency band within which the electric thruster is capable of exceeding the requirements for gravitational wave detection.

Development of a validation technique for road surface profile applicable to point cloud data

In recent years, various information and communication technology (ICT) devices measuring three-dimensional (3D) point cloud data have been developed and widely used for the application of pavement surface investigation. However, ICT devices have generally been developed not only for measuring road surface profiles but for various geo-reference point clouds. In this background, the validation of surface profiles acquired with ICT devices fulfils an important role in proving the reliability of measurement result composed by point clouds. This study proposes a wavelet transform agreement (WTA) which involves a normalization factor of profile amplitude for further improvement in the wavelet-based coherence technique. The WTA analysis allows evaluating similarity/dissimilarity of two profiles considering both the location and wavelength simultaneously. For this purpose, a terrestrial laser scanner (TLS), a mobile mapping system (MMS), and an unmanned aerial vehicle (UAV) are employed to prove the advantage of WTA in practical applications. As a result, the advantages of WTA analysis are clearly recognized in the optimization for the measurement interval of TLS, the multi-line measurement of MMS for ride quality improvement of a pavement, and the efficient operation of UAV in terms of the flight altitude. This paper also shows the identification of aging development for surface roughness over time in terms of locations and wavelengths. These findings help not only to guarantee the accuracy of profile measurements but to realize the sophisticated way of using 3D point clouds acquired with ICT devices. The outcomes of this study contribute to the increase of productivity for pavement works with improving the quality of surface profile measurement. • Wavelet agreement modifies wavelet transform coherence for road profile analysis. • Profile validation becomes reliable with wavelet agreement analysis. • Wavelet agreement performs profile validation keeping locations and wavelengths. • Wavelet-based method has an affinity with three-dimensional point clouds. • Profile validation improves operational efficiency of ICT devices.

Luminosity functions consistent with a pulsar-dominated Galactic Center excess

A new population of millisecond pulsars is a long-standing proposed explanation for the excess of GeV-scale gamma rays emanating from the region surrounding the center of the Milky Way (the “Galactic Center excess”). We examine several simple parameterizations of possible luminosity functions for this population, as well as several benchmark luminosity functions proposed in the literature, and compare the predicted populations of resolved point sources to the Fermi 4FGL-DR2 point source catalog and a sub-population recently identified using wavelet-based methods. We provide general results that can be used to translate upper limits on the number of resolved point sources associated with the excess, and the fraction of the flux in the excess that can be attributed to resolved sources, into limits on the luminosity function parameter space. We discuss a number of important systematic uncertainties, including in the detection threshold model and the total flux attributed to the excess. We delineate regions of parameter space (containing existing benchmark models) where there is no apparent tension with current data, and the number of total pulsars needed to explain the excess is in the range of \U0001d4aa(104-5). In the future, lowered point source detection thresholds could be achieved either by new analysis methods or new data. An order-of-magnitude reduction in the sensitivity threshold (which may already be achieved by novel analyses probing sub-threshold source populations) could hope to resolve more than 30% of the flux of the excess even in pessimistic scenarios.

Speckle noise reduction for structural vibration measurement with laser Doppler vibrometer on moving platform

Speckle noise is a major problem for structural vibration measurements with Laser Doppler vibrometer on moving platform (LDVom) due to its highly random, frequent, and broadband nature, especially at high speeds. This paper develops a new post-processing framework to reduce speckle noise based on a case study of LDVom measurements on railway tracks. First, the characteristics of the speckle noise are studied. As the speed increases, the speckle noise occurs more frequently, with shorter intervals, shorter durations, greater amplitudes, and broader frequency bands. Then, a three-step despeckle framework is proposed, consisting of spike detection, imputation, and smoothing. This framework works by detecting and replacing spikes, recovering false positives, and smoothing false negatives and residual noise. To showcase this framework, we use a wavelet-based method for Step 1, an ARIMA-based method for Step 2, and a Butterworth filter for Step 3. Besides, the parameter selection strategies and the alternative methods are discussed. Next, the methods are validated through qualitative comparison and quantitative evaluation using a Monte Carlo-based strategy. We demonstrate that the proposed methods effectively reduce the speckle noise at speeds of at least 20 km/h while avoiding the pseudo vibrations. Finally, we show that the LDVom successfully captures the track vibrations at dominant frequencies of 500 ∼ 700 Hz with good repeatability between different laps and good agreement with trackside measurements.

Time-frequency effect of investor sentiment, economic policy uncertainty, and crude oil on international stock markets: evidence from wavelet quantile analysis

ABSTRACT This paper employs the wavelet-based quantile method to examine the time and frequency effect of investor sentiment, economic policy uncertainty, and crude oil on emerging and developed stock markets over the monthly sample range from September 2005 to December 2020. We first explore the relationship between various markets, and our empirical results reveal a strong long-term spillover effect of sentiment on returns from developed to emerging markets. Meanwhile, we find the negative influence of EPU gradually strengthens from the short-term towards the long-term. Further, oil shocks to stock returns are highly related to investment horizons and market circumstances. Specifically, the correlation is negative in the medium-term while positive in the short- and long-term, and more evident when stock markets are in a bearish or bullish state. In short, investors should take the structure dependence in terms of time and frequency when participating in financial markets.

A Gaussian wavelet-based method for extracting rockfall motion information in consecutive impact tests on flexible barrier systems

Flexible barriers are vulnerable to consecutive rockfall impacts, particularly in mountainous areas. The barriers deformation, energy absorption, and anti-impact performance can be evaluated from the rockfall motion information. However, a slight interference in rockfall displacement signals, generated during the actual measurement, could result in a distortion of the rockfall velocity and acceleration extracted through conventional derivative calculations. Consecutive impact tests on steel-wire ring nets were conducted, and the motion of the impact rock was captured from a high-speed video. The random noise in the impact signal was quantified using the signal-to-noise ratio and was distinguished in the frequency domain. Furthermore, to increase the derivative calculation accuracy, a Gaussian wavelet-based method is proposed, and an amplitude parameter is introduced into the wavelet transform procedure. The self-consistency of the proposed method was achieved using a combined differentiation–integration iteration process. Analytical signals of a single-degree-of-freedom system under a sine-wave impulse were used to validate the proposed method. We observed that the wavelet scale parameters were strongly related to the impact signal frequency band, which accounted for 90% – 99% of the total energy in the frequency domain. Finally, the Gaussian wavelet-based method was applied to the real impact signals of a rockfall. The results indicated that the proposed method is an effective and reliable tool for extracting the velocity and acceleration information of falling rocks during the consecutive impact process.

M‐Band Wavelet‐Based Imputation of scRNA‐seq Matrix and Multi‐view Clustering of Cells

Wavelet analysis has been recognized as a cutting‐edge and promising tool in the fields of signal processing and data analysis. However, application of wavelet‐based method in single‐cell RNA sequencing (scRNA‐seq) data is little known. Here, we present M‐band wavelet‐based imputation of scRNA‐seq matrix and multi‐view clustering of cells. We applied combination of M‐band wavelet analysis and uniform manifold approximation and projection (UMAP) to a panel of single cell sequencing datasets by breaking up the data matrix into a trend (low frequency or low resolution) component and M‐1 fluctuation (high frequency or high resolution) components. Our hybrid analysis enables us to examine multi‐view clustering of cell types, identity, and functional states. Distinct to standard scRNA‐seq workflow, our wavelet‐based approach is a new addition to resolve the notorious chaotic sparsity of scRNA‐seq matrix and to uncover rare cell types with a fine‐resolution.

Modification of a Wavelet-Based Method for Detecting Ebullitive Methane Fluxes in Eddy-Covariance Observations: Application at Two Rice Fields

Modification of a Wavelet-Based Method for Detecting Ebullitive Methane Fluxes in Eddy-Covariance Observations: Application at Two Rice Fields