Multi-scale Wavelet Research Articles

Clustering of inertial particles in turbulent flow through a porous unit cell

Direct numerical simulation is used to investigate effects of turbulent flow in the confined geometry of a face-centred cubic porous unit cell on the transport, clustering and deposition of fine particles at different Stokes numbers ( $St = 0.01, 0.1, 0.5, 1, 2$ ) and at a pore Reynolds number of 500. Particles are advanced using one-way coupling and the collision of particles with pore walls is modelled as perfectly elastic with specular reflection. Tools for studying inertial particle dynamics and clustering developed for homogeneous flows are adapted to take into account the embedded, curved geometry of the pore walls. The pattern and dynamics of clustering are investigated using the volume change of Voronoi tesselation in time to analyse the divergence and convergence of the particles. Similar to the case of homogeneous, isotropic turbulence, the cluster formation is present at large volumes, while cluster destruction is prominent at small volumes and these effects are amplified with the Stokes number. However, unlike homogeneous, isotropic turbulence, the formation of a large number of very small volumes was observed at all Stokes numbers and attributed to the collision of particles with the pore wall. Multiscale wavelet analysis of the particle number density indicates that the peak of the energy density spectrum, representative of enhanced particle clustering, shifts towards larger scales with an increase in the Stokes number. Scale-dependent skewness and flatness quantify the intermittent void and cluster distribution, with cluster formation observed at small scales for all Stokes numbers, and void regions at large scales for large Stokes numbers.

Control of leading-edge separation on bioinspired airfoil with fluttering coverts.

In this work, the aerodynamic role of the artificial covert feathers (i.e., coverts) on an airfoil is experimentally studied in a wind tunnel to investigate the flow control effect on the leading-edge separation. We apply flexible featherlike devices on a high-angle-of-attack airfoil. We use a hot-wire anemometer to measure the velocity profiles and turbulent fluctuations in the downstream wake flow. As a baseline of flow separation, a two-dimensional NACA 0018 airfoil model is set at the angle of attack of 15 ° at the chord-based Reynolds number of 1.0×10^{5}, causing strong leading-edge and trailing-edge shear layers and a low-speed wake flow area in between as large as 0.35 chord length. When deployed on the upper wing surface, the flexible coverts adaptively flutter under the influence of the local unsteady airflow. Hot-wire measurement results show that the leading-edge coverts effectively suppress the flow separation and reduce the size of the wake flow area. The change of power spectral density shows that the predominant peaks as the fundamental and harmonic frequencies are both attenuated due to the suppression of unsteady motions of the shear layers. On the other hand, the fluttering coverts at the trailing edge modify the trailing-edge shear layer by redistributing the turbulent kinetic energy to the high-frequency components. By simultaneous double-point measurement, we find that the leading-edge and trailing-edge shear layers are drawn closer to each other, and the two shear layers show an increased peak in the coherence spectrum. Further multiscale wavelet analysis shows that the perturbations at the 60% chord length increase the large-scale amplitude modulation of small-scale turbulence and therefore they stabilize the leading-edge and trailing-edge shear layers. Meanwhile, the flow intermittency outside of the wake flow area is attenuated as well. The effective flow control effects in the present work are in good agreement with the previous direct observations of bird flight in literature that the coverts on the upper wing surface play an important role in flow separation control during high-angle-of-attack flight. These findings advance the understanding of aerodynamic contribution of the covers on bird wings and reveal the engineering potential of bioinspired coverts for flow separation control of aircrafts and unmanned air vehicles.

Mineral prospectivity mapping based on wavelet neural network and Monte Carlo simulations in the Nanling W-Sn metallogenic province

The Nanling Range in South China is endowed with abundant W-Sn and other important rare metal resources associated with granitic intrusions, but the rate of new major mineral discoveries has been drastically diminished over the last decades. Data-driven mineral prospectivity mapping (MPM) using machine learning is emerging as a powerful tool in support of mineral exploration targeting at regional or camp scale. However, MPM based on supervised learning faces some general problems, notably including subtle information obscured in exploration data and imbalanced training samples. In this paper, we proposed a novel ensemble scheme for MPM using wavelet neural network (WNN) and Monte Carlo simulation (MCs) to address the forementioned issues. Specifically, the purpose of using WNN based on multiscale wavelet analysis is to capture weak or hidden (geophysical and geochemical) information caused by concealed ore deposits, while an undersampling MCs (UMCs) algorithm is employed to assess uncertainties caused by data imbalance and lessen its impact on MPM. Subtle (weak and mixing) information related to concealed mineralization, including geophysical and geochemical anomalies, were extracted using wavelet analysis at first, and then a dozen of predictive evidences was integrated based on WNN using UMCs for producing a W-Sn perspectivity map. The results suggest that WNN has a higher prediction accuracy (∼90%) in comparison to the artificial neural network (ANN) (∼85%). Moreover, the improved AUC value (∼0.9) of WNN based on UMCs compared to the classic ANN (∼0.82) and WNN (∼0.85) suggests that the proposed ensemble algorithm improves the geological generalization of machine learning. Revisiting WNN predictions by uncertainties produced more sharply focused exploration targets of W-Sn deposits (covering ∼5% of the study area). The resulting predictive map provides important clues of W-Sn deposit occurrences which could guide and stimulate future mineral exploration in the Nanling Range.

Multiscale Wavelet Transfer Entropy With Application to Corticomuscular Coupling Analysis

Functional coupling between the motor cortex and muscle activity is commonly detected and quantified by cortico-muscular coherence (CMC) or Granger causality (GC) analysis, which are applicable only to linear couplings and are not sufficiently sensitive: some healthy subjects show no significant CMC and GC, and yet have good motor skills. The objective of this work is to develop measures of functional cortico-muscular coupling that have improved sensitivity and are capable of detecting both linear and non-linear interactions. A multiscale wavelet transfer entropy (TE) methodology is proposed. The methodology relies on a dyadic stationary wavelet transform to decompose electroencephalogram (EEG) and electromyogram (EMG) signals into functional bands of neural oscillations. Then, it applies TE analysis based on a range of embedding delay vectors to detect and quantify intra- and cross-frequency band cortico-muscular coupling at different time scales. Our experiments with neurophysiological signals substantiate the potential of the developed methodologies for detecting and quantifying information flow between EEG and EMG signals for subjects with and without significant CMC or GC, including non-linear cross-frequency interactions, and interactions across different temporal scales. The obtained results are in agreement with the underlying sensorimotor neurophysiology. These findings suggest that the concept of multiscale wavelet TE provides a comprehensive framework for analyzing cortex-muscle interactions. The proposed methodologies will enable developing novel insights into movement control and neurophysiological processes more generally.

Visual Saliency via Multiscale Analysis in Frequency Domain and Its Applications to Ship Detection in Optical Satellite Images.

This article proposes a bottom-up visual saliency model that uses the wavelet transform to conduct multiscale analysis and computation in the frequency domain. First, we compute the multiscale magnitude spectra by performing a wavelet transform to decompose the magnitude spectrum of the discrete cosine coefficients of an input image. Next, we obtain multiple saliency maps of different spatial scales through an inverse transformation from the frequency domain to the spatial domain, which utilizes the discrete cosine magnitude spectra after multiscale wavelet decomposition. Then, we employ an evaluation function to automatically select the two best multiscale saliency maps. A final saliency map is generated via an adaptive integration of the two selected multiscale saliency maps. The proposed model is fast, efficient, and can simultaneously detect salient regions or objects of different sizes. It outperforms state-of-the-art bottom-up saliency approaches in the experiments of psychophysical consistency, eye fixation prediction, and saliency detection for natural images. In addition, the proposed model is applied to automatic ship detection in optical satellite images. Ship detection tests on satellite data of visual optical spectrum not only demonstrate our saliency model's effectiveness in detecting small and large salient targets but also verify its robustness against various sea background disturbances.

Inversion of Soil Iron Oxide Based on Multi-Scale Continuous Wavelet Decomposition

Inversion of Soil Iron Oxide Based on Multi-Scale Continuous Wavelet Decomposition

An Attention-Based Wavelet Convolution Neural Network for Epilepsy EEG Classification.

As a kind of non-invasive, low-cost, and readily available brain examination, EEG has attached significance to the means of clinical diagnosis of epilepsy. However, the reading of long-term EEG records has brought a heavy burden to neurologists and experts. Therefore, automatic EEG classification for epileptic patients plays an essential role in epilepsy diagnosis and treatment. This paper proposes an Attention Mechanism-based Wavelet Convolution Neural Network for epilepsy EEG classification. Attention Mechanism-based Wavelet Convolution Neural Network firstly uses multi-scale wavelet analysis to decompose the input EEGs to obtain their components in different frequency bands. Then, these decomposed multi-scale EEGs are input into the Convolution Neural Network with an attention mechanism for further feature extraction and classification. The proposed algorithm achieves 98.89% triple classification accuracy on the Bonn EEG database and 99.70% binary classification accuracy on the Bern-Barcelona EEG database. Our experiments prove that the proposed algorithm achieves a state-of-the-art classification effect on epilepsy EEG.

Automatic P-Wave Arrival Picking Based on Inaction Method

Accurately picking the arrival of the P-wave is of great significance for earthquake relief and emergency rescue. The picking accuracy of some previous methods was easily disturbed by noise. We propose an automatic picking algorithm for seismic P-wave first arrivals based on the inaction method (IM) and the Akaike information criterion (AIC), called the IMAIC method, to alleviate the above problems. We use the IMAIC method to directly extract the seismic phase characteristics from the normal time-frequency transform (NTFT) spectrum to pick the P-wave arrival, which does not require inverse transformation of the NTFT. The proposed method essentially implements bandpass filtering to avoid noise interference to the greatest extent possible while optimally preserving the important features of the signal, such as the sharp direct P-wave arrival. We applied the IMAIC method to 9909 aftershock records from Wenchuan in 2008 to verify its reliability and robustness, taking the manually picked P-wave arrival as a reference. The average deviation is -0.010 ± 0.170 s when using the proposed IMAIC method. Furthermore, a comparative study of P-wave arrivals that are automatically derived using multiscale wavelet analysis and singular value decomposition (SVD)-like picking algorithms with the same data set demonstrates the effectiveness of the IMAIC method. The proposed method offers much promise for picking seismic phase onsets, even when using data sets with a low signal-to-noise ratio (SNR).

Hermite-Shannon-Cosine Interval Wavelet and Its Application in Adaptive Distribute Interpolation on Curves

<p indent="0mm">The dynamic curve is a common tool to describe the transformation law of various phenomena. To capture the characteristic points dynamically and approximate the dynamic curve accurately, a Shannon-Cosine wavelet function with interpolation, smoothness, tight support, and symmetry is constructed. Firstly, by means of the wavelike property and continuity of the Shannon wavelet function, a parameterized window function is designed based on the integral median theorem, in which the support and smoothness of Shannon-Cosine wavelet can be chosen to meet the requirement of the approximated curves. Secondly, based on the theory analysis and numerical experiments, the discontinuity near the boundary of the curve is identified as the major factors which result in the boundary effect appeared on the wavelet transform on the curve, and then the interval wavelet is constructed by using the two-point cubic Hermite interpolation function. Finally, the multi-scale Shannon-Cosine wavelet is used to perform multi-scale adaptive subdivision and approximation of the propagation of shock wave curve and the reflected Burger curve. It is able to capture the characteristic points of the curve adaptively, which can be used to reconstruct the curve. Burger curve is taken as the example to test the proposed method, the numerical experiments show that, compared with other methods, the method of Hermite Shannon-Cosine interval wavelet approximation curve has higher numerical accuracy and lower algorithm complexity.

A method for measuring ice thickness of wind turbine blades based on edge detection

In recent years, with the successive development of mountain wind power resources in the high humidity regions, the problem of ice covering on wind turbine blades has become increasingly prominent. Wind turbine blade icing will affect blade aerodynamic performance and reduce power generation. In this paper, a method for measuring the ice thickness of wind turbine blades based on edge detection was proposed. As the icing images of blades have characteristics like low contrast, unclearness and blurred edges, the images were preprocessed by methods like defogging, gray-scale transformation, histogram correction, Gaussian filtering, and Laplace edge enhancement. Aiming at the characteristics of wind turbine icing images with many noises and many small edges, a multiscale wavelet edge detection algorithm was used to detect the blade icing images. Based on the pixel coordinates of the ice edge and the edge of the blade, through the pre-calibration, a method for calculating the ice thickness of the leading edge of the blade based on the pixel coordinate difference /real length ratio was proposed. Multiple measurement tests were performed in the natural icing environment. The average ice thickness measurement error value of short distance (0.5 m)/long distance (35 m) is 0.31 mm/8.9 mm, and the average ice thickness measurement error rate is 2.62% /6.0%.

Evaluation of Severity of Infectious Pneumonia for Newborn Using Ultrasound Image under Adaptive Image Denoising Algorithm

This study was to analyze the ultrasound imaging characteristics of infectious pneumonia of newborn in different conditions and the differences in neurobehavioral development. An adaptive image denoising (AID) algorithm was constructed based on multiscale wavelet features. It was compared with the transform domain denoising (TDD) algorithm and spatial domain denoising (SDD) algorithm and applied to ultrasound images of newborns with infectious pneumonia. It was found that the peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and feature similarity index (FSIM) of the constructed algorithm were higher than those of the TDD and SDD algorithms ( P &lt; 0.05 ). The ultrasound scores of newborns in noncritical group (group A, 1.54 ± 0.62 scores) were all lower than those of the critical group (group B, 3.96 ± 0.41 scores) and extremely critical group (group C, 4.25 ± 0.35 scores) ( P &lt; 0.05 ). The behavioral ability, passive muscle tension, active muscle tension, and original reflection of the newborns in group A were better than other groups ( P &lt; 0.05 ). It indicated that the constructed algorithm showed better denoising effect on ultrasound images, which could effectively evaluate the severity of newborns’ infectious pneumonia.

Study on theoretical analysis of C4F7N infrared spectra and detection method of mixing ratio of the gas mixture

SF6 gas is widely used in power industry because of its good insulation, but it's an extremely potent greenhouse gas. To actively respond to climate change, the research of new environment-friendly gas insulating medium is an important research direction. C4F7N gas is the most potential environmentally friendly insulating gas instead of SF6 applied in high-voltage electrical equipment. C4F7N/CO2 gas mixture insulation equipment has been gradually promoted and used. The insulation performance of the gas mixture can be obtained by determining the content of C4F7N in the gas mixture. Therefore, the detection of mixture ratio of C4F7N gas has important engineering significance. In this paper, the geometric structure of C4F7N molecule is optimized based on density functional theory. Four methods of GGA-PBE, GGA-BLYP, GGA-PW91 and B3LYP were selected to determine the best density functional theory method for calculating the spectral properties of C4F7N molecules. A method for detecting the mixture ratio of C4F7N/CO2 based on infrared spectroscopy is proposed. The results show that: the B3LYP method is the best for the calculation of C4F7N infrared spectrum. A peak processing algorithm based on multi-scale wavelet transform was proposed. After the infrared overlapping peaks of C4F7N/CO2 gas mixture in the band of 750 ∼ 785 cm−1 were processed, the fitting effect has been improved overall. After peak processing, the band consists of four subpeaks, the inversion error can be reduced from 4.8 to 2.7 by using the sub-peak 2 as the eigenvalue of concentration inversion. The research results provide an effective method for detecting the mixing ratio of C4F7N/CO2 gas mixture.

Medical Image Segmentation Algorithm Based on Multi-scale Color Wavelet Texture

In order to improve the segmentation accuracy of brain tumor magnetic resonance medical image, a segmentation method of brain tumor magnetic resonance medical image based on multi-scale color wavelet texture features is proposed. The segmentation model of brain tumor magnetic resonance medical image is established, and the motion damage information of brain tumor magnetic resonance medical image is adaptively fused in the ultrasound imaging environment. The medical image information is enhanced by using the motion skeletal muscle block matching technology. According to the suspicious point feature matching method of brain tumor, the fusion detection and processing of brain tumor magnetic resonance medical image are carried out. The multi-scale color wavelet texture feature detection method is used to extract the image features of brain tumor MRI points, and the CT bright spot features are used to analyze the features of brain tumor MRI medical images. Combined with the adaptive neural network training method, the automatic detection of brain tumor magnetic resonance medical image is completed, and the suspected brain tumor points are extracted, so as to realize the segmentation of brain tumor magnetic resonance medical image. Simulation results show that the proposed method can effectively improve the segmentation accuracy of brain tumor MRI medical image, and has high resolution and accuracy for suspicious brain tumor detection.

Temporal characterization of minute-level PM2.5 variation within a local monitoring network using DWT-DTW

Meticulously understanding the local processes of particulate pollution can help evaluate and mitigate its impact on residents. However, this issue is not sufficiently addressed on intra-community scales, as the characterization and comparison of short-term variations in urban environment is challenged by dynamic misalignment. Our study integrates discrete wavelet transforms (DWT) and dynamic time warping (DTW) to tackle this problem, and formulate practical pollution process indicators from a time-domain perspective. Specifically, original PM2.5 series are decomposed into multi-scale wavelet approximates, which are temporally realigned using DTW. Then, background variation series is estimated by seeking commonality among the majority of stations on time and frequency domains. Indicators are calculated by comparing local PM2.5 variation and estimated background variation, thus describing the local processes of background pollution episodes and discovering possible local pollution incidents. On this basis, empirical analysis in a campus network identified distinct information conveyed on different temporal scales. Case study discovered four phases within a 3-day period based on changes in dominating temporal scale of the background series, which is consistent with known pollution processes. Respective investigations of each phase show good capability in reflecting the influence of terrain, meteorology and dominant emission sources. Inter-station comparisons suggest significant influence from micro-scale spatial environment even when subject to exterior emissions. In general, the method can provide pertinent indicators for evaluation, prediction and optimization efforts in local pollution mitigation. The empirical results imply potentials of urban design measures for such mitigation, on which our future studies will focus.

Sparsity-guided multi-scale empirical wavelet transform and its application in fault diagnosis of rolling bearings

Sparsity-guided multi-scale empirical wavelet transform and its application in fault diagnosis of rolling bearings

Adaptive Multi-Scale Wavelet Neural Network for Time Series Classification

Wavelet transform is a well-known multi-resolution tool to analyze the time series in the time-frequency domain. Wavelet basis is diverse but predefined by manual without taking the data into the consideration. Hence, it is a great challenge to select an appropriate wavelet basis to separate the low and high frequency components for the task on the hand. Inspired by the lifting scheme in the second-generation wavelet, the updater and predictor are learned directly from the time series to separate the low and high frequency components of the time series. An adaptive multi-scale wavelet neural network (AMSW-NN) is proposed for time series classification in this paper. First, candidate frequency decompositions are obtained by a multi-scale convolutional neural network in conjunction with a depthwise convolutional neural network. Then, a selector is used to choose the optimal frequency decomposition from the candidates. At last, the optimal frequency decomposition is fed to a classification network to predict the label. A comprehensive experiment is performed on the UCR archive. The results demonstrate that, compared with the classical wavelet transform, AMSW-NN could improve the performance based on different classification networks.

Rolling Bearing Fault Diagnosis Based on VMD-MPE and PSO-SVM

The goal of the paper is to present a solution to improve the fault detection accuracy of rolling bearings. The method is based on variational mode decomposition (VMD), multiscale permutation entropy (MPE) and the particle swarm optimization-based support vector machine (PSO-SVM). Firstly, the original bearing vibration signal is decomposed into several intrinsic mode functions (IMF) by using the VMD method, and the feature energy ratio (FER) criterion is introduced to reconstruct the bearing vibration signal. Secondly, the multiscale permutation entropy of the reconstructed signal is calculated to construct multidimensional feature vectors. Finally, the constructed multidimensional feature vector is fed into the PSO-SVM classification model for automatic identification of different fault patterns of the rolling bearing. Two experimental cases are adopted to validate the effectiveness of the proposed method. Experimental results show that the proposed method can achieve a higher identification accuracy compared with some similar available methods (e.g., variational mode decomposition-based multiscale sample entropy (VMD-MSE), variational mode decomposition-based multiscale fuzzy entropy (VMD-MFE), empirical mode decomposition-based multiscale permutation entropy (EMD-MPE) and wavelet transform-based multiscale permutation entropy (WT-MPE)).

Identification of autonomous nonlinear dynamical system based on discrete-time multiscale wavelet neural network

Identification of autonomous nonlinear dynamical system based on discrete-time multiscale wavelet neural network

Flow regime recognition in a long pipeline-riser system based on signals at the top of the riser

To identify conveniently multiphase flow regimes in subsea pipeline-risers, we study in this paper experimentally two-phase flows in a 1657 m long pipeline with an S-shaped riser to simulate field experiment, within a wide range of gas and liquid velocities. Three flow regimes, namely severe slugging, transitional flows, and stable flows, are analyzed based on three differential pressure and one pressure signals at the top of the riser; comparatively speaking, the positions of these signals in the experimental system are similar to those of the sea level signals in industrial fields, which are easy and less expensive to obtain. The obtained signals are decomposed into six scales via a multi-scale wavelet analysis, and further four statistical parameters on each scale are extracted, including mean values, standard deviations, ranges, and mean values of absolute. We compared the effects of six SVM classifiers with different kernel functions on the recognition rate of flow regimes, and it is found the recognition rates of SVM classifier with quadratic and cubic kernel functions are the highest. Further, the principal component analysis is employed to reduce the dimension of statistical parameters and it indicates that the recognition rate tends to increase with the rising number of principal components from 1 to 6, and it remains constant if the principal component number is further increased. Moreover, The results suggest that the recognition rate obtained from the pressure difference between the top of the riser and the separator peaks, and then it comes that from the pressure signal at the top of the riser, and that for the pressure difference signal at the top of the riser is the least satisfying one. As for the optimal differential pressure signals between the top of the riser and the separator, the results show that the recognition rate increases rapidly from 70.2% to 90.4% when the sample duration rising from 2.3 s to 18.6 s, and when the sample duration exceeds 74.4 s, the recognition rate exceeds 92.9% and remains unchanged.

Multi-Spectral Fusion and Denoising of Color and Near-Infrared Images Using Multi-Scale Wavelet Analysis.

We formulate multi-spectral fusion and denoising for the luminance channel as a maximum a posteriori estimation problem in the wavelet domain. To deal with the discrepancy between RGB and near infrared (NIR) data in fusion, we build a discrepancy model and introduce the wavelet scale map. The scale map adjusts the wavelet coefficients of NIR data to have the same distribution as the RGB data. We use the priors of the wavelet scale map and its gradient as the contrast preservation term and gradient denoising term, respectively. Specifically, we utilize the local contrast and visibility measurements in the contrast preservation term to transfer the selected NIR data to the fusion result. We also use the gradient of NIR wavelet coefficients as the weight for the gradient denoising term in the wavelet scale map. Based on the wavelet scale map, we perform fusion of the RGB and NIR wavelet coefficients in the base and detail layers. To remove noise, we model the prior of the fused wavelet coefficients using NIR-guided Laplacian distributions. In the chrominance channels, we remove noise guided by the fused luminance channel. Based on the luminance variation after fusion, we further enhance the color of the fused image. Our experimental results demonstrated that the proposed method successfully performed the fusion of RGB and NIR images with noise reduction, detail preservation, and color enhancement.