Wavelet Multiresolution Analysis Research Articles

Diagnostics of changes in the dynamics of complex systems from transient processes based on multiresolution wavelet analysis

With the use of multiresolution wavelet analysis, the possibilities of diagnosing changes in the dynamical regimes of complex systems from transient processes depending on the rate of variations of control parameters are studied. Estimates are made of the minimum sample size that allows diagnosing a change in the dynamical regime of systems with self-sustained oscillations on the example of transient processes during the formation or destruction of synchronous chaotic oscillations. Keywords: multiresolution analysis, random process, nonstationarity, wavelet.

Wavelet Multiresolution Analysis Based Speech Emotion Recognition System Using 1D CNN LSTM Networks

Wavelet Multiresolution Analysis Based Speech Emotion Recognition System Using 1D CNN LSTM Networks

Диагностика изменений динамики сложных систем по переходным процессам на основе многомасштабного вейвлет-анализа

With the use of multiresolution wavelet analysis, the possibilities of diagnosing changes in the dynamical regimes of complex systems from transient processes depending on the rate of variations of control parameters are studied. Estimates are made of the minimum sample size that allows diagnosing a change in the dynamical regime of systems with self-sustained oscillations on the example of transient processes during the formation or destruction of synchronous chaotic oscillations.

Hurst exponent dynamics of S&P 500 returns: Implications for market efficiency, long memory, multifractality and financial crises predictability by application of a nonlinear dynamics analysis framework

In this study, we conduct a rolling window approach to wavelet-filtered (denoised) S&P500 returns (2000−2020) to obtain time-varying Hurst exponents. We discuss implications of Hurst exponent dynamics such as the complete invalidity of the efficient market hypothesis (EMH), an explicative rationale for momentum crashes and potentials for crises predictability. We analyse the dynamics of the Hurst exponents by applying a novel nonlinear dynamics analysis framework for non-stationary and nonlinear time series. The latter framework includes statistical tests, a recurrence quantification analysis (RQA), a wavelet multi-resolution analysis (MRA) and a multifractal detrended fluctuation analysis (MFDFA) paired with subsequent multifractal analyses. Besides, we display empirical findings taken out of the academic literature and critically elaborate on the impact of our findings and future prospects.

A three-dimensional B-spline wavelet finite element method for structural vibration analysis

In this study, a three-dimensional (3-D) B-spline wavelet finite element method (WFEM) is proposed by combining the wavelet theory and 3-D finite element method (FEM). Owing to the semi-orthogonality and multi-resolution analysis of spline wavelet over the solution domain, a cuboid with uniform distribution nodes is established for the 3-D B-spline wavelet on the interval (BSWI) element. The governing equations of vibration for the elastic structures are derived by introducing the 3-D B-spline wavelet theory into the displacement components of each node. A procedure for assembling the BSWI elements is presented by redefining the index element node functions. Numerical studies including the vibration analysis of solid and hollow beams and plates under different boundary conditions are performed to show the performance of the present method. A comprehensive comparison of the predicted vibration characteristics obtained by the present method, traditional FEM, and reference data is presented to verify the accuracy and efficiency of the 3-D B-spline WFEM. The core of the present method is involving the 3-D B-spline wavelet to replace the polynomial interpolation functions in the traditional FEM, which enhances computational accuracy during the vibration analysis of the elastic structures.

Multifractal formalism combined with multiresolution wavelet analysis of physiological signals

Multifractal formalism combined with multiresolution wavelet analysis of physiological signals

Multiresolution wavelet analysis of transients: numerical simulations and application to EEG

Multiresolution wavelet analysis of transients: numerical simulations and application to EEG

A Method for Representing Non-Standard Waveform in Factory Tests Using Impulse Waveforms

The standard 1.2/50 lightning impulse test has been important for factory testing equipment and evaluating their performance in electrical systems. In practice, however, such equipment is subject to non-standard waveform (NSW) of high frequencies, which may not be covered by standard tests. To overcome this difficulty, the present article outlines a method that simulates NSW in laboratory tests. Based on multiresolution wavelet analysis, the method considers the correlation between amplitude and entropy in the decomposition levels between waveforms. To that end, changes are proposed to the following parameters of standard impulse tests: amplitude, cut-off instant, and front time. The results show that, mostly, the combination of a lightning impulse waveform (LIW) with impulse waves cut at different times, sufficiently represent the NSW. Only when the NSW's density falls predominantly in a frequency range above 3.125 MHz, will there be need for a complementary LIW with a steep front time. The method's application allows manufacturers and concessionaires to subject the equipment to conditions that properly represent the NSW effects, through lightning impulse tests carried out at the factory.

Image Reconstruction with Multiscale Interest Points Based on a Conditional Generative Adversarial Network

A new image reconstruction (IR) algorithm from multiscale interest points in the discrete wavelet transform (DWT) domain was proposed based on a modified conditional generative adversarial network (CGAN). The proposed IR-DWT-CGAN model generally integrated a DWT module, an interest point extraction module, an inverse DWT module, and a CGAN. First, the image was transformed using the DWT to provide multi-resolution wavelet analysis. Then, the multiscale maxima points were treated as interest points and extracted in the DWT domain. The generator was a U-net structure to reconstruct the original image from a very coarse version of the image obtained from the inverse DWT of the interest points. The discriminator network was a fully convolutional network, which was used to distinguish the restored image from the real one. The experimental results on three public datasets showed that the proposed IR-DWT-CGAN model had an average increase of 2.9% in the mean structural similarity, an average decrease of 39.6% in the relative dimensionless global error in synthesis, and an average decrease of 48% in the root-mean-square error compared with several other state-of-the-art methods. Therefore, the proposed IR-DWT-CGAN model is feasible and effective for image reconstruction with multiscale interest points.

Volumetric Rendering on Wavelet-Based Adaptive Grid

Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.

Misfire Detection in Automotive Engines Using a Smartphone through Wavelet and Chaos Analysis.

Besides the failures that cause accidents, there are the ones responsible for preventing the car’s motion capacity. These failures cause inconveniences to the passengers and expose them to the dangers of the road. Although modern vehicles are equipped with a failure detection system, it does not provide an online approach to the drivers. Third-party devices and skilled labor are necessary to manage the data for failure characterization. One of the most common failures in engines is called misfire, and it happens when the spark is weak or inexistent, compromising the whole set. In this work, two algorithms are compared, based on Wavelet Multiresolution Analysis (WMA) and another using an approach performing signal analysis based on Chaos using the density of maxima (SAC-DM) to identify misfare in a combustion engine of a working automotive vehicle. Experimental tests were carried out in a car to validate the techniques for the engine without failure, with failure in one piston, and with two failed pistons. The results made it possible to obtain the failure diagnosis for 100% of the cases for both WMA and SAC-DM methods, but a shorter time window when using the last one.

The Statistical Analysis of Anomalous Anticyclone in Ocean Atmosphere and Economy Based on Target Tracking Algorithm

Based on the importance of climate change in the environmental and economic fields, this study analyzes the impact of climate change on the economy based on the current situation, including the impact on sensitive industries and the impact on each district, in order to study the impact of abnormal atmospheric anticyclones on the economy. Furthermore, this study enhances the image-tracking algorithm, fuses the registered radar picture using the wavelet multiresolution analysis approach, and decomposes the registered radar image using the Mallat algorithm to retrieve the low- and high-frequency components of the image. Because the information included in the frequency components after wavelet decomposition differs, this study uses appropriate fusion algorithms for the decomposed low-frequency and high-frequency components, respectively, to produce panoramic photographs with acceptable visual effects. Through experimental research, it can be seen that the statistical analysis model of anomalous anticyclone in ocean atmosphere and economy based on the target tracking algorithm proposed in this study has a good simulation operation effect, and it also verifies that there is a certain correlation between the atmospheric anomalous anticyclone and the economy.

GeoGravGOCE: A standalone MATLAB GUI for processing GOCE satellite gradient data

The exploitation of data from the Global Ocean Circulation Explorer (GOCE) mission still offers unique insights in Earth system processes despite the fact that the mission has been completed more than eight years ago. The use of GOCE data requires tedious and cumbersome processing in order to extract them from their original format, process them in the various reference frames and filter them to derive final products at the orbital altitude. GeoGravGOCE is an open-source software, developed in MATLAB, which aims to provide a friendly Graphical User Interface (GUI) to process the original GOCE gradiometric observations, i.e., second-order derivatives of the gravitational potential as provided by the European Space Agency. It is composed of four main tabs, which first allows the GOCE gradient pre-processing and the transformation of gradients from a geopotential models to the gradiometric reference frame. Then, the spectral filtering and the mutual transformations of gravity gradients between the four reference systems used in satellite gravimetry can be carried out.. Three main filtering methods are implemented within the software, referring to: Finite Impulse Response (FIR), Infinite Impulse Response (IIR), and Wavelet Multi-Resolution Analysis (WL-MRA) filters. The user is free to select the desired degree of filtering and evaluate the derived results in terms of both the power spectral density of the filtered signals and their spatial distribution. The present work gives an analytical outline of the program, along with its various functionalities, while results derived from the processing of original GOCE data are presented as well. GeoGravGOCE is a free software under the GNU license and can be freely accessed via the project webpage http://olimpia.topo.auth.gr/GeoGravGOCE/.

Effect of a front inclined hole on multiscale vortical structures around a wall-mounted cube

To reveal the multiscale wake structures of a wall-mounted cube and the effects of a front inclined hole (FIH), a combination of wavelet multiresolution analysis and vortex identification techniques is applied to analyze time-resolved particle image velocimetry data. The cube model has a side length D = 50 mm and the Reynolds number ReD = 7800. The inlet of the FIH is located at a height 0.71D on the front surface of the cube, and the outlet is located at the center of the free end. Statistical analysis indicates that an FIH can reduce the recirculation zone around the cube, suppress downwash flow, and alter the development of free-end shear flow. The turbulence intensity and turbulent kinetic energy in the wake also decrease significantly in the presence of an FIH. The wavelet multiresolution analysis shows that the main structures of the flow field experience a transformation from small to intermediate and then large scales from the shear layer around the standard cube to its wake. However, in the presence of an FIH, the scale of the flow structure near the free end becomes smaller, the large-scale structure in the wake is weakened, and the transition from small to intermediate scales is no longer obvious. The wavelet vortex dynamics analysis reveals the evolutions of vortex structures with different scales. In the presence of an FIH, the trend of large- and intermediate-scale coherent structures moving to the bottom wall is weakened, while the streamwise extent of small-scale structures is greater. In the large-scale component of the wake, a transverse secondary vortex is observed, which is formed by the combined action of a shedding transverse vortex and downwash flow.

An Innovative Dynamic Mobility Sampling Scheme Based on Multiresolution Wavelet Analysis in IoT Networks

Mobility is a key aspect of modern networking systems. To determine how to better manage the available resources, many architectures aim to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> know the future positions of mobile nodes. This can be determined, for example, from mobile sensors in a smart city environment or wearable devices carried by pedestrians. If we consider infrastructure networks, frequently changing the coverage cell may lead to service disruptions if a predictive approach is not deployed in the system. All predictive systems are based on the storage of old mobility samples to adequately train the model. Our focus is based on the possibility to determine an approach for adaptively sampling mobility patterns based on the intrinsic features of the human/node behavior. Several works in the literature examine mobility prediction mobile networks, but all of them are dedicated to the study of time features in mobility traces: none took into account the spectral content of historical mobility patterns for predictive purposes. In contrast, we take into account this spectral content in mobility samples. Through a set of wavelet transforms, we adapted the sampling frequency dynamically and obtained a considerable set of advantages (space, energy, accuracy, etc.). In fact, this issue covers an important role in the IoT paradigm, where energy consumption is one of the main variables requiring optimization (frequent and unnecessary mobility samplings can disrupt battery life). We performed several simulations using real-world traces to confirm the merit of our proposal.

FIR, IIR and Wavelet Algorithms for the Rigorous Filtering of GOCE SGG Data to the GOCE MBW

Gravity field and steady-state Ocean Circulation Explorer (GOCE) data are strongly affected by noise and long-wavelength errors outside the satellite measurement bandwidth (MBW). One of the main goals in utilizing GOCE data for gravity field modeling is the application of filtering techniques that can remove gross errors and reduce low-frequency errors and high-frequency noise while preserving the original signal. This paper aims to present and analyze three filtering strategies used to de-noise the GOCE Level 2 data from long-wavelength correlated errors and noise. These strategies are Finite Impulse Response (FIR), Infinite Impulse Response (IIR), and Wavelet Multi-resolution Analysis (WL), which have been applied to GOCE residual second order derivatives of the gravity potential. Several experiments were performed for each filtering scheme in order to identify the ideal filtering parameters. The outcomes indicate that all the suggested filtering strategies proved to be effective in removing low-frequency errors while preserving the signals in the GOCE MBW, with FIR filtering providing the overall best results.

A novel traffic accident detection method with comprehensive traffic flow features extraction.

With the rapidly increasing of automobiles, traffic accidents are gradually becoming more frequent. This creates a great need for effective traffic anomaly detection algorithms. Existing methods shed light on directly inferring the abnormalities from traffic flow, which is short in features extraction and representation of traffic flows. In this paper, we propose three new traffic flow features, namely the road congestion, the traffic intensity, and the traffic state instability, for more comprehensive traffic status representation and anomaly detection. Residual analysis, quadratic discrimination, multi-resolution wavelet analysis are integrated for the extraction of the aforementioned features, which will be applied for the downstream tasks of traffic anomaly detection. Experimental results reveal that accident identification based on the proposed features is more effective than the raw traffic flow, which is supposed to provide an alternative approach for further applications and studies.

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.

Acquisition and Classification of Lung Sounds for Improving the Efficacy of Auscultation Diagnosis of Pulmonary Diseases.

PurposeLung diseases are the third leading cause of death worldwide. Stethoscope-based auscultation is the most commonly used, non-invasive, inexpensive, and primary diagnostic approach for assessing lung conditions. However, the manual auscultation-based diagnosis procedure is prone to error, and its accuracy is dependent on the physician’s experience and hearing capacity. Moreover, the stethoscope recording is vulnerable to different noises that can mask the important features of lung sounds which may lead to misdiagnosis. In this paper, a method for the acquisition of lung sound signals and classification of the top 7 lung diseases has been proposed for improving the efficacy of auscultation diagnosis of pulmonary disease.MethodsAn electronic stethoscope has been constructed for signal acquisition. Lung sound signals were then collected from people with COPD, upper respiratory tract infections (URTI), lower respiratory tract infections (LRTI), pneumonia, bronchiectasis, bronchiolitis, asthma, and healthy people. Lung sounds were analyzed using a wavelet multiresolution analysis. To choose the most relevant features, feature selection using one-way ANOVA was performed. The classification accuracy of various machine learning classifiers was compared, and the Fine Gaussian SVM was chosen for final classification due to its superior performance. Model optimization was accomplished through the application of Bayesian optimization techniques.ResultsA test classification accuracy of 99%, specificity of 99.2%, and sensitivity of 99.04%, have been achieved for the 7 lung diseases using the optimized Fine Gaussian SVM classifier.ConclusionOur experimental results demonstrate that the proposed method has the potential to be used as a decision support system for the classification of lung diseases, especially in those areas where the expertise and the means are limited.

WMR-DepthwiseNet: A Wavelet Multi-Resolution Depthwise Separable Convolutional Neural Network for COVID-19 Diagnosis.

Timely discovery of COVID-19 could aid in formulating a suitable treatment plan for disease mitigation and containment decisions. The widely used COVID-19 test necessitates a regular method and has a low sensitivity value. Computed tomography and chest X-ray are also other methods utilized by numerous studies for detecting COVID-19. In this article, we propose a CNN called depthwise separable convolution network with wavelet multiresolution analysis module (WMR-DepthwiseNet) that is robust to automatically learn details from both spatialwise and channelwise for COVID-19 identification with a limited radiograph dataset, which is critical due to the rapid growth of COVID-19. This model utilizes an effective strategy to prevent loss of spatial details, which is a prevalent issue in traditional convolutional neural network, and second, the depthwise separable connectivity framework ensures reusability of feature maps by directly connecting previous layer to all subsequent layers for extracting feature representations from few datasets. We evaluate the proposed model by utilizing a public domain dataset of COVID-19 confirmed case and other pneumonia illness. The proposed method achieves 98.63% accuracy, 98.46% sensitivity, 97.99% specificity, and 98.69% precision on chest X-ray dataset, whereas using the computed tomography dataset, the model achieves 96.83% accuracy, 97.78% sensitivity, 96.22% specificity, and 97.02% precision. According to the results of our experiments, our model achieves up-to-date accuracy with only a few training cases available, which is useful for COVID-19 screening. This latest paradigm is expected to contribute significantly in the battle against COVID-19 and other life-threatening diseases.