Use Of Wavelet Analysis Research Articles

Hybrid wavelet-neural network models for time series

The use of wavelet analysis contributes to better modeling for financial time series in the sense of both frequency and time. In this study, S&P500 and NASDAQ data are separated into several components utilizing multiresolution analysis (MRA). Subsequently, using an appropriate neural network structure, each component is modeled. In addition, wavelets are used as an activation function in long short-term memory (LSTM) networks to form a hybrid model. The hybrid model is merged with MRA as a proposed method in this paper. Four distinct strategies are employed: LSTM, LSTM+MRA, hybrid LSTM-Wavenet, and hybrid LSTM-Wavenet+MRA. Results show that the use of MRA and wavelets as an activation function together reduces the error the most.

A wavelet-enhanced adaptive hierarchical FFT-based approach for the efficient solution of microscale boundary value problems

This contribution focuses on the development of an adaptive hierarchical FFT-based approach for the efficient solution of microscale boundary value problems. To this end, the classic Moulinec–Suquet scheme is revisited and enhanced by making use of wavelet analysis. Governing fields are represented in a wavelet basis and higher level stress approximations in a nested set of approximation spaces are successively derived by making use of wavelet transforms. By adaptively refining the computational grid based on the solution profile, localised features can be resolved accurately while the overall number of material model evaluations is significantly reduced. The performance is demonstrated by a detailed study of representative boundary value problems in one- and two-dimensional domains, whereby a reduction in the number of material model evaluations of up to 95% has been achieved.

Estimation of the Basin Outflow by Wavelet Neural Network, Conjunctive Use of Wavelet Analysis and Artificial Neural Network

Estimation of the Basin Outflow by Wavelet Neural Network, Conjunctive Use of Wavelet Analysis and Artificial Neural Network

Analysis of Low-Density Heat Flux Data by the Wavelet Method

When evaluating the energy efficiency of buildings and implementing the necessary measures to increase energy efficiency levels, thermal technical characteristics are determined. For this purpose, in situ measurements of the thermal resistance of external enclosing structures were carried out. One of the methods most often used by researchers is the non-destructive method—the heat flow meter (HFM) method regulated by ISO 9869. In the case of surveying a building with a high level of thermal resistance, researchers are faced with low-density heat flux measurements, which is always a difficult task due to significant fluctuations and the influence of external factors on the measurement results. This is due to the fact that it is difficult to determine what is a useful signal and what is a consequence of the effects of non-stationarity and heat transfer conditions. The article provides an example of low-density heat flux measurements when determining the thermal resistance of a building and proposes a data pre-processing procedure that allows for the reduction of heat flux fluctuations, which has a significant impact on the final result at low density. The proposed use of wavelet analysis in the pre-processing of low-density heat flux measurement data makes it possible to reconstruct them or reduce disturbances that occur during research. A comparison of the obtained results with the results of the calculation according to ISO 9869-1 showed a decrease in the standard deviation of the measurements from 5.74 to 2.81%. The results of this study can be used to reduce the noise of low-density heat flux and, as a result, reduce the standard deviation of the measurement when applying the HFM method of determining the thermal resistance of external enclosing structures.

Application of the wavelet transformation theory in the algorithm for constructing a quasigeoid model

Purpose. To investigate the interaction of geodesic and normal altitude indicators according to quasigeoid data, the joint use of space measurements and those performed on the Earths surface in the implementation of geodetic tasks. In this article, the task is to create a calculation algorithm for further research on the quasigeoid model and the application of the model in solving geodetic problems. Methodology. Reliable determination of the height anomaly requires great accuracy, therefore, the theory of wavelet-transformation was used in the model of the variant of space technologies as an alternative to the laborious leveling of the Earths surface, which characterizes the actual fluctuations from the normal of the Earths gravitational field, when calculating the mean square deviations of the plumb line is an urgent task. Findings. A block diagram of the calculation algorithm has been compiled using a software package to solve the boundary problem of physical geodesy, in which the Earths surface is subject to modern space measurements. Originality. The use of wavelet analysis for processing information from satellite data in geodesy improves the results of image classification, and the coefficients of the wavelet transformation can be used as indicators for recognizing the coordinates of points with high accuracy. Practical value. Application of the theory of wavelet transformations as a powerful mathematical tool for solving problems of geodetic information, data compression and recovery, increasing computing performance, encoding information.

Do commodity markets catch a cold from stock markets? Modelling uncertainty spillovers using Google search trends and wavelet coherence

We investigate stock market uncertainty spillovers to commodity markets using wavelet coherence and a general stock market-related Google search trends (GST)-based index to proxy for uncertainty. GST reflect stock market uncertainty over short-, medium- and long-term horizons. Periods of association between GST and the VIX, a widely used proxy for stock market uncertainty, coincide with economic, financial, and geopolitical events. The association between the VIX and GST has grown over time. In line with economic psychology, this implies that during times of heightened uncertainty investors increasingly search for stock market-related information. Our analysis further reveals that some commodities are more susceptible to uncertainty spillovers from stock markets, notably energy commodities. We demonstrate how GST may be used to isolate the impact of specific events and show that COVID-19 had a disproportionate impact on commodity price volatility. We also find that energy, livestock and precious metals are increasingly integrated with stock markets. Spillover analysis repeated using the VIX produces similar results and reflects information that is also reflected in GST, confirming an uncertainty narrative. The use of wavelet analysis and GST to proxy for general and event specific uncertainty offers an alternative perspective to traditional econometric approaches and may be of interest to econometricians, analysts, investors and researchers.

Statistical Evaluation of the Influences of Precipitation and River Level Fluctuations on Groundwater in Yoshino River Basin, Japan

Precise evaluation of the correlations among precipitation, groundwater and river water enhance our understanding on regional hydrological circulation and water resource management. The innovative and efficient use of wavelet analysis has been able to identify significant interactions in the spatial and temporal domains and to estimate the recharge travel time. In this paper, a wavelet analysis was utilized to analyse 43 years of monthly, and 2 years of daily, precipitation, river level and groundwater level data in the Yoshino River Basin, Japan. There were two main results: (1) There was a significant influence of precipitation and river on groundwater, with a periodicity of 4–128 days, 1 year and 2–7 years. The periodicity of 1 year was correlated with seasonal variability. The significant interaction at 4–128 days mainly occurred in the rainy season. The 2–7-year oscillation of aquifer water levels was determined by precipitation. (2) The recharge-water travel times in the study area estimated from the arrow patterns in the precipitation–groundwater wavelet coherence (WTC) were consistent for each observation well. The response times of the aquifer to precipitation were 1 day and 3–6 days in 2013 and 2014, respectively. The different time lags were likely determined by the timing of maximum daily precipitation.

Use of wavelet analysis in the study of the bottom relief of the Peter the Great Bay of the Sea of Japan

Use of wavelet analysis in the study of the bottom relief of the Peter the Great Bay of the Sea of Japan

Method of Wavelet Analysis of Time Series to Assess the Effectiveness of the Country’s Energy Security

This article addresses the problems of energy security at the level of Russian regions, which is a particularly urgent in modern economic conditions characterized by global digitalization processes. In this case, the problem arises the need to develop mathematical tools for planning and assessing energy security in conditions of high uncertainty and fluctuations of the studied parameters of the external environment.The paper presents the mathematical justification for the use of wavelet analysis and the construction of spaces of scaling functions in order to obtain the theorem of multifunctional analysis of economic parameters and indicators of regional energy security, based on many intervals and determining the corresponding wavelet spaces.

Measurement of the angular motion parameters of the mirror of the scanning device

A scanning device for a space-based environmental monitoring system has been investigated. The main attention is paid to the study of the parameters of the angular motion of the mirror of the scanning device, the uniformity of rotation of which largely determines the quality of the image of the Earth's surface. The principle and results of measuring the parameters of the mirror rotation carried out in a wide angular range are considered. The measurements were performed using a dynamic goniometer-autocollimator, which has been calibrated at the State Standard of Plane Angle Unit GET 22-2014. The repeatability of the average angular velocity of the scanning device mirror and the repeatability of the initial scanning angle are calculated. Nonstationarity in mathematical expectation and variance in random deviations of the angular motion of the mirror from the linear law of scanning is noted. The use of wavelet analysis revealed the frequency of excitation of oscillations in the low-frequency region of the spectrum. The possibility of using the a dynamic goniometer-autocollimator for measuring not only the angular position of the scanning device mirror, but also the angular velocity is shown.

Wavelet Transforms of Diagnosable Signals from Ship Power Complexes in a MATLAB Environment

The use of digital technologies in the systems of diagnostics and monitoring of units of a ship’s propulsion plant can significantly increase the efficiency and quality of assessing the technical condition of operated objects in the online mode as well as expand the class of practical problems to be solved. Digital processing of signals of complex configuration at a qualitatively new level is an indispensable condition for a critical improvement in the course of processing the current values of diagnosable parameters, increasing the reliability and trouble-free performance of a ship’s technical equipment during operation. A method of approximation has been discussed in the paper. Moreover, the paper provides an algorithm for analyzing the signal of the indicator diagram of a marine diesel engine, the spectrum of which contains high-frequency components and short-term pulses indicating deviations from the normal operating mode, the assessment of which is practically impossible with the traditionally applied methods of spectral analysis of signals. The approximation method is based on the use of wavelet analysis, which makes it possible to deeply explore such modes. Examples of using wavelet analysis to approximate one-dimensional signals of elements and systems of a ship’s power complexes are given.

Properties of the Variability of the Solar Constant as an Index of Solar Activity

The properties of the solar constant variability are considered according to the results of satellite observations ( http://lasp.colorado.edu/home/sorce/data/tsi-data/ ). The obtainment of satellite data with an accuracy of 0.01% that is devoid of atmospheric influence allows a detailed analysis of variations in this index of solar activity and space weather for solar-activity cycles 21–24. The use of wavelet analysis demonstrates the properties of the 11-year cycle in the variation of the solar constant. With the exclusion of variations of the 11-year cycle, it is possible to study short-period processes in each solar cycle. The variations in the solar constant demonstrate their own local spectrum of power periods, which differs from the activity periods according to sunspot observations. The most significant decrease in the solar constant occurs during the passage in the center of the solar disk of large groups of spots and activity complexes that block the solar constant. Thus, the basic properties of the intrinsic variability of the solar constant differ from the properties of the magnetic cycle.

Effect of Local Vibrations on Plantar Skin Blood Flow Responses During Weight-bearing Standing in Healthy Volunteers

The objective of this study was to examine the effects of local vibrations on plantar skin blood flow (SBF) responses during weight-bearing standing. Wavelet analysis of plantar SBF was used to analyze microvascular regulation in response to standing with and without local vibrations. Fifteen (15) healthy participants (26.5 ± 5.7 years; 4 male and 11 female) received a local vibration intervention (35 Hz, 1 mm, 2 g vibration) and a sham vibration to the skin of the right first metatarsal head during 10-minute standing. Laser Doppler flowmetry was used to measure SBF before and after 10 minutes of standing. SBF after standing was expressed as a ratio of SBF before standing to minimize blood flow variations. The use of wavelet analysis allowed the authors to examine the frequency bands corresponding to the physiological controls in the vibration and sham areas of the foot, including metabolic (0.0095-0.02 Hz), neurogenic (0.02-0.05 Hz), myogenic (0.05-0.15 Hz), respiratory (0.15-0.4 Hz), and cardiac (0.4-2.0 Hz) regulations. Plantar SBF ratio changes in the vibration protocol (1.83 ± 0.27) were significantly higher compared with the sham protocol (0.97 ± 0.08) (P < .01). SBF before and after the 35 Hz vibrations were 41.96 ± 14.02 perfusion units (range 6.68-208.9 perfusion units) and 61.16 ± 14.74 perfusion units (range 7.76-155.37 perfusion units), respectively. SBF before and after the sham vibration were 37.32 ± 9.29 perfusion units (range 5.74-120.44 perfusion units) and 33.97 ± 8.11 perfusion units (range 6.95-108.44 perfusion units), respectively. Wavelet analysis of SBF oscillations showed a significant difference in all regulations: metabolic (P < .05), neurogenic (P < .05), myogenic (P < .05), respiratory (P < .05), and cardiac (P < .05) in response to 35 Hz local vibrations compared with the sham vibration. Local vibrations (35 Hz frequency, 1 mm amplitude) to the plantar tissues during 10 minutes of weight-bearing standing resulted in a significant increase in after-standing plantar SBF compared with sham vibration. The control mechanisms contributing to this increase in SBF were metabolic, neurogenic, myogenic, respiratory, and cardiac regulations. These findings confirm results of preclinical studies and support the need for additional research to examine the potential protective effects of local vibration to decrease the risk of plantar ulcers.

The Use of Wavelet Analysis to Improve the Accuracy of Pavement Layer Thickness Estimation Based on Amplitudes of Electromagnetic Waves.

The article discusses one of the methods of dielectric constant determination in a continuous way, which is the determination of its value based on the amplitude of the wave reflected from the surface. Based on tests performed on model asphalt slabs, it was presented how the value of the dielectric constant changes depending on the atmospheric conditions of the measured surface (dry, covered with water film, covered with ice, covered with snow, covered with de-icing salt). Coefficients correcting dielectric constants of hot mix asphalt (HMA) determined in various surface atmospheric conditions were introduced. It was proposed to determine the atmospheric conditions of the pavement with the use of wavelet analysis in order to choose the proper dielectric constant correction coefficient and therefore improve the accuracy of the pavement layer thickness estimation based on the ground penetrating radar (GPR) method.

On wavelet-based statistical process monitoring

This paper presents an overview of wavelet-based techniques for statistical process monitoring. The use of wavelet has already had an effective contribution to many applications. The increase of data availability has led to the use of wavelet analysis as a tool to reduce, denoise, and process the data before using statistical models for monitoring. The most recent review paper on wavelet-based methods for process monitoring had the goal to review the findings up to 2004. In this paper, we provide a recent reference for researchers and engineers with a different focus. We focus on: (i) wavelet statistical properties, (ii) control charts based on wavelet coefficients, and (iii) wavelet-based process monitoring methods within a machine learning framework. It is clear from the literature that wavelets are widely used with multivariate methods compared to univariate methods. We also found some potential research areas regarding the use of wavelet in image process monitoring and designing control charts based on wavelet statistics, and listed them in the paper.

Passive Airborne Fourier Transform Infrared Remote Detection of Methanol by Use of Wavelet Analysis as A Feature Extraction Method

Wavelet analysis was evaluated as a data preprocessing tool in the construction of automated classifiers for the detection of volatile organic compounds from passive Fourier transform infrared remote sensing data collected in a downward-looking mode from an aircraft platform. The discrete wavelet transform was applied to single-beam spectra and patterns were formed with either the wavelet coefficients directly or with spectra reconstructed with selected resolution levels of the wavelet decomposition. Automated classifiers were constructed with support vector machines (SVM) and used to detect releases of methanol from an industrial site. A key issue in this work was the desire to use data collected during controlled experiments on the ground to train the SVM classifiers. Spectral backgrounds in these ground-collected data are different than those encountered as the aircraft flies, however, and the development of successful classification models requires spectral preprocessing to suppress background signatures. Biorthogonal wavelets were used to generate patterns and resulted in SVM models that produced no missed methanol detections and false detection rates of less than 0.1% when applied to prediction data not used in the development of the model. The SVM classifiers constructed with wavelet processing were compared to one based on unprocessed spectra and also to one computed with spectra preprocessed with Butterworth high-pass digital filters.

Use of wavelet analysis for an objective evaluation of the formation of pills in nonwoven fabrics

A quantitative technique to measure pill formation on fabrics has been developed using a wavelet analysis. This technique permits the damage of fabrics to be evaluated with a minimum of human interpretation. A two-dimensional, discrete-wavelet transform was applied to images of nonwoven fabrics, and an optimal approach was found by which the background information could be eliminated from the digital data to obtain characteristic information about the pills. This information, corresponding to the degree of damage, is expressed in terms of a gray-value ratio that is extracted from the details of the wavelet characterization. It has been shown that the resultant parameter correlates well with an independent, qualitative assessment of damage.

Use of Wavelet Analysis for Determining the Stability of the Banking System

The possibility and feasibility of using wavelet analysis to disclose the stability of the banking system operation were justified in the article. The main stages of wavelet analysis for disclosing the stability of the banking system operation were defined.

Physical Optics Methods of Recording Weak Structural Responses of Dispersed Clay Systems to the Effect of Microwave Radiation

A complex of physical optics methods that includes x-ray phase analysis, colorimetry, and wavelet analysis is proposed. Weak structural responses of dispersed clay systems to the effect of microwave radiation are recorded by means of the complex. Through the use of a combination of x-ray phase analysis and colorimetric gradation, it is possible to establish phase and polymorphic conversions, and with the use of wavelet analysis, the evolution of the morphology of dispersed particles. The efficiency of the proposed complex of physical optics methods for studying secondary phase morphologies in the millimeter, micrometric, and submicrometric scales is demonstrated.

WO-GRID METHOD OF STRUCTURAL ANALYSIS BASED ON DISCRETE HAAR BASIS. PART 1: ONE-DIMENSIONAL PROBLEMS

The distinctive paper is devoted to the two-grid method of structural analysis based on discrete Haar basis (in particular, the simplest one-dimensional problems are under consideration). A brief review of publications of recent years of Russian and foreign specialists devoted to the current trends in the use of wavelet analysis in construction mechanics is given. Approximations of the mesh functions in discrete Haar bases of zero and first levels are described (the mesh function is represented as the sum in which one term is its approximation of the first level, and the second term is so-called complement (up to the initial state) on the grid of the first level). Projectors are constructed for the spaces of vector functions of the original grid to the space of their approximation on the first-level grid and its complement (the detailing component) to the initial state. Basic scheme of the two-grid method is presented. This method allows solution of boundary problems of structural mechanics with the use of matrix operators of significantly smaller dimension. It should be noted that discrete analogue of the initial operator equation (defined on a given interval) is a system of linear algebraic equations (SLAE) constructed within finite difference method (FDM) or the finite element method (FEM). Next, the transition to the resolving SLAE is done. Block Gauss method is used for its direct solution (forward-backward algorithm is realized). We consider a numerical solution of the boundary problem of bending of the Bernoulli beam lying on an elastic foundation (within Winkler model) as a practically important one-dimensional sample. There is good consistency of the results obtained by the proposed method and by standard finite difference method.