Fourier Analysis Techniques Research Articles

Fast harmonic analysis for PHIL experiments with decentralized real-time controllers

This paper proposes and implements, a harmonic analysis technique used in microgrids for inverter power control when measured voltage and current signals are passed over a communication link with considerable latency. Using frequency-shifting and filtering techniques, the measurement is converted to magnitude and phase information and passed over an asynchronous communication link to another controller, where the original waveform is recovered with delay compensation. The method allows accurate power calculations and grid synchronization over distributed prosumer controllers. The proposed method can work at different execution rates, depending on real time (RT) workload, and is shown to be robust against step changes, harmonics and communication delays. The method is demonstrated with two PHIL experiments at the CoSES, TU Munich lab in grid connected and island mode.

Three-Point Boundary Value Problems of Coupled Nonlocal Laplacian Equations

This paper discusses a kind of coupled nonlocal Laplacian evolution equation with Caputo time-fractional derivatives and proportional delays. Green function and mild solution are firstly established by employing the approach of eigenvalues’ expansions and Fourier analysis technique. By the properties of eigenvalues and Mittag–Leffler functions, several vital estimations of Green functions are presented. In view of these estimations and some appropriate assumptions, the existence and uniqueness of the mild solution are studied by utilizing the Leray–Schauder fixed-point theorem and the Banach fixed-point theorem. Finally, an example is provided to illustrate the effectiveness of our main results.

Spectrally modulated polarimetry with wavelength domain analysis.

Spectrally modulated Stokes polarimeters use a pair of high-order crystal retarders to generate a spectrally dependent modulation of the polarization of light. In these systems, the detected intensity versus wavenumber spectrum is usually referred to as a channeled spectrum, and the Fourier inversion of this spectrum allows the determination of Stokes parameters of light without needing any other mechanical or active device for polarization control. This work proposes a spectrally modulated polarimeter beyond the concept of a channeled wavenumber spectrum, so effectively detaching the spectral modulation from the Fourier analysis technique. The wavelength domain analysis we use is best suited for dispersive spectrometers offering intensity versus wavelength measurements. The technique is illustrated with the measurement of very small optical rotations produced by sucrose solutions. The proposed technique is easily extendable to spectrally modulated Mueller polarimeters.

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy.

Cells can crawl, self-heal, and tune their stiffness due to their remarkably dynamic cytoskeleton. As such, reconstituting networks of cytoskeletal biopolymers may lead to a host of active and adaptable materials. However, engineering such materials with precisely tuned properties requires measuring how the dynamics depend on the network composition and synthesis methods. Quantifying such dynamics is challenged by variations across the time, space, and formulation space of composite networks. The protocol here describes how the Fourier analysis technique, differential dynamic microscopy (DDM), can quantify the dynamics of biopolymer networks and is particularly well suited for studies of cytoskeleton networks. DDM works on time sequences of images acquired using a range of microscopy modalities, including laser-scanning confocal, widefield fluorescence, and brightfield imaging. From such image sequences, one can extract characteristic decorrelation times of density fluctuations across a span of wave vectors. A user-friendly, open-source Python package to perform DDM analysis is also developed. With this package, one can measure the dynamics of labeled cytoskeleton components or of embedded tracer particles, as demonstrated here with data of intermediate filament (vimentin) networks and active actin-microtubule networks. Users with no prior programming or image processing experience will be able to perform DDM using this software package and associated documentation.

An Amplitude-Frequency Curve-Based Parameter Sensitivity Analysis for the Conveying Fluid Pipe

Sensitivity analysis is a common way to research the parameters’ impact on complex systems, for instance national economy, environment, ecosystem, etc. The parametric analysis of a conveying fluid pipe is a challenge because it is a complex high-order partial differential system. In this brief, a mechanism-based method is proposed to analyze the parameter sensitivity of the conveying fluid pipe. Firstly, the mathematical model in a high-order partial differential form of the conveying fluid pipe under a harmonic load is deduced and transformed into a nonlinear ordinary differential equation form through the Galerkin truncation. The amplitude-frequency curve of the target system is established by harmonic balance method and matrix analysis technique. Then, the parameter sensitivity is discussed by the analytical results of the amplitude-frequency curve through Newton’s method. Finally, some examples are applied to intuitively illustrate the conveying fluid pipe’s parameter sensitivity.

Cauchy problem for nonlocal diffusion equations modelling Lévy flights

In the present paper, we study the time-space fractional diffusion equation involving the Caputo differential operator and the fractional Laplacian. This equation describes the Lévy flight with the Brownian motion component and the drift component. First, the asymptotic behavior of the fundamental solution of the fractional diffusion equation is considered. Then, we use the fundamental solution to obtain the representation formula of solutions of the Cauchy problem. In the last, the L 2 -decay estimates for solutions are proved by employing the Fourier analysis technique.

Ionospheric Current Variations by Empirical Orthogonal Function Analysis: Solar Activity Dependence and Longitudinal Differences

AbstractThe solar quiet (Sq) ionospheric current variations exhibit spatial and temporal patterns that can be identified by the prevailing eigenmodes based on the empirical orthogonal function (EOF) analysis. In this study, the Sq current function over the American and European/African sectors are derived using ground magnetometer data from 2006 to 2019 based on the spherical harmonic analysis technique. Subsequently, we decomposed the Sq current function into eigenmodes by applying the EOF analysis, where the first three eigenmodes capture 96% of the overall Sq current variance. Additionally, these eigenmodes are utilized to model the Sq current function and compare its properties between the two longitudinal sectors. We observed that the EOF model could reconstruct the observed Sq current function with the first three eigenmodes in both longitudinal sectors. Moreover, the EOF model unveils a clear association of the Sq current function with several driven features, such as magnetic latitude, local time, season, and solar activity. Both longitudinal sectors had comparable Sq current patterns under varying solar activity, while their amplitudes varied. Besides, the newly developed model could reproduce a refined Sq current variability over the two longitudinal sectors as long as the observed Sq variations have sufficient duration. Our EOF model shows that the variations of the Sq current function with solar activity can be explained by the first three eigenmodes, which could be used as a basis for further numerical modeling of the Sq current variations.

Which Parts of the Male Genitalia are More Diagnostic in Terms of Bumblebee Taxonomy?

The insect genitalia work as a perfect taxonomical tool as it is one of the most stable prezygotic isolation powers among species. The details of morphological characters are potentially useful in the recognition and diagnosis of species but sometimes it can be really difficult to find out the details of visible features. Within this context, male genitalia of bumblebees from the Kashmir Himalaya were compared using a model pool of 28 species with 38 taxa from eight subgenera. Three structures that have a function in copulation (penis valve from the postero-dorsal aspect and from the outer lateral aspect, volsella from the interio-ventral aspect, and gonostylus from the dorsal aspect) were inspected and the outline-based geometric morphometric technique of elliptical Fourier analysis were performed. Principal Components Analysis (PCA) and Canonical Variates Analysis (CVA) were used to explain the diagnostic power of these structures for the taxonomy of bumblebees at the subgeneric rank. It was found that the lateral aspect of the penis valve shows greater diagnostic power than the other genital structures investigated. This approach may help future studies by contributing towards solving problems in taxonomy and semi-automatic taxonomical systems.

Struwe-like solutions for an evolutionary model of magnetoviscoelastic fluids

In this work we investigate the existence and uniqueness of Struwe-like solutions for a system of partial differential equations modeling the dynamics of magnetoviscoelastic fluids. The considered system couples a Navier-Stokes type equation with a dissipative equation for the deformation tensor and a Landau–Lifshitz–Gilbert type equation for the magnetization field.The main purpose is to establish a well-posedness theory in a two-dimensional periodic domain under standard assumption of critical regularity for the (possibly large) initial data. We prove that the considered weak solutions are everywhere smooth, except for a discrete set of time values.The proof of the uniqueness is based on suitable energy estimates for the solutions within a functional framework which is less regular than the one of the Struwe energy level. These estimates rely on several techniques of harmonic analysis and paradifferential calculus.

Quench position reconstruction through harmonic field analysis in superconducting magnets

The performances of superconducting magnets for particle accelerators are limited by instabilities or disturbances which lead to the transition of the superconducting material to the normal resistive state and the activation of the quench protection system to prevent damage to the magnet. To locate the position of the state transition, voltage taps or quench antennas are the most commonly used technologies for their reliability and accuracy. However, during the production phase of a magnet, the number of voltage taps is commonly reduced to simplify the construction process and quench antennas are generally used only for dipoles or quadrupoles to limit the antenna design complexity. To increase the accuracy in the reconstruction of the quench event position, a novel method, suitable for magnets with independent superconducting coils and quench protected without the use of quench heaters, is proposed in this paper. This method, based on standard magnetic measurement techniques for field harmonic analysis, can locate the position of the superconductor transition inside the magnet after the quench event when the magnet has been discharged. Analyzing the not allowed harmonics produced in the field quality at zero current, the position of the quenched coils can be retrieved for any magnet orders without increasing the complexity of the dedicated measurement technique.

Empirical Modeling of Ionospheric Current Using Empirical Orthogonal Function Analysis and Artificial Neural Network

AbstractGiven the potential importance of solar quiet (Sq) ionospheric current in geomagnetic field modeling, it is vital to obtain accurate parameters characterizing its variations, particularly the spatial and temporal variations. In this paper, we derived the Sq current function based on the spherical harmonic analysis (SHA) technique using a 14‐year (2006–2019) quiet geomagnetic field record over the American sector. The empirical orthogonal function (EOF) analysis was then applied to deduce temporal and spatial variations of the Sq current. It is observed that the first EOF mode of the Sq current function is dominated by solar activity, while the second and third EOF modes exhibit annual and semiannual variations, respectively. Also, the artificial neural network (ANN) model of Sq current function was constructed to validate the EOF model predictions. While the Sq current intensity predicted by the ANN model is underestimated by 2.83%, the EOF model underpredicted the Sq current intensity by 1.92% relative to the observation. The root mean square error (RMSE) of the EOF model is 0.64 kA. This RMSE is about 79% smaller than that of the ANN model. In addition, both the EOF and ANN models capture the variation of the total Sq current (Jtotal) intensity with respect to solar activity. In principle, the EOF model had an optimal performance at nearly 98% accuracy, with the ANN model exhibiting almost the same degree of accuracy, which appears to be a reference point for ionospheric conditions when looking for space weather applications.

ANALYSIS OF EXPORT FREIGHT TRANSPORTATION OF UKRAINE IN THE RAILWAY AND SEA CONNECTION

The paper analyzes the export transportation of goods by rail and transshipment in seaports of Ukraine using the methods of mathematical statistics. At present, the export of Ukrainian goods to the countries of the world in terms of traffic exceeds imports several times and is the most dynamically developing international trade sector. Despite the unstable political and economic, and since last year also the sanitary-ecological situation in Ukraine and in the world, exports still have a stable positive dynamics among the total volumes of international traffic. The analysis of export cargo with transshipment in seaports showed that for the sixth year in a row grain cargo ranks first among others in terms of exports. On the railway the key type of cargoes in transportations in recent years also became grain which rates of transportation increase annually. The export component of international trade is also based on ferrous metals, ores, oils, chemical and mineral fertilizers, and mechanical engineering products. The total share of the export component for the EU market as Ukraine's main international trading partner increased from 27.3% in 2008 to 37.3% in 2020. Among the problems hindering the further increase in transshipment in seaports is the still underdeveloped infrastructure, despite the available opportunities to increase technical capacity, and as a result - the limited range of cargo and types of vessels for service, and the use of outdated technologies of ship handling and cargo operations in ports. Ukraine's international trade development projects include attracting investors to port infrastructure through concession tenders in seaports, introduction of private locomotive traction on railways, measures to ensure safety of navigation and maintaining the necessary depths in ports, addressing the shortage of rolling stock on railways, infrastructure development port railway stations. The application of the Fourier analysis technique to detect cyclical fluctuations in transport processes made it possible to obtain a forecast function of grain cargo volumes in certain time intervals, which can be used to develop measures to smooth out uneven traffic flows and reduce uncertainties in transport.

Asymptotic behavior of critical dissipative quasi-geostrophic equation in Fourier space

In this paper we show the global existence for critical dissipative quasi-geostrophic equations if ‖θ0ˆ‖L1 is small enough; among others we prove the analyticity of such a solution. If in addition the initial condition verifies |D|−δθ0∈L1(R2) with 0<δ<1, then the solution remains regular and limt→∞⁡tδ‖θˆ(t)‖L1=0. Fourier analysis and standard techniques are used.

Impulse denoising based on noise accumulation and harmonic analysis techniques

In the article, we propose a robust impulse denoising method based on noise accumulation and harmonic analysis techniques (NAHAT filter). Noise accumulation technique is used to improve the ability to detect noisy pixels, and a harmonic function is used to gain the accuracy of restoring gray values of the detected noisy pixels. The proposed method can remove impulse noise very effectively even under high-density impulse noise levels. Moreover, the proposed method can preserve image structures such as the edges and textures well. Based on experimental results, the proposed method obtains good performance under various noise levels as well as outperforms other similar state-of-the-art impulse denoising methods.

Cauchy Problem for General Time Fractional Diffusion Equation

Abstract In the present work, we consider the Cauchy problem for the time fractional diffusion equation involving the general Caputo-type differential operator proposed by Kochubei [11]. First, the existence, the positivity and the long time behavior of solutions of the diffusion equation without source term are established by using the Fourier analysis technique. Then, based on the representation of the solution of the inhomogenous linear ordinary differential equation with the general Caputo-type operator, the general diffusion equation with source term is studied.

Weighted estimates for the Bergman projection on the Hartogs triangle

We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on the Hartogs triangle. The estimates of the operator norm are in terms of a Bekollé-Bonami type constant. As an application of the results obtained, we give, for example, an upper bound for the Lp norm of the Bergman projection on the generalized Hartogs triangle Hm/n in C2.

Stall inception in a contra-rotating fan under radially distorted inflows

The fan of a gas turbine engine is often subject to distortion due to non-uniformities in the incoming flow which could eventually result in an early stall of the fan. Contra-rotating fans have potential aerodynamic advantages and could replace the conventional fan configurations of gas turbine engines. Understanding the phenomenon prior to stall is important to characterise the behaviour of the stage at low mass flow rates. This paper investigates the phenomena leading to stall in a low-aspect ratio contra-rotating fan stage operating at different speed combinations under radially distorted inflows. Unsteady casing static pressure measurements obtained at a location upstream of rotor-1 leading edge are analysed using wavelet and Fourier analysis techniques. The results primarily concluded that a higher speed of rotation of rotor-2 could possibly suppress the pre-stall disturbances. The fluid structures leading to stall are initially associated with the blade passing frequency (BPF). These frequencies stretch to lower frequencies during the onset of fully developed stall and fully developed stall finally occurs at low frequencies.

Mitigation of Harmonics in Power Transmission Network using Filters

In the novel times, with the surge in use of power electronics, power quality with system efficiency is playing a symbolic role for the advancement of electric supply. The fundamental purpose of the electric utility is to provide a sinusoidal voltage at constant magnitude throughout the system. This objective is convoluted because of the loads present in the system which produce harmonic currents. Due to these harmonic currents, distorted voltages and currents are carried out which affect the reliability and efficiency of the system in several ways. The sinusoidal waveform produced by electric utilities is distorted due to harmonics and increased use of non-linear loads. The deterioration of the power quality and reliability of the power system is due to the presence of these harmonics in the power system. Hence, we need a proper analytical approach to study, classify and characterize the harmonics present in the system and develop a suitable and effective mitigation method to reduce the harmonics in the power system to standard limits of harmonics prescribed by the IEEE and IEC standards. The study of the level of harmonics present in the system, their causes and effects are known as harmonic analysis or harmonics study. Based on the observations of harmonic analysis we develop mitigation techniques to reduce these harmonics. One such method is the implementation of filters. By implementing harmonic filters, we mitigate the harmonics present in the system by providing a low impedance path. The methodological procedure behind effective design and implementation of filters is achieved by performing load flow analysis to obtain the system data and harmonic analysis to obtain data of harmonics present in the system. Based on the data obtained, the type of filter and the optimal placement of filter is decided to mitigate the harmonics. The mitigation of harmonics can report significant benefits for industries, data centers, etc. in terms of overall installation cost and protection against interruptions and equipment faults in the power system. The overall process of Harmonic analysis and mitigation techniques are performed using Mi-Power software.

Reformulation of Parker–Oldenburg's method for Earth's spherical approximation

SUMMARY Parker–Oldenburg's method is perhaps the most commonly used technique to estimate the depth of density interface from gravity data. To account for large density variations reported, for instance, at the Moho interface, between the ocean seawater density and marine sediments, or between sediments and the underlying bedrock, some authors extended this method for variable density models. Parker–Oldenburg's method is suitable for local studies, given that a functional relationship between gravity data and interface geometry is derived for Earth's planar approximation. The application of this method in (large-scale) regional, continental or global studies is, however, practically restricted by errors due to disregarding Earth's sphericity. Parker–Oldenburg's method was, therefore, reformulated also for Earth's spherical approximation, but assuming only a uniform density. The importance of taking into consideration density heterogeneities at the interface becomes even more relevant in the context of (large-scale) regional or global studies. To address this issue, we generalize Parker–Oldenburg's method (defined for a spherical coordinate system) for the depth of heterogeneous density interface. Furthermore, we extend our definitions for gravity gradient data of which use in geoscience applications increased considerably, especially after launching the Gravity field and steady-state Ocean Circulation Explorer (GOCE) gravity-gradiometry satellite mission. For completeness, we also provide expressions for potential. The study provides the most complete review of Parker–Oldenburg's method in planar and spherical cases defined for potential, gravity and gravity gradient, while incorporating either uniform or heterogeneous density model at the interface. To improve a numerical efficiency of gravimetric forward modelling and inversion, described in terms of spherical harmonics of Earth's gravity field and interface geometry, we use the fast Fourier transform technique for spherical harmonic analysis and synthesis. The (newly derived) functional models are tested numerically. Our results over a (large-scale) regional study area confirm that the consideration of a global integration and Earth's sphericty improves results of a gravimetric forward modelling and inversion.

Ultrasonic Thickness Measurements Using Machine Learning

Abstract Thickness measurements using an ultrasonic contact test is a well-known nondestructive evaluation technique. However, its implementation in a robotic system with a closed-loop feedback control for artificial intelligent measurements requires precise information of positioning and force of the ultrasonic probe. In this work, we describe an ultrasonic probe developed in our lab that uses a semispherical soft membrane made from an elastomer. The aim is to develop a methodology for precise positioning and force control of a dry contact ultrasonic probe based on the ultrasonic signal information processed using sparse matrix optimization and Fourier analysis techniques. The results show that the proposed methodology makes easy to achieve a fine tuning of the probe orientation with high sensitivity to load and misalignment in order to perform accurate thickness measurements.