Fourier Series Decomposition Research Articles

Variable frequency triple-phase-shift modulation strategy for minimizing RMS current in dual-active-bridge DC-DC converters

For dual-active-bridge (DAB) DC-DC converters, a variable frequency triple-phase-shift (VF-TPS) modulation strategy based on a particle swarm optimization (PSO) algorithm was proposed to solve the problem of the low efficiency of TPS modulation in larger power conditions. To facilitate the implementation of the PSO algorithm, the mathematical expressions between the transmission power or the RMS square of the inductance current and four control variables including the switching frequency and three phase-shift duty cycles are simplified by the Fourier series decomposition method. An objective function of the particle fitness is presented to find the optimal control variables at any reference transmission power, which achieves the minimum inductance RMS current in the full power range and improves the efficiency under heavy loads. In addition, the PSO algorithm is used to design the appropriate switching frequency range and inductance. Finally, a 1.2 kW DAB converter prototype was established, and experimental results verify the correctness and feasibility of the modulation strategy.

Animating Fourier series decomposition of a character with LuaTeX and MPLIB

In this article, we will see how, thanks to METAPOST and MPLIB and LuaTeX, we can build an animation illustrating in a mechanical way the Fourier decomposition of a closed contour. This is a translation by the author of the original article in French, published in La Lettre GUTenberg number 41 of the French TeX user group.

Dean Vortex for Laminar Flows in Curved Pipes with Various Cross-Sections

Curved pipes flows are encountered in different areas such as heat transfer, chaotic mixing, separation of mixtures in pipes, or blood circulation among others and exhibit a variety of characteristics depending on the ranges of Dean numbers and pipe curvatures. Studies on curved pipes flows usually consider the cases of circular, elliptical, and rectangular shapes for the cross sections of the pipe. The present work extends the availability of asymptotic analytical solutions to new ranges of cross-sectional shapes while considering fully developed steady state flows at low Dean numbers. The new shapes are given by a polar equation R* (q) satisfying the relation 1-R^(*2) (q)+dR^(*y) (q)sin(yq)=0 where d and y are parameters. The zero-order azimuthal velocity profiles for various cross-sections are given by exact analytical solutions. Solutions for the nonhomogeneous biharmonic equation for the secondary flows are given by using exact expressions for the particular solutions. Furthermore, the Fourier series decomposition of the solution is adopted to determine the integration constants that allow satisfying the non-slip boundary conditions. Solutions are presented for semi triangular (y=3) , square (y=4), and pentagonal (y=5) cross sections shapes. It is found that the velocity distribution and the Dean’s vortexes intensities are modified in function of the cross-section shapes.

Numerical Simulation of a Counter-Rotative Open Rotor Using Phase-Lagged Conditions: Initial Validation on a Single Rotor Case

Abstract This paper presents the large Eddy simulation (LES) of a propeller representative of the first rotor of a counter rotative open rotor (CROR) configuration based on a multiple frequency phase-lagged approach in conjunction with a proper orthogonal decomposition (POD) data storage. This method enables to perform unsteady simulations on multistage turbomachinery configurations including multiple frequency flows with a reduction of the computational domain composed of one single blade passage for each row. This approach is advantageous when no circumferential periodicity occurs in the blade rows of the configuration and a full 360 deg simulation would be required. The data storage method is based on a POD decomposition replacing the traditional Fourier series decomposition (FSD). The inherent limitation of phase-shifted periodicity assumption remains with POD data storage but this compression method alleviates some issues associated with the Fourier transform, especially spectrum issues. The paper is first dedicated to compare the flow field obtained with the LES with phase-lagged condition against full-matching URANS, LES simulations, and experimental data available around the blade and in the wake of the rotor. The study shows a close agreement of the phase-lagged LES simulation with other simulations performed and a thicker wake compared with the experiments with lower turbulent activity. The analysis of the losses generated in the configuration, based on an entropy formulation and a splitting between boundary layer and secondary flow structures, shows the strong contribution of the blade boundary layer in the losses generated.

Joint Estimation of Multiple Time Interleaved ADC Timing Offsets Based on Fourier Series Decomposition

A method for reducing the complexity of estimating multiple timing offset in time interleaved analog to digital converter based on Fourier series decomposition is proposed. The timing offset of different slices of the time interleaved analog to digital converter can be understood as points on a curve, which represents the timing offset per slice. Thus, the estimation of the timing offset can also be achieved by fitting of the timing-offset-curve. The timing offset curve can be represented by a kernel regression coefficient which are orthonormal on a limited set, thus replacing the estimation of timing offset per slice with the estimation of the regression kernel coefficients. In this paper, the idea of estimating kernel coefficients by using Fourier series analysis is presented and analyzed. When the timing offset of different slices are highly correlated, it is shown that an improvement of 3 dB can be achieved with ~75% reduction in complexity, 6 dB improvement with ~60% reduction and 10 dB with ~40% reduction in respect to similar linear methods.

ПОВЫШЕНИЕ ЭНЕРГОЭФФЕКТИВНОСТИ ПРОИЗВОДСТВА ЗА СЧЕТ ПРИМЕНЕНИЯ СИЛОВЫХ ФИЛЬТРОВ ВЫСШИХ ГАРМОНИК

Актуальность. В настоящее время все большее количество технологических процессов и производств в нефтегазовой отрасли реализуется на базе высокопроизводительного оборудования с полупроводниковыми преобразователями электрической энергии, в число которых, например, входят частотно-регулируемые электроприводы переменного тока или бесперебойные источники питания, которые относятся к классу нелинейных нагрузок и могут вызывать большое количество негативных явлений в работе распределительных сетей, включающих в себя несимметрию фазных напряжений и токов, резонансные процессы, тепловые потери в нейтральном проводе, перегрев двигателей и трансформаторов и т. д. Для улучшения электромагнитной совместимости различного рода электроприемников в составе промышленных систем электроснабжения довольно часто используют пассивные конденсаторные батареи для коррекции коэффициента мощности, которые малоэффективны в случае нелинейных процессов. Кроме этого, данный тип компенсационных устройств продолжает потреблять реактивную энергию при отсутствии каких-либо нагрузок и не удовлетворяет современным требованиям в области энергосбережения. Описанные выше недостатки в работе трехфазных систем переменного тока требуют разработки новых схемотехнических решений, методов анализа энергетических процессов и синтеза алгоритмов силовой фильтрации, позволяющих обеспечить нормированные показатели качества электрической энергии в распределительных сетях низкого и среднего классов напряжения вне зависимости от конкретного вида электрических цепей нагрузки. Цель исследования заключается в комплексном анализе существующих технических решений, направленных на повышение электромагнитной совместимости распределительных сетей, а также в описании основных ограничений в работе силовых фильтрокомпенсирующих устройств применительно к промышленным объектам минерально-сырьевого комплекса; в разработке базовых структур активных силовых фильтров с пониженными требованиями по производительности, объему памяти и быстродействию программно-аппаратной части системы управления, практическое применение которых обеспечивает нормированное качество электрической энергии при изменении режимов работы технологического оборудования или конфигурации питающей линии. Объекты: автономные или децентрализованные электроэнергетические системы переменного тока с преобразовательными устройствами силовой электроники и частотно-регулируемыми электроприводами, а также элементами силовой цепи с нелинейными характеристиками, например, реакторами или трансформаторами с насыщенными сердечниками, в которых присутствуют значительные искажения в мгновенной форме трехфазных сигналов; пассивные и активные силовые фильтры высших гармоник. Методы: некоммутативная алгебра кватернионов; четырехмерное гиперкомплексное пространство; методы спектрального анализа и разложения в ряд Фурье. Результат: краткий обзор различных подходов и технических средств к повышению качества электрической энергии в системах электроснабжения промышленных объектов минерально-сырьевого сектора, а также системы управления,рамках которых достигается синусоидальный закон изменения во времени сетевых токов с нулевым или опережающим/отстающим угловым сдвигом при одновременном соблюдении условия симметрии по мгновенным значениям.

A Simple Unsupervised, Real-time Clustering Method for Arterial Blood Pressure Signal Classification.

Biomedical signal analysis often depends on methods to detect and distinguish abnormal or high noise/artifact signal from normal signal. A novel unsupervised clustering method suitable for resource constrained embedded computing contexts, classifies arterial blood pressure (ABP) beat cycles as normal or abnormal. A cycle detection algorithm delineates beat cycles, so that each cycle can be modeled by a continuous time Fourier series decomposition. The Fourier series parameters are a discrete vector representation for the cycle along with the cycle period. The sequence of cycle parameter vectors is a non-uniform discrete time representation for the ABP signal that provides feature input for a clustering algorithm. Clustering uses a weighted distance function of normalized cycle parameters to ignore cycle differences due to natural and expected physiological modulations, such as respiratory modulation, while accounting for differences due to other causes, such as patient movement artifact. Challenging cardiac surgery patient signal examples indicate effectiveness.

Progress Toward Efficient Compression Algorithms for Application in Flight Simulation Environments

Modern computational fluid dynamic simulations of flows about naval vessels produce an enormous amount of flow-field data. The computations are performed in order to model details of the erratic unsteady flows that can occur about naval superstructures. The flow-field data can then be used in flight simulators for naval pilot training purposes. Often, however, far too much data are generated for the flight simulators to process in real-time. This paper demonstrates the use of both proper orthogonal decomposition and Fourier series decomposition approaches for airwake dataset compression. The proper orthogonal decomposition method is used for compressing airwake data in the time domain, and Fourier series decomposition is used for compressing airwake data in the spatial coordinates. The approaches are applied to airwake data for a simplified frigate vessel model. A separate aircraft tanker configuration is also examined in order to demonstrate that the level of numerical precision can have an effect on the dataset compression results. Both approaches are effective at reducing airwake dataset size while preserving the dominant flow-field features, and both approaches are inexpensive and straightforward to implement. The level of dataset compression ultimately depends on the level of accuracy required by the user.

Gaia Data Release 2

Context. More than half a million of the 1.69 billion sources in Gaia Data Release 2 (DR2) are published with photometric time series that exhibit light variations during the 22 months of observation. Aims. An all-sky classification of common high-amplitude pulsators (Cepheids, long-period variables, δ Scuti/SX Phoenicis, and RR Lyrae stars) is provided for stars with brightness variations greater than 0.1 mag in G band. Methods. A semi-supervised classification approach was employed, firstly training multi-stage random forest classifiers with sources of known types in the literature, followed by a preliminary classification of the Gaia data and a second training phase that included a selection of the first classification results to improve the representation of some classes, before the improved classifiers were applied to the Gaia data. Dedicated validation classifiers were used to reduce the level of contamination in the published results. A relevant fraction of objects were not yet sufficiently sampled for reliable Fourier series decomposition, consequently classifiers were based on features derived from statistics of photometric time series in the G, GBP, and GRP bands, as well as from some astrometric parameters. Results. The published classification results include 195 780 RR Lyrae stars, 150 757 long-period variables, 8550 Cepheids, and 8882 δ Scuti/SX Phoenicis stars. All of these results represent candidates whose completeness and contamination are described as a function of variability type and classification reliability. Results are expressed in terms of class labels and classification scores, which are available in the vari_classifier_result table of the Gaia archive.

Motion in frequency domain for harmonic balance simulation of electrical machines

PurposeThe high computational effort of steady-state simulations limits the optimization of electrical machines. Stationary solvers calculate a fast but less accurate approximation without eddy-currents and hysteresis losses. The harmonic balance approach is known for efficient and accurate simulations of magnetic devices in the frequency domain. But it lacks an efficient method for the motion of the geometry.Design/methodology/approachThe high computational effort of steady-state simulations limits the optimization of electrical machines. Stationary solvers calculate a fast but less accurate approximation without eddy-currents and hysteresis losses. The harmonic balance approach is known for efficient and accurate simulations of magnetic devices in the frequency domain. But it lacks an efficient method for the motion of the geometry.FindingsThe three-phase symmetry reduces the simulated geometry to the sixth part of one pole. The motion transforms to a frequency offset in the angular Fourier series decomposition. The calculation overhead of the Fourier integrals is negligible. The air impedance approximation increases the accuracy and yields a convergence speed of three iterations per decade.Research limitations/implicationsOnly linear materials and two-dimensional geometries are shown for clearness. Researchers are encouraged to adopt recent harmonic balance findings and to evaluate the performance and accuracy of both formulations for larger applications.Practical implicationsThis method offers fast-frequency domain simulations in the optimization process of rotating machines and so an efficient way to treat time-dependent effects such as eddy-currents or voltage-driven coils.Originality/valueThis paper proposes a new, efficient and accurate method to simulate a rotating machine in the frequency domain.

Squdel Function: Square Wave Approximation Without Ringing

A function that is well suited to describe a square wave as well as a sequence of delta functions is presented. The squdel function has a closed rational form instead of a series approximation. Bandwidth limitations are readily incorporated in this function without producing undesirable ringing artifacts. The squdel function is infinitely differentiable and analytic for a squareness parameter as close as required to the square function provided that the limit is not taken. Even its Fourier series decomposition does not exhibit overshooting when truncated. Two-dimensional soft pixel structures are shown to be economically modeled with this function.

Onset of chaos in helical vortex breakdown at low Reynolds number

The dynamics of the helical vortex breakdown has revealed a Ruelle-Takens-Newhouse route to chaos coming from the nonlinear interactions of pure hydrodynamic modes. Global stability analysis, Fourier series decomposition, and time series analysis have been used to shed light on the dynamical states.

Data-driven based estimation of HVAC energy consumption using an improved Fourier series decomposition in buildings

Many data-driven algorithms are being explored in the field of building energy performance estimation. Choosing an appropriate method for a specific case is critical to guarantee a successful energy operation management such as measurement and verification. Currently, little research work on assessment of different data-driven algorithms using real time measurement data sets is available. In this paper, five commonly used data-driven algorithms, ARX, SS, N4S, discretized variable BN and continuous variable BN, are used to estimate HVAC related electricity energy consumption in a university dormitory. In practice, total energy consumption data is easily accessible, while separated HVAC energy consumption data is not commonly available due to expensive sub-metering and/or the complexity of mechanical and electrical layouts. A virtual sub-meter based on a decomposition method is proposed to separate HVAC energy consumption from the total building energy consumption, which is derived from an improved Fourier series based decomposition method.

Sensitive analysis of harmonics on the assessment of thermal diffusivity of building materials of a periodic state

Thermal efficiency of buildings requires a perfect knowledge of the thermal properties of materials which compose building envelope. To this end, the use of reliable testing methods for thermal diffusivity measurements of buildings materials is fundamental. Currently, periodic methods are based on the exploitation of fundamental harmonic, resulting from Fourier series decomposition. The objective of this paper is to demonstrate that fundamental is necessary and sufficient in order to characterize the thermal diffusivity. For those purposes, a sensitive analysis of harmonic contributions from Fourier series is supported by a substantial experimental campaign. Moreover, some dissymmetrical tests were carried out in order to highlight the preponderant influence of fundamental, compared to other harmonics. The analysis of contributions of harmonics shows that the evolution of thermal diffusivity is very slightly dependent on the number of harmonics. Then, the exploitation of fundamental is necessary and sufficient, and the characterization test protocol is validated by experimental results and by the comparison with commonly accepted values for these kinds of materials.

Evaluation points of the complex frequency characteristics of a dynamic object using pulse testing impact

In the report we consider the problem of periodic identification of dynamic object is a single test pulse at a fixed interval of observation. The authors analyze the decomposition in Fourier series of the observed signal at the output of the object and the signal at the input to the observation interval. It is shown that the relationship of the amplitudes of the harmonics with the same number of output and input signals with certain accuracy can indicate the coordinates of corresponding points of complex frequency characteristics of the object. This precision depends on the observation interval and the inertial properties of the object. The advantage of this approach is its good noise immunity, and relatively low time for identification. Conditions imposed on the observed duration of the transition process at the output of the dynamic object with the given parameters of the testing pulse, which allows the required accuracy to estimate the coordinates of complex frequency characteristics of the industrial site and to adapt the controller settings.

Three dimensional transient Green's functions in a thermoelastic transversely isotropic half‐space

AbstractA transversely isotropic thermoelastic half‐space in both mechanical and thermal points of view is considered as the domain of the initial boundary value problem involved in this paper. The governing partial differential equations of thermoelasticity in a cylindrical coordinate system are uncoupled with the aid of a complete set of displacement‐potential and temperature‐potential functions, which with the help of Fourier series decomposition and Hankel‐Laplace integral transforms, are reduced to ordinary differential equations in terms of depth. Then, the general solutions due to an arbitrary patch‐load and surface heat flux are investigated for the case of a point load varying with time as Heaviside step function and a point heat flux varying with time as Dirac delta function in order to compute the related Green's functions. The governing equations for the potential functions are in such a way that different longitudinal and transverse waves are recognized and the transport properties can be discovered from the governing equations. Some numerical illustrations are also presented to depict the dependency of response on the thermal properties as well as the anisotropy of the medium.

Spot volatility estimation using the Laplace transform

A new non-parametric estimator of the instantaneous volatility is defined relying on the link between the Laplace transform of the price process and that of the volatility process for Brownian semimartingale models. The proposed estimation method is a global one, in the spirit of methods based on Fourier series decomposition, with a plus for improving the precision of the volatility estimates near the boundary of the time interval. Consistency and asymptotic normality of the proposed estimator are proved. A simulation study confirms the theoretical results and Monte Carlo evidence of the favorable performance of the proposed estimator in the presence of microstructure noise effects is presented.

Multivariate Geostatistical Grid-Free Simulation of Natural Phenomena

Conventional geostatistical simulation methods are implemented in a way that is inherently gridded and sequence dependent. A variant of spectral simulation method is revisited from a linear model of regionalization standpoint to simulate realizations of coregionalized variables that are expressed as a function of the coordinates of the simulation locations, data values, and imposed spatial structure. The resulting grid-free simulation (GFS) methodology expresses a realization at any set of regularly or irregularly distributed nodes. GFS consists of two main steps: unconditional grid-free simulation and dual cokriging-based conditioning. The unconditional multivariate simulation is represented by a linear model of coregionalization, where weights are derived from the covariance function of the modeled system, and random factors are computed as a sum of equally weighted line processes within a turning bands paradigm. These stochastic line processes are expressed as a linear model of regionalization, weights are from the Fourier series decomposition of line covariance functions, and random factors have a cosine function form requiring coordinates of simulation locations and the random phases. The resulting conditionally simulated values are uniquely tied to simulation locations by an analytical form. Newly assimilated data change current realizations only locally within the correlation range. The GFS parameters are carefully chosen from a series of examples, and the associated theory is illustrated with a three-dimensional case study.

A harmonic one-dimensional element for non-linear thermo-mechanical analysis of axisymmetric structures under asymmetric loads: The case of hot strip rolling

This work presents a one-dimensional harmonic finite element for the transient elasto-plastic analysis of axisymmetric structures loaded by non-axisymmetric thermal and mechanical loads. The one-dimensional element exploits a semi-analytical approach, based on Fourier series decomposition of the applied loads. The initial stress method is used for the non-linear solution of elasto-plastic analysis. As a case study, the proposed one-dimensional harmonic element is applied for modelling a two-dimensional circle under thermal and mechanical loadings rotating over its surface, which is used as an approximation of a work roll in hot strip rolling. With the one-dimensional harmonic element, the cyclic thermo-mechanical behaviour of the work roll can be simulated by considering localized plasticity caused by thermo-mechanical loads representative of strip and back-up roll. Compared to two-dimensional models already used in the literature, the one-dimensional element allows a significant reduction in the computational time to be achieved; it follows that the whole transient thermo-mechanical response can be simulated, thus permitting a more complete evaluation of the stress–strain response that is necessary for fatigue life assessment.

Thermal stress state of rock massif with a spherical cavity taking into account inhomogeneity of the medium

The case of continuous one-dimensional heterogeneity of deformation characteristics of a material of the pedigree array with the spherical cavity, received by means of explosion, are continuous functions of one of co-ordinates – radius is considered. Solution of an initial set of equations concerning displacements is sought in the form of decomposition in Fourier series in Legendre polynomials. Using the method of separation of variables, we can reduce the problem to a system of two ordinary differential equations with variable coefficients, which can be solved numerically. Stress analysis was performed in the homogeneous and inhomogeneous array surrounding the spherical cavity. A comparative analysis of the results is carried out.