Harmonic Analysis Method Research Articles

Real-time polarization measurement based on spatially modulated polarimeter and deep learning

Spatially modulated polarimeter (SMP) can be employed to obtain the polarization states of light by a single shot of intensity image, and it is stable, robust and easy to use. In order to simplify the calculation procedures and improve the measurement speed, we introduce the deep learning (DL) method into SMP. In this work, a convolutional neural network (CNN) based on VGGNet architecture has been trained by simulated samples that are generated by a theoretical model of a spatially modulated system. Then the trained CNN is utilized to evaluate the Stokes parameters of the input light beam according to its spatially modulated image obtained in the real experiment. The mean absolute error between the evaluated values and the true values of the normalized Stokes parameters can be less than 0.02, and the evaluation of each image takes only 0.03–0.04 s. Compared with the traditional Fourier analysis method, the DL method is close in accuracy while greatly enhanced in speed, making real-time polarization measurement achievable.

On the open sea propagation of two-dimensional rotational water waves generated by a moving bed

We study the propagation of two-dimensional tsunami waves triggered by a seaquake in the open sea in the presence of underlying wind-generated currents, corresponding to background flows of constant vorticity. A suitable scaling of the governing equations introduces dimensionless parameters, of particular interest being the setting of linear waves that only depend on the vertical movement of the sea bed. We use Fourier analysis methods to extract formulae for the function f which describes the vertical displacement of the water's free surface. We show that the results are particularly useful in the physically relevant shallow-water regime: in the irrotational case the predictions fit well with the observed behaviour of some historical tsunamis. In other situations, the stationary-phase principle gives insight into the asymptotic behaviour of f.

The temporal variations in principal and shallow-water tidal constituents and their application in tidal level calculation: an example in Zhoushan Archipelagoes with complex bathymetry

Temporal variations in tides are critical for ocean dynamics and engineering activities around coastal areas. Based on the data observed from 8 tide-gauge stations spanning 2 years (2016–2017), variations in principal (M2, S2, K1, O1) and shallow-water (M4, MS4, M6, 2MS6) tidal constituents in the Zhoushan Archipelagoes were studied by applying both classic and moving harmonic analysis methods. The temporal variations in the S2 and K1 harmonic parameters show annual cycles, while those of M2 and O1 are dominated by semi-annual cycles at most stations. The variations in shallow-water tides are more complex: larger discrepancies were observed among all stations and the variations in the harmonic parameters of the same constituent also varied differently. The phase lag variations were attributed mainly to changes in wind and runoff. Regarding the amplitude variations, the mean sea level and stratification played a considerable role; in addition, the effect of runoff on the semi-annual variation of amplitudes was significant. The predicted tidal levels and engineering water levels are improved when the temporal variations in harmonic parameters were considered, thereby benefiting practical application and related issues in coastal engineering and management.

Harmonic Magnetic Field Analysis Method and Modeling of Double-Sided Air-Cored Superconducting Linear Synchronous Motor for EDS Train

This study introduces a novel methodology based on the idea of double Fourier series and coil segmentation, performed based on governing equations, with harmonic magnetic field analysis of a double-sided air-cored superconducting linear synchronous motor for electrodynamic suspension train. This method can solve the harmonic magnetic field generated by arbitrarily shaped coils. First, with rectangular-shaped coils and race-track-shaped coils as examples, the process of calculating harmonic magnetic field using the proposed method is introduced comprehensively, and the influence of the end effect is also considered. Second, based on the solution results of the harmonic magnetic field, a modeling method that can quickly solve no-load superconducting flux linkage, no-load back EMF, and three-dimensional (3-D) electromagnetic forces without losing accuracy is presented, which is verified by finite element simulation. Finally, two static tests are designed. The effectiveness of the proposed method is verified by the test results of static thrust and static normal force.

Explicit high-order compact difference method for solving nonlinear hyperbolic equations with three types of boundary conditions

In this paper, an explicit compact difference method is constructed to solve nonlinear hyperbolic equations with initial and three types of boundary conditions. Firstly, a nonlinear explicit fourth-order compact difference scheme is derived by truncation error residual correction and the fourth-order Padé approximation. The corresponding scheme for the linear hyperbolic equation is proven to be conditionally stable by the Fourier analysis method. Then, to improve the computational efficiency, the nonlinear scheme is linearized to obtain a linear explicit fourth-order compact difference scheme. Finally, numerical experiments are conducted to verify the stability and accuracy of the presented method.

A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation

In this article, we developed a new higher-order implicit finite difference iterative scheme (FDIS) for the solution of the two dimension (2-D) time fractional Cable equation (FCE). In the new proposed FDIS, the time fractional and space derivatives are discretized using the Caputo fractional derivative and fourth-order implicit scheme, respectively. Moreover, the proposed scheme theoretical analysis (convergence and stability) is also discussed using the Fourier analysis method. Finally, some numerical test problems are presented to show the effectiveness of the proposed method.

Label-free high-resolution white light quantitative phase nanoscopy system.

We present a high-resolution white light quantitative phase nanoscopy (WLQPN) system that can be utilized to visualize nanoparticles and subcellular features of the biological specimens. The five-phase shifting technique, along with deconvolution, is adopted to obtain super-resolution in phase imaging. The phase shifting technique can provide full detector resolution, making it beneficial as compared to the well-known Fourier analysis method. The Fourier transform method requires minimum angle of , where is maximum achievable spatial frequency. It limits the highest achievable resolution to much below the actual diffraction limit of the system. Thus, to obtain a high-resolution phase map of the biological specimen, a two-step process is adopted. First, the phase map is recovered using the five-phase shifting algorithm, with full detector spatial resolution. Second, the complex field is obtained from the recovered phase map and further processed using the Richardson Lucy total variation deconvolution algorithm to obtain super-resolution phase images. The present technique was tested on 1951 USAF resolution chart, 200 nm polystyrene beads and Escherichia coli bacteria using a 50×, 0.55NA objective lens. The 200 nm polystyrene beads are visually resolvable and subcellular features of the E. coli bacteria are also observed, suggesting a significant improvement in the resolution.

A DC TO AC CONVERTER WITH A HIGH FREQUENCY LEVEL

Two block diagrams of DC-AC converters with a voltage curve of a given frequency close to the sinusoidal shape without a high-frequency section and with a high-frequency section are considered. In the converter circuit without a high-frequency link, an autonomous voltage inverter (AVI) is used, and in the converter circuit with a high-frequency link, a high-frequency AVI (AVI HF) and a direct frequency converter with quasi-single-band modulation (DFC QF) are used. In both of these converter circuits, for electromagnetic isolation between the DC voltage source and the load, a power transformer is envisaged, to match the input and output voltages. To improve, ensure and obtain on the load the output voltage curve close to the sinusoidal shape, filters are used, which is the simplest way of improvement without a selective elimination of distorting harmonics of non-sinusoidal periodic voltage with multiple switching of valves, without pulse-width modulation, and so on with the complication of voltage inverter and DFC control systems. At the same time, in the first converter circuit, one filter is used: connected between the output of the inverter and the input of the output transformer, and in the second converter circuit, two filters are used, one of which is connected between the output of the AVI HF and the high-frequency transformer, and the other - between the output of the DFC with the QF load. Since the output voltages of AVI and DFC are non-sinusoidal periodic functions, using the methods of harmonic analysis and switching functions, mathematical descriptions of the output voltages of AVI and DFC are obtained in the form of a trigonometric Fourier series. A numerical assessment of the weight and size parameters of transformers and filters in relative units is carried out. It is shown that the use of a converter with a high-frequency link based on AVI HF and DFC with QF allows to significantly reduce the mass and dimensions of power electromagnetic elements.

Harmonic Resonance Analysis of Shale Gas Distribution Network with Phased Load

Based on the background of achieving carbon peaking and carbon neutrality, the development and application of new high-power compressors, electric grid drilling RIGS and electric fracturing pump system provide new equipment support for the electric, green and intelligent development of shale gas fields in China. However, the harmonic pollution of shale gas grid becomes more serious due to the converter and frequency conversion device in the system, which easily causes harmonic resonance problem. Therefore, the harmonic resonance of shale gas grid is comprehensively analyzed and treated. Firstly, the working mechanism of compressor, electric drilling RIGS of the harmonic impedance model of electric fracturing pump system is established. Secondly, the main research methods of harmonic resonance analysis are introduced, and the basic principle of modal analysis is explained. Modal analysis method was used to analyze. Finally, harmonic resonance is suppressed. The results show that there may be multiple resonant frequency points in the distribution network changes, but these changes are relatively clear; if the original resonant frequency point of the resonant loop does not exist, the resonant frequency point disappears. The optimal configuration strategy of passive filter can effectively suppress harmonic resonance of distribution network in shale gas field.

Визначення принципів упорядкування навчальних консультацій у закладах вищої освіти

The article considers the issue of improving the efficiency of educational information acquisition by future electrical engineering students. Several methods for forming the timetable of tutorials are analyzed, which ensure the increase of fundamental and practical knowledge levels, the ability to work with technical equipment, and solve non-standard situations that might happen in working conditions. Streamlining of tutorials timetable was proved by the main principle of optimization of this process. The research was carried out on the example of teaching technical subjects of study to students during the academic semester. Subjects of the study were taught cyclically within two weeks. Processing of the results was carried out by methods of mathematical modeling and harmonic analysis. The obtained results were verified using a cybernetic model of the learning process by introducing the proposed optimal timetable of tutorials into the general timetable of classes. The survey proved the efficiency of educational information acquisition by electrical engineering students. As criteria for evaluating the efficiency of educational information acquisition, it is proposed to consider the mathematical expectation and dispersion of acquisition on the cycle interval. Based on the optimization approach and using the methods of harmonic analysis and mathematical modeling, the principle of increasing the efficiency of assimilation of educational information by electrical students, i.e. placing different forms of organization of training in a stable schedule, is determined. It has been proven that the introduction of additional consultations into the schedule according to the developed principle allows to even out the discreteness of information delivery, which increases the mathematical expectation of learning by 50% and reduces the variance by 1.8 times, significantly increasing the level of student training. Key words: human and machine systems, information acquisition, information presentation schedule, dispersion, cybernetic model.

Anomalously large seasonal modulations of shallow water tides at Lamu, Kenya

Understanding seasonal tidal changes is vital for accurate tidal prediction which is essential for numerous practical purposes, such as flood warning and navigation. It is common knowledge that main constituents show significant seasonal modulations in the global ocean due to non-astronomical factors such as river discharge, sea ice and ocean stratification. Less known, and less studied, is the seasonal variability of shallow water constituents. In this paper, we revisit the abnormally large semi-annual modulation of shallow water constituents at Lamu indicated by a previous study. We find that large semi-annual modulations of shallow water tides at Lamu are mostly not physical, but artifacts induced by unresolved nearby nonlinear shallow water tides due to short length of records. We also propose a novel method based on the ‘credo of smoothness’ to extract real semi-annual modulations of shallow water tides. Tidal harmonic analysis and other widely-used time series methods are generally frequency-depend, which means that they can only extract the amplitude and phase of one specific tidal frequency, but cannot distinguish different origins of a tidal constituent. It is suggested that care must be taken to ensure the obtained tidal amplitude/phase series are really reflecting tidal changes and are not artifacts of frequency-depend methods.

Application of BP Neural Networks in Tide Forecasting

Tidal phenomenon is a significant dynamical phenomenon in the ocean, and the accurate prediction of tide is an important task for various maritime activities. This paper proposes analysis method considering tidal periodicity and apply it to the actual tide prediction. The results prove that this method can solve the delay problem in tide prediction, improve the accuracy of prediction. Compared with the tidal harmonic analysis method, the prediction result of this method is more accurate and requires less data for short-term tidal forecast. Although this study can only provide an accurate forecast for 3 days, it is enough to deal with risks. How to improve the accuracy of long-term prediction is one of the future research directions.

Improving the dependability of the servo drives of unmanned aerial vehicles through optimized operating modes

Aim. Improving the reliability of servo drives through partial redundancy of structural components. Methods. The paper uses methods of harmonic analysis, technical system dependability theory. Results. The mean times to failure of servo drives that differ in terms of the level of redundancy of structural elements (external connectors, feedback sensors, control boards, electric motors and load gears) were compared. It was shown that structural element redundancy along with the capability to switch to still-operable elements in the course of servo drive operation enable a triple increase of the failure tolerance. The authors suggested criteria for identifying the moment of time for decision-making regarding an electric servo’s structure modification before the moment of failure of the redundant element of such servo. Conclusion. The method suggested in the paper allows formalizing the process of electric servo structure modification for the purpose of ensuring the required level of failure tolerance.

Propagation characteristics and quantification analysis of harmonic current in large‐scale wind farms

AbstractThese days, the harmonic problem of wind power grid‐connected systems is becoming increasingly prominent due to the increase in the number of large‐scale centralized grid‐connected wind farms and the gradual trend of high‐proportion power electronics for source‐grid loads. The harmonic oscillation caused by power electronic equipment provides large‐scale propagating in the system, and the harmonic interaction makes the harmonic propagation more complex. First, the harmonic interaction of the system is simplified into the radiation relationship between the wind farm and each branch to solve the harmonic current propagation problem caused by the interaction in the multiple wind farms. Then, the branch harmonic current propagation analysis method is used to transfer harmonic impedance and generate the branch harmonic current decoupling. Second, a harmonic current propagation coefficient is proposed to quantitatively analyze the relationship between the harmonic current of the wind farm and the branch. Thereby, the quantitative analysis of the propagation characteristics for the wind farm harmonic current in the system branch is obtained. Finally, abundant simulations verify the effectiveness and feasibility of the proposed method.

Equivalent Current Systems of Quiet Ionosphere during the 24th Solar Cycle Derived from the Geomagnetic Records in China

External and internal equivalent current systems of solar quiet (Sq) were obtained using the spherical harmonic analysis (SHA) method with a “mirror” technique based on geomagnetic records from 46 stations in China during 2008–2019. It is the first attempt to investigate Sq currents using so many stations in the China region for a long period. On the basis of criterion Kp ≤ 2+, geomagnetic vector data were selected to represent monthly Sq variations. After calculating the equivalent currents for each month and each Lloyd season, Sq variation was analyzed in relation to the solar cycle and season. The intensities of both external and internal Sq currents were found consistent with solar activity for the same month or season, while the positions of the current foci were evidently unaffected by solar activity. The intensities of Sq currents also exhibited primary semiannual (annual) variation in the periods of high (low) solar activity. The latitude of the internal current vortex showed evident seasonal variation in Lloyd seasons with high (low) values in the D (J) season, while the external current vortex exhibited no obvious seasonal variation. The strongest correlation between external and internal foci was found in D season, and the internal current foci usually appeared 20–40 min earlier than the external ones. Owing to the complex mechanisms behind Sq variation, some findings will need further analysis in the future.

Fast time optical variability in Be/X-ray binaries

Context. Classical Be stars, regardless of spectral subtype, display multi-periodic light modulations in the frequency range 0.1–12 c d−1 when observed with a high cadence and a long duration. This behavior is attributed to non-radial pulsations and/or the rotation of the Be star. A similar study on the optical counterparts to Be/X-ray binaries is yet to be carried out. Aims. The main goal of this work is to investigate the fast photometric variability of the optical counterparts to Be/X-ray binaries and compare the general patterns of such variability with the Galactic population of classical Be stars. Methods. The main core of our analysis is based on space-based observations performed by TESS. We analyzed 21 sources with TESS. High-cadence photometry with two ground-based telescopes was also performed for 15 sources. The TESS light curves were created from the full-frame images using the Lightkurve package. The ground-based light curves were obtained through differential photometry between the target and a number of non-variable stars in the same field of view. Standard Fourier analysis and least-squares fitting methods were employed in the frequency analysis. Results. All sources exhibit intra-night light variations with intensity variations of 0.01–0.06 mag in the ground-based observations and up to 5% in flux in TESS observations. This variability manifests itself as multi-periodic signals in the frequency range 0.2–12 c d−1. We find that the patterns of variability of the Be stars in Be/X-ray binaries agree with that of classical early-type Be stars in terms of the general shape of the periodograms. Based on the general shape and number of peaks in the periodograms, Be/X-ray binaries can be classified into different types. The most common case is the presence of groups of closely spaced frequencies (67%), followed by sources that exhibit isolated signals (18%). The remaining source type displays frequency spectra characterized by a mixed pattern of stochastic variability and high-frequency peaks. Conclusions. This study reveals that short-term optical photometric variability is a very common, if not ubiquitous, feature intrinsic to the Be optical companions in Be/X-ray binaries. This variability is mainly attributed to pulsations that originate in the stellar interior.

Distribution of seasonal signals in the deep South China Sea

The upper South China Sea (SCS) circulation is characterized by seasonal variability due to the monsoon, and in fact, some studies have shown that the deep SCS circulation could also vary seasonally. Based on SODA product, this study presents the distribution of seasonal signals at 2100 m in the deep SCS by the method of harmonic analysis. Seasonal signals are evident in most areas, sufficient to explain more than 20% of the total variation. The amplitude pattern of U displays a four-core structure on the meridional band of 114°–118°E, and high amplitudes of V are located in the middle basin. The annual harmonics of U along 12.75°N have several characteristics: notable seasonal signals in the deep ocean, phase isolines that slope downward to the west implying upward and westward phase propagation, and amplitude maxima that are parallel to phase isolines. These features suggest that seasonal signals in the deep SCS originate from the upper ocean and the vertically propagating Rossby waves provide a mechanism.

An accurate and efficient local one-dimensional method for the 3D acoustic wave equation

Abstract We establish an accurate and efficient scheme with four-order accuracy for solving three-dimensional (3D) acoustic wave equation. First, the local one-dimensional method is used to transfer the 3D wave equation into three one-dimensional wave equations. Then, a new scheme is obtained by the Padé formulas for computation of spatial second derivatives and the correction of the truncation error remainder for discretization of temporal second derivative. It is compact and can be solved directly by the Thomas algorithm. Subsequently, the Fourier analysis method and the Lax equivalence theorem are employed to prove the stability and convergence of the present scheme, which shows that it is conditionally stable and convergent, and the stability condition is superior to that of most existing numerical methods of equivalent order of accuracy in the literature. It allows us to reduce computational cost with relatively large time step lengths. Finally, numerical examples have demonstrated high accuracy, stability, and efficiency of our method.

Tidal level prediction using combined methods of Harmonic Analysis and Deep Neural Networks in Southern Coastline of Iran

Predicting tides and water levels had always been such an important topic for researchers and professionals since the study of tidal level has pivotal role in supporting marine economy, port construction projects and maritime transportation. Tidal water levels are a combination of astronomical (deterministic part) and non-astronomical (stochastic part) water levels. In this study, we combined Harmonic Analysis (HA) with three Deep Neural Networks (DNNs), namely the Long-Short Term Memory (LSTM), Convolution Neural Network (CNN), and Multilayer Perceptron (MLP). The HA method is used for predicting the astronomical components, while DNNs are used to predict the non-astronomical water level. We have used tide gauge data from three stations along the southern coastline of Iran to demonstrate the effectiveness and accuracy of our model. We utilized RMSE, MAE, R2 (r-squared), and MAPE to evaluate the performance of the model. Finally, The LSTM network shown superior performance in most of the cases, although other networks also show good results. All three DNNs have R2 of 0.99, and the RMSE, MAE, and MAPE indicate that errors are low.

A torque ripple reduction method using field current injection for doubly salient motor

Doubly salient motor (DSM) is widely used owing to attractively in high-speed operation capability. However, there is a shortcoming of torque ripple for the non-sinusoidal nonlinear structure, for the purpose of solving this problem, this paper presents a torque ripple reduction strategy by field current injection for doubly salient motor. Initially, the armature current control method of the DSM adopts the multi-sine superposition (MSWS) driving scheme, combined with finite element and Fourier analysis methods to establish the output torque and torque ripple model, where the torque of the DSM is mainly composed of the 1st, 2nd, and 4th harmonic component, and the torque ripple is mainly composed of 3rd harmonics component. Then, a field current injection approach is presented, and calculate the magnitude and phase of the injected component, which serves as a quantitative analysis foundation for torque ripple suppression. Finally, the experimental results illustrate the superiority of the presented method in torque ripple optimization.