A Tunable Resolution MUSIC Algorithm for Interharmonics Analysis

The harmonic and interharmonic analysis recommendations are contained in the latest IEC standards on power quality. Measurement and analysis experiences have shown that great difficulties arise in the interharmonic detection and measurement with acceptable levels of accuracy. In order to improve the resolution of spectrum analysis, the traditional method (e.g. discrete Fourier transform) is to take more sampling cycles, e.g. 10 sampling cycles corresponding to the spectrum interval of 5 Hz while the fundamental frequency is 50 Hz. However, this method is not suitable to the interharmonic measurement, because the frequencies of interharmonic components are non-integer multiples of the fundamental frequency, which makes the measurement additionally difficult. In this paper, the tunable resolution multiple signal classification (TRMUSIC) algorithm is presented, which the spectrum can be tuned to exhibit high resolution in targeted regions. Some simulation examples show that the resolution for two adjacent frequency components is usually sufficient to measure interharmonics in power systems with acceptable computation time. The proposed method is also suited to analyze interharmonics when there exists an undesirable asynchronous deviation and additive white noise.

The runoff characteristics and harmonic analysis of the soil moisture dynamics in Robinia pseudoacacia stand

Robinia pseudoacacia stands act as a typical ecological protection forest in hilly semi-arid area of China. Two fields of surface runoff were separately set up in R. pseudoacacia stand and its clearcut area in the western Liaoning Province (1850-12225 E, 4024-4234 N) for measuring the characteristics of runoff and sediment as well as soil moisture dynamics. Contractive analysis of the two land types showed that there existed a significant difference in volumes of runoff and sediment between the sites of R. pseudoacacia stand and its clearcut area. The runoff volume and sediment volume in clearcut area were much bigger than those in R. pseudoacacia stand, with an increase amount of 40%-177% for runoff and 180%-400% for sediment. Hydrograph of surface runoff of typical rainfall showed that the peak value of runoff in R. pseudoacacia stand was decreased by 1.0-2.5?0-3m3s-1 compared with that in its clearcut area, and the occurring time of peak value of runoff in R. pseudoacacia stand was 10-20 min later than that in its clearcut area. Harmonic analysis of soil moisture dynamics indicated that the soil moisture in R. pseudoacacia stand was 2.3 % higher than that in clearcut area, and the soil moisture both in R. pseudoacacia stand and its clearcut area could be divided into dry season and humid season and varied periodically with annual rainfall precipitation. It was concluded that R. pseudoacacia stand plays a very important role in storing water, increasing soil moisture, and reducing surface runoff and soil erosion.

Wavelet analysis method of harmonics and electromagnetic interference in coal mines

In this study we propose an analytical method based on orthogonal wavelet transforms for detecting harmonic noise and Electromagnetic Interference (EMI) from power supply systems and equipment in coal mines. The method will separate interference from signals through wavelet packet decomposition and then accomplish wavelet packet synthesis towards decomposition results after filtering, to remove harmonic noise and electromagnetic interference. Detailed simulation experiments are presented to study power harmonics and Electrical Fast Transient Burst (EFT/B) interference and to validate the effectiveness of our proposed method. The experimental results show that the proposed method, suitable for mutant and non-stationary signal detection, can accurately analyze harmonic interference and EMI in coal mines, as well as establish EMI source models and perform underground Electromagnetic Compatibility (EMC) prediction analyses.

Improving convergence of incremental harmonic balance method using homotopy analysis method

We have deduced incremental harmonic balance an iteration scheme in the （IHB） method using the harmonic balance plus the Newton-Raphson method. Since the convergence of the iteration is dependent upon the initial values in the iteration, the convergent region is greatly restricted for some cases. In this contribution, in order to enlarge the convergent region of the IHB method, we constructed the zeroth-order deformation equation using the homotopy analysis method, in which the IHB method is employed to solve the deformation equation with an embedding parameter as the active increment. Taking the Duffing and the van der Pol equations as examples, we obtained the highly accurate solutions. Importantly, the presented approach renders a convenient way to control and adjust the convergence.

A Precise Algorithm for Non-Integer Harmonics Analysis Based on FFT and Neural Network

By means of an arificial neural network (ANN) model, higher measurement accuracy of integer harmonics can be obtained. Combining the windowed fast Fourier transform (FFT) algorithm with the improved ANN model, we present a new precise algorithm for non-integer harmonics analysis. According to the result obtained from the Hanning-windowed FFT algorithm, we choose the initial values of orders of harmonics for the neural network. Through such processing, the time of iterations is shortened and the convergence rate of neural network is raised thereby. The simulation results show that close non-integer harmonics can be separated from a signal with higher accuracy and better real-time by using the algorithm presented in the paper. Key words fast Fourier transform (FFT) - artificial neural network (ANN) - Hanning-window - harmonics analysis CLC number TM 935 Foundation item: Supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of China (2001-182) and the Science Foundation of Naval University of Engineering(HGDJJ03001).Biography: WANG Gong-bao (1962-), male, Professor, research direction: artificial neural network, wavelet analysis and their applications to signal processing in electric power systems.

Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis

Deformation of the flexspline is the basis of analyzing tooth trajectory and designing tooth profile.Considering the tooth influence on the position of equivalent neutral layer,a piecewise method for calculating the deformation of flexspline assembled with a cam wave generator is presented in this paper.Firstly,a mechanic model of a ring of uniform thickness in contact with a rigid cam is established.The displacements of the ring inside and outside an unknown wrapping angle are determined by the geometric constraints of the cam profile and the equilibrium rela-tionship,respectively.Meanwhile,the wrapping angle is solved according to the boundary conditions.The assembly forces are derived to investigate the circumferential elongation and strain.Then,considering the tooth effects on the neutral layer of flexspline,the tooth is positioned on the equivalent neutral layer,which is the non-elongation layer within one gear pitch but offset from the geometric mid-layer.The equivalent neutral layer is positioned by the empirical formula of the offset ratio,which is summarized by the orthogonal simulation on finite element models of racks.Finally,finite element models of a ring-shaped and a cup-shaped flexspline assembled with elliptical cam are established to verify the effectiveness and accuracy of the piecewise method.The results show that,compared with the geometric method,the tooth positioning deviation calculated by the piecewise method can be reduced by about 70%with a more accurate deformation description from the geometric condition and mechanic condition inside and outside the wrapping angle.

GLOBAL OCEAN TIDES FROM GEOSAT ALTIMETRY BY QUASI-HARMONIC ANALYSIS

Global ocean tides data were derived from Geosat altimeter data by means of the Quasi Harmonic Constituent Method (QHCM). Tidal solutions with resolution of 1°/3 in longitude and latitude were obtained for constituents M 2, S 2, O 1, K 1, M 4 and MS 4. The mean sea heights above the reference ellipsoid were also obtained consequently. The obtained tidal constants were compared with those from deep sea and island tide gauge data. The rms differences between the harmonic constants derived from Geosat altimetry and deep sea tide gauges for M 2, S 2, O 1 and K 1 ranged from 1.4 cm to 2.6 cm, although the GM altimeter data have significant errors due to instrument malfunction and other reasons. M 2 tide obtained was the most accurate one among all the tides. Comparison also showed that island tidal constants cannot represent well the tidal distribution in the ocean near the island, because of the significant local effect on tides.

Analysis of the Harmonic Response of a Modulation Permanent Magnetic Transmission Equipment Based on ANSYS

This paper analyzes the structure and transmission principles of a modulation permanent magnet gear transmission. Its 3D data model is built based on the known optimized parameters from research team. Its structure of the harmonic response is analyzed and discussed under the software ANSYS. The displacement response and the initial 6 order response frequency and phase angle are obtained. The change rule of these responses is known under the forced vibration.

Modeling and Interpreting CHAMP Magnetic Anomaly Field over China Continent Using Spherical Cap Harmonic Analysis

Based on the CHAMP Magsat data set, spherical cap harmonic analysis was used to model the magnetic fields over China continent. The data set used in the analysis includes the 15′×15′ gridded values of the CHAMP anomaly fields (latitude φ=25°N to 50°N and longitude λ=78°E to 135°E). The pole of the cap is located at φ=35°N and λ=110°E with half-angle of 30°. The maximum index (K max) of the model is 30 and the total number of model coefficients is 961, which corresponds to the minimum wavelength at the earth's surface about 400 km. The root mean square (RMS) deviations between the calculated and observed values are ～ 4 nT for ΔX, ～ 3 nT for ΔY and ～ 3.5 nT for ΔZ, respectively. Results show that positive anomalies are found mainly at the Tarim basin with ～6- 8 nT, the Yangtze platform and North China platform with ～4 nT, and the Songliao basin with ～4-6 nT. In contrast, negative anomaly is mainly located in the Tibet orogenic belt with the amplitude ～ (-6)-(-8) nT. Upward continuation of magnetic anomalies was used to semi-quantitatively separate the magnetic anomalies in different depths of crust. The magnetic anomalies at the earth's surface are from -6 to 10 nT for upper crust, middle crust -27 to 42 nT and lower crust -12 to 18 nT, respectively. The strikes of the magnetic anomalies for the upper crust are consistent with those for the middle crust, but not for the lower crust. The high positive magnetic anomalies mainly result from the old continental nucleus and diastrophic block (e.g. middle Sichuan continental nucleus, middle Tarim basin continental nucleus, Junggar diastrophic block and Qaidam diastrophic block). The amplitudes of the magnetic anomalies of the old continental nucleus and diastrophic block are related to evolution of deep crust. These results improve our understanding of the crustal structure over China continent.

Analysis of the Electric Locomotives Neutral-section Passing Harmonic Resonance

For the further analysis and suppression of the electric locomotives neutral-section passing overvoltage, on the basis of theoretical analysis of the neutral-section passing harmonic resonance conditions, this paper establishes simplified harmonic resonance simulation models of the electric locomotives neutral-section passing using MATLAB/Simulink, and makes the overvoltage simulation analysis of the existing electric locomotives neutral-section passing system in the event of a harmonic resonance. Results show that when the system harmonic resonance occurs, the operating overvoltage of the neutral-section passing is serious intensified by the overvoltage of the harmonic resonance, which will make the voltage of the pantograph collector head exceeding 100kV. This amplitude of the overvoltage will breakdown the air gap, which will be a serious threat to the safety operation of the electric railway. However, this kind of neutral-section passing overvoltage hasn’t cause the attention in the field and theoretical studies, which need more analysis and verification in the further study.

Verification of Existence of Harmonic Suppression in Error Separation by Prony Spectrum Analysis

Prony spectrum analysis is employed in this paper to analyze the harmonics of estimation of radial runout of axis in error separation. The result of analysis verifies the existence of harmonic suppression in multi-step method, thereby advancing the study of harmonic suppression which stayed at the theoretical level for years.

NEW THREE PHASE VFVA SINE WAVE GENERATOR AND PWM HARMONICS ANALYSIS

The new three phase VFVA sine wave generator is presented in this paper. A new sampling holding three phase VFVA sine wave generator’s principle, circuit and experimentation waveform are introduced. The principle of this sampling holding circuit is simple and the realization of har’dware circuit is easy. Here we describe the three phase reference sine wave which is produced by this generator’s circuit and is required by PWM inverter is described in this paper, and also introduced the speed control and harmonir analysis of PWM inverter variable frequency.

Tidal harmonic analysis of TOPEX/POSEIDON data in the Northwest Pacific by introducing difference-ratio relations

The difference-ratio relations are introduced to separate tidal constituents that are aliaseddue to the sampling interval and sampling span of the TOPEX/POSEIDON altimeter. It is found that some tidal constituents such as K_1 and SSA, though aliased at along track points, are not aliased at crossover points beeause the data at crossover points are double those at along track points. So the harmonic analysis method can be employed directly for the analysis of time series at crossover points. Then the difference-ratio relations from crossover points are introduced to analyze the time series at along track points. The TOPEX/POSEIDON data in the Northwest Pacific are analyzed with this method. The results from this method agree well with tidal constants from tidal gauges.

IMAGING OF EEG BY SPHERICAL HARMONIC ANALYSIS

A new three dimensional imaging method for electroencephalogram(EEG) is suggested. It consists of the solution of an inward spherical harmonic continuation. The principle of the new method is introduced in Section II, then a few numerical simulation tests are shown and the feasibility of the new method is confirmed by the simulation results.

AN HARMONIC ANALYSIS FOR OPERATORS IN THE CASE OF A LOCALLY COMPACT ABELIAN GROUP：F．AND M．RIESZ THEOREMS

Let G be a locally compact Abelian group, B a homogeneous Banach algebra without the order on G. at denotes the set of all integrable operators with respect to right translation on B(see [2]). Under some convenient conditions we obtain the following results:both the first F. and M. Riesz Theorem for operators in and the second F. and M. Riesz Theorem for operators in hold.

Operational Modal Analysis of a Ship Model in the Presence of Harmonic Excitation

A ship is operated under an extremely complex environment, and waves and winds are assumed to be the stochastic excitations. Moreover, the propeller, host and mechanical equipment can also induce the harmonic responses. In order to reduce structural vibration, it is important to obtain the modal parameters information of a ship. However, the traditional modal parameter identification methods are not suitable since the excitation information is difficult to obtain. Natural excitation technique-eigensystem realization algorithm （NExT-ERA） is an operational modal identification method which abstracts modal parameters only from the response signals, and it is based on the assumption that the input to the structure is pure white noise. Hence, it is necessary to study the influence of harmonic excitations while applying the NExT-ERA method to a ship structure. The results of this research paper indicate the practical experiences under ambient excitation, ship model experiments were successfully done in the modal parameters identification only when the harmonic frequencies were not too close to the modal frequencies.

Quantitative and Qualitative Analysis of Bose—Einstein Condensation in Harmonic Traps

A simple and direct approach to handle summation is presented. With this approach, we analytically investigate Bose–Einstein condensation of ideal Bose gas trapped in an isotropic harmonic oscillator potential. We get the accurate expression of which is very close to (0.43% larger than) the experimental data. We find the curve of internal energy of the system vs. temperature has a turning point which marks the beginning of a condensation. We also find that there exists specific heat jump at the transition temperature, no matter whether the system is macroscopic or finite. This phenomenon could be a manifestation of a phase transition in finite systems.

Two-step harmonic analysis for capturing seasonally-varying amplitudes and phase lags of the predominant tidal constituents

Recent studies have revealed that the predominant tidal constituents have seasonal variations at some locations.However,how to accurately obtain these variations remains a problem for the traditional harmonic analysis(HA)due to the tradeoff between length of time window and resolution of constituents.Therefore,a method named as"two-step HA"is developed in this study,which consists of both long-and short-time-window HA.Through a series of ideal experiments,practical application at two tidal gauges and comparison with the traditional HA,the feasibility and accuracy of the two-step HA are verified:The two-step HA performs better than the traditional HA in estimating monthly amplitudes and phases for the predominant constituents,whether they have seasonal variability or not.In addition to capturing variations of the predominant constituents at tidal gauges,the two-step HA would be useful in investigation of the coherence and incoherence of internal tides.

Algorithm for Harmonic Tidal Analysis along T/P Tracks： Taking Differences of Observed Sea Surface Heights at Adjacent Points as Observations

An algorithm （differential mode） is presented for the improvement of harmonic tidal analysis along T/P tracks, in which the differences between the observed sea surface heights at adjacent points are taken as observations. Also, the observation equations are constrained with the results of the crossover analysis; the parameter estimations are performed at 0.1° latitude intervals by the least squares. Cycle 10 to 330 T/P altimeter data covering the China Sea and the Northwest Pacific Ocean （2°-50° N,105°-150° E） are adopted for a refined along-track harmonic tidal analysis, and harmonic constants of 12 constituents in 8 474 points are obtained, which indicates that the algorithm can efficiently remove non-tidal effects in the altimeter observations, and improve the precision of tide parameters. Moreover, parameters along altimetry tracks represent a smoother distribution than those obtained by traditional algorithms. The root mean squares of the fitting errors between the tidal height model and the observations reduce from 11 cm to 1.3 cm.

Harmonic Analysis in Discrete Dynamical Systems

In this paper we review several contributions made in the field of discrete dynamical systems, inspired by harmonic analysis. Within discrete dynamical systems, we focus exclusively on quadratic maps, both one-dimensional (1D) and two-dimensional (2D), since these maps are the most widely used by experimental scientists. We first review the applications in 1D quadratic maps, in particular the harmonics and antiharmonics introduced by Metropolis, Stein and Stein (MSS). The MSS harmonics of a periodic orbit calculate the symbolic sequences of the period doubling cascade of the orbit. Based on MSS harmonics, Pastor, Romera and Montoya (PRM) introduced the PRM harmonics, which allow to calculate the structure of a 1D quadratic map. Likewise, we review the applications in 2D quadratic maps. In this case both MSS harmonics and PRM harmonics deal with external arguments instead of with symbolic sequences. Finally, we review pseudoharmonics and pseudoantiharmonics, which enable new interesting applications.