Spherical harmonic analysis(SHA)and synthesis(SHS)are widely used by researchers in various fields.Both numerical integration and least-squares methods can be employed for analysis and synthesis.However,these approach...Spherical harmonic analysis(SHA)and synthesis(SHS)are widely used by researchers in various fields.Both numerical integration and least-squares methods can be employed for analysis and synthesis.However,these approaches,when calculated via summation,are computationally intensive.Although the Fast Fourier Transform(FFT)algorithm is efficient,it is traditionally limited to processing global grid points starting from zero longitude.In this paper,we derive an improved FFT algorithm for spherical harmonic analysis and synthesis.The proposed algorithm eliminates the need for grid points to start at zero longitude,thereby expanding the applicability of FFT-based methods.Numerical experiments demonstrate that the new algorithm retains the computational efficiency of conventional FFT while achieving accuracy comparable to the summation method.Consequently,it enables direct harmonic coefficient calculation from global grid data without requiring interpolation to align with zero longitude.Additionally,the algrithm can generate grid points with equi-angular spacing using the improved FFT algorithm,starting from non-zero longitudes.To address the loss of orthogonality in latitude due to discrete spherical grids,a quadrature weight factor-dependent on grid type(e.g.,regular or Gauss grid)-is incorporated,as summarized in this study.展开更多
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 wes...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.展开更多
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...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.展开更多
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 suc...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.展开更多
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...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.展开更多
According to the rotor vortex theory,the rotor circulation and the rotor induced velocity are developed into Fourier series.The circulation distribution along blade spanwise is expressed in terms of segment-by-segment...According to the rotor vortex theory,the rotor circulation and the rotor induced velocity are developed into Fourier series.The circulation distribution along blade spanwise is expressed in terms of segment-by-segment linear functions.In consequence the induced velocity equations and the circulation equations are derived.The engineering application of the rotor vortex theory is provided.Then the induced velocity and its harmonic components are obtained to provide a quantitative basis for the vortex model.For calculating each harmonic component of the induced velocity a simplified method is put forward which considers the effects of each order circulation with neglecting those of higher order.The method saves the computer time and is of significant benefit.展开更多
The signal spectral leakage and fence effect are prone to take place during the power harmonic analysis by fast fourier transform(FFT) under asynchronous sampling.The inhibiting ability of classical window functions i...The signal spectral leakage and fence effect are prone to take place during the power harmonic analysis by fast fourier transform(FFT) under asynchronous sampling.The inhibiting ability of classical window functions is restricted by side-lobe behaviors. A new type window function called time domain mutual-multiplication window, is obtained by multiplication operation of several window functions. A novel approach of harmonic analysis is developed through analyzing performances of main-lobe and side-lobe of the new window. Simulation results show that the time domain mutual-multiplication window can significantly suppress frequency spectral leakage and improve the accuracy of harmonic parameter estimation.展开更多
Regional gravity field modeling with high-precision and high-resolution is one of the most important scientific objectives in geodesy, and can provide fundamental information for geophysics, geodynamics, seismology, a...Regional gravity field modeling with high-precision and high-resolution is one of the most important scientific objectives in geodesy, and can provide fundamental information for geophysics, geodynamics, seismology, and mineral exploration. Rectangular harmonic analysis （RHA） is proposed for regional gravity field modeling in this paper. By solving the Laplace＇s equation of gravitational potential in local Cartesian coordinate system, the rectangular harmonic expansions of disturbing potential, gravity anomaly, gravity disturbance, geoid undulation and deflection of the vertical are derived, and so are the formula for signal degree variance and error degree variance of the rectangular harmonic coefficients （RHC）. We also present the mathematical model and detailed algorithm for the solution of RHC using RHA from gravity observations. In order to reduce the edge effects caused by periodic continuation in RHA, we propose the strategy of extending the size of computation domain. The RHA-based modeling method is validated by conducting numerical experiments based on simulated ground and airborne gravity data that are generated from geopotential model EGM2008 and contaminated by Gauss white noise with standard deviation of 2 mGal. The accuracy of the 2.5＇×2.5＇ geoid undulations computed from ground and airborne gravity data is 1 and 1.4 cm, respectively. The standard error of the gravity disturbances that downward continued from the flight height of 4 km to the geoid is only 3.1 reGal. Numerical results confirm that RHA is able to provide a reliable and accurate regional gravity field model, which may be a new option for the representation of the fine structure of regional gravity field.展开更多
We give an introduction to basic harmonic analysis and representation theory for homogeneous spaces Z = G/H attached to a real reductive Lie group G. A special emphasis is made to the case where Z is real spherical.
As a means of quantitative interpretation,forward calculations of the global lithospheric magnetic field in the Spherical Harmonic(SH)domain have been widely used to reveal geophysical,lithological,and geothermal vari...As a means of quantitative interpretation,forward calculations of the global lithospheric magnetic field in the Spherical Harmonic(SH)domain have been widely used to reveal geophysical,lithological,and geothermal variations in the lithosphere.Traditional approaches either do not consider the non-axial dipolar terms of the inducing field and its radial variation or do so by means of complicated formulae.Moreover,existing methods treat the magnetic lithosphere either as an infinitesimally thin layer or as a radially uniform spherical shell of constant thickness.Here,we present alternative forward formulae that account for an arbitrarily high maximum degree of the inducing field and for a magnetic lithosphere of variable thickness.Our simulations based on these formulae suggest that the satellite magnetic anomaly field is sensitive to the non-axial dipolar terms of the inducing field but not to its radial variation.Therefore,in forward and inverse calculations of satellite magnetic anomaly data,the non-axial dipolar terms of the inducing field should not be ignored.Furthermore,our results show that the satellite magnetic anomaly field is sensitive to variability in the lateral thickness of the magnetized shell.In particular,we show that for a given vertically integrated susceptibility distribution,underestimating the thickness of the magnetic layer overestimates the induced magnetic field.This discovery bridges the greatest part of the alleged gap between the susceptibility values measured from rock samples and the susceptibility values required to match the observed magnetic field signal.We expect the formulae and conclusions of this study to be a valuable tool for the quantitative interpretation of the Earth's global lithospheric magnetic field,through an inverse or forward modelling approach.展开更多
In this paper,a 12/14-pole permanent magnet in-wheel motor is studied for potential in-wheel application,and the torque and loss are improved simultaneously based on designing and optimizing the corresponding dominant...In this paper,a 12/14-pole permanent magnet in-wheel motor is studied for potential in-wheel application,and the torque and loss are improved simultaneously based on designing and optimizing the corresponding dominant harmonics.The key of this study is to evaluate the contributions of harmonics on torque and loss,and further determines the harmonics related to them.Based on this,the torque enhancement factor and loss suppression factor are defined based on the selected dominant harmonics.And,the two factors are set as the optimization objectives,aiming at improving the characteristics of torque and loss.At the same time,to achieve an efficient optimization,a layered optimization method is presented,which includes magnet source layer and permeance layer.Based on the optimization,the motor torque is improved effectively,while the rotor iron loss is also reduced significantly.Then,a prototype motor is manufactured for experimental test.Finally,the simulation analysis and test results verify the validation of the studied motor and the proposed optimization method based on dominant harmonics.展开更多
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 pres...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.展开更多
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 observ...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.展开更多
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 response...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.展开更多
Double-shaft-driven needle punching machine is a specialized equipment designed for processing C/C crucible preforms.Its main needle punching module is operated by two sets of reciprocating crank-slider mechanisms.The...Double-shaft-driven needle punching machine is a specialized equipment designed for processing C/C crucible preforms.Its main needle punching module is operated by two sets of reciprocating crank-slider mechanisms.The intense vibration during needle punching not only generates huge noise,but also substantially reduces the quality of the preform.It is imperative to perform a dynamic analysis and optimization of the entire needle punching machine.In this paper,the three-dimensional(3D)model of the entire double-shaft-driven needle punching machine for C/C crucible preforms is established.Based on the modal analysis theory,the modal characteristics of the needle punching machine under various operating conditions are analyzed and its natural frequencies and vibration modes are determined.The harmonic response analysis is then employed to obtain the amplitude of the needle plate at different frequencies,and the structural weak points of the needle punching machine are identified and improved.The feasibility of the optimized scheme is subsequently reevaluated and verified.The results indicate that the first six natural frequencies of the machine increase,and the maximum amplitude of the needle plate decreases by 70.3%.The enhanced dynamic characteristics of the machine significantly improve its performance,enabling more efficient needle punching of C/C crucible preforms.展开更多
Tidal data of Tanggu marine environment monitoring stations for 59 years （1950-2008） was processed by using harmonic analysis, harmonic constants curves were discussed. And by using FFT spectral analysis periodicity...Tidal data of Tanggu marine environment monitoring stations for 59 years （1950-2008） was processed by using harmonic analysis, harmonic constants curves were discussed. And by using FFT spectral analysis periodicity and causation of its harmonic constants were analyzed. Alter astronomic tide signal was eliminated, residual water level was decomposed by using FFT spectral analysis, and then we got the periodic variation of mean residual water level over the past 50 years and discussed mean sea level changing trends of Tianjin offshore. The results show that variety of amplitude of M2 tidal constituent reveals 20 years, 4-6 years, 2-3-year periods, and it was obviously influenced by engineering construction since reform and opening age. Residual water level fluctuations reveal 20 years, 5-6 years, 2-3 years and 1 year periods. Sea level of Tianjin offshore displays a progressive ascending trend with rate about 3.4mm/a, which was influenced mainly by sea level rise and land subsidence.展开更多
In order to better understand the general tidal features in the venturi-shaped area between Zhenhai and Shenjiamen in the northern coastal region of Zhejiang Province in the East China Sea, the tidal data were obtaine...In order to better understand the general tidal features in the venturi-shaped area between Zhenhai and Shenjiamen in the northern coastal region of Zhejiang Province in the East China Sea, the tidal data were obtained from both the three permanent tide stations of Zhenhai, Dinghai and Shenjiamen, and four temporary tide stations of Mamu, Chuanshan, Guoju and Liuheng, along with the current speed being observed at Luotou Waterway. Results from harmonic analysis show that: (1) The area was dominated by shallow water tides with irregular semi-diurnal features, and the smallest tidal range occurred in the area near a crossing line between Zhenhai and Dinghai stations, indicating that a tidal node existed in the southern Hangzhou Bay; (2) Formulae, HS2/HM2 >0.4 and gM2-(gK1+gO1)=270° (where H and g are harmonic constants), could be used as judging criteria for high and low tidal level diurnal inequalities; (3) The duration difference between ebb and flood tides could be roughly assessed by the ratio of HM4 vs. HM2; and the larger the ratio is, the bigger the duration difference is. At the same time, the duration period could be assessed by 2gM2-gM4, the epoch difference between M2 and M4 tidal constituents. If 2gM2-gM4 <180°, then the ebb duration is longer than the flood duration; if 180°< 2gM2-gM4 <360°, the result is reversed; (4) Taking Dinghai station as a center point, the highest tidal levels and the average high tidal levels, as well as the average tidal ranges at all stations became higher and larger both southeastwards and northwestwards, while the lowest tidal levels and the average low tidal levels appeared to be lower both southeastwards and northwestwards; and (5) The tidal patterns were not all in line with the tidal current patterns. As a conclusion, the smallest tidal range occurred in the narrow part of the venturi-shaped area. Along the both sides of the area, the highest tidal level and tidal range became higher and larger, while the lowest tidal level became lower with the increase of the distance from the narrow throat area. This is somehow different from the theory that the tidal level increases gradually when it moves towards the top narrow area of a V-shaped bay or estuary.展开更多
基金supported by The National Natural Science Foundation of China(42374004).
文摘Spherical harmonic analysis(SHA)and synthesis(SHS)are widely used by researchers in various fields.Both numerical integration and least-squares methods can be employed for analysis and synthesis.However,these approaches,when calculated via summation,are computationally intensive.Although the Fast Fourier Transform(FFT)algorithm is efficient,it is traditionally limited to processing global grid points starting from zero longitude.In this paper,we derive an improved FFT algorithm for spherical harmonic analysis and synthesis.The proposed algorithm eliminates the need for grid points to start at zero longitude,thereby expanding the applicability of FFT-based methods.Numerical experiments demonstrate that the new algorithm retains the computational efficiency of conventional FFT while achieving accuracy comparable to the summation method.Consequently,it enables direct harmonic coefficient calculation from global grid data without requiring interpolation to align with zero longitude.Additionally,the algrithm can generate grid points with equi-angular spacing using the improved FFT algorithm,starting from non-zero longitudes.To address the loss of orthogonality in latitude due to discrete spherical grids,a quadrature weight factor-dependent on grid type(e.g.,regular or Gauss grid)-is incorporated,as summarized in this study.
基金This paper was supported by Chinese 863 Plan Water-Saving Agriculture (2002AA2Z4321),the Key Knowledge Innovation Project (SCXZY0103) and The Tenth-five Plan of Liaoning Province (2001212001).
文摘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.
基金ThispaperissupportedbytheChinese" 973"Program (No .2 0 0 3CD71 650 6)
文摘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.
基金his study was supported by the National Natural Science Foundation of China under contract No.40006001.
文摘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.
基金The National Natural Science Foundation of China under contract No.41806012。
文摘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.
文摘According to the rotor vortex theory,the rotor circulation and the rotor induced velocity are developed into Fourier series.The circulation distribution along blade spanwise is expressed in terms of segment-by-segment linear functions.In consequence the induced velocity equations and the circulation equations are derived.The engineering application of the rotor vortex theory is provided.Then the induced velocity and its harmonic components are obtained to provide a quantitative basis for the vortex model.For calculating each harmonic component of the induced velocity a simplified method is put forward which considers the effects of each order circulation with neglecting those of higher order.The method saves the computer time and is of significant benefit.
文摘The signal spectral leakage and fence effect are prone to take place during the power harmonic analysis by fast fourier transform(FFT) under asynchronous sampling.The inhibiting ability of classical window functions is restricted by side-lobe behaviors. A new type window function called time domain mutual-multiplication window, is obtained by multiplication operation of several window functions. A novel approach of harmonic analysis is developed through analyzing performances of main-lobe and side-lobe of the new window. Simulation results show that the time domain mutual-multiplication window can significantly suppress frequency spectral leakage and improve the accuracy of harmonic parameter estimation.
基金jointly supported by the National Basic Research Program of China (Grant No. 2013CB733301)the National Science and Technology Support Program of China (Grant No. 2012BAB16B01)+1 种基金the National Natural Science Foundation of China (Grant No. 41204008)the Basic Research Program of National Administration of Surveying, Mapping and Geoinformation of China
文摘Regional gravity field modeling with high-precision and high-resolution is one of the most important scientific objectives in geodesy, and can provide fundamental information for geophysics, geodynamics, seismology, and mineral exploration. Rectangular harmonic analysis （RHA） is proposed for regional gravity field modeling in this paper. By solving the Laplace＇s equation of gravitational potential in local Cartesian coordinate system, the rectangular harmonic expansions of disturbing potential, gravity anomaly, gravity disturbance, geoid undulation and deflection of the vertical are derived, and so are the formula for signal degree variance and error degree variance of the rectangular harmonic coefficients （RHC）. We also present the mathematical model and detailed algorithm for the solution of RHC using RHA from gravity observations. In order to reduce the edge effects caused by periodic continuation in RHA, we propose the strategy of extending the size of computation domain. The RHA-based modeling method is validated by conducting numerical experiments based on simulated ground and airborne gravity data that are generated from geopotential model EGM2008 and contaminated by Gauss white noise with standard deviation of 2 mGal. The accuracy of the 2.5＇×2.5＇ geoid undulations computed from ground and airborne gravity data is 1 and 1.4 cm, respectively. The standard error of the gravity disturbances that downward continued from the flight height of 4 km to the geoid is only 3.1 reGal. Numerical results confirm that RHA is able to provide a reliable and accurate regional gravity field model, which may be a new option for the representation of the fine structure of regional gravity field.
文摘We give an introduction to basic harmonic analysis and representation theory for homogeneous spaces Z = G/H attached to a real reductive Lie group G. A special emphasis is made to the case where Z is real spherical.
基金supported by the National Natural Science Foundation of China(Grant Nos.42250103 and 42174090)the Opening Fund of Key Laboratory of Geological Survey and Evaluation of Ministry of Education(Grant No.GLAB2023ZR02)the Ministry of Science and Technology(MOST)Special Fund from the State Key Laboratory of Geological Processes and Mineral Resources(Grant No.MSFGPMR2022-4)。
文摘As a means of quantitative interpretation,forward calculations of the global lithospheric magnetic field in the Spherical Harmonic(SH)domain have been widely used to reveal geophysical,lithological,and geothermal variations in the lithosphere.Traditional approaches either do not consider the non-axial dipolar terms of the inducing field and its radial variation or do so by means of complicated formulae.Moreover,existing methods treat the magnetic lithosphere either as an infinitesimally thin layer or as a radially uniform spherical shell of constant thickness.Here,we present alternative forward formulae that account for an arbitrarily high maximum degree of the inducing field and for a magnetic lithosphere of variable thickness.Our simulations based on these formulae suggest that the satellite magnetic anomaly field is sensitive to the non-axial dipolar terms of the inducing field but not to its radial variation.Therefore,in forward and inverse calculations of satellite magnetic anomaly data,the non-axial dipolar terms of the inducing field should not be ignored.Furthermore,our results show that the satellite magnetic anomaly field is sensitive to variability in the lateral thickness of the magnetized shell.In particular,we show that for a given vertically integrated susceptibility distribution,underestimating the thickness of the magnetic layer overestimates the induced magnetic field.This discovery bridges the greatest part of the alleged gap between the susceptibility values measured from rock samples and the susceptibility values required to match the observed magnetic field signal.We expect the formulae and conclusions of this study to be a valuable tool for the quantitative interpretation of the Earth's global lithospheric magnetic field,through an inverse or forward modelling approach.
文摘In this paper,a 12/14-pole permanent magnet in-wheel motor is studied for potential in-wheel application,and the torque and loss are improved simultaneously based on designing and optimizing the corresponding dominant harmonics.The key of this study is to evaluate the contributions of harmonics on torque and loss,and further determines the harmonics related to them.Based on this,the torque enhancement factor and loss suppression factor are defined based on the selected dominant harmonics.And,the two factors are set as the optimization objectives,aiming at improving the characteristics of torque and loss.At the same time,to achieve an efficient optimization,a layered optimization method is presented,which includes magnet source layer and permeance layer.Based on the optimization,the motor torque is improved effectively,while the rotor iron loss is also reduced significantly.Then,a prototype motor is manufactured for experimental test.Finally,the simulation analysis and test results verify the validation of the studied motor and the proposed optimization method based on dominant harmonics.
文摘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.
基金Supported by the National Natural Science Foundation of China （No. 40671161） and the Open Research Fund Program of the Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, China（No.1469990324233-03-04）.
文摘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.
基金Supported by the National Natural Science Foundation of China（51079027）
文摘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.
文摘Microscopic imaging based on second-harmonic generation has been proving to be a powerful tool for biomedical studies, especially in that tissues with
基金Open Project of Shanghai Key Laboratory of Lightweight Composite,China(No.2232021A4-04)。
文摘Double-shaft-driven needle punching machine is a specialized equipment designed for processing C/C crucible preforms.Its main needle punching module is operated by two sets of reciprocating crank-slider mechanisms.The intense vibration during needle punching not only generates huge noise,but also substantially reduces the quality of the preform.It is imperative to perform a dynamic analysis and optimization of the entire needle punching machine.In this paper,the three-dimensional(3D)model of the entire double-shaft-driven needle punching machine for C/C crucible preforms is established.Based on the modal analysis theory,the modal characteristics of the needle punching machine under various operating conditions are analyzed and its natural frequencies and vibration modes are determined.The harmonic response analysis is then employed to obtain the amplitude of the needle plate at different frequencies,and the structural weak points of the needle punching machine are identified and improved.The feasibility of the optimized scheme is subsequently reevaluated and verified.The results indicate that the first six natural frequencies of the machine increase,and the maximum amplitude of the needle plate decreases by 70.3%.The enhanced dynamic characteristics of the machine significantly improve its performance,enabling more efficient needle punching of C/C crucible preforms.
文摘Tidal data of Tanggu marine environment monitoring stations for 59 years （1950-2008） was processed by using harmonic analysis, harmonic constants curves were discussed. And by using FFT spectral analysis periodicity and causation of its harmonic constants were analyzed. Alter astronomic tide signal was eliminated, residual water level was decomposed by using FFT spectral analysis, and then we got the periodic variation of mean residual water level over the past 50 years and discussed mean sea level changing trends of Tianjin offshore. The results show that variety of amplitude of M2 tidal constituent reveals 20 years, 4-6 years, 2-3-year periods, and it was obviously influenced by engineering construction since reform and opening age. Residual water level fluctuations reveal 20 years, 5-6 years, 2-3 years and 1 year periods. Sea level of Tianjin offshore displays a progressive ascending trend with rate about 3.4mm/a, which was influenced mainly by sea level rise and land subsidence.
基金Supported by Study on the Temporal and Spatial Distributions of Temperature and Salinity in Xiangshan Bay and the Northern Zhejiang Coastal Waters in the East China Sea of the Education Department of Zhejiang Provincial Government of China (Project No. 20061134)Study on Environment Dynamics and Nutrient Circulation in Xiangshan Bay and its Surrounding Areas in the East China Sea of the Second Institute of Oceanography, State Oceanic Administration, China (Project No. SOED0605)
文摘In order to better understand the general tidal features in the venturi-shaped area between Zhenhai and Shenjiamen in the northern coastal region of Zhejiang Province in the East China Sea, the tidal data were obtained from both the three permanent tide stations of Zhenhai, Dinghai and Shenjiamen, and four temporary tide stations of Mamu, Chuanshan, Guoju and Liuheng, along with the current speed being observed at Luotou Waterway. Results from harmonic analysis show that: (1) The area was dominated by shallow water tides with irregular semi-diurnal features, and the smallest tidal range occurred in the area near a crossing line between Zhenhai and Dinghai stations, indicating that a tidal node existed in the southern Hangzhou Bay; (2) Formulae, HS2/HM2 >0.4 and gM2-(gK1+gO1)=270° (where H and g are harmonic constants), could be used as judging criteria for high and low tidal level diurnal inequalities; (3) The duration difference between ebb and flood tides could be roughly assessed by the ratio of HM4 vs. HM2; and the larger the ratio is, the bigger the duration difference is. At the same time, the duration period could be assessed by 2gM2-gM4, the epoch difference between M2 and M4 tidal constituents. If 2gM2-gM4 <180°, then the ebb duration is longer than the flood duration; if 180°< 2gM2-gM4 <360°, the result is reversed; (4) Taking Dinghai station as a center point, the highest tidal levels and the average high tidal levels, as well as the average tidal ranges at all stations became higher and larger both southeastwards and northwestwards, while the lowest tidal levels and the average low tidal levels appeared to be lower both southeastwards and northwestwards; and (5) The tidal patterns were not all in line with the tidal current patterns. As a conclusion, the smallest tidal range occurred in the narrow part of the venturi-shaped area. Along the both sides of the area, the highest tidal level and tidal range became higher and larger, while the lowest tidal level became lower with the increase of the distance from the narrow throat area. This is somehow different from the theory that the tidal level increases gradually when it moves towards the top narrow area of a V-shaped bay or estuary.
