By studying the e ects of geometric precision on kinematic accuracy, an error mapping model has been established, based on the hypothesis that a motion pair and its installation surface are rigid. However, when using ...By studying the e ects of geometric precision on kinematic accuracy, an error mapping model has been established, based on the hypothesis that a motion pair and its installation surface are rigid. However, when using this assumption,there is a significant error induced in high-precision computer numerical control(CNC) machine tools as compared with reality. One of the most important reasons for this error is failing to consider the error averaging e ect of motion pair elements. Therefore, this work examines a high-precision horizontal machining center as its research object, and analyzes the error averaging mechanism of a rolling guide pair under a deformation of the rolling elements. The carriage bearing forces caused by guideway straightness errors are obtained by constructing a geometric error model of a single carriage. The relationship between guideway straightness errors and carriage bearing forces is described by a transfer function in the spatial frequency domain, and its characteristics are analyzed. It quantifies the so-called error averaging e ect of the rolling guide system and, on this basis, a static model for four carriages is established to reflect the error averaging e ect of the rolling guide pair on the position and orientation errors of the motion pair. In addition, it is found that the wavelengths and phase di erences of guideway errors a ect this error averaging mechanism, but the amplitude and preload have little influence thereon. The experiment result shows that the kinematic straightness errors in the x-and y-directions were approximately 1/3 to 1/2 of the guideway straightness errors in the corresponding directions. The results can be used to guide the precision design and assembly of machine tools.展开更多
The first-passage statistics of Duffing-Rayleigh- Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed int...The first-passage statistics of Duffing-Rayleigh- Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed into two time homogeneous diffusion Markovian processes of amplitude and phase after stochastic averaging. The diffusion process method for first-passage problem is used and the corresponding backward Kolmogorov equation and Pontryagin equation are constructed and solved to yield the conditional reliability function and mean first-passage time with suitable initial and boundary conditions. The analytical results are confirmed by Monte Carlo simulation.展开更多
In this paper, a modified averaging scheme is presented for a class of time-delayed vibration systems with slow variables. The new scheme is a combination of the averaging techniques proposed by Hale and by Lehman and...In this paper, a modified averaging scheme is presented for a class of time-delayed vibration systems with slow variables. The new scheme is a combination of the averaging techniques proposed by Hale and by Lehman and Weibel, respectively. The averaged equation obtained from the modified scheme is simple enough but it retains the required information for the local nonlinear dynamics around an equilibrium. As an application of the present method, the delay value for which a secondary Hopf bifurcation occurs is successfully located for a delayed van der Pol oscillator.展开更多
Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and th...Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way.Then a MADM method based on generalized ordered weighted averaging operators is proposed.The proposed method is illustrated with a numerical example.展开更多
Time domain averaging(TDA) is essentially a comb filter,it cannot extract the specified harmonics which may be caused by some faults,such as gear eccentric.Meanwhile,TDA always suffers from period cutting error(PCE) t...Time domain averaging(TDA) is essentially a comb filter,it cannot extract the specified harmonics which may be caused by some faults,such as gear eccentric.Meanwhile,TDA always suffers from period cutting error(PCE) to different extent.Several improved TDA methods have been proposed,however they cannot completely eliminate the waveform reconstruction error caused by PCE.In order to overcome the shortcomings of conventional methods,a flexible time domain averaging(FTDA) technique is established,which adapts to the analyzed signal through adjusting each harmonic of the comb filter.In this technique,the explicit form of FTDA is first constructed by frequency domain sampling.Subsequently,chirp Z-transform(CZT) is employed in the algorithm of FTDA,which can improve the calculating efficiency significantly.Since the signal is reconstructed in the continuous time domain,there is no PCE in the FTDA.To validate the effectiveness of FTDA in the signal de-noising,interpolation and harmonic reconstruction,a simulated multi-components periodic signal that corrupted by noise is processed by FTDA.The simulation results show that the FTDA is capable of recovering the periodic components from the background noise effectively.Moreover,it can improve the signal-to-noise ratio by 7.9 dB compared with conventional ones.Experiments are also carried out on gearbox test rigs with chipped tooth and eccentricity gear,respectively.It is shown that the FTDA can identify the direction and severity of the eccentricity gear,and further enhances the amplitudes of impulses by 35%.The proposed technique not only solves the problem of PCE,but also provides a useful tool for the fault symptom extraction of rotating machinery.展开更多
The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational law...The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.展开更多
This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize co...This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.展开更多
The paper studies the parametric stochastic roll motion in the random waves.The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed....The paper studies the parametric stochastic roll motion in the random waves.The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed.Random sea surface is treated as a narrow-band stochastic process,and the stochastic parametric excitation is studied based on the effective wave theory.The nonlinear restored arm function obtained from the numerical simulation is expressed as the approximate analytic function.By using the stochastic averaging method,the differential equation of motion is transformed into Ito’s stochastic differential equation.The steady-state probability density function of roll motion is obtained,and the results are validated with the numerical simulation and model test.展开更多
A stochastic averaging method for predicting the response of quasi partially integrable and non-resonant Hamiltoniansystems to fractional Gaussian noise （fGla） with the Hurst index 1/2〈H〈l is proposed. The average...A stochastic averaging method for predicting the response of quasi partially integrable and non-resonant Hamiltoniansystems to fractional Gaussian noise （fGla） with the Hurst index 1/2〈H〈l is proposed. The averaged stochastic differential equa-tions （SDEs） for the first integrals of the associated Hamiltonian system are derived. The dimension of averaged SDEs is less thanthat of the original system. The stationary probability density and statistics of the original system are obtained approximately fromsolving the averaged SDEs numerically. Two systems are worked out to illustrate the proposed stochastic averaging method. It isshown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of originalsystem agree well, and the computational time for the former results is less than that for the latter ones.展开更多
A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise （fGn） with the Hurst index 1/2 〈 H 〈 1 is proposed. First, the definition and the ba...A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise （fGn） with the Hurst index 1/2 〈 H 〈 1 is proposed. First, the definition and the basic property of fGn and related fractional Brownian motion （iBm） are briefly introduced. Then, the averaged fractional stochastic differential equations （SDEs） for the first integrals and combinations of angle variables of the associated Hamiltonian systems are derived. The stationary probability density and statistics of the original systems are then obtained approximately by simulating the averaged SDEs numerically. An example is worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well.展开更多
Climate change in mountainous regions has significant impacts on hydrological and ecological systems. This research studied the future temperature, precipitation and snowfall in the 21^（st） century for the Tianshan ...Climate change in mountainous regions has significant impacts on hydrological and ecological systems. This research studied the future temperature, precipitation and snowfall in the 21^（st） century for the Tianshan and northern Kunlun Mountains（TKM） based on the general circulation model（GCM） simulation ensemble from the coupled model intercomparison project phase 5（CMIP5） under the representative concentration pathway（RCP） lower emission scenario RCP4.5 and higher emission scenario RCP8.5 using the Bayesian model averaging（BMA） technique. Results show that（1） BMA significantly outperformed the simple ensemble analysis and BMA mean matches all the three observed climate variables;（2） at the end of the 21^（st） century（2070–2099） under RCP8.5, compared to the control period（1976–2005）, annual mean temperature and mean annual precipitation will rise considerably by 4.8°C and 5.2%, respectively, while mean annual snowfall will dramatically decrease by 26.5%;（3） precipitation will increase in the northern Tianshan region while decrease in the Amu Darya Basin. Snowfall will significantly decrease in the western TKM. Mean annual snowfall fraction will also decrease from 0.56 of 1976–2005 to 0.42 of 2070–2099 under RCP8.5; and（4） snowfall shows a high sensitivity to temperature in autumn and spring while a low sensitivity in winter, with the highest sensitivity values occurring at the edge areas of TKM. The projections mean that flood risk will increase and solid water storage will decrease.展开更多
Gross primary production(GPP) plays a crucial part in the carbon cycle of terrestrial ecosystems.A set of validated monthly GPP data from 1957 to 2010 in 0.5°× 0.5° grids of China was weighted from the ...Gross primary production(GPP) plays a crucial part in the carbon cycle of terrestrial ecosystems.A set of validated monthly GPP data from 1957 to 2010 in 0.5°× 0.5° grids of China was weighted from the Multi-scale Terrestrial Model Intercomparison Project using Bayesian model averaging(BMA).The spatial anomalies of detrended BMA GPP during the growing seasons of typical El Nino years indicated that GPP response to El Nino varies with Pacific Decadal Oscillation(PDO) phases: when the PDO was in the cool phase,it was likely that GPP was greater in northern China(32°–38°N,111°–122°E) and less in the Yangtze River valley(28°–32°N,111°–122°E);in contrast,when PDO was in the warm phase,the GPP anomalies were usually reversed in these two regions.The consistent spatiotemporal pattern and high partial correlation revealed that rainfall dominated this phenomenon.The previously published findings on how El Nino during different phases of PDO affecting rainfall in eastern China make the statistical relationship between GPP and El Nino in this study theoretically credible.This paper not only introduces an effective way to use BMA in grids that have mixed plant function types,but also makes it possible to evaluate the carbon cycle in eastern China based on the prediction of El Nino and PDO.展开更多
The choices of the parameterizations for each component in a microwave emission model have significant effects on the quality of brightness temperature （Tb） sim- ulation. How to reduce the uncertainty in the Tb simu...The choices of the parameterizations for each component in a microwave emission model have significant effects on the quality of brightness temperature （Tb） sim- ulation. How to reduce the uncertainty in the Tb simulation is investigated by adopting a statistical post-processing procedure with the Bayesian model averaging （BMA） ensemble approach. The simulations by the community microwave emission model （CMEM） cou- pled with the community land model version 4.5 （CLM4.5） over China's Mainland are con- ducted by the 24 configurations from four vegetation opacity parameterizations （VOPs）, three soil dielectric constant parameterizations （SDCPs）, and two soil roughness param- eterizations （SRPs）. Compared with the simple arithmetical averaging （SAA） method, the BMA reconstructions have a higher spatial correlation coefficient （larger than 0.99） than the C-band satellite observations of the advanced microwave scanning radiometer on the Earth observing system （AMSR-E） at the vertical polarization. Moreover, the BMA product performs the best among the ensemble members for all vegetation classes, with a mean root-mean-square difference （RMSD） of 4 K and a temporal correlation coefficient of 0.64.展开更多
To ensure agreement between theoretical calculations and experimental data,parameters to selected nuclear physics models are perturbed and fine-tuned in nuclear data evaluations.This approach assumes that the chosen s...To ensure agreement between theoretical calculations and experimental data,parameters to selected nuclear physics models are perturbed and fine-tuned in nuclear data evaluations.This approach assumes that the chosen set of models accurately represents the‘true’distribution of considered observables.Furthermore,the models are chosen globally,indicating their applicability across the entire energy range of interest.However,this approach overlooks uncertainties inherent in the models themselves.In this work,we propose that instead of selecting globally a winning model set and proceeding with it as if it was the‘true’model set,we,instead,take a weighted average over multiple models within a Bayesian model averaging(BMA)framework,each weighted by its posterior probability.The method involves executing a set of TALYS calculations by randomly varying multiple nuclear physics models and their parameters to yield a vector of calculated observables.Next,computed likelihood function values at each incident energy point were then combined with the prior distributions to obtain updated posterior distributions for selected cross sections and the elastic angular distributions.As the cross sections and elastic angular distributions were updated locally on a per-energy-point basis,the approach typically results in discontinuities or“kinks”in the cross section curves,and these were addressed using spline interpolation.The proposed BMA method was applied to the evaluation of proton-induced reactions on ^(58)Ni between 1 and 100 MeV.The results demonstrated a favorable comparison with experimental data as well as with the TENDL-2023 evaluation.展开更多
In this paper,we aim to derive an averaging principle for stochastic differential equations driven by time-changed Lévy noise with variable delays.Under certain assumptions,we show that the solutions of stochasti...In this paper,we aim to derive an averaging principle for stochastic differential equations driven by time-changed Lévy noise with variable delays.Under certain assumptions,we show that the solutions of stochastic differential equations with time-changed Lévy noise can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence and in convergence in probability,respectively.The convergence order is also estimated in terms of noise intensity.Finally,an example with numerical simulation is given to illustrate the theoretical result.展开更多
This paper provides a direct and fast acquisition algorithm of civilian long length（CL） codes in the L2 civil（L2C） signal. The proposed algorithm simultaneously reduces the number of fast Fourier transformation（...This paper provides a direct and fast acquisition algorithm of civilian long length（CL） codes in the L2 civil（L2C） signal. The proposed algorithm simultaneously reduces the number of fast Fourier transformation（FFT） correlation through hyper code technique and the amount of points in every FFT correlation by using an averaging correlation method. To validate the proposed acquisition performance, the paper applies this algorithm to the real L2C signal collected by the global positioning system（GPS） L2C intermediate frequency（IF） signal sampler—SIS100L2C. The acquisition results show that the proposed modified algorithm can acquire the code phase accurately with less calculation and its acquisition performance is better than the single hyper code method.展开更多
The ability to estimate terrestrial water storage(TWS)is essential for monitoring hydrological extremes(e.g.,droughts and floods)and predicting future changes in the hydrological cycle.However,inadequacies in model ph...The ability to estimate terrestrial water storage(TWS)is essential for monitoring hydrological extremes(e.g.,droughts and floods)and predicting future changes in the hydrological cycle.However,inadequacies in model physics and parameters,as well as uncertainties in meteorological forcing data,commonly limit the ability of land surface models(LSMs)to accurately simulate TWS.In this study,the authors show how simulations of TWS anomalies(TWSAs)from multiple meteorological forcings and multiple LSMs can be combined in a Bayesian model averaging(BMA)ensemble approach to improve monitoring and predictions.Simulations using three forcing datasets and two LSMs were conducted over China's Mainland for the period 1979–2008.All the simulations showed good temporal correlations with satellite observations from the Gravity Recovery and Climate Experiment during 2004–08.The correlation coefficient ranged between 0.5 and 0.8 in the humid regions(e.g.,the Yangtze river basin,Huaihe basin,and Zhujiang basin),but was much lower in the arid regions(e.g.,the Heihe basin and Tarim river basin).The BMA ensemble approach performed better than all individual member simulations.It captured the spatial distribution and temporal variations of TWSAs over China's Mainland and the eight major river basins very well;plus,it showed the highest R value(>0.5)over most basins and the lowest root-mean-square error value(<40 mm)in all basins of China.The good performance of the BMA ensemble approach shows that it is a promising way to reproduce long-term,high-resolution spatial and temporal TWSA data.展开更多
The linewidth of electromagnetically induced transparency（EIT） in a coated Rb vapor cell was studied under a magnetic field gradient.The nonlinear broadening of the EIT linewidth with the magnetic field gradient was...The linewidth of electromagnetically induced transparency（EIT） in a coated Rb vapor cell was studied under a magnetic field gradient.The nonlinear broadening of the EIT linewidth with the magnetic field gradient was observed.It was found that the motional averaging of the field gradient was more pronounced at higher laser intensities and larger beam sizes.In the same regime,there was a small linewidth decrease with the increasing magnetic field gradient.We have established a Monte-Carlo model,which gave results in good qualitative agreement with our experiment.Physics pictures for the above phenomena were also suggested.These results provide an understanding of the EIT linewidth behavior under motional averaging,and should be useful for applications in quantum optics and metrology based on coated vapor cells.展开更多
This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orb...This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orbits between the spacecraft mean motion and the central body＇s rotation. Averaging conditions for these cases are given. As a major extension, a few classes of near resonant orbits are analyzed by the averaging method. Then some resulted conclusions of these averaging analyses are applied to understand the stabil- ity regions in a numerical experiment. Some stability conclu- sions are obtained. As a typical example, it is shown in detail that near circular 1 ： 2 resonant orbit is always unstable.展开更多
基金Supported by National Science and Technology Major Project of China(Grant No.2015ZX04005001)Tianjin Provincial Nature Science Foundation of China(Grant No.16JCZDJC38400)
文摘By studying the e ects of geometric precision on kinematic accuracy, an error mapping model has been established, based on the hypothesis that a motion pair and its installation surface are rigid. However, when using this assumption,there is a significant error induced in high-precision computer numerical control(CNC) machine tools as compared with reality. One of the most important reasons for this error is failing to consider the error averaging e ect of motion pair elements. Therefore, this work examines a high-precision horizontal machining center as its research object, and analyzes the error averaging mechanism of a rolling guide pair under a deformation of the rolling elements. The carriage bearing forces caused by guideway straightness errors are obtained by constructing a geometric error model of a single carriage. The relationship between guideway straightness errors and carriage bearing forces is described by a transfer function in the spatial frequency domain, and its characteristics are analyzed. It quantifies the so-called error averaging e ect of the rolling guide system and, on this basis, a static model for four carriages is established to reflect the error averaging e ect of the rolling guide pair on the position and orientation errors of the motion pair. In addition, it is found that the wavelengths and phase di erences of guideway errors a ect this error averaging mechanism, but the amplitude and preload have little influence thereon. The experiment result shows that the kinematic straightness errors in the x-and y-directions were approximately 1/3 to 1/2 of the guideway straightness errors in the corresponding directions. The results can be used to guide the precision design and assembly of machine tools.
基金the Foundation of ECUST(East China University of Science and Technology)for Outstanding Young Teachers(YH0157105)
文摘The first-passage statistics of Duffing-Rayleigh- Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed into two time homogeneous diffusion Markovian processes of amplitude and phase after stochastic averaging. The diffusion process method for first-passage problem is used and the corresponding backward Kolmogorov equation and Pontryagin equation are constructed and solved to yield the conditional reliability function and mean first-passage time with suitable initial and boundary conditions. The analytical results are confirmed by Monte Carlo simulation.
基金FANEDD of China (200430)the National Natural Science Foundation of China (10372116,10532050)
文摘In this paper, a modified averaging scheme is presented for a class of time-delayed vibration systems with slow variables. The new scheme is a combination of the averaging techniques proposed by Hale and by Lehman and Weibel, respectively. The averaged equation obtained from the modified scheme is simple enough but it retains the required information for the local nonlinear dynamics around an equilibrium. As an application of the present method, the delay value for which a secondary Hopf bifurcation occurs is successfully located for a delayed van der Pol oscillator.
基金supported by the National Natural Science Foundation of China (70871117 70571086)
文摘Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way.Then a MADM method based on generalized ordered weighted averaging operators is proposed.The proposed method is illustrated with a numerical example.
基金supported by National Natural Science Foundation of China(Grant Nos.5112502251005173)+1 种基金PhD Programs Foundation of Ministry of Education of China(Grant No.20110201110025)the Fundamental Research Funds for the Central Universities of China
文摘Time domain averaging(TDA) is essentially a comb filter,it cannot extract the specified harmonics which may be caused by some faults,such as gear eccentric.Meanwhile,TDA always suffers from period cutting error(PCE) to different extent.Several improved TDA methods have been proposed,however they cannot completely eliminate the waveform reconstruction error caused by PCE.In order to overcome the shortcomings of conventional methods,a flexible time domain averaging(FTDA) technique is established,which adapts to the analyzed signal through adjusting each harmonic of the comb filter.In this technique,the explicit form of FTDA is first constructed by frequency domain sampling.Subsequently,chirp Z-transform(CZT) is employed in the algorithm of FTDA,which can improve the calculating efficiency significantly.Since the signal is reconstructed in the continuous time domain,there is no PCE in the FTDA.To validate the effectiveness of FTDA in the signal de-noising,interpolation and harmonic reconstruction,a simulated multi-components periodic signal that corrupted by noise is processed by FTDA.The simulation results show that the FTDA is capable of recovering the periodic components from the background noise effectively.Moreover,it can improve the signal-to-noise ratio by 7.9 dB compared with conventional ones.Experiments are also carried out on gearbox test rigs with chipped tooth and eccentricity gear,respectively.It is shown that the FTDA can identify the direction and severity of the eccentricity gear,and further enhances the amplitudes of impulses by 35%.The proposed technique not only solves the problem of PCE,but also provides a useful tool for the fault symptom extraction of rotating machinery.
基金supported by the National Natural Science Foundation of China (70771025)the Fundamental Research Funds for the Central Universities of Hohai University (2009B04514)Humanities and Social Sciences Foundations of Ministry of Education of China(10YJA630067)
文摘The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.
文摘This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.
基金the State Administration of Science,Technology and Industry for National Defense of China(Grant No.B2420132001).
文摘The paper studies the parametric stochastic roll motion in the random waves.The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed.Random sea surface is treated as a narrow-band stochastic process,and the stochastic parametric excitation is studied based on the effective wave theory.The nonlinear restored arm function obtained from the numerical simulation is expressed as the approximate analytic function.By using the stochastic averaging method,the differential equation of motion is transformed into Ito’s stochastic differential equation.The steady-state probability density function of roll motion is obtained,and the results are validated with the numerical simulation and model test.
基金supported by the National Natural Science Foundation of China(Nos.11172259,11272279,11321202,and 11432012)
文摘A stochastic averaging method for predicting the response of quasi partially integrable and non-resonant Hamiltoniansystems to fractional Gaussian noise （fGla） with the Hurst index 1/2〈H〈l is proposed. The averaged stochastic differential equa-tions （SDEs） for the first integrals of the associated Hamiltonian system are derived. The dimension of averaged SDEs is less thanthat of the original system. The stationary probability density and statistics of the original system are obtained approximately fromsolving the averaged SDEs numerically. Two systems are worked out to illustrate the proposed stochastic averaging method. It isshown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of originalsystem agree well, and the computational time for the former results is less than that for the latter ones.
基金supported by the National Natural Science Foundation of China under grants nos.:11272279,11321202 and 11432012
文摘A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise （fGn） with the Hurst index 1/2 〈 H 〈 1 is proposed. First, the definition and the basic property of fGn and related fractional Brownian motion （iBm） are briefly introduced. Then, the averaged fractional stochastic differential equations （SDEs） for the first integrals and combinations of angle variables of the associated Hamiltonian systems are derived. The stationary probability density and statistics of the original systems are then obtained approximately by simulating the averaged SDEs numerically. An example is worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well.
基金supported by the Thousand Youth Talents Plan(Xinjiang Project)the National Natural Science Foundation of China(41630859)the West Light Foundation of Chinese Academy of Sciences(2016QNXZB12)
文摘Climate change in mountainous regions has significant impacts on hydrological and ecological systems. This research studied the future temperature, precipitation and snowfall in the 21^（st） century for the Tianshan and northern Kunlun Mountains（TKM） based on the general circulation model（GCM） simulation ensemble from the coupled model intercomparison project phase 5（CMIP5） under the representative concentration pathway（RCP） lower emission scenario RCP4.5 and higher emission scenario RCP8.5 using the Bayesian model averaging（BMA） technique. Results show that（1） BMA significantly outperformed the simple ensemble analysis and BMA mean matches all the three observed climate variables;（2） at the end of the 21^（st） century（2070–2099） under RCP8.5, compared to the control period（1976–2005）, annual mean temperature and mean annual precipitation will rise considerably by 4.8°C and 5.2%, respectively, while mean annual snowfall will dramatically decrease by 26.5%;（3） precipitation will increase in the northern Tianshan region while decrease in the Amu Darya Basin. Snowfall will significantly decrease in the western TKM. Mean annual snowfall fraction will also decrease from 0.56 of 1976–2005 to 0.42 of 2070–2099 under RCP8.5; and（4） snowfall shows a high sensitivity to temperature in autumn and spring while a low sensitivity in winter, with the highest sensitivity values occurring at the edge areas of TKM. The projections mean that flood risk will increase and solid water storage will decrease.
基金supported by the National Key Research and Development Program of China (Grant Nos.2016YFA0602501 and 2018YFA0606004)the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos.XDA20040301 and XDA20020201)。
文摘Gross primary production(GPP) plays a crucial part in the carbon cycle of terrestrial ecosystems.A set of validated monthly GPP data from 1957 to 2010 in 0.5°× 0.5° grids of China was weighted from the Multi-scale Terrestrial Model Intercomparison Project using Bayesian model averaging(BMA).The spatial anomalies of detrended BMA GPP during the growing seasons of typical El Nino years indicated that GPP response to El Nino varies with Pacific Decadal Oscillation(PDO) phases: when the PDO was in the cool phase,it was likely that GPP was greater in northern China(32°–38°N,111°–122°E) and less in the Yangtze River valley(28°–32°N,111°–122°E);in contrast,when PDO was in the warm phase,the GPP anomalies were usually reversed in these two regions.The consistent spatiotemporal pattern and high partial correlation revealed that rainfall dominated this phenomenon.The previously published findings on how El Nino during different phases of PDO affecting rainfall in eastern China make the statistical relationship between GPP and El Nino in this study theoretically credible.This paper not only introduces an effective way to use BMA in grids that have mixed plant function types,but also makes it possible to evaluate the carbon cycle in eastern China based on the prediction of El Nino and PDO.
基金Project supported by the China Special Fund for Meteorological Research in the Public Interest(No.GYHY201306045)the National Natural Science Foundation of China(Nos.41305066 and41575096)
文摘The choices of the parameterizations for each component in a microwave emission model have significant effects on the quality of brightness temperature （Tb） sim- ulation. How to reduce the uncertainty in the Tb simulation is investigated by adopting a statistical post-processing procedure with the Bayesian model averaging （BMA） ensemble approach. The simulations by the community microwave emission model （CMEM） cou- pled with the community land model version 4.5 （CLM4.5） over China's Mainland are con- ducted by the 24 configurations from four vegetation opacity parameterizations （VOPs）, three soil dielectric constant parameterizations （SDCPs）, and two soil roughness param- eterizations （SRPs）. Compared with the simple arithmetical averaging （SAA） method, the BMA reconstructions have a higher spatial correlation coefficient （larger than 0.99） than the C-band satellite observations of the advanced microwave scanning radiometer on the Earth observing system （AMSR-E） at the vertical polarization. Moreover, the BMA product performs the best among the ensemble members for all vegetation classes, with a mean root-mean-square difference （RMSD） of 4 K and a temporal correlation coefficient of 0.64.
基金funding from the Paul ScherrerInstitute,Switzerland through the NES/GFA-ABE Cross Project。
文摘To ensure agreement between theoretical calculations and experimental data,parameters to selected nuclear physics models are perturbed and fine-tuned in nuclear data evaluations.This approach assumes that the chosen set of models accurately represents the‘true’distribution of considered observables.Furthermore,the models are chosen globally,indicating their applicability across the entire energy range of interest.However,this approach overlooks uncertainties inherent in the models themselves.In this work,we propose that instead of selecting globally a winning model set and proceeding with it as if it was the‘true’model set,we,instead,take a weighted average over multiple models within a Bayesian model averaging(BMA)framework,each weighted by its posterior probability.The method involves executing a set of TALYS calculations by randomly varying multiple nuclear physics models and their parameters to yield a vector of calculated observables.Next,computed likelihood function values at each incident energy point were then combined with the prior distributions to obtain updated posterior distributions for selected cross sections and the elastic angular distributions.As the cross sections and elastic angular distributions were updated locally on a per-energy-point basis,the approach typically results in discontinuities or“kinks”in the cross section curves,and these were addressed using spline interpolation.The proposed BMA method was applied to the evaluation of proton-induced reactions on ^(58)Ni between 1 and 100 MeV.The results demonstrated a favorable comparison with experimental data as well as with the TENDL-2023 evaluation.
基金supported by the National NaturalScience Foundation of China(12071003,11901005)the Natural Science Foundation of Anhui Province(2008085QA20)。
文摘In this paper,we aim to derive an averaging principle for stochastic differential equations driven by time-changed Lévy noise with variable delays.Under certain assumptions,we show that the solutions of stochastic differential equations with time-changed Lévy noise can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence and in convergence in probability,respectively.The convergence order is also estimated in terms of noise intensity.Finally,an example with numerical simulation is given to illustrate the theoretical result.
基金supported by the Fundamental Research Fund for the Central Universities(NS2013016)
文摘This paper provides a direct and fast acquisition algorithm of civilian long length（CL） codes in the L2 civil（L2C） signal. The proposed algorithm simultaneously reduces the number of fast Fourier transformation（FFT） correlation through hyper code technique and the amount of points in every FFT correlation by using an averaging correlation method. To validate the proposed acquisition performance, the paper applies this algorithm to the real L2C signal collected by the global positioning system（GPS） L2C intermediate frequency（IF） signal sampler—SIS100L2C. The acquisition results show that the proposed modified algorithm can acquire the code phase accurately with less calculation and its acquisition performance is better than the single hyper code method.
基金supported by the National Natural Science Foundation of China(Grant Nos.41405083 and 91437220)the Natural Science Foundation of Hunan Province,China(Grant No.2015JJ3098)+1 种基金the Key Research Program of Frontier Sciences,CAS(QYZDY-SSW-DQC012)the Fund Project for The Education Department of Hunan Province(Grant No.16A234)
文摘The ability to estimate terrestrial water storage(TWS)is essential for monitoring hydrological extremes(e.g.,droughts and floods)and predicting future changes in the hydrological cycle.However,inadequacies in model physics and parameters,as well as uncertainties in meteorological forcing data,commonly limit the ability of land surface models(LSMs)to accurately simulate TWS.In this study,the authors show how simulations of TWS anomalies(TWSAs)from multiple meteorological forcings and multiple LSMs can be combined in a Bayesian model averaging(BMA)ensemble approach to improve monitoring and predictions.Simulations using three forcing datasets and two LSMs were conducted over China's Mainland for the period 1979–2008.All the simulations showed good temporal correlations with satellite observations from the Gravity Recovery and Climate Experiment during 2004–08.The correlation coefficient ranged between 0.5 and 0.8 in the humid regions(e.g.,the Yangtze river basin,Huaihe basin,and Zhujiang basin),but was much lower in the arid regions(e.g.,the Heihe basin and Tarim river basin).The BMA ensemble approach performed better than all individual member simulations.It captured the spatial distribution and temporal variations of TWSAs over China's Mainland and the eight major river basins very well;plus,it showed the highest R value(>0.5)over most basins and the lowest root-mean-square error value(<40 mm)in all basins of China.The good performance of the BMA ensemble approach shows that it is a promising way to reproduce long-term,high-resolution spatial and temporal TWSA data.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61078013 and J1103204)the Shanghai Pujiang Program,China (Grant No. 10PJ1401400)+1 种基金the National Basic Research Program of China (Grant Nos. 2011CB921604 and 2012CB921604)the Fudan University,China
文摘The linewidth of electromagnetically induced transparency（EIT） in a coated Rb vapor cell was studied under a magnetic field gradient.The nonlinear broadening of the EIT linewidth with the magnetic field gradient was observed.It was found that the motional averaging of the field gradient was more pronounced at higher laser intensities and larger beam sizes.In the same regime,there was a small linewidth decrease with the increasing magnetic field gradient.We have established a Monte-Carlo model,which gave results in good qualitative agreement with our experiment.Physics pictures for the above phenomena were also suggested.These results provide an understanding of the EIT linewidth behavior under motional averaging,and should be useful for applications in quantum optics and metrology based on coated vapor cells.
基金partially supported by an innovation fund from Chinese academy of space technology and a grant from the Jet Propulsion Laboratory
文摘This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orbits between the spacecraft mean motion and the central body＇s rotation. Averaging conditions for these cases are given. As a major extension, a few classes of near resonant orbits are analyzed by the averaging method. Then some resulted conclusions of these averaging analyses are applied to understand the stabil- ity regions in a numerical experiment. Some stability conclu- sions are obtained. As a typical example, it is shown in detail that near circular 1 ： 2 resonant orbit is always unstable.
