The global error minimization is a variational method for obtaining approximate analytical solutions to nonlinear oscillator equations which works as follows. Given an ordinary differential equation, a trial solution ...The global error minimization is a variational method for obtaining approximate analytical solutions to nonlinear oscillator equations which works as follows. Given an ordinary differential equation, a trial solution containing unknowns is selected. The method then converts the problem to an equivalent minimization problem by averaging the squared residual of the differential equation for the selected trial solution. Clearly, the method fails if the integral which defines the average is undefined or infinite for the selected trial. This is precisely the case for such non-periodic solutions as heteroclinic (front or kink) and some homoclinic (dark-solitons) solutions. Based on the fact that these types of solutions have vanishing velocity at infinity, we propose to remedy to this shortcoming of the method by averaging the product of the residual and the derivative of the trial solution. In this way, the method can apply for the approximation of all relevant type of solutions of nonlinear evolution equations. The approach is simple, straightforward and accurate as its original formulation. Its effectiveness is demonstrated using a Helmholtz-Duffing oscillator.展开更多
This paper investigates the possible sources of errors associated with tropical cyclone （TC） tracks forecasted using the Global/Regional Assimilation and Prediction System （GRAPES）. The GRAPES forecasts were made ...This paper investigates the possible sources of errors associated with tropical cyclone （TC） tracks forecasted using the Global/Regional Assimilation and Prediction System （GRAPES）. The GRAPES forecasts were made for 16 landfaIling TCs in the western North Pacific basin during the 2008 and 2009 seasons, with a forecast length of 72 hours, and using the default initial conditions （＂initials＂, hereafter）, which are from the NCEP-FNL dataset, as well as ECMWF initials. The forecasts are compared with ECMWF forecasts. The results show that in most TCs, the GRAPES forecasts are improved when using the ECMWF initials compared with the default initials. Compared with the ECMWF initials, the default initials produce lower intensity TCs and a lower intensity subtropical high, but a higher intensity South Asia high and monsoon trough, as well as a higher temperature but lower specific humidity at the TC center. Replacement of the geopotential height and wind fields with the ECMWF initials in and around the TC center at the initial time was found to be the most efficient way to improve the forecasts. In addition, TCs that showed the greatest improvement in forecast accuracy usually had the largest initial uncertainties in TC intensity and were usually in the intensifying phase. The results demonstrate the importance of the initial intensity for TC track forecasts made using GRAPES, and indicate the model is better in describing the intensifying phase than the decaying phase of TCs. Finally, the limit of the improvement indicates that the model error associated with GRAPES forecasts may be the main cause of poor forecasts of landfalling TCs. Thus, further examinations of the model errors are required.展开更多
Firstly, the new combined error model of cumulative geoid height influenced by four error sources, including the inter-satellite range-rate of an interferometric laser （K-band） ranging system, the orbital position a...Firstly, the new combined error model of cumulative geoid height influenced by four error sources, including the inter-satellite range-rate of an interferometric laser （K-band） ranging system, the orbital position and velocity of a global positioning system （GPS） receiver and non-conservative force of an accelerometer, is established from the perspectives of the power spectrum principle in physics using the semi-analytical approach. Secondly, the accuracy of the global gravitational field is accurately and rapidly estimated based on the combined error model; the cumulative geoid height error is 1.985× 10^-1 m at degree 120 based on GRACE Level 1B measured observation errors of the year 2007 published by the US Jet Propulsion Laboratory （JPL）, and the cumulative geoid height error is 5.825 × 10^-2 m at degree 360 using GRACE Follow-On orbital altitude 250 km and inter-satellite range 50 km. The matching relationship of accuracy indexes from GRACE Follow-On key payloads is brought forward, and the dependability of the combined error model is validated. Finally, the feasibility of high-accuracy and high-resolution global gravitational field estimation from GRACE Follow-On is demonstrated based on different satellite orbital altitudes.展开更多
<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the...<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>展开更多
In real machining, the tool paths are composed of a series of short line segments, which constitute groups of sharp corners correspondingly leading to geometry discontinuity in tangent. As a result, high acceleration ...In real machining, the tool paths are composed of a series of short line segments, which constitute groups of sharp corners correspondingly leading to geometry discontinuity in tangent. As a result, high acceleration with high fluctuation usually occurs. If these kinds of tool paths are directly used for machining, the feedrate and quality will be greatly reduced. Thus, generating continuous tool paths is strongly desired. This paper presents a new error-controllable method for generating continuous tool path. Different from the traditional method focusing on fitting the cutter locations, the proposed method realizes globally smoothing the tool path in an error-controllable way. Concretely, it does the smoothing by approaching the newly produced curve to the linear tool path by taking the tolerance requirement as a constraint. That is, the error between the desired tool path and the G01 commands are taken as a boundary condition to ensure the finally smoothed curve being within the given tolerance. Besides, to improve the smoothing ability in case of small corner angle, an improved local smoothing method is also proposed by symmetrically assigning the control points to the two adjacent linear segments with the constrains of tolerance and G3 continuity. Experiments on an open five-axis machine are developed to verify the advantages of the proposed methods.展开更多
A novel hybrid approach for earthquake location is proposed which uses a combined coarse global search and fine local inversion with a minimum search routine, plus an examination of the root mean squares （RMS） error...A novel hybrid approach for earthquake location is proposed which uses a combined coarse global search and fine local inversion with a minimum search routine, plus an examination of the root mean squares （RMS） error distribution. The method exploits the advantages of network ray tracing and robust formulation of the Frrchet derivatives to simultaneously update all possible initial source parameters around most local minima （including the global minimum） in the solution space, and finally to determine the likely global solution. Several synthetic examples involving a 3-D complex velocity model and a challenging source-receiver layout are used to demonstrate the capability of the newly-developed method. This new global-local hybrid solution technique not only incorporates the significant benefits of our recently published hypocenter determination procedure for multiple earthquake parameters, but also offers the attractive features of global optimal searching in the RMS travel time error distribution. Unlike the traditional global search method, for example, the Monte Carlo approach, where millions of tests have to be done to fmd the final global solution, the new method only conducts a matrix inversion type local search but does it multiple times simultaneously throughout the model volume to seek a global solution. The search is aided by inspection of the RMS error distribution. Benchmark tests against two popular approaches, the direct grid search method and the oct-tree important sampling method, indicate that the hybrid global-local inversion yields comparable location accuracy and is not sensitive to modest level of noise data, but more importantly it offers two-order of magnitude speed-up in computational effort. Such an improvement, combined with high accuracy, make it a promising hypocenter determination scheme in earthquake early warning, tsunami early warning, rapid hazard assessment and emergency response after strong earthquake occurrence.展开更多
This paper describes a strategy for merging daily precipitation information from gauge observations, satellite estimates （SEs）, and numerical predictions at the global scale. The strategy is designed to remove syste...This paper describes a strategy for merging daily precipitation information from gauge observations, satellite estimates （SEs）, and numerical predictions at the global scale. The strategy is designed to remove systemic bias and random error from each individual daily precipitation source to produce a better gridded global daily precipitation product through three steps. First, a cumulative distribution function matching procedure is performed to remove systemic bias over gauge-located land areas. Then, the overall biases in SEs and model predictions （MPs） over ocean areas are corrected using a rescaled strategy based on monthly precipitation. Third, an optimal interpolation （OI）-based merging scheme （referred as the HL-OI scheme） is used to combine unbiased gahge observations, SEs, and MPs to reduce random error from each source and to produce a gauge--satellite-model merged daily precipitation analysis, called BMEP-d （Beijing Climate Center Merged Estimation of Precipitation with daily resolution）, with complete global coverage. The BMEP-d data from a four-year period （2011- 14） demonstrate the ability of the merging strategy to provide global daily precipitation of substantially improved quality. Benefiting from the advantages of the HL-OI scheme for quantitative error estimates, the better source data can obtain more weights during the merging processes. The BMEP-d data exhibit higher consistency with satellite and gauge source data at middle and low latitudes, and with model source data at high latitudes. Overall, independent validations against GPCP-1DD （GPCP one-degree daily） show that the consistencies between B MEP-d and GPCP-1DD are higher than those of each source dataset in terms of spatial pattern, temporal variability, probability distribution, and statistical precipitation events.展开更多
The unequal error protection （UEP） is applied in distributed speech recognition （DSR） system and three schemes are proposed. All of these three schemes are evaluated on the GSM simulating platform for recognizing ...The unequal error protection （UEP） is applied in distributed speech recognition （DSR） system and three schemes are proposed. All of these three schemes are evaluated on the GSM simulating platform for recognizing mandarin digit strings and compared with the equal error protection （EEP） scheme. Experiments show that UEP can protect the data transmitted in DSR system more effectively, which results in a higher word accurate rate of DSR system.展开更多
The extent to which specific climatic factors influence evapotranspiration under subhumid conditions in Hungary was investigated. The reference evapotranspiration, calculated with the internationally accepted Penman-M...The extent to which specific climatic factors influence evapotranspiration under subhumid conditions in Hungary was investigated. The reference evapotranspiration, calculated with the internationally accepted Penman-Monteith equation proposed by FAO, was considered. The results show that the influence of radiation, which provides energy for evaporation, is the strongest factor and that the influence of global radiation alone is very strong. Taking into account that radiation was measured under rather limited conditions in space and time, global radiation was calculated using the Hargreaves method based on temperature. Accordingly, we have defined a formula based on temperature-based global radiation and verified the data obtained with the Penman-Monteith formula calculated for 14 meteorological stations. The verification gave good results, therefore the method can be used for practical purposes in the subhumid conditions of Hungary based on the data of the nearest meteorological station.展开更多
文摘The global error minimization is a variational method for obtaining approximate analytical solutions to nonlinear oscillator equations which works as follows. Given an ordinary differential equation, a trial solution containing unknowns is selected. The method then converts the problem to an equivalent minimization problem by averaging the squared residual of the differential equation for the selected trial solution. Clearly, the method fails if the integral which defines the average is undefined or infinite for the selected trial. This is precisely the case for such non-periodic solutions as heteroclinic (front or kink) and some homoclinic (dark-solitons) solutions. Based on the fact that these types of solutions have vanishing velocity at infinity, we propose to remedy to this shortcoming of the method by averaging the product of the residual and the derivative of the trial solution. In this way, the method can apply for the approximation of all relevant type of solutions of nonlinear evolution equations. The approach is simple, straightforward and accurate as its original formulation. Its effectiveness is demonstrated using a Helmholtz-Duffing oscillator.
基金supported by the National Science and Technology Support Program(Grant.No.2012BAC22B03)the National Natural Science Foundation of China(Grant No.41475100)+1 种基金the Youth Innovation Promotion Association of Chinese Academy of Sciencesthe Japan Society for the Promotion of Science KAKENHI(Grant.No.26282111)
文摘This paper investigates the possible sources of errors associated with tropical cyclone （TC） tracks forecasted using the Global/Regional Assimilation and Prediction System （GRAPES）. The GRAPES forecasts were made for 16 landfaIling TCs in the western North Pacific basin during the 2008 and 2009 seasons, with a forecast length of 72 hours, and using the default initial conditions （＂initials＂, hereafter）, which are from the NCEP-FNL dataset, as well as ECMWF initials. The forecasts are compared with ECMWF forecasts. The results show that in most TCs, the GRAPES forecasts are improved when using the ECMWF initials compared with the default initials. Compared with the ECMWF initials, the default initials produce lower intensity TCs and a lower intensity subtropical high, but a higher intensity South Asia high and monsoon trough, as well as a higher temperature but lower specific humidity at the TC center. Replacement of the geopotential height and wind fields with the ECMWF initials in and around the TC center at the initial time was found to be the most efficient way to improve the forecasts. In addition, TCs that showed the greatest improvement in forecast accuracy usually had the largest initial uncertainties in TC intensity and were usually in the intensifying phase. The results demonstrate the importance of the initial intensity for TC track forecasts made using GRAPES, and indicate the model is better in describing the intensifying phase than the decaying phase of TCs. Finally, the limit of the improvement indicates that the model error associated with GRAPES forecasts may be the main cause of poor forecasts of landfalling TCs. Thus, further examinations of the model errors are required.
基金supported by the National Natural Science Foundation of China (Grant No 40674038)the Funds of the Chinese Academy of Sciences for Key Topics in Innovation Engineering (Grant Nos KZCX2-YW-143 and KZCX2-YW-202)+1 种基金the National High Technology Research and Development Program of China (863) (Grant Nos 2009AA12Z138 and 2006AA09Z153)the Grant-in-Aid for Scientific Research of Japan (Grant No B19340129)
文摘Firstly, the new combined error model of cumulative geoid height influenced by four error sources, including the inter-satellite range-rate of an interferometric laser （K-band） ranging system, the orbital position and velocity of a global positioning system （GPS） receiver and non-conservative force of an accelerometer, is established from the perspectives of the power spectrum principle in physics using the semi-analytical approach. Secondly, the accuracy of the global gravitational field is accurately and rapidly estimated based on the combined error model; the cumulative geoid height error is 1.985× 10^-1 m at degree 120 based on GRACE Level 1B measured observation errors of the year 2007 published by the US Jet Propulsion Laboratory （JPL）, and the cumulative geoid height error is 5.825 × 10^-2 m at degree 360 using GRACE Follow-On orbital altitude 250 km and inter-satellite range 50 km. The matching relationship of accuracy indexes from GRACE Follow-On key payloads is brought forward, and the dependability of the combined error model is validated. Finally, the feasibility of high-accuracy and high-resolution global gravitational field estimation from GRACE Follow-On is demonstrated based on different satellite orbital altitudes.
文摘<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>
基金supported by the National Natural Science Foundation of China under Grant Nos.51675440 and 11620101002National Key Research and Development Program of China under Grant No.2017YFB1102800the Fundamental Research Funds for the Central Universities under Grant No.3102018gxc025
文摘In real machining, the tool paths are composed of a series of short line segments, which constitute groups of sharp corners correspondingly leading to geometry discontinuity in tangent. As a result, high acceleration with high fluctuation usually occurs. If these kinds of tool paths are directly used for machining, the feedrate and quality will be greatly reduced. Thus, generating continuous tool paths is strongly desired. This paper presents a new error-controllable method for generating continuous tool path. Different from the traditional method focusing on fitting the cutter locations, the proposed method realizes globally smoothing the tool path in an error-controllable way. Concretely, it does the smoothing by approaching the newly produced curve to the linear tool path by taking the tolerance requirement as a constraint. That is, the error between the desired tool path and the G01 commands are taken as a boundary condition to ensure the finally smoothed curve being within the given tolerance. Besides, to improve the smoothing ability in case of small corner angle, an improved local smoothing method is also proposed by symmetrically assigning the control points to the two adjacent linear segments with the constrains of tolerance and G3 continuity. Experiments on an open five-axis machine are developed to verify the advantages of the proposed methods.
基金funded by the National Natural Science Foundation of China (No.40774020)the Key Research Program from Ministry of Education of China (No.107137)
文摘A novel hybrid approach for earthquake location is proposed which uses a combined coarse global search and fine local inversion with a minimum search routine, plus an examination of the root mean squares （RMS） error distribution. The method exploits the advantages of network ray tracing and robust formulation of the Frrchet derivatives to simultaneously update all possible initial source parameters around most local minima （including the global minimum） in the solution space, and finally to determine the likely global solution. Several synthetic examples involving a 3-D complex velocity model and a challenging source-receiver layout are used to demonstrate the capability of the newly-developed method. This new global-local hybrid solution technique not only incorporates the significant benefits of our recently published hypocenter determination procedure for multiple earthquake parameters, but also offers the attractive features of global optimal searching in the RMS travel time error distribution. Unlike the traditional global search method, for example, the Monte Carlo approach, where millions of tests have to be done to fmd the final global solution, the new method only conducts a matrix inversion type local search but does it multiple times simultaneously throughout the model volume to seek a global solution. The search is aided by inspection of the RMS error distribution. Benchmark tests against two popular approaches, the direct grid search method and the oct-tree important sampling method, indicate that the hybrid global-local inversion yields comparable location accuracy and is not sensitive to modest level of noise data, but more importantly it offers two-order of magnitude speed-up in computational effort. Such an improvement, combined with high accuracy, make it a promising hypocenter determination scheme in earthquake early warning, tsunami early warning, rapid hazard assessment and emergency response after strong earthquake occurrence.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41275076, 41305057, 41175066, 41175086, and 40905046)the Beijing Natural Science Foundation (Grant No. 8144046)+1 种基金the National High Technology Research and Development Program of China (Grant Nos. 2009AA122005 and 2009BAC51B03)the National Basic Research Program of China (Grant No. 2010CB 951902)
文摘This paper describes a strategy for merging daily precipitation information from gauge observations, satellite estimates （SEs）, and numerical predictions at the global scale. The strategy is designed to remove systemic bias and random error from each individual daily precipitation source to produce a better gridded global daily precipitation product through three steps. First, a cumulative distribution function matching procedure is performed to remove systemic bias over gauge-located land areas. Then, the overall biases in SEs and model predictions （MPs） over ocean areas are corrected using a rescaled strategy based on monthly precipitation. Third, an optimal interpolation （OI）-based merging scheme （referred as the HL-OI scheme） is used to combine unbiased gahge observations, SEs, and MPs to reduce random error from each source and to produce a gauge--satellite-model merged daily precipitation analysis, called BMEP-d （Beijing Climate Center Merged Estimation of Precipitation with daily resolution）, with complete global coverage. The BMEP-d data from a four-year period （2011- 14） demonstrate the ability of the merging strategy to provide global daily precipitation of substantially improved quality. Benefiting from the advantages of the HL-OI scheme for quantitative error estimates, the better source data can obtain more weights during the merging processes. The BMEP-d data exhibit higher consistency with satellite and gauge source data at middle and low latitudes, and with model source data at high latitudes. Overall, independent validations against GPCP-1DD （GPCP one-degree daily） show that the consistencies between B MEP-d and GPCP-1DD are higher than those of each source dataset in terms of spatial pattern, temporal variability, probability distribution, and statistical precipitation events.
基金Sponsored bythe National Natural Science Foundation of China (60372089) the Basic Research Foundation of Beijing Institute of Technology(BIT-UBF-200301F03)
文摘The unequal error protection （UEP） is applied in distributed speech recognition （DSR） system and three schemes are proposed. All of these three schemes are evaluated on the GSM simulating platform for recognizing mandarin digit strings and compared with the equal error protection （EEP） scheme. Experiments show that UEP can protect the data transmitted in DSR system more effectively, which results in a higher word accurate rate of DSR system.
文摘The extent to which specific climatic factors influence evapotranspiration under subhumid conditions in Hungary was investigated. The reference evapotranspiration, calculated with the internationally accepted Penman-Monteith equation proposed by FAO, was considered. The results show that the influence of radiation, which provides energy for evaporation, is the strongest factor and that the influence of global radiation alone is very strong. Taking into account that radiation was measured under rather limited conditions in space and time, global radiation was calculated using the Hargreaves method based on temperature. Accordingly, we have defined a formula based on temperature-based global radiation and verified the data obtained with the Penman-Monteith formula calculated for 14 meteorological stations. The verification gave good results, therefore the method can be used for practical purposes in the subhumid conditions of Hungary based on the data of the nearest meteorological station.
