To enhance the integrity, an analytic method （AM） which has less execution time is proposed to calculate the user differential range error （UDRE） used by the user to detect the potential risk. An ephemeris and clo...To enhance the integrity, an analytic method （AM） which has less execution time is proposed to calculate the user differential range error （UDRE） used by the user to detect the potential risk. An ephemeris and clock correction calculation method is introduced first. It shows that the most important thing of computing UDRE is to find the worst user location （WUL） in the service volume. Then, a UDRE algorithm using AM is described to solve this problem. By using the covariance matrix of the error vector, the searching of WUL is converted to an analytic geometry problem. The location of WUL can be obtained directly by mathematical derivation. Experiments are conducted to compare the performance between the proposed AM algorithm and the exhaustive grid search （EGS） method used in the master station. The results show that the correctness of the AM algorithm can be proved by the EGS method and the AM algorithm can reduce the calculation time by more than 90%. The computational complexity of this proposed algorithm is better than that of EGS. Thereby this algorithm is more suitable for computing UDRE at the master station.展开更多
An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller tha...An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps. Two methods of imposing initial conditions are given, which avoids the tediousness when derivative initial conditions are imposed, and the numerical comparisons indicate that the first method, in which the analog equations of initial displacements and velocities are used to directly replace the differential quadra- ture （DQ） analog equations of ODEs at the first and the last sampling points, respectively, is much more accurate than the second method, in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points. On the contrary to the conventional step-by-step direct integration schemes, the solutions at all sampling points can be obtained simultaneously by DQTEM, and generally, one differential quadrature time element may be enough for the whole time domain. Extensive numerical comparisons validate the effi- ciency and accuracy of the proposed method.展开更多
Combining difference method and boundary integral equation method,we propose a new numerical method for solving initial-boundary value problem of second order hyperbolic partial differential equations defined on a bou...Combining difference method and boundary integral equation method,we propose a new numerical method for solving initial-boundary value problem of second order hyperbolic partial differential equations defined on a bounded or unbounded domain in R~3 and obtain the error estimates of the approximate solution in energy norm and local maximum norm.展开更多
An optimized data-matching machine learning algorithm is developed to provide high-prediction accuracy of total burned areas for specific wildfire incidents.It is applied to a well-studied forest-fire dataset from Por...An optimized data-matching machine learning algorithm is developed to provide high-prediction accuracy of total burned areas for specific wildfire incidents.It is applied to a well-studied forest-fire dataset from Portugal Montesinho Natural Park considering 13 input variables.The total burned area distribution of the 517 burn events in that dataset is highly positively skewed.The model is transparent and avoids regressions and hidden layers.This increases its detailed datamining capabilities.It matches the highest burned-area prediction accuracy achieved for this datasetwith a wide range of traditionalmachine learning algorithms.The two-stage prediction process provides informative feature selection that establishes the relative influences of the input variables on burned-area predictions.Optimizing with mean absolute error(MAE)and root mean square error(RMSE)as separate objective functions provides complementary information with which to data mine each total burnedarea incident.Such insight offers potential agricultural,ecological,environmental and forestry benefits by improving the understanding of the key influences associated with each burn event.Data mining the differential trends of cumulative absolute error and squared error also provides detailed insight with which to determine the suitability of each optimized solution to accurately predict burned-areas events of specific types.Such prediction accuracy and insight leads to confidence in how each prediction is derived.It provides knowledge to make appropriate responses and mitigate specific burn incidents,as they occur.Such informed responses should lead to short-term and long-term multi-faceted benefits by helping to prevent certain types of burn incidents being repeated or spread.展开更多
文摘To enhance the integrity, an analytic method （AM） which has less execution time is proposed to calculate the user differential range error （UDRE） used by the user to detect the potential risk. An ephemeris and clock correction calculation method is introduced first. It shows that the most important thing of computing UDRE is to find the worst user location （WUL） in the service volume. Then, a UDRE algorithm using AM is described to solve this problem. By using the covariance matrix of the error vector, the searching of WUL is converted to an analytic geometry problem. The location of WUL can be obtained directly by mathematical derivation. Experiments are conducted to compare the performance between the proposed AM algorithm and the exhaustive grid search （EGS） method used in the master station. The results show that the correctness of the AM algorithm can be proved by the EGS method and the AM algorithm can reduce the calculation time by more than 90%. The computational complexity of this proposed algorithm is better than that of EGS. Thereby this algorithm is more suitable for computing UDRE at the master station.
基金supported by the National Natural Science Foundation of China (11172028,10772014)
文摘An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps. Two methods of imposing initial conditions are given, which avoids the tediousness when derivative initial conditions are imposed, and the numerical comparisons indicate that the first method, in which the analog equations of initial displacements and velocities are used to directly replace the differential quadra- ture （DQ） analog equations of ODEs at the first and the last sampling points, respectively, is much more accurate than the second method, in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points. On the contrary to the conventional step-by-step direct integration schemes, the solutions at all sampling points can be obtained simultaneously by DQTEM, and generally, one differential quadrature time element may be enough for the whole time domain. Extensive numerical comparisons validate the effi- ciency and accuracy of the proposed method.
基金China State Major Key Project for Basic Researches
文摘Combining difference method and boundary integral equation method,we propose a new numerical method for solving initial-boundary value problem of second order hyperbolic partial differential equations defined on a bounded or unbounded domain in R~3 and obtain the error estimates of the approximate solution in energy norm and local maximum norm.
文摘An optimized data-matching machine learning algorithm is developed to provide high-prediction accuracy of total burned areas for specific wildfire incidents.It is applied to a well-studied forest-fire dataset from Portugal Montesinho Natural Park considering 13 input variables.The total burned area distribution of the 517 burn events in that dataset is highly positively skewed.The model is transparent and avoids regressions and hidden layers.This increases its detailed datamining capabilities.It matches the highest burned-area prediction accuracy achieved for this datasetwith a wide range of traditionalmachine learning algorithms.The two-stage prediction process provides informative feature selection that establishes the relative influences of the input variables on burned-area predictions.Optimizing with mean absolute error(MAE)and root mean square error(RMSE)as separate objective functions provides complementary information with which to data mine each total burnedarea incident.Such insight offers potential agricultural,ecological,environmental and forestry benefits by improving the understanding of the key influences associated with each burn event.Data mining the differential trends of cumulative absolute error and squared error also provides detailed insight with which to determine the suitability of each optimized solution to accurately predict burned-areas events of specific types.Such prediction accuracy and insight leads to confidence in how each prediction is derived.It provides knowledge to make appropriate responses and mitigate specific burn incidents,as they occur.Such informed responses should lead to short-term and long-term multi-faceted benefits by helping to prevent certain types of burn incidents being repeated or spread.
