A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle ...A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.展开更多
Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problem...Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms.展开更多
The dual algorithm for minimax problems is further studied in this paper.The resulting theoretical analysis shows that the condition number of the corresponding Hessian of the smooth modified Lagrange function with ch...The dual algorithm for minimax problems is further studied in this paper.The resulting theoretical analysis shows that the condition number of the corresponding Hessian of the smooth modified Lagrange function with changing parameter in the dual algorithm is proportional to the reciprocal of the parameter,which is very important for the efficiency of the dual algorithm.At last,the numerical experiments are reported to validate the analysis results.展开更多
In this study,a Dual Smoothing Ionospheric Gradient Monitor Algorithm(DSIGMA)was developed for Code-Carrier Divergence(CCD)faults of dual-frequency Ground-Based Augmentation Systems(GBAS)based on the Bei Dou Navigatio...In this study,a Dual Smoothing Ionospheric Gradient Monitor Algorithm(DSIGMA)was developed for Code-Carrier Divergence(CCD)faults of dual-frequency Ground-Based Augmentation Systems(GBAS)based on the Bei Dou Navigation Satellite System(BDS).Divergence-Free(DF)combinations of the signals were used to form test statistics for a dualfrequency DSIGMA.First,the single-frequency DSIGMA was reviewed,which supports the GBAS approach service type D(GAST-D)for protection against the effect of large ionospheric gradients.The single-frequency DSIGMA was used to create a novel input scheme for the dual-frequency DSIGMA by introducing DF combinations.The steady states of the test statistics were also analysed.The monitors were characterized using BDS measurement data,whereby standard deviations of 0.0432 and 0.0639 m for the proposed two test statistics were used to calculate the monitor threshold.An extensive simulation was designed to assess the monitor performance by comparing the Probability of Missed Detection(PMD)according to the differential error with the range domain PMD limits under different fault modes.The results showed that the proposed algorithm has a higher integrity performance than the single-frequency monitor.The minimum detectable divergence with the same missed probability is less than 50%that of GAST-D.展开更多
This paper focuses on fixed-interval smoothing for stochastic hybrid systems.When the truth-mode mismatch is encountered,existing smoothing methods based on fixed structure of model-set have significant performance de...This paper focuses on fixed-interval smoothing for stochastic hybrid systems.When the truth-mode mismatch is encountered,existing smoothing methods based on fixed structure of model-set have significant performance degradation and are inapplicable.We develop a fixedinterval smoothing method based on forward-and backward-filtering in the Variable Structure Multiple Model(VSMM)framework in this paper.We propose to use the Simplified Equivalent model Interacting Multiple Model(SEIMM)in the forward and the backward filters to handle the difficulty of different mode-sets used in both filters,and design a re-filtering procedure in the model-switching stage to enhance the estimation performance.To improve the computational efficiency,we make the basic model-set adaptive by the Likely-Model Set(LMS)algorithm.It turns out that the smoothing performance is further improved by the LMS due to less competition among models.Simulation results are provided to demonstrate the better performance and the computational efficiency of our proposed smoothing algorithms.展开更多
In this paper, we investigate a smoothing-type algorithm for solving the symmetric cone linear program ((SCLP) for short) by making use of an augmented system of its optimality conditions. The algorithm only needs...In this paper, we investigate a smoothing-type algorithm for solving the symmetric cone linear program ((SCLP) for short) by making use of an augmented system of its optimality conditions. The algorithm only needs to solve one system of linear equations and to perform one line search at each iteration. It is proved that the algorithm is globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, the algorithm may correctly detect solvability of (SCLP). Furthermore, if (SCLP) has a solution, then the algorithm will generate a solution of (SCLP), and if the problem is strongly infeasible, the algorithm will correctly detect infeasibility of (SCLP).展开更多
A large quantity of unmanned aerial vehicle(UAV)trajectory data related to air traffic information has important value in engineering fields.However,the cost of data and trajectory processing limits the applications,a...A large quantity of unmanned aerial vehicle(UAV)trajectory data related to air traffic information has important value in engineering fields.However,the cost of data and trajectory processing limits the applications,and as the number of UAVs increases rapidly,future UAVs'path data will be very large.Therefore,this paper designs a multi-UAV route re-generation method based on trajectory data,which can realize the UAVs'path data compression,de-aggregation,and regeneration tasks.Based on the trajectory data,the three-dimensional Douglas-Peucker algorithm is used to compress the trajectory data to reduce the storage space.The improved B-spline path smoothing algorithm based on the reversing control point is used to depolymerize and smooth the path.Simulation experiments show that the above multi-UAV route re-generation algorithm can obtain a more optimized path while maintaining the important characteristics of the original path.展开更多
文摘A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.
基金The project supported by the National Natural Science foundation of china(10225212,50178016.10302007)the National Kev Basic Research Special Foundation and the Ministry of Education of China
文摘Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms.
文摘The dual algorithm for minimax problems is further studied in this paper.The resulting theoretical analysis shows that the condition number of the corresponding Hessian of the smooth modified Lagrange function with changing parameter in the dual algorithm is proportional to the reciprocal of the parameter,which is very important for the efficiency of the dual algorithm.At last,the numerical experiments are reported to validate the analysis results.
基金financial support from the National Natural Science Foundation of China(Nos.61871012,U1833125)a project from the Ministry of Industry and Information Technology(Airborne RAIM/ARAIM Technology)+2 种基金Open Fund Project of Intelligent Operation Key Laboratory of Civil Aviation Airport Group(No.KLAGIO20180405)the Young Top Talent Support Program of Beihang Universitythe Beijing Nova Program of Science and Technology(No.Z191100001119134)。
文摘In this study,a Dual Smoothing Ionospheric Gradient Monitor Algorithm(DSIGMA)was developed for Code-Carrier Divergence(CCD)faults of dual-frequency Ground-Based Augmentation Systems(GBAS)based on the Bei Dou Navigation Satellite System(BDS).Divergence-Free(DF)combinations of the signals were used to form test statistics for a dualfrequency DSIGMA.First,the single-frequency DSIGMA was reviewed,which supports the GBAS approach service type D(GAST-D)for protection against the effect of large ionospheric gradients.The single-frequency DSIGMA was used to create a novel input scheme for the dual-frequency DSIGMA by introducing DF combinations.The steady states of the test statistics were also analysed.The monitors were characterized using BDS measurement data,whereby standard deviations of 0.0432 and 0.0639 m for the proposed two test statistics were used to calculate the monitor threshold.An extensive simulation was designed to assess the monitor performance by comparing the Probability of Missed Detection(PMD)according to the differential error with the range domain PMD limits under different fault modes.The results showed that the proposed algorithm has a higher integrity performance than the single-frequency monitor.The minimum detectable divergence with the same missed probability is less than 50%that of GAST-D.
基金supported in part by the National Natural Science Foundation of China(No.61773306)the National Key Research and Development Plan,China(Nos.2021YFC2202600 and 2021YFC2202603)。
文摘This paper focuses on fixed-interval smoothing for stochastic hybrid systems.When the truth-mode mismatch is encountered,existing smoothing methods based on fixed structure of model-set have significant performance degradation and are inapplicable.We develop a fixedinterval smoothing method based on forward-and backward-filtering in the Variable Structure Multiple Model(VSMM)framework in this paper.We propose to use the Simplified Equivalent model Interacting Multiple Model(SEIMM)in the forward and the backward filters to handle the difficulty of different mode-sets used in both filters,and design a re-filtering procedure in the model-switching stage to enhance the estimation performance.To improve the computational efficiency,we make the basic model-set adaptive by the Likely-Model Set(LMS)algorithm.It turns out that the smoothing performance is further improved by the LMS due to less competition among models.Simulation results are provided to demonstrate the better performance and the computational efficiency of our proposed smoothing algorithms.
基金Supported by the National Natural Science Foundation of China(No.11171252,11301375 and 71301118)Research Fund for the Doctoral Program of Higher Education of China(No.20120032120076)Tianjin Planning Program of Philosophy and Social Science(No.TJTJ11-004)
文摘In this paper, we investigate a smoothing-type algorithm for solving the symmetric cone linear program ((SCLP) for short) by making use of an augmented system of its optimality conditions. The algorithm only needs to solve one system of linear equations and to perform one line search at each iteration. It is proved that the algorithm is globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, the algorithm may correctly detect solvability of (SCLP). Furthermore, if (SCLP) has a solution, then the algorithm will generate a solution of (SCLP), and if the problem is strongly infeasible, the algorithm will correctly detect infeasibility of (SCLP).
文摘A large quantity of unmanned aerial vehicle(UAV)trajectory data related to air traffic information has important value in engineering fields.However,the cost of data and trajectory processing limits the applications,and as the number of UAVs increases rapidly,future UAVs'path data will be very large.Therefore,this paper designs a multi-UAV route re-generation method based on trajectory data,which can realize the UAVs'path data compression,de-aggregation,and regeneration tasks.Based on the trajectory data,the three-dimensional Douglas-Peucker algorithm is used to compress the trajectory data to reduce the storage space.The improved B-spline path smoothing algorithm based on the reversing control point is used to depolymerize and smooth the path.Simulation experiments show that the above multi-UAV route re-generation algorithm can obtain a more optimized path while maintaining the important characteristics of the original path.