For the vector attitude determination, the traditional optimal algorithms which are based on quaternion estimator(QUEST) measurement noise model are complicated for just two observations. In our application, the mag...For the vector attitude determination, the traditional optimal algorithms which are based on quaternion estimator(QUEST) measurement noise model are complicated for just two observations. In our application, the magnetometer and accelerometer are not two comparable kinds of sensors and both are not small field-of-view sensors as well. So in this paper a new unit measurement model is derived. According to the Wahba problem, the optimal weights for each measurement are obtained by the error variance researches. Then an improved quaternion Gauss–Newton method is presented and adopted to acquire attitude. Eventually, simulation results and experimental validation employed to test the proposed method demonstrate the usefulness of the improved algorithm.展开更多
The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing...The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing Newton-type algorithm is proposed for solving the generalized complementarity problem.Under suitable assumptions, the proposed algorithm is well-defined and global convergent.展开更多
By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by...By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by the proposed algorithm is bounded and this algorithm is proved to be globally convergent under an assumption that the P NCP has a nonempty solution set.This assumption is weaker than the ones used in most existing smoothing algorithms.In particular,the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P NCP without any additional assumption.展开更多
In this paper,a Novel Compliant Actuator(NCA)-driven Upper-Limb Exoskeleton(ULE)with force controllable,impact resistance,and back drivability is designed to ensure the safety of the subject during Human-Robot Interac...In this paper,a Novel Compliant Actuator(NCA)-driven Upper-Limb Exoskeleton(ULE)with force controllable,impact resistance,and back drivability is designed to ensure the safety of the subject during Human-Robot Interaction(HRI)processing.Based on the designed NCA-driven ULE,this paper constructs a Model Predictive Control Scheme(MPCS)for force trajectory tracking,which minimises future tracking errors by solving an optimal control problem with inequality constraints.In addition,an Error-Accumulation Improved Newton Algorithm(EAINA)is proposed to solve the MPCS for suppressing various noises and external disturbances.The proposed EAINA is theoretically proved to have small steady state for noise conditions and stability of the EAINA using Lyapunov method.Finally,experimental results verify that the proposed MPCS solved by the EAINA in the NCA-driven ULE achieves robustness,fast convergence,strong tolerance and stability for trajectory rehabilitation task.展开更多
The system of generalized absolute value equations(GAVE)has attracted more and more attention in the optimization community.In this paper,by introducing a smoothing function,we develop a smoothing Newton algorithm wit...The system of generalized absolute value equations(GAVE)has attracted more and more attention in the optimization community.In this paper,by introducing a smoothing function,we develop a smoothing Newton algorithm with non-monotone line search to solve the GAVE.We show that the non-monotone algorithm is globally and locally quadratically convergent under a weaker assumption than those given in most existing algorithms for solving the GAVE.Numerical results are given to demonstrate the viability and efficiency of the approach.展开更多
Based on the extraction equilibrium and mass balances in countercurrent extraction systems, a novel method was studied for dealing with the extraction equilibrium and the mass distribution in a multi-component(gamma-c...Based on the extraction equilibrium and mass balances in countercurrent extraction systems, a novel method was studied for dealing with the extraction equilibrium and the mass distribution in a multi-component(gamma-component) system. The relationships of mass distribution (x(i), y(i), i = 1, ..., lambda) between two phases were expressed by 2 lambda dimensional simultaneous equations. These simultaneous equations can be converted to a one-dimension nonlinear equation, then it was solved by Newton-Raphson algorithm within a few number of iteration. Compared with the regular calculation method for the 2 lambda dimensional simultaneous equations, Newton-Raphson algorithm can decrease the number of iteration, increase the convergence of the equations and accelerate the speed of simulation. It was verified in many multi-component systems with satisfactory results. As an example, a five-component system is demonstrated in this paper.展开更多
Distributed generation (DG) is gaining in importance due to the growing demand for electrical energy and the key role it plays in reducing actual energy losses, lowering operating costs and improving voltage stability...Distributed generation (DG) is gaining in importance due to the growing demand for electrical energy and the key role it plays in reducing actual energy losses, lowering operating costs and improving voltage stability. In this paper, we propose to inject distributed power generation into a distribution system while minimizing active energy losses. This injection should be done at a grid node (which is a point where energy can be injected into or recovered from the grid) that will be considered the optimal node when total active losses in the radial distribution system are minimal. The focus is on meeting energy demand using renewable energy sources. The main criterion is the minimization of active energy losses during injection. The method used is the algorithm of bee colony (ABC) associated with Newtonian energy flow transfer equations. The method has been implemented in MATLAB for optimal node search in IEEE 14, 33 and 57 nodes networks. The active energy loss results of this hybrid algorithm were compared with the results of previous searches. This comparison shows that the proposed algorithm allows to have reduced losses with the power injected that we have found.展开更多
为了优化基于设计图纸建立的结构有限元模型,得到结构的基准有限元模型,提出了一种基于牛顿插值法的高维模型表示(High-dimensional Model representation based on Newton Interpolation, NEWTHDMR)的结构有限元模型修正方法。NEWT-HDM...为了优化基于设计图纸建立的结构有限元模型,得到结构的基准有限元模型,提出了一种基于牛顿插值法的高维模型表示(High-dimensional Model representation based on Newton Interpolation, NEWTHDMR)的结构有限元模型修正方法。NEWT-HDMR可以描述结构参数与响应之间的黑箱函数关系以取代有限元软件,联合结构真实响应残差和构造目标函数;结合Jaya算法,通过迭代求解结构待修正参数的修正值,进而修正结构有限元模型。利用简支梁数值模型验证本文提出方法的有效性,并分析对比一阶NEWT–HDMR和二阶NEWT-HDMR在修正精度上的差异。结果表明,NEWT-HDMR模型修正结果可以满足工程要求且二阶NEWT-HDMR修正精度更高,验证该方法在结构有限元模型修正中应用的可行性和可靠性。展开更多
Coordinate descent method is a unconstrained optimization technique. When it is applied to support vector machine (SVM), at each step the method updates one component of w by solving a one-variable sub-problem while...Coordinate descent method is a unconstrained optimization technique. When it is applied to support vector machine (SVM), at each step the method updates one component of w by solving a one-variable sub-problem while fixing other components. All components of w update after one iteration. Then go to next iteration. Though the method converges and converges fast in the beginning, it converges slow for final convergence. To improve the speed of final convergence of coordinate descent method, Hooke and Jeeves algorithm which adds pattern search after every iteration in coordinate descent method was applied to SVM and a global Newton algorithm was used to solve one-variable subproblems. We proved the convergence of the algorithm. Experimental results show Hooke and Jeeves' method does accelerate convergence specially for final convergence and achieves higher testing accuracy more quickly in classification.展开更多
An improved hybrid Time of Arrival (ToA)/ Angle of Arrival (AoA) location algorithm by adopting Gauss-Newton iterative algorithm is proposed. It is with the advantage of fast convergence and combining with the grid-se...An improved hybrid Time of Arrival (ToA)/ Angle of Arrival (AoA) location algorithm by adopting Gauss-Newton iterative algorithm is proposed. It is with the advantage of fast convergence and combining with the grid-search-based method to optimize the initial object coordinates of the iteration, meanwhile, under the condition of small measurement errors caused by noises of ToA and AoA, the algorithm performance can be improved effectively. In the Non-Line-of-Sight (NLoS) environments of the Wireless Sensor Network (WSN), simulation results show that improved accuracy is gained with moderate flexibility and fast steady convergence compared with the existing algorithms.展开更多
摘要For the vector attitude determination, the traditional optimal algorithms which are based on quaternion estimator(QUEST) measurement noise model are complicated for just two observations. In our application, the magnetometer and accelerometer are not two comparable kinds of sensors and both are not small field-of-view sensors as well. So in this paper a new unit measurement model is derived. According to the Wahba problem, the optimal weights for each measurement are obtained by the error variance researches. Then an improved quaternion Gauss–Newton method is presented and adopted to acquire attitude. Eventually, simulation results and experimental validation employed to test the proposed method demonstrate the usefulness of the improved algorithm.
基金Supported by LIU Hui Centre for Applied Mathematics of Nankai University and Tianjin University
摘要The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing Newton-type algorithm is proposed for solving the generalized complementarity problem.Under suitable assumptions, the proposed algorithm is well-defined and global convergent.
基金Supported by China Postdoctoral Science Foundation(No.20060390660)Science and Technology Development Plan of Tianjin(No.06YFGZGX05600)+1 种基金Scientific Research Foundation of Liu Hui Center for Applied MathematicsNankai University-Tianjin University.
摘要By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by the proposed algorithm is bounded and this algorithm is proved to be globally convergent under an assumption that the P NCP has a nonempty solution set.This assumption is weaker than the ones used in most existing smoothing algorithms.In particular,the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P NCP without any additional assumption.
基金supported by the National Natural Science Foundation of China(Nos.62373065,61873304,62173048,and 62106023)the Key Science and Technology Projects of Jilin Province,China(No.20230204081YY).
摘要In this paper,a Novel Compliant Actuator(NCA)-driven Upper-Limb Exoskeleton(ULE)with force controllable,impact resistance,and back drivability is designed to ensure the safety of the subject during Human-Robot Interaction(HRI)processing.Based on the designed NCA-driven ULE,this paper constructs a Model Predictive Control Scheme(MPCS)for force trajectory tracking,which minimises future tracking errors by solving an optimal control problem with inequality constraints.In addition,an Error-Accumulation Improved Newton Algorithm(EAINA)is proposed to solve the MPCS for suppressing various noises and external disturbances.The proposed EAINA is theoretically proved to have small steady state for noise conditions and stability of the EAINA using Lyapunov method.Finally,experimental results verify that the proposed MPCS solved by the EAINA in the NCA-driven ULE achieves robustness,fast convergence,strong tolerance and stability for trajectory rehabilitation task.
基金supported by the Natural Science Foundation of Fujian Province(Grant No.2021J01661)by the National Natural Science Foundation of China(Grant No.11901024)+5 种基金supported by the National Natural Science Foundation of China(Grant No.12201275)by the Ministry of Education in China of Humanities and Social Science Project(Grant No.21YJCZH204)by the Liaoning Provincial Department of Education(Grant No.JYTZD2023072)supported by the National Natural Science Foundation of China(Grant No.12131004)by the Ministry of Science and Technology of China(Grant No.2021YFA1003600)supported by the National Key Research and Development Program of China(Grant No.2019YFC0312003).
摘要The system of generalized absolute value equations(GAVE)has attracted more and more attention in the optimization community.In this paper,by introducing a smoothing function,we develop a smoothing Newton algorithm with non-monotone line search to solve the GAVE.We show that the non-monotone algorithm is globally and locally quadratically convergent under a weaker assumption than those given in most existing algorithms for solving the GAVE.Numerical results are given to demonstrate the viability and efficiency of the approach.
摘要Based on the extraction equilibrium and mass balances in countercurrent extraction systems, a novel method was studied for dealing with the extraction equilibrium and the mass distribution in a multi-component(gamma-component) system. The relationships of mass distribution (x(i), y(i), i = 1, ..., lambda) between two phases were expressed by 2 lambda dimensional simultaneous equations. These simultaneous equations can be converted to a one-dimension nonlinear equation, then it was solved by Newton-Raphson algorithm within a few number of iteration. Compared with the regular calculation method for the 2 lambda dimensional simultaneous equations, Newton-Raphson algorithm can decrease the number of iteration, increase the convergence of the equations and accelerate the speed of simulation. It was verified in many multi-component systems with satisfactory results. As an example, a five-component system is demonstrated in this paper.
摘要Distributed generation (DG) is gaining in importance due to the growing demand for electrical energy and the key role it plays in reducing actual energy losses, lowering operating costs and improving voltage stability. In this paper, we propose to inject distributed power generation into a distribution system while minimizing active energy losses. This injection should be done at a grid node (which is a point where energy can be injected into or recovered from the grid) that will be considered the optimal node when total active losses in the radial distribution system are minimal. The focus is on meeting energy demand using renewable energy sources. The main criterion is the minimization of active energy losses during injection. The method used is the algorithm of bee colony (ABC) associated with Newtonian energy flow transfer equations. The method has been implemented in MATLAB for optimal node search in IEEE 14, 33 and 57 nodes networks. The active energy loss results of this hybrid algorithm were compared with the results of previous searches. This comparison shows that the proposed algorithm allows to have reduced losses with the power injected that we have found.
摘要为了优化基于设计图纸建立的结构有限元模型,得到结构的基准有限元模型,提出了一种基于牛顿插值法的高维模型表示(High-dimensional Model representation based on Newton Interpolation, NEWTHDMR)的结构有限元模型修正方法。NEWT-HDMR可以描述结构参数与响应之间的黑箱函数关系以取代有限元软件,联合结构真实响应残差和构造目标函数;结合Jaya算法,通过迭代求解结构待修正参数的修正值,进而修正结构有限元模型。利用简支梁数值模型验证本文提出方法的有效性,并分析对比一阶NEWT–HDMR和二阶NEWT-HDMR在修正精度上的差异。结果表明,NEWT-HDMR模型修正结果可以满足工程要求且二阶NEWT-HDMR修正精度更高,验证该方法在结构有限元模型修正中应用的可行性和可靠性。
基金supported by the National Natural Science Foundation of China (6057407560705004)
摘要Coordinate descent method is a unconstrained optimization technique. When it is applied to support vector machine (SVM), at each step the method updates one component of w by solving a one-variable sub-problem while fixing other components. All components of w update after one iteration. Then go to next iteration. Though the method converges and converges fast in the beginning, it converges slow for final convergence. To improve the speed of final convergence of coordinate descent method, Hooke and Jeeves algorithm which adds pattern search after every iteration in coordinate descent method was applied to SVM and a global Newton algorithm was used to solve one-variable subproblems. We proved the convergence of the algorithm. Experimental results show Hooke and Jeeves' method does accelerate convergence specially for final convergence and achieves higher testing accuracy more quickly in classification.
基金supported by National Natural Science Foundation of China under Grant No.61172073State Key Laboratory of Networking and Switching Technology (Beijing Universityof Posts and Telecommunications) under Grant No.SKLNST-2009-1-09+1 种基金Open Research Fund of National Mobile Communications Research Laboratory, Southeast University, P. R.ChinaChina Fundamental Research Funds for the Central Universities:Beijing Jiaotong University
摘要An improved hybrid Time of Arrival (ToA)/ Angle of Arrival (AoA) location algorithm by adopting Gauss-Newton iterative algorithm is proposed. It is with the advantage of fast convergence and combining with the grid-search-based method to optimize the initial object coordinates of the iteration, meanwhile, under the condition of small measurement errors caused by noises of ToA and AoA, the algorithm performance can be improved effectively. In the Non-Line-of-Sight (NLoS) environments of the Wireless Sensor Network (WSN), simulation results show that improved accuracy is gained with moderate flexibility and fast steady convergence compared with the existing algorithms.