Efforts have been made to solve the Dirac equation with axially deformed scalar and vector WoodsSaxon potentials in the coordinate space with the imaginary time step method. The results of the singleparticle energies ...Efforts have been made to solve the Dirac equation with axially deformed scalar and vector WoodsSaxon potentials in the coordinate space with the imaginary time step method. The results of the singleparticle energies thus obtained are consistent with those calculated with the basis expansion method, which demonstrates the feasibility of the imaginary time step method for the relativistic static problems.展开更多
The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficu...The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.展开更多
The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integ...The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integration schemes derived by the singlepoint precise integration method given in this paper are proved unconditionally stable.Comparisons between the schemes derived by the finite difference method and theschemes by the method employed in the present paper are made for diffusion andconvective-diffusion equations. Nunierical examples show the superiority of the singlepoint integration method.展开更多
This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditiona...This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.展开更多
大规模双馈风电场作为实现我国“双碳”目标的陆上风电主力,其高比例电力电子设备的接入对电力系统电磁暂态高精度仿真技术提出日益严苛的要求,面向上百台发电单元的双馈场站全拓扑精细化微秒级仿真研究仍相对空白。基于现场可编程门阵...大规模双馈风电场作为实现我国“双碳”目标的陆上风电主力,其高比例电力电子设备的接入对电力系统电磁暂态高精度仿真技术提出日益严苛的要求,面向上百台发电单元的双馈场站全拓扑精细化微秒级仿真研究仍相对空白。基于现场可编程门阵列(field programmable gate array,FPGA)微秒级小步长并行仿真能力,提出一种面向双馈风电场站的发电单元FPGA并行仿真方法。首先,进行双馈感应电机微秒级高并行度离散化建模与换流器受控源建模;接着,对节点导纳矩阵分块降维以实现发电单元内部分网并行,并从整体电路解算层面提出单元级并行仿真框架;最后,考虑实时数字仿真器(real time digital simulator,RTDS)与FPGA仿真平台特点,分配发电单元的微秒级小步长仿真任务并搭建联合仿真硬件框架;通过对比RTDS标准模型与RTDS+FPGA联合仿真模型,验证所提并行仿真方法的准确性。展开更多
摆振会降低起落架的使用寿命,影响乘坐舒适性,甚至会引起机体损坏,导致飞机失事。为了抑制起落架摆振,本文采用时滞反馈非线性能量汇(nonlinear energy sink,NES)对起落架摆振进行多目标优化。以某轻型飞机起落架为研究对象,设计了基于...摆振会降低起落架的使用寿命,影响乘坐舒适性,甚至会引起机体损坏,导致飞机失事。为了抑制起落架摆振,本文采用时滞反馈非线性能量汇(nonlinear energy sink,NES)对起落架摆振进行多目标优化。以某轻型飞机起落架为研究对象,设计了基于NES的时滞反馈半主动控制减摆器,并建立了前起落架摆振系统分析动力学方程。通过线性多步法求解出时滞反馈半主动控制摆振系统的特征根,分析了减摆器可控阻尼系数对特征根最大实部的影响。以时滞量为设计变量,将振幅衰减时间和第四周期振幅的线性加权组合确定为目标函数。采用粒子群算法对该优化目标进行全局搜索,得到相应的最优时滞量,并与遗传算法得到的结果进行对比,验证了最优时滞量的可靠性,并在时域内对减摆器的减摆效果进行了验证。结果表明,与无时滞控制系统相比,采用最优时滞反馈的半主动控制系统的前起落架摆振幅值显著降低。展开更多
This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is ...This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is modeled by partial differential equations (PDEs) and involve optimization of some quantity. The PDEs are in most cases nonlinear and solved using numerical methods. Since such numerical solutions are being used routinely, the recent trend has been to develop numerical methods and algorithms so that the optimization problems can be solved numerically as well using the same PDE-solver. We present here one such numerical method which is based on simultaneous pseudo-time stepping. The efficiency of the method is increased with the help of a multigrid strategy. Application example is included for an aerodynamic shape optimization problem.展开更多
The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, ...The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, a linear state feedback controller making the closed-loop system globally asymptotically stable is constructed.展开更多
相较于传统的两步法,动力学一步法能充分利用观测数据的原始信息,理论上可获得更合理的时变重力场产品,同时也因其涉及的参数维度更多样、函数模型更复杂,一直是当前研究的热点和难点.本文研究并实现了动力学一步法恢复时变重力场,给出...相较于传统的两步法,动力学一步法能充分利用观测数据的原始信息,理论上可获得更合理的时变重力场产品,同时也因其涉及的参数维度更多样、函数模型更复杂,一直是当前研究的热点和难点.本文研究并实现了动力学一步法恢复时变重力场,给出了合理的数据处理策略,而后基于GRACE-FO(GRACE Follow-On)星载GPS数据和KBR(K/Ka Band Ranging)距离变率数据反演了2021—2022年60阶全球月时变重力场模型.对于一步法中诸多技术细节,本文重点分析了先验权和经验参数对轨道确定和模型反演的影响,研究表明:当采用30 s采样率的GPS数据时,需适当对GPS数据降权,以免引入过多噪声,码伪距、载波相位和KBR距离变率数据的先验权比应为1:104:1014;为了保证轨道和模型质量,在反演过程中有必要引入经验参数以吸收残余的摄动力误差,相较其他经验参数(分段周期经验加速度、几何经验参数),分段常经验加速度在保证定轨精度的同时可更有效地吸收模型中的噪声.此外,在采用相同动力学参数配置时,动力学一步法反演的时变重力场模型无论是与官方模型的一致性还是内符合精度均优于两步法.最后,综合评估了整个时间跨度的轨道和时变重力场模型质量,结果显示,动力学一步法确定的轨道可满足厘米级需求,双星的卫星激光测距残差标准差均为1.6 cm,重力场模型与官方机构CSR(Center for Space Research)、JPL(Jet Propulsion Laboratory)、GFZ(GeoForschungsZentrum Potsdam)最新发布的RL06.1模型一致性较好,在保留完整时变信号特征的前提下,噪声表现与CSR模型相当,优于JPL、GFZ模型.展开更多
基金Supported by National Natural Science Foundation of China (10435010, 10775004, 10221003)Major State Basic Research Development Program (2007CB815000)
文摘Efforts have been made to solve the Dirac equation with axially deformed scalar and vector WoodsSaxon potentials in the coordinate space with the imaginary time step method. The results of the singleparticle energies thus obtained are consistent with those calculated with the basis expansion method, which demonstrates the feasibility of the imaginary time step method for the relativistic static problems.
基金financial support from Hunan Provincial Natura1 Science Foundation of China,Grant Number:02JJY2085,for this study
文摘The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.
文摘The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integration schemes derived by the singlepoint precise integration method given in this paper are proved unconditionally stable.Comparisons between the schemes derived by the finite difference method and theschemes by the method employed in the present paper are made for diffusion andconvective-diffusion equations. Nunierical examples show the superiority of the singlepoint integration method.
基金The project supported by the National Key Basic Research and Development Foundation of the Ministry of Science and Technology of China （G2000048702, 2003CB716707）the National Science Fund for Distinguished Young Scholars （10025208）+1 种基金 the National Natural Science Foundation of China （Key Program） （10532040） the Research Fund for 0versea Chinese （10228028）.
文摘This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.
文摘大规模双馈风电场作为实现我国“双碳”目标的陆上风电主力,其高比例电力电子设备的接入对电力系统电磁暂态高精度仿真技术提出日益严苛的要求,面向上百台发电单元的双馈场站全拓扑精细化微秒级仿真研究仍相对空白。基于现场可编程门阵列(field programmable gate array,FPGA)微秒级小步长并行仿真能力,提出一种面向双馈风电场站的发电单元FPGA并行仿真方法。首先,进行双馈感应电机微秒级高并行度离散化建模与换流器受控源建模;接着,对节点导纳矩阵分块降维以实现发电单元内部分网并行,并从整体电路解算层面提出单元级并行仿真框架;最后,考虑实时数字仿真器(real time digital simulator,RTDS)与FPGA仿真平台特点,分配发电单元的微秒级小步长仿真任务并搭建联合仿真硬件框架;通过对比RTDS标准模型与RTDS+FPGA联合仿真模型,验证所提并行仿真方法的准确性。
文摘摆振会降低起落架的使用寿命,影响乘坐舒适性,甚至会引起机体损坏,导致飞机失事。为了抑制起落架摆振,本文采用时滞反馈非线性能量汇(nonlinear energy sink,NES)对起落架摆振进行多目标优化。以某轻型飞机起落架为研究对象,设计了基于NES的时滞反馈半主动控制减摆器,并建立了前起落架摆振系统分析动力学方程。通过线性多步法求解出时滞反馈半主动控制摆振系统的特征根,分析了减摆器可控阻尼系数对特征根最大实部的影响。以时滞量为设计变量,将振幅衰减时间和第四周期振幅的线性加权组合确定为目标函数。采用粒子群算法对该优化目标进行全局搜索,得到相应的最优时滞量,并与遗传算法得到的结果进行对比,验证了最优时滞量的可靠性,并在时域内对减摆器的减摆效果进行了验证。结果表明,与无时滞控制系统相比,采用最优时滞反馈的半主动控制系统的前起落架摆振幅值显著降低。
文摘This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is modeled by partial differential equations (PDEs) and involve optimization of some quantity. The PDEs are in most cases nonlinear and solved using numerical methods. Since such numerical solutions are being used routinely, the recent trend has been to develop numerical methods and algorithms so that the optimization problems can be solved numerically as well using the same PDE-solver. We present here one such numerical method which is based on simultaneous pseudo-time stepping. The efficiency of the method is increased with the help of a multigrid strategy. Application example is included for an aerodynamic shape optimization problem.
基金Supported by the "973" Project of P. R. China (G1998020300)
文摘The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, a linear state feedback controller making the closed-loop system globally asymptotically stable is constructed.
文摘相较于传统的两步法,动力学一步法能充分利用观测数据的原始信息,理论上可获得更合理的时变重力场产品,同时也因其涉及的参数维度更多样、函数模型更复杂,一直是当前研究的热点和难点.本文研究并实现了动力学一步法恢复时变重力场,给出了合理的数据处理策略,而后基于GRACE-FO(GRACE Follow-On)星载GPS数据和KBR(K/Ka Band Ranging)距离变率数据反演了2021—2022年60阶全球月时变重力场模型.对于一步法中诸多技术细节,本文重点分析了先验权和经验参数对轨道确定和模型反演的影响,研究表明:当采用30 s采样率的GPS数据时,需适当对GPS数据降权,以免引入过多噪声,码伪距、载波相位和KBR距离变率数据的先验权比应为1:104:1014;为了保证轨道和模型质量,在反演过程中有必要引入经验参数以吸收残余的摄动力误差,相较其他经验参数(分段周期经验加速度、几何经验参数),分段常经验加速度在保证定轨精度的同时可更有效地吸收模型中的噪声.此外,在采用相同动力学参数配置时,动力学一步法反演的时变重力场模型无论是与官方模型的一致性还是内符合精度均优于两步法.最后,综合评估了整个时间跨度的轨道和时变重力场模型质量,结果显示,动力学一步法确定的轨道可满足厘米级需求,双星的卫星激光测距残差标准差均为1.6 cm,重力场模型与官方机构CSR(Center for Space Research)、JPL(Jet Propulsion Laboratory)、GFZ(GeoForschungsZentrum Potsdam)最新发布的RL06.1模型一致性较好,在保留完整时变信号特征的前提下,噪声表现与CSR模型相当,优于JPL、GFZ模型.
