为精确模拟浅水波非线性演化过程中的动边界,提出一种基于位移的Hamilton变分原理,并进而导出一种基于位移的浅水方程(Shallow Water Equation based on Displacement,SWE-D).SWE-D以位移为基本未知量,可以精确满足动边界处的零水深要...为精确模拟浅水波非线性演化过程中的动边界,提出一种基于位移的Hamilton变分原理,并进而导出一种基于位移的浅水方程(Shallow Water Equation based on Displacement,SWE-D).SWE-D以位移为基本未知量,可以精确满足动边界处的零水深要求并精确捕捉动态边界位置,且解具有协调性.在Hamilton变分原理的框架下,分别采用有限元和保辛积分算法对该浅水方程进行空间离散和时间积分,可有效地处理不平水底情况,保证对非线性演化进行长时间仿真的精度.数值算例表明该方法适用于浅水动边界问题的数值模拟.展开更多
针对模型参数不准确条件下的全自动着舰控制技术进行了研究,设计了一种基于保辛伪谱算法(symplectic pseudospectral method, SP)和带遗忘因子递推最小二乘法(recursive least squares with forgetting factor, FFRLS)的舰载机着舰自校...针对模型参数不准确条件下的全自动着舰控制技术进行了研究,设计了一种基于保辛伪谱算法(symplectic pseudospectral method, SP)和带遗忘因子递推最小二乘法(recursive least squares with forgetting factor, FFRLS)的舰载机着舰自校正模型预测控制方法(self-tuning model predictive control, ST-MPC)。针对舰载机的着舰控制模型,在MPC方法的框架下,首先设计了一种基于预测轨迹形状与位置偏差的引导轨迹,用以消除航母甲板运动和实时误差的影响。同时,基于SP算法设计了滚动优化模块并引入雄鸡尾流扰动补偿以抑制舰尾流干扰;进一步,通过FFRLS算法结合巴特沃斯低通滤波器,对模型中影响控制性能的敏感参数进行实时估计用以提高着舰控制算法的鲁棒性。仿真结果表明,在有多种干扰影响且控制模型参数不准确时,所设计的ST-MPC算法,能够将着舰高度误差控制在±0.15 m以内,其控制精度远高于传统的线性二次型最优调节器和极点配置算法,且算法的计算效率满足实时在线跟踪的要求。展开更多
Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite differ...Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations.Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.展开更多
文摘为精确模拟浅水波非线性演化过程中的动边界,提出一种基于位移的Hamilton变分原理,并进而导出一种基于位移的浅水方程(Shallow Water Equation based on Displacement,SWE-D).SWE-D以位移为基本未知量,可以精确满足动边界处的零水深要求并精确捕捉动态边界位置,且解具有协调性.在Hamilton变分原理的框架下,分别采用有限元和保辛积分算法对该浅水方程进行空间离散和时间积分,可有效地处理不平水底情况,保证对非线性演化进行长时间仿真的精度.数值算例表明该方法适用于浅水动边界问题的数值模拟.
文摘针对模型参数不准确条件下的全自动着舰控制技术进行了研究,设计了一种基于保辛伪谱算法(symplectic pseudospectral method, SP)和带遗忘因子递推最小二乘法(recursive least squares with forgetting factor, FFRLS)的舰载机着舰自校正模型预测控制方法(self-tuning model predictive control, ST-MPC)。针对舰载机的着舰控制模型,在MPC方法的框架下,首先设计了一种基于预测轨迹形状与位置偏差的引导轨迹,用以消除航母甲板运动和实时误差的影响。同时,基于SP算法设计了滚动优化模块并引入雄鸡尾流扰动补偿以抑制舰尾流干扰;进一步,通过FFRLS算法结合巴特沃斯低通滤波器,对模型中影响控制性能的敏感参数进行实时估计用以提高着舰控制算法的鲁棒性。仿真结果表明,在有多种干扰影响且控制模型参数不准确时,所设计的ST-MPC算法,能够将着舰高度误差控制在±0.15 m以内,其控制精度远高于传统的线性二次型最优调节器和极点配置算法,且算法的计算效率满足实时在线跟踪的要求。
基金Supported by the National Natural Science Foundation of China under Grant No.91130013Hunan Provincial Innovation Foundation under Grant No.CX2012B010+1 种基金the Innovation Fund of National University of Defense Technology under Grant No.B120205the Open Foundation of State Key Laboratory
文摘Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations.Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.
