概率约束评估的功能度量法的混沌控制

功能度量法是基于可靠度的结构优化设计中评估概率约束的一种方法,其改进均值(AMV)迭代格式具有简洁、高效的优点,但对一些非线性功能函数搜索最小功能目标点时可能陷入周期振荡或混沌解,本文利用混沌反馈控制的稳定转换法对功能度量法的AMV迭代格式实施收敛控制.首先展示一些功能函数应用功能度量法AMV格式迭代计算产生了周期解和混沌解现象,并对迭代算法进行了混沌动力学分析.然后利用稳定转换法对功能度量法迭代失败的参数区间进行混沌控制,使嵌入周期和混沌轨道的不稳定不动点稳定化,获得了稳定收敛解,实现了迭代解的周期振荡、分岔和混沌控制.     

基于多项式约束的三角平动点平面周期轨道设计方法

平动点是圆型限制性三体问题中的五个平衡解.其中,三角平动点在平面问题中具有"中心×中心"的动力学特性,其附近存在着大量的周期轨道,研究这些周期轨道的构建方法在深空探测中具有理论及工程意义.本文从振动角度分析周期轨道,通过多项式展开法构建出主坐标下周期轨道两个运动方向之间的渐近关系.从新的角度分析了系统的动力学特性和平面周期运动两个方向内在关联以及物理规律.这种多项式形式的关系式,可以作为约束条件用于数值微分修正算法中,通过迭代的方式寻找周期轨道.数值仿真算例验证了方法的正确性及精确性.文章从振动的角度对周期轨道进行分析,改进了微分修正算法.提出的方法可以被拓展至圆型/椭圆型限制性三体问题的三维周期轨道构建中.     

基于多项式约束的三角平动点平面周期轨道设计方法1）

平动点是圆型限制性三体问题中的五个平衡解.其中,三角平动点在平面问题中具有“中心×中心”的动力学特性,其附近存在着大量的周期轨道,研究这些周期轨道的构建方法在深空探测中具有理论及工程意义.本文从振动角度分析周期轨道,通过多项式展开法构建出主坐标下周期轨道两个运动方向之间的渐近关系.从新的角度分析了系统的动力学特性和平面周期运动两个方向内在关联以及物理规律.这种多项式形式的关系式,可以作为约束条件用于数值微分修正算法中,通过迭代的方式寻找周期轨道.数值仿真算例验证了方法的正确性及精确性.文章从振动的角度对周期轨道进行分析,改进了微分修正算法.提出的方法可以被拓展至圆型/椭圆型限制性三体问题的三维周期轨道构建中.     

MA对偶-信赖域算法在非线性不等式约束优化问题中的应用研究

针对含有非线性不等式约束条件的优化问题,提出了MA对偶-信赖域算法。在每次迭代过程中,基于信赖域方法和问题的逼近属性,构造了原优化问题中目标函数和约束函数的移动渐进线函数,由此建立简单的子优化问题。运用对偶方法求解子问题得到原优化问题的下降方向,再用线搜索方法取得搜索步长,最后得到下一步的迭代点。应用数学推理证明了该算法的全局收敛性。以悬臂梁最小柔度问题为例,应用MA对偶-信赖域算法对优化问题进行了求解,数值算例的结果表明,MA对偶-信赖域算法在求解非线性约束优化问题时比MMA和GCMMA算法的迭代次数少,收敛速度快。     

一种带有末端弹体姿态角约束的非线性制导律

针对带有末端多约束的三维非线性制导问题,设计了一种通用模型预测静态规划制导算法。该制导算法通过向后迭代求解权矩阵微分方程对控制量进行更新,将动态优化问题转化为静态优化问题,计算效率得以提高。阐述了通用模型预测静态规划制导算法的基本原理,详细给出了基于通用模型预测静态规划算法的制导律设计过程。所设计的制导律满足末端法向加速度约束,因此,间接满足末端弹体姿态角约束。仿真时考虑目标的机动方式和落角约束,仿真结果表明,末端位移偏差小于0.5 m,末端落角可控制在0.01°范围内,末端法向加速度小于0.01 m/s2,该制导律能够很好地满足末端位移、落角和法向加速度约束。     

结合光流跟踪和三焦点张量约束的双目视觉里程计

针对城市街道准确实时定位的问题,提出将光流跟踪与三焦点张量约束结合的双目视觉里程计方法。为提高运算效率,将图像序列分为关键帧与非关键帧,对关键帧进行常规的特征点检测与匹配,对非关键帧用Lucas-Kanade光流跟踪特征点对。推导了基于前后帧、左右视图三焦点张量约束的观测方程,顾及动力学方程,组成卡尔曼滤波模型。考虑到观测方程的非线性,采用迭代Sigma点卡尔曼滤波进行解算,解算过程中用RANSAC稳健估计策略提纯匹配,以增强系统整体稳健性。实验结果表明:提出的算法在基本不损失精度(X方向优于5 m,Y方向优于4 m)的情况下,计算速度提升6.2倍,单帧图像平均处理时间由0.3115 s下降为0.0503 s,能够满足城市定位实时准确的需求。     

双面约束多点摩擦多体系统的建模和数值方法

提出了一种建立具有固定双面约束多点摩擦的多体系统动力学方程的方法. 用笛卡尔坐标阵描述系统的位形,根据局部方法的递推关系建立系统的约束方程,应用第一类Lagrange方程建立该系统的动力学方程,使得具有摩擦的约束面的法向力与Lagrange乘子一一对应,便于摩擦力的分析与计算,并用矩阵形式给出了摩擦力的广义力的一般表达式. 应用增广法将微分-代数方程组转化为常微分方程组,并用分块矩阵的形式给出,以便于方程的编程与计算.给出了一种改进的试算法,可提高计算效率. 最后给出了一个算例,应用试算法和RK法对算例进行了数值仿真.      

单机开式复合约束绳系吊装的动点坐标与绳力的通用程序算法分析

主要介绍单机开式复合约束绳系吊装计算的通用程序算法。利用Picard迭代法建立了单机开式复合约束绳系动点坐标的通用迭代算法,以及绳力计算的通用算式,并描述了实现通用算法的关键编程技术;典型算例结果分析表明,通用程序算法是非常有效的,Picard迭代法具有重要的工程应用价值。     

一种基于约束共轭梯度的闪光照相图像复原算法

针对闪光照相图像模糊较大、成像信噪比低的特点,提出了一种基于约束共轭梯度（CCG）的闪光照相图像复原算法。针对闪光照相的特点,引入基于非负、中值滤波和偏微分方程（PDE）的光滑约束条件,把闪光照相图像复原问题转化为约束优化问题,并利用约束共轭梯度法迭代求图像复原的最优解。数值试验表明,该算法能较好再现图像边缘信息,复原出的图像在信噪比和视觉方面都有较大提高。     

基于半光滑牛顿法的润滑液膜有限元空化算法

针对润滑液膜中空化问题,引入Fischer-Burmeister函数,提出一种求解满足质量守恒雷诺方程的半光滑牛顿迭代算法.该算法将空化问题的非线性互补关系转化为等式约束方程,避免了迭代计算中的不等式约束识别问题.算法可将空化约束方程与雷诺方程、力平衡方程、变形方程等同时纳入牛顿迭代方程组,有效解决了传统松弛迭代算法需要多重嵌套循环带来的效率低下问题及压力与膜厚的强耦合性带来的收敛困难问题.计算实例表明,该算法计算效率高、收敛性好,且易应用于弹流润滑分析中,在滑动轴承和机械端面密封等多种物理模型下均有良好的适用性.     

并行加速的局部变分迭代法及其轨道计算应用

为满足航天工程对轨道计算精度和实时性的高要求,近年来发展出了可以通过大步长积分修正实现快速精确求解的积分修正类方法.积分修正类方法有可并行计算的特点,然而在串行计算环境下会受到计算资源的限制,无法充分发挥其可并行加速的优势.此外,合理的计算参数通常难以预先确定,也使积分修正类方法大步长快速计算的优势难以充分体现.针对以上问题,利用积分修正类方法可并行计算的特点,提出了并行加速的局部变分迭代法PA-LVIM,通过将传统局部变分迭代法LVIM的并行计算量均摊到多个计算节点上,显著提高了计算速度.此外,还使用根据系统状态二阶导数分布确定计算参数的打磨法优化了PA-LVIM的计算参数,进一步发挥了其大步长快速计算的优势.求解了三个经典的轨道递推问题,仿真结果表明, PA-LVIM的加速效果明显,且经打磨法优化计算参数后,其计算效率又进一步得到提高,将当前主流方法的计算效率提高了5倍以上.     

非线性MEMS微梁的重心有理插值迭代配点法分析

文章利用重心有理插值迭代配点法分析计算非线性MEMS微梁问题。通过处理MEMS微梁的几何通过假设初始函数,将微梁非线性控制方程转换为线性化微分方程,建立逼近非线性微分方程的线性化迭代格式。采用重心有理插值配点法求解线性化微分方程,提出了数值分析MEMS微梁非线性弯曲问题的重心插值迭代配点法。给出了非线性微分方程的直接线性化和Newton线性化计算公式,详细讨论了非线性积分项的计算方法和公式。利用重心有理插值微分矩阵,建立了矩阵-向量化的重心插值迭代配点法的计算公式。数值算例结果表明,重心插值迭代配点法求解微梁非线性弯曲问题,具有计算公式简单、程序实施方便和计算精度高的特点。     

平动点Halo轨道航天器保持的多目标优化

针对日地系统平动点附近Halo轨道航天器保持任务,考虑航天器的能量消耗与轨道保持精度需求,采用多目标优化方法设计了改进时变控制器用于航天器Halo轨道保持任务。首先,基于圆形限制性三体模型推导了航天器的相对动力学方程并基于此设计了线性时变控制器。然后,采用多目标优化方法对时变控制器参数进行优化,得到满足航天器能量消耗与轨道保持精度之间平衡的Pareto最优解。最后,通过对考虑模型与环境干扰情况的数值模拟,结果表明多目标优化方法对平动点Halo轨道航天器保持任务达到低能能耗与高精度目标,具有一定的应用价值。     

Adaptive mesh refinement and load balancing based on multi-level block-structured Cartesian mesh

We developed a framework for a distributed-memory parallel computer that enables dynamic data management for adaptive mesh refinement and load balancing. We employed simple data structure of the building cube method (BCM) where a computational domain is divided into multi-level cubic domains and each cube has the same number of grid points inside, realising a multi-level block-structured Cartesian mesh. Solution adaptive mesh refinement, which works efficiently with the help of the dynamic load balancing, was implemented by dividing cubes based on mesh refinement criteria. The framework was investigated with the Laplace equation in terms of adaptive mesh refinement, load balancing and the parallel efficiency. It was then applied to the incompressible Navier–Stokes equations to simulate a turbulent flow around a sphere. We considered wall-adaptive cube refinement where a non-dimensional wall distance y⁺ near the sphere is used for a criterion of mesh refinement. The result showed the load imbalance due to y⁺ adaptive mesh refinement was corrected by the present approach. To utilise the BCM framework more effectively, we also tested a cube-wise algorithm switching where an explicit and implicit time integration schemes are switched depending on the local Courant-Friedrichs-Lewy (CFL) condition in each cube.     

Accurate and robust adaptive mesh refinement for aerodynamic simulation with multi‐block structured curvilinear mesh

A multi‐block curvilinear mesh‐based adaptive mesh refinement (AMR) method is developed to satisfy the competing objectives of improving accuracy and reducing cost. Body‐fitted curvilinear mesh‐based AMR is used to capture flow details of various length scales. A series of efforts are made to guarantee the accuracy and robustness of the AMR system. A physics‐based refinement function is proposed, which is proved to be able to detect both shock wave and vortical flow. The curvilinear mesh is refined with cubic interpolation, which guarantees the aspect ratio and smoothness. Furthermore, to enable its application in complex configurations, a sub‐block‐based refinement strategy is developed to avoid generating invalid mesh, which is the consequence of non‐smooth mesh lines or singular geometry features. A newfound problem of smaller wall distance, which negatively affects the stability and is never reported in the literature, is also discussed in detail, and an improved strategy is proposed. Together with the high‐accuracy numerical scheme, a multi‐block curvilinear mesh‐based AMR system is developed. With a series of test cases, the current method is verified to be accurate and robust and be able to automatically capture the flow details at great cost saving compared with the global refinement. Copyright © 2015 John Wiley & Sons, Ltd.     

A crack tip tracking algorithm for cohesive interface element analysis of fatigue delamination propagation in composite materials

A novel approach is proposed for the use of cohesive elements in the analysis of delamination propagation in composite materials under high-cycle fatigue loading. The method is applicable to delamination propagation within the Paris-law regime and is suitable for the analysis of three-dimensional structures typical of aerospace applications. The major advantages of the proposed formulation are its complete independence of the cohesive zone length – which is a geometry-dependent parameter – and its relative insensitivity to mesh refinement. This is only possible via the introduction of three nonlocal algorithms, which provide (i) automated three-dimensional tracking of delamination fronts, (ii) an estimation of direction of crack propagation and (iii) accurate and mesh-insensitive integration of strain energy release rate. All calculations are updated at every increment of an explicit time-integration finite element solution, which models the envelopes of forces and displacements with an assumption of underlying constant cyclic loading. The method was implemented as a user-defined subroutine in the commercial finite element software LS-Dyna and supports the analysis of complex three-dimensional models. Results are presented for benchmark cases such as specimens with central cut plies and centrally-loaded circular plates. Accurate predictions of delamination growth rates are observed for different mesh topologies in agreement with the Paris-laws of the material.     

Collocated discrete least squares meshless (CDLSM) method for the solution of transient and steady‐state hyperbolic problems

A collocated discrete least squares meshless method for the solution of the transient and steady‐state hyperbolic problems is presented in this paper. The method is based on minimizing the sum of the squared residuals of the governing differential equation at some points chosen in the problem domain as collocation points. The collocation points are generally different from nodal points, which are used to discretize the problem domain. A moving least squares method is employed to construct the shape functions at nodal points. The coefficient matrix is symmetric and positive definite even for non‐symmetric hyperbolic differential equations and can be solved efficiently with iterative methods. The proposed method is a truly meshless method and does not require numerical integration. Advantages of the collocation points are shown to be threefold: First, the collocation points are shown to be responsible for stabilizing the method in particular when problems with shocked solution are attempted. Second, the collocation points are also shown to improve the accuracy of the solution even for problems with smooth solutions. Third, the collocation points are shown to contribute to the efficiency of the method when solving steady‐state problems via faster convergence of the resulting algorithm. The ability of the method and in particular the effect of collocation points are tested against a series of one‐dimensional transient and steady‐state benchmark examples from the literature and the results are presented. A sensitivity analysis is also carried out to investigate the effect of the base polynomials on the accuracy and convergence characteristics of the method in solving steady‐state problems. The results show the ability of the proposed method to accurately solve difficult hyperbolic problems considered. The method is also shown to be particularly stable for problems with shocked solution due to the inherent stabilizing mechanism of the method. Copyright © 2008 John Wiley & Sons, Ltd.     

Strong-form framework for solving boundary value problems with geometric nonlinearity

In this paper, we present a strong-form framework for solving the boundary value problems with geometric nonlinearity, in which an incremental theory is developed for the problem based on the Newton-Raphson scheme. Conventionally, the finite element methods (FEMs) or weak-form based meshfree methods have often been adopted to solve geometric nonlinear problems. However, issues, such as the mesh dependency, the numerical integration, and the boundary imposition, make these approaches computationally inefficient. Recently, strong-form collocation methods have been called on to solve the boundary value problems. The feasibility of the collocation method with the nodal discretization such as the radial basis collocation method (RBCM) motivates the present study. Due to the limited application to the nonlinear analysis in a strong form, we formulate the equation of equilibrium, along with the boundary conditions, in an incremental-iterative sense using the RBCM. The efficacy of the proposed framework is numerically demonstrated with the solution of two benchmark problems involving the geometric nonlinearity. Compared with the conventional weak-form formulation, the proposed framework is advantageous as no quadrature rule is needed in constructing the governing equation, and no mesh limitation exists with the deformed geometry in the incremental-iterative process.     

Domain decomposition methods in computational fluid dynamics

The divide-and-conquer paradigm of iterative domain decomposition or substructuring has become a practical tool in computational fluid dynamics applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. We illustrate these features on the classic model problem of flow over a backstep using Newton's method as the non-linear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately and can be combined synergistically. We include sample performance results from an Intel iPSC/860 hypercube implementation.     

A collocation method for convection dominated flows

A collocation method based on multiple regions with moving boundaries placed in a flow field in which convection effects dominate, is proposed. By making the moving boundaries of the regions coincide with moving sharp fronts present in the solution of convection dominated problems, and thereby allowing higher concentration of meshes to be placed about the fronts, the proposed method is able to achieve very high accuracy. By having a moving mesh, the Peclet number characterizing the flow field depends upon velocity relative to a moving mesh in a region. Consequently by choosing proper velocities of the moving boundaries, the value of this Peclet number can be made as small as desired. The traditional collocation method based on centred discretization, when applied to each region in the field, produces oscillation free solutions even when the values of Peclet number based on absolute velocity are extremely large. In view of these characteristics the method appears to be an excellent candidate for the solution of any two-phase flow problem containing sharp fronts.