基于压力的高阶精度隐式格式的研究及应用

１．引 言 在研究自然界和工程应用领域的物理流动问题时，一般根据流体流动的马赫数范围，采用不同的数学模型．相应地，在计算流体力学（ＣＦＤ：Ｃｏｍｐｕｔａｔｉｏｎａｌ Ｆｌｕｉｄ Ｄｙｎａｍｉｃｓ）中，针对不同的数学模型，建立和发展了差分格式和求解算法．其中时间推进法与其它方法相比，在数学的严密性、物理特性和所能采用的差分格式等方面具有许多优点，是亚音速、跨音速和超音速等可压缩流动问题中应用非常广泛的算法．尤其自七十年代以来，随着高分辨率高精度差分格式和高计算效率时间推进格式的建立和发展，时间推进法在…     

融合反向学习和黄金正弦的改进粒子群算法

提出一种融合反向学习和黄金正弦的改进粒子群算法。通过反向学习策略优化初始种群的质量，提高算法的收敛速度；结合黄金正弦算法优化位置更新公式，并通过双面镜理论处理边界外的粒子，使粒子在搜索空间内分布更均匀，增强算法的搜索能力；利用柯西变异的方法对全局最优粒子的位置进行扰动，提高粒子跳出局部最优的能力。对8个测试函数进行实验，并与其他的五种算法进行比较，结果表明，本文改进之后的粒子群优化算法有着更快的收敛速度和更高的寻优精度。     

一种基于灰度的梯度边界检测优化算法*

为降低基于梯度的边界检测算法的复杂度,常使用两种梯度近似算法。但这些梯度近似值受边界方向的影响较大,降低了边界检测的性能。提出了通用梯度近似算法的数学模型和两种优化准则,进而推导出两种梯度近似的优化算法。分析表明：与常用算法相比,优化算法在各向同性的性能方面提高4.4倍,在梯度幅度的逼近度提高57倍。同时,给出了优化算法的简单快捷的实现方法。     

非线性边界和等式约束条件下的高维函数优化算法研究

本文建立了基于模式搜索法的非线性边界约束条件下多参数函数的优化算法。通过综合模式搜索法、最速下降法和转轴法解决了在高维空间中的优化算法和非线性边界约束的算法问题。同时使用广义拉格朗日乘子法解决了非线性等式约束条件的计算方法。通过在四轨道隶玻色子模型计算中的应用,验证了该计算方法的有效性。由于该方法综合了多种经典优化算法,因此可以广泛适用于在非线性复杂边界约束条件下的多参数函数的优化计算。     

车辆自主导航中的道路边界识别算法

道路边界识别是车辆基于道路区域或边界信息自动导航的首要问题．根据驾驶员视觉处理经验和车辆运动轨迹方程，总结出道路边界识别的先验知识与预测知识，在所选取的二次曲线道路形状模型基础上,分别利用边界识别算法和跟踪识别算法得到车辆起步和稳定行驶过程中的实时道路边界信息，为车辆控制器计算出位置偏差和方向偏差两个参数，以实现车辆基于前向单目视觉的自主导航．通过对实际路面试验结果的分析，证明了该方法的有效性和准确性．     

基于链路交点相对位置信息的轻量级覆盖空洞检测算法

针对无线传感器网络（WSN）覆盖空洞导致网络性能和服务质量下降的问题，提出了一种基于链路交点相对位置信息的覆盖空洞检测算法（CHDARPI）。首先，定义空洞边界节点并计算相邻边界节点间链路的交点相对位置（RPI）值；然后，采用基于未完全覆盖交点数量（NICI）优先的策略选择空洞检测的发起节点，保证了连通覆盖空洞的并发检测。最后，在空洞检测过程中，将空洞检测消息局限于空洞边界节点之内，并根据转发节点方向角的大小制定不同场景下的转发策略，保证了空洞检测的效率。仿真结果表明：与现有基于边界节点的分布式覆盖空洞检测算法（DCHD）和基于分布式最小极角的覆盖空洞检测算法（DLPA）相比，CHDARPI在平均空洞检测时间和检测能耗方面分别至少下降了15.2%和16.7%。     

基于线性不等式的数据划分方法的优化

计算和数据划分是串行程序并行化时所要解决的一个重要问题，如何对程序中引用的数据进行合理的分布以最大限度的发现程序的并行性减少数据重分布的通信开销，是并行编译优化的重点。给出的数据和计算的优化分解方法是基于Anderson-Lam的分解算法上改进得到的。根据Anderson-Lam的算法得到数据和计算划分后，以线性不等式的形式表示，然后通过分析循环嵌套中能够进行边界冗余的只读数组，重新构造数据划分不等式，根据此不等式进行数据分布，实现具有边界冗余的只读数组的数据划分，有效地减少了数据收发的通信量。     

可压缩全速湍流流动的边界数值处理方法研究

计算流体力学问题的边界条件处理方法关系到数值仿真结果的精确度。为解决算法的精度,提出了三维可压缩湍流流动的边界条件数值处理方法,对所研究的边界类型包括进口边界、出口边界和固体壁面,流动的速度范围涉及亚音速、跨音速和超音速。流场数值仿真采用SIMPLE算法,湍流采用k-ε模型仿真。将边界总结为沟通型和孤立型边界两种类型,对每一控制方程分别阐述特定的数值处理方法。应用提出的边界处理方法对单圆弧凸包通道进行数值仿真获得了合理的结果,跨音速和超音速情形下准确地计算出了流场中存在的激波。     

散乱点数据的Bayesian曲面重建

针对带噪声的点云数据提出了一种基于贝叶斯（Bayesian）统计理论的曲面重建算法。算法的主要思想是在可能的重建概率空间上寻找最大后验概率。首先，分别计算测量过程数学模型和曲面先验概率模型；其次，通过共轭梯度优化算法确定每一个点的最大后验重建位置；最后，应用Surface Splatting 算法绘制点模型。实验结果表明，该先验概率模型不仅能去除扫描点云数据的噪声，同时还能增强曲面的细节特征。和已有的研究工作相比，本算法能获得更好的重建结果。     

基于Pareto最优解的零件制作方向优化研究

分析了快速成型工艺中零件制作方向对制件表面质量、所需支撑面积和零件制造时间的影响,分别建立了它们的优化数学模型。采用了基于Pareto最优解的多目标优化遗传算法NSGA－II进行优化计算,通过与单目标优化方法求得最优结果的对比,表明用多目标优化方法进行零件制作方向的优化计算,不仅可以求出比单目标方法更优的解,而且通过一次优化计算就可得到多个较优的零件制作方向。     

箱体类塑件注射模三维造型方法

基于ＡｕｔｏＣＡＤ Ｒ１２工作平台,以箱体类塑件为对象开发了一种注射模ＣＡＤ系统,该系统提出了一种新的高级体素单元－切片体素;提出了利用二维塑件图形来获得三维塑件几何造型的图形数据输入方法和能完成复杂成型零件的三维几何造型技术;设计了相关的系统数据库接口,实现了系统各模块内部数据的集成统一等关键技术;给出了模具三维装配造型和装配图纸生成实例。     

Geometric analysis of collaborative optimization

Instead of the past mathematical analyses, an intuitive geometric analysis of the collaborative optimization (CO) algorithm is presented in this paper, which reveals some geometric properties of CO and gives a direct geometric interpretation of the reason for the reported computational difficulties in CO. The analysis shows that if the system-level optimum point at one iteration is outside the feasible region of the original optimization problem, at the next iteration, the system-level optimization problem may be infeasible due to the system-level consistency equality constraints. One way to solve the problem of the infeasibility is to relax the system-level consistency equality constraints using inequality constraints. However it is a delicate job to determine a rational relaxed tolerance because feasibility and consistency have conflicting requirements for the tolerance, that is, the more relaxed the better for feasibility while the stricter the better for consistency. Based on the geometric analysis, a method of variable relaxed tolerance is put forward to solve this problem. In this method, an adaptive adjustment of the tolerance is made at each iteration according to the quantified inconsistency between two subsystems. In the last section, the capabilities and limitations of the proposed method are illustrated by three examples.     

Near-minimal test sets for the detection of single gate faults

A new algorithm is presented for the detection of single gate faults in combinational networks. A gate fault is any unknown transformation of the Boolean function realized by a particular gate or single-output subnetwork. Detection of such faults is accomplished by verifying the truth table of the correct gate function.The concept of real transform of a Boolean function is utilized to obtain in each iteration an optimal test, namely, a test that performs as much of the fault detection task as possible. The resulting test set is near-minimal and complete.The algorithm can handle multi-output networks, integrated network components and mixed (gate, stuck-at) fault models.     

Two-loop reinforcement learning algorithm for finite-horizon optimal control of continuous-time affine nonlinear systems

This article proposes three novel time-varying policy iteration algorithms for finite-horizon optimal control problem of continuous-time affine nonlinear systems. We first propose a model-based time-varying policy iteration algorithm. The method considers time-varying solutions to the Hamiltonian–Jacobi–Bellman equation for finite-horizon optimal control. Based on this algorithm, value function approximation is applied to the Bellman equation by establishing neural networks with time-varying weights. A novel update law for time-varying weights is put forward based on the idea of iterative learning control, which obtains optimal solutions more efficiently compared to previous works. Considering that system models may be unknown in real applications, we propose a partially model-free time-varying policy iteration algorithm that applies integral reinforcement learning to acquiring the time-varying value function. Moreover, analysis of convergence, stability, and optimality is provided for every algorithm. Finally, simulations for different cases are given to verify the convenience and effectiveness of the proposed algorithms.     

基于控制参数化的注塑工业过程最优反馈控制方法

本文针对一类典型的注塑工业过程系统, 研究了注塑填充过程中产生的熔体流动速度最优跟踪控制问题, 提出了一种基于控制参数化的计算最优反馈控制器设计方法以实现注塑过程中熔融聚合物流动前沿位移的最优跟 踪控制, 进而达到改善注塑零件性能的高效生产目标. 首先, 面向注塑工艺复杂生产过程建立了动态过程系统数学 模型, 提出了注塑机内部熔融聚合物流动前沿位置的动态最优跟踪控制问题; 其次, 设计了一种多级反馈控制律, 通 过控制参数化方法将控制反馈核进行了参数化表示, 将控制器设计问题转化为一序列最优参数决策问题; 然后, 通 过状态灵敏度方程分析方法, 求解出了目标函数及约束条件关于决策变量参数梯度信息的显式表达式, 并基于所提 供的梯度信息结合序列二次规划算法进行了高效优化迭代求解; 最后, 通过实验仿真验证了本文所提出的最优反 馈控制器设计方法的可行性和有效性.     

Instrumented film-insert injection compression molding for lens encapsulation of liquid crystal displays

A film-insert injection compression molding process was introduced to encapsulate cholesteric liquid crystal displays with flexible and rigid lens for full protection of displays to replace the currently used time consuming hand lamination technique. For this purpose, a new interchangeable cavity instrumented hot runner mold was designed and constructed. This complex method was carefully optimized considering challenges arising from an insert multilayer display with +80% liquid crystal content as well as different thermal expansion coefficients between the layers and the lens material as a high potential of delamination and warpage. Concerning the desired physical properties including transparency, low melt viscosity and melting temperature as well as a wide range of hardness grades from soft (flexible) to hard (rigid), three different hardness grades of thermoplastic polyurethanes were found to be the best candidates for this lens application. During proposed lens encapsulation, the pressure changes were evaluated with screw and mold movements using position detection via displacement transducers attached to track the mold closure and screw forward motion. The quality of encapsulation and shrinkage related problems, as well as their elimination, were all discussed. Display substrate material selection criteria for lowered warpage were defined with supporting thermal characterizations. Among the process parameters, tested also by applying the design of experiments with Taguchi method, mold temperature was found to be the most influential parameter on warpage, followed by pin gate opening time, packing pressure, and cooling time.     

Solution of fuzzy integrated production and marketing planning based on extension principle

The integration of production and marketing planning is crucial in practice for increasing a firm’s profit. However, the conventional inventory models determine the selling price and demand quantity for a retailer’s maximal profit with exactly known parameters. When the demand quantity, unit cost, and production rate are represented as fuzzy numbers, the profit calculated from the model should be fuzzy as well. Unlike previous studies, this paper develops a solution method to find the fuzzy profit of the integrated production and marketing planning problem when the demand quantity, unit cost, and production rate are represented as fuzzy numbers. Based on Zadeh’s extension principle, we transform the problem into a pair of two-level mathematical programming models to calculate the lower bound and upper bound of the fuzzy profit. According to the duality theorem of geometric programming technique, the two-level mathematical program is transformed into the one-level conventional geometric program to solve. At a specific α-level, we can derive the global optimum solutions for the lower and upper bounds of the fuzzy profit by applying well-developed theories of geometric programming. Examples are given to illustrate the whole idea proposed in this paper.     

Solution of fuzzy integrated production and marketing planning based on extension principle

The integration of production and marketing planning is crucial in practice for increasing a firm’s profit. However, the conventional inventory models determine the selling price and demand quantity for a retailer’s maximal profit with exactly known parameters. When the demand quantity, unit cost, and production rate are represented as fuzzy numbers, the profit calculated from the model should be fuzzy as well. Unlike previous studies, this paper develops a solution method to find the fuzzy profit of the integrated production and marketing planning problem when the demand quantity, unit cost, and production rate are represented as fuzzy numbers. Based on Zadeh’s extension principle, we transform the problem into a pair of two-level mathematical programming models to calculate the lower bound and upper bound of the fuzzy profit. According to the duality theorem of geometric programming technique, the two-level mathematical program is transformed into the one-level conventional geometric program to solve. At a specific α-level, we can derive the global optimum solutions for the lower and upper bounds of the fuzzy profit by applying well-developed theories of geometric programming. Examples are given to illustrate the whole idea proposed in this paper.     

A method of representing dimensions and tolerances on solid based freeform surfaces

Dimensions and tolerances are an integral part of the product definition of any component controlling its functionality and manufacturability.This paper puts forward a mathematical method of representing tolerances and dimensions on a (BREP) solid modeller. It differs from previous work in the area in that it enables tolerances to be applied to a general free-form surface, in particular aerofoil geometry.The method is based on three tolerance formats, a position tolerance, a form tolerance and a datumform tolerance. It combines a matrix method for the representation of geometric positioning and tolerancing with a graph theoretic approach for spatial analysis. Its application with a BREP modelling system is mentioned and its application within inspection analysis.     

Model-based visual feedback control for a hand-eye coordinatedrobotic system

The integration of a single camera into a robotic system to control the relative position and orientation between the robot's end-effector and a moving part in real time is discussed. Only monocular vision techniques are considered because of current limitations in the speed of computer vision analysis. The approach uses geometric models of both the part and the camera, as well as the extracted image features, to generate the appropriate robot control signals for tracking. Part and camera models are also used during the teaching stage to predict important image features that appear during task completion