平面 NURBS 曲线的椭圆弧自适应逼近

给出了用椭圆弧及双椭圆弧自适应逼近平面NURBS曲线的算法。算法所得到的椭圆样条能够G1连续 ,双椭圆样条还能够保形。与现行的圆弧逼近算法相比 ,本算法不需要求解非线性方程组 ,而是由给定的插补误差自动计算参数增量 ,得到椭圆曲线的特征点 ,还可以将误差控制在预期的范围之内 ;与现行的直线插补方法相比 ,不需要额外的时间和空间 ,也适用于CNC环境。本算法在腔体加工、二维轮廓加工等方面有特别的实用价值。     

Minimizing makespan on a single batch processing machine with nonidentical job sizes

We deal with the problem of minimizing makespan on a single batch processing machine. In this problem, each job has both processing time and size (capacity requirement). The batch processing machine can process a number of jobs simultaneously as long as the total size of these jobs being processed does not exceed the machine capacity. The processing time of a batch is just the processing time of the longest job in the batch. An approximation algorithm with worst‐case ratio 3/2 is given for the version where the processing times of large jobs (with sizes greater than 1/2) are not less than those of small jobs (with sizes not greater than 1/2). This result is the best possible unless P = NP. For the general case, we propose an approximation algorithm with worst‐case ratio 7/4. A number of heuristics by Uzosy are also analyzed and compared. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 226–240, 2001     

Parallel machine scheduling with job assignment restrictions

In the classical multiprocessor scheduling problem independent jobs must be assigned to parallel, identical machines with the objective of minimizing the makespan. This article explores the effect of assignment restrictions on the jobs for multiprocessor scheduling problems. This means that each job can only be processed on a specific subset of the machines. Particular attention is given to the case of processing times restricted to one of two values, 1 and λ, differing by at most 2. A matching based polynomial time ε‐approximation algorithm is developed that has a performance ratio tending to . This algorithm is shown to have the best possible performance, tending to 3/2, for processing times 1 and 2. For the special case of nested processing sets, i.e., when the sets of machines upon which individual jobs may be assigned are non‐overlapping, the behavior of list scheduling algorithms is explored. Finally, for assignment restrictions determined by just one characteristic of the machines, such as disc storage or memory constraint in the case of high performance computing, we contribute an algorithm that provides a 3/2 worst case bound and runs in time linear in the number of jobs. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

状态—参数联合估计方法及其在液体火箭发动机健康监控中的应用

基于传统的扩展卡尔曼滤波器（ＥＫＦ）,本文提出了一种带次优渐消因子的ＥＫＦ用于非线性时变随机动态系统状态与参数的联合估计。应用于液体火箭发动机健康监控算法的仿真研究表明,本文所提出的联合估计器具有较好的收敛性、实时性和动态跟踪能力。此外,文中还讨论了联合估计器应用于实际系统的有关问题。     

应用分解法分析二阶锁相环路

本文介绍了一种新的非线性分析方法──分解法,并通过引入数学机械化的方法,将其应用于非理想二阶锁相环路的分析,推导了捕捉过程中相位差、频率差的逼近解析解,分析了环路的稳定性,得到了环路稳态相差、稳态频差和捕捉时间等参数。     

火炮射表数据处理方法评述

主要介绍火炮射表数据处理方法,对国内目前较为流行的两种射表逼近方法进行了全面、系统的分析与比较,指出了逐步回归射表逼近方法存在的缺陷和不足。对国外近几年采用的插值法文中也进行了比较详细的讨论,并指出了未来的研究问题。     

用非线性规划求解有限推力最优交会

利用非线性规划方法研究了航天器的有限推力最优交会问题。这种方法利用了近年来发展起来的直接优化技术,用分段多项式来表示整个轨道的状态和控制向量,将最优控制问题转化为非线性规划问题。在应用这种方法时,先将整个轨道分为若干推力段和无推力段,然后利用配置方法产生推力段的约束段,利用状态转移矩阵来产生无推力段的约束。最后,对共面轨道情况下的交会进行了数值仿真,验证了方法的有效性和鲁棒性。     

非线性超晶格中波的传播

通过二维实映射研究了非线性Kronig-Penney超晶格中波的传播。数值计算得到非线性系数不同、以及透射波幅不同时的映射图。结果表明,非线性系数对波传播有明显的调制作用,而透射波幅对非线性系数的有效性有明显的改变。     

复杂非线性隔冲减振系统计算分析

基于结构动力学理论,提出了一种用于分析计算复杂非线性隔冲减振系统的双模型两步计算法。该方法将冲击振动分成2个阶段:冲击作用阶段和自由振动阶段。冲击作用阶段,采用两自由度模型进行响应计算,该两自由度模型可有效地解决基础冲击输入问题;自由振动阶段,采用单自由度模型进行响应计算,设备在该阶段以冲击终了时刻的速度和位移为初始条件进行振动。文中还对一个典型的复杂非线性系统的冲击过程进行了数值计算.该方法亦可用于线性隔冲减振系统的计算分析.     

A mathematical programming approach for improving the robustness of least sum of absolute deviations regression

This paper discusses a novel application of mathematical programming techniques to a regression problem. While least squares regression techniques have been used for a long time, it is known that their robustness properties are not desirable. Specifically, the estimators are known to be too sensitive to data contamination. In this paper we examine regressions based on Least‐sum of Absolute Deviations (LAD) and show that the robustness of the estimator can be improved significantly through a judicious choice of weights. The problem of finding optimum weights is formulated as a nonlinear mixed integer program, which is too difficult to solve exactly in general. We demonstrate that our problem is equivalent to a mathematical program with a single functional constraint resembling the knapsack problem and then solve it for a special case. We then generalize this solution to general regression designs. Furthermore, we provide an efficient algorithm to solve the general nonlinear, mixed integer programming problem when the number of predictors is small. We show the efficacy of the weighted LAD estimator using numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006