论证一类不等式问题 展示数学发现的方法

通过对一个不等式的加强和完善,探求出推广这一类问题的途径,解决了一类不等式问题。     

Safe distances

This work highlights the problem in military operations of setting safety limits for friendly forces, neutral forces, or civilians, to avoid sustaining unnecessary casualties both in wartime and in training. We present and investigate an analytic model which both enables the quantitative understanding of the inherent problems, and which furnishes a reasonably flexible tool in the hands of the analyst. Characteristic numerical results are displayed and analyzed: They show in particular that prevailing crude approximations are inadequate. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 259–269, 2001     

基于正交最小二乘估计的非线性时间序列的预测

在对非线性时间序列的短期预测中经常采用局部线性化的预测算法 ,原有的算法使用普通最小二乘法 (LS)估计近似线性模型的参数。对于存在噪声的数据 ,该算法的数值稳定性较差。本文在对非线性空间进行局部线性化的基础上 ,采用正交最小二乘方法 (OLS)对线性模型同时进行结构选择与参数辨识 ,改善了数值的病态特性 ,增强了算法的稳定性     

一类不匹配不确定非线性系统鲁棒变结构控制

针对一类具有不匹配非参数化不确定性的非线性系统 ,设计出一种鲁棒变结构控制器。该控制器能够保证当时间 t趋于无穷时 ,闭环控制系统的输出跟踪误差趋于零。仿真实例说明了该控制器具有满意的控制效果     

助推-滑翔式导弹中段弹道方案的初步分析

建立了助推—滑翔式弹道中段的无量纲运动方程。采用非线性规划方法实现弹道优化。首先求解不同初始速度、速度倾角和最大升阻比的最大射程弹道,然后考虑驻点热流、过载约束,求解总气动加热最小和射程最大的最优弹道。基于前者的计算结果分析了初始条件对最大射程弹道的影响。将考虑约束的再入滑翔弹道与弹道式再入的特征参数比较,表明再入滑翔弹道的峰值热流较小,而总气动加热增加,但再入滑翔飞行时间在一般锥形体再入机动飞行器的热防护系统可承受的时间范围内。     

Log‐concave and concave distributions in reliability

Nonparametric classes of life distributions are usually based on the pattern of aging in some sense. The common parametric families of life distributions also feature monotone aging. In this paper we consider the class of log‐concave distributions and the subclass of concave distributions. The work is motivated by the fact that most of the common parametric models of life distributions (including Weibull, Gamma, log‐normal, Pareto, and Gompertz distributions) are log‐concave, while the remaining life of maintained and old units tend to have a concave distribution. The classes of concave and log‐concave distributions do not feature monotone aging. Nevertheless, these two classes are shown to have several interesting and useful properties. We examine the closure of these classes under a number of reliability operations, and provide sharp reliability bounds for nonmaintained and maintained units having life distribution belonging to these classes. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 419–433, 1999     

基于NFxPEM算法的调制气流声源的非线性补偿研究

针对调制气流声源存在较强的谐波畸变,将声源系统等效为Hammerstein非线性模型,利用该模型下的预失真技术对声源进行非线性补偿研究。根据辨识的Hammerstein模型中静态非线性部分带有直流分量的特点,给出了考虑直流分量补偿的预失真算法,并用数值仿真验证了算法的准确性和直流分量补偿的必要性。在非线性补偿实验中,根据单频信号辨识得到Hammerstein模型参数,采用NFxPEM算法求得对应的预失真Wiener模型参数和预失真波形。实验结果表明,与直接发射相比,补偿发射后声波的功率谱中谐波能量有所下降,而基频能量有小幅度的上升,说明了研究思路的正确性。     

基于小波的信噪分离方法

本文在 Ｄｏｎｏｈｏ 提出的从噪声中恢复信号的非线性小波方法的基本原理的基础上, 并针对非线性小波方法的核心问题——浮动阈值的设定提出了新的算法。通过算例证明, 所设计的浮动阈值在实际应用中效果较好, 特别在低信噪比时信号恢复效果明显优于现常用的浮动阈值设计方法。     

疲劳裂纹闭合的非线性超声在线测量

建立了外部载荷作用下用非线性振动-声场调制指数表征裂纹尺寸的数学模型。根据对外载荷与塑性致闭应力共同作用下裂纹面的开闭响应的分析,提出了裂纹张开和闭合应力的在线测量方法。在一块含中心穿透裂纹的铝合金薄板试件上进行了裂纹闭合参数的测量实验,实验结果表明,使用振动-声场调制技术在线测量裂纹闭合参数是可行且有效的,且该方法还能用于分析小裂纹的特殊开闭行为。     

Optimal motion planning in rapid‐fire combat situations with attacker uncertainty

This article provides a modeling framework for quantifying cost and optimizing motion plans in combat situations with rapid weapon fire, multiple agents, and attacker uncertainty characterized by uncertain parameters. Recent developments in numerical optimal control enable the efficient computation of numerical solutions for optimization problems with multiple agents, nonlinear dynamics, and a broad class of objectives. This facilitates the application of more realistic, equipment‐based combat models, which track both more realistic models, which track both agent motion and dynamic equipment capabilities. We present such a framework, along with a described algorithm for finding numerical solutions, and a numerical example.