高维非线性电路平衡点稳定性研究

提出了一种新的分析具有分解形式的高维非线性电路平衡点全局渐近稳定的方法.这种方法以矩阵分解为工具,结合平衡点的渐近稳定判据,用分解矩阵的稳定性决定平衡点的全局渐近稳定性.与目前该问题所采用的LIYAPUNOV直接法相比,该方法具有无须判断平衡点的唯一性,判别方法直接明了等优点.电路维数越大时,此方法越有其优势.同时,该方法对于其他形式的非线性系统的分析,也有重要的启发性及应用价值.     

基于马尔科夫链的一种评价方法

应用了数理统计与随机过程理论,从分析动态系统的状态以及状态转移情况给出了一种合理的评价方法,经过实例验证,该方法效果较好.     

一个具有相互独立、不同分布服务时间序列的排队模型

讨论的排队模型 ,放宽了GI/G/1系统中“服务时间独立同分布”的限制 ,只要求各服务时间相互独立 ,因而较GI/G/1排队模型能更合理地拟合实际问题 .在此较宽的条件下 ,利用补充变量的方法 ,求得了该排队系统队长的瞬时分布     

氧化锆陶瓷Ⅱ-Ⅲ复合型裂纹的综合相变增韧作用

采用综合相变准则和应变能释放率判据对氧化锆陶瓷Ⅱ-Ⅲ复合型裂纹的增韧结果进行了理论计算。分别给出了静止裂纹和定常扩展裂纹相变增韧的理论表达式。结果表明:综合相变对静止裂纹有微小的负屏蔽效应,对扩展裂纹的增初结果与材料的剪切模量、相变尾区高度和相变体积分数成正比,并且增韧值随着K_Ⅲ/K_Ⅱ比值的增大而减小,表明相变对Ⅱ型裂纹的增韧效果相对Ⅲ型裂纹更显著。     

基于Solidworks二次开发的两栖车辆浮态设计及静稳性分析

建立了描述车辆姿态向量和重力向量的两个坐标系,研究了姿态向量与坐标变换之间的关系,根据Solid-Works提供的函数,利用二分法求解了给定姿态下的浮心位置;以浮心计算为基础,通过对车辆的受力分析和运动分析,确定了车辆浮态的计算方法;利用SolidWorks的API函数进行二次开发,形成了计算静稳性的程序,并进行了实例计算。结果表明：与传统的作图法相比较,该方法计算结果更精确,计算速度更快。     

状态空间表达下控制系统的稳态误差

经典控制理论对系统稳态误差的讨论从传递函数入手,重点是对系统开环传递函数的研究,当系统的输入是任意函数时,引入动态误差系数方法来研究稳态误差,但是当输入具有高阶导数时,动态误差系数将很难得到.现代控制理论中的状态空间表达下求系统的稳态误差很好地解决了这个问题.利用矩阵之间的运算来表示动态误差系数,并且可以得到任意输入下的稳态误差值,在线性定常系统下的推导结果还可以适用于线性时变系统,具有一定的普遍性.     

一种变质心高速旋转炮弹鲁棒姿态控制律

针对采用变质心技术的高速旋转炮弹的姿态控制问题,提出一种基于扩张状态观测器的动态面控制方法。根据由弹体和单滑块组成的多体系统的特点,建立了系统的姿态动力学模型,并对其进行了合理的简化。将系统的滚转通道引起的强耦合、建模误差及外部扰动等视为未知不确定干扰,并且考虑由于炮弹尺寸限制而引起的多体系统控制输入(滑块位移)的有限性,设计了扩张状态观测器和辅助系统,分别对系统的干扰进行观测以及处理控制输入的有限性,综合动态面控制技术设计了姿态控制律,最后基于李雅普诺夫稳定性原理证明了控制器的稳定性。仿真结果表明,该控制器能够在克服干扰的前提下快速稳定地跟踪指令信号,具有良好的控制精度和鲁棒性。     

备件冷储备方案下装备群任务可靠性建模

针对具有相同结构功能的装备群系统可靠性评估问题,根据任务周期内对装备完好数的要求,合理表示了系统状态转移过程。以部件任务期间状态变化为研究对象,将系统等效表示为多阶段任务系统,即串行k/N(G)系统。在确定系统可行状态过程基础上,分别建立了部件寿命分布在3种不同情形下的系统任务可靠性模型,并分析了备件冷储备方案的影响。为确定系统任务期间备件携带量提供决策支持,最后给出了一个应用实例。     

Generalizing the survival signature to unrepairable homogeneous multi‐state systems

The notion of signature has been widely applied for the reliability evaluation of technical systems that consist of binary components. Multi‐state system modeling is also widely used for representing real life engineering systems whose components can have different performance levels. In this article, the concept of survival signature is generalized to a certain class of unrepairable homogeneous multi‐state systems with multi‐state components. With such a generalization, a representation for the survival function of the time spent by a system in a specific state or above is obtained. The findings of the article are illustrated for multi‐state consecutive‐k‐out‐of‐n system which perform its task at three different performance levels. The generalization of the concept of survival signature to a multi‐state system with multiple types of components is also presented. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 593–599, 2017     

The probability of the existence of a feasible flow in a stochastic transportation network

Stochastic transportation networks arise in various real world applications, for which the probability of the existence of a feasible flow is regarded as an important performance measure. Although the necessary and sufficient condition for the existence of a feasible flow represented by an exponential number of inequalities is a well‐known result in the literature, the computation of the probability of all such inequalities being satisfied jointly is a daunting challenge. The state‐of‐the‐art approach of Prékopa and Boros, Operat Res 39 (1991) 119–129 approximates this probability by giving its lower and upper bounds using a two‐part procedure. The first part eliminates all redundant inequalities and the second gives the lower and upper bounds of the probability by solving two well‐defined linear programs with the inputs obtained from the first part. Unfortunately, the first part may still leave many non‐redundant inequalities. In this case, it would be very time consuming to compute the inputs for the second part even for small‐sized networks. In this paper, we first present a model that can be used to eliminate all redundant inequalities and give the corresponding computational results for the same numerical examples used in Prékopa and Boros, Operat Res 39 (1991) 119–129. We also show how to improve the lower and upper bounds of the probability using the multitree and hypermultitree, respectively. Furthermore, we propose an exact solution approach based on the state space decomposition to compute the probability. We derive a feasible state from a state space and then decompose the space into several disjoint subspaces iteratively. The probability is equal to the sum of the probabilities in these subspaces. We use the 8‐node and 15‐node network examples in Prékopa and Boros, Operat Res 39 (1991) 119–129 and the Sioux‐Falls network with 24 nodes to show that the space decomposition algorithm can obtain the exact probability of these classical examples efficiently. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 479–491, 2016