Application of Markov renewal theory and semi-Markov decision processes in maintenance modeling and optimization of multi-unit systems

In this paper, a condition-based maintenance model for a multi-unit production system is proposed and analyzed using Markov renewal theory. The units of the system are subject to gradual deterioration, and the gradual deterioration process of each unit is described by a three-state continuous time homogeneous Markov chain with two working states and a failure state. The production rate of the system is influenced by the deterioration process and the demand is constant. The states of the units are observable through regular inspections and the decision to perform maintenance depends on the number of units in each state. The objective is to obtain the steady-state characteristics and the formula for the long-run average cost for the controlled system. The optimal policy is obtained using a dynamic programming algorithm. The result is validated using a semi-Markov decision process formulation and the policy iteration algorithm. Moreover, an analytical expression is obtained for the calculation of the mean time to initiate maintenance using the first passage time theory.     

On efficient algorithms for finding efficient salvo policies

We consider the salvo policy problem, in which there are k moments, called salvos, at which we can fire multiple missiles simultaneously at an incoming object. Each salvo is characterized by a probability p_i: the hit probability of a single missile. After each salvo, we can assess whether the incoming object is still active. If it is, we fire the missiles assigned to the next salvo. In the salvo policy problem, the goal is to assign at most n missiles to salvos in order to minimize the expected number of missiles used. We consider three problem versions. In Gould's version, we have to assign all n missiles to salvos. In the Big Bomb version, a cost of B is incurred when all salvo's are unsuccessful. Finally, we consider the Quota version in which the kill probability should exceed some quota Q. We discuss the computational complexity and the approximability of these problem versions. In particular, we show that Gould's version and the Big Bomb version admit pseudopolynomial time exact algorithms and fully polynomial time approximation schemes. We also present an iterative approximation algorithm for the Quota version, and show that a related problem is NP-complete.     

线性代数中一个向量等式的新应用

本文利用向量等式：对线性代数中的两个重要结论作出新的证明。本文给出的证明，不但方法上具有新意，而且其解决过程也会使我们对问题本身有新的认识和理解。     

The building evacuation problem with shared information

In this article, the Building Evacuation Problem with Shared Information (BEPSI) is formulated as a mixed integer linear program, where the objective is to determine the set of routes along which to send evacuees (supply) from multiple locations throughout a building (sources) to the exits (sinks) such that the total time until all evacuees reach the exits is minimized. The formulation explicitly incorporates the constraints of shared information in providing online instructions to evacuees, ensuring that evacuees departing from an intermediate or source location at a mutual point in time receive common instructions. Arc travel time and capacity, as well as supply at the nodes, are permitted to vary with time and capacity is assumed to be recaptured over time. The BEPSI is shown to be NP‐hard. An exact technique based on Benders decomposition is proposed for its solution. Computational results from numerical experiments on a real‐world network representing a four‐story building are given. Results of experiments employing Benders cuts generated in solving a given problem instance as initial cuts in addressing an updated problem instance are also provided. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

一种改进的事件驱动系统框架

在给出事件驱动系统安全漏洞的基础上,指出了产生漏洞的根本原因是:系统忽视了输入系统的事件序列之间存在的相关性;系统无条件信任任何事件源产生的事件.针对这两个原因,相应提出了事件序列形式安全分析模型及基于事件源的可信度评估模型,依据这两个模型,构建了一种改进的事件驱动系统框架.     

基于支持向量机的功率变换器开关管开路故障诊断

提出一种基于支持向量机的功率变换器开关管开路故障诊断方法。利用支持向量机建立分类模型,模型以相电流功率谱为输入量,7种故障状态为输出量,选用高斯核,使用基于二叉树分类器的分类算法。将诊断结果与基于BP神经网络的诊断结果进行比较,结果表明基于支持向量机的分类器在功率变换器开关管开路故障诊断中具有更高的准确率和更好的泛化能力。     

Adjacency‐based local top‐down search method for finding maximal efficient faces in multiple objective linear programming

It is well‐known that the efficient set of a multiobjective linear programming (MOLP) problem can be represented as a union of the maximal efficient faces of the feasible region. In this paper, we propose a method for finding all maximal efficient faces for an MOLP. The new method is based on a condition that all efficient vertices (short for the efficient extreme points and rays) for the MOLP have been found and it relies on the adjacency, affine independence and convexity results of efficient sets. The method uses a local top‐down search strategy to determine maximal efficient faces incident to every efficient vertex for finding maximal efficient faces of an MOLP problem. To our knowledge, the proposed method is the first top‐down search method that uses the adjacency property of the efficient set to find all maximal efficient faces. We discuss this and other advantages and disadvantages of the algorithm. We also discuss some computational experience we have had with our computer code for implementing the algorithm. This computational experience involved solving several MOLP problems with the code.     

浅海中时谐水平电偶极子在空气中的极低频磁场

为深入分析空气中的极低频磁场,用时谐水平电偶极子等效船舶被主轴调制的水下腐蚀相关电流。根据Maxwell方程组和电磁场边界条件建立浅海条件下电偶极子在空气中的矢量磁位模型,进一步推导了磁场表达式,并利用快速汉克尔变换计算磁场的传播规律。测量了水池碳棒电极和海上钛基电极的磁场,验证了磁场的实用性和模型的有效性。     

采用PWPF调节器的再入飞行器最优控制分配方法

针对具有反作用控制系统(Reaction Control System,RCS)和气动舵两类控制机构的再入飞行器,提出一种基于脉宽脉频(Pulse-Width Pulse-Frequency,PWPF)调节器的最优控制分配方法。将RCS的输入信号转化为连续变化量,RCS与气动舵的控制分配问题被描述为二次规划问题,并采用有效集方法对其求解。采用离散法和PWPF调节器将优化结果转化为RCS的开关机状态。与混合整数规划问题相比,连续二次规划问题更容易求解,计算速度更快。通过对二次规划问题的重构,该算法能有效地应对故障情况。