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.     

Integrating decisions with advance supply information in an assemble-to-order system

We study a periodic-review assemble-to-order (ATO) system with multiple components and multiple products, in which the inventory replenishment for each component follows an independent base-stock policy and stochastic product demands are satisfied according to a First-Come-First-Served rule. We assume that the replenishment for various component suffers from lead time uncertainty. However, the decision maker has the so-called advance supply information (ASI) associated with the lead times and thus can take advantage of the information for system optimization. We propose a multistage stochastic integer program that incorporates ASI to address the joint optimization of inventory replenishment and component allocation. The optimal base-stock policy for the inventory replenishment is determined using the sample average approximation algorithm. Also, we provide a modified order-based component allocation (MOBCA) heuristic for the component allocation. We additionally consider a special case of the variable lead times where the resulting two-stage stochastic programming model can be characterized as a single-scenario case of the proposed multistage model. We carry out extensive computational studies to quantify the benefits of integrating ASI into joint optimization and to explore the possibility of employing the two-stage model as a relatively efficient approximation scheme for the multistage model.     

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.     

转向机动条件下利用拖船航迹的拖线阵阵形估计

针对水动力模型(water-pulley模型)适用范围有限的问题,提出一种对拖船航迹进行平滑得到拖线阵声阵段运动轨迹,进而实现阵形估计的方法。通过分析缆的稳态振荡响应特性,近似认为声阵段上各点沿同一轨迹运动;设计平滑窗将拖船回转机动航迹平滑为声阵段航迹,并将其拓展应用于拖船转向机动的情况;利用平滑窗的一部分对距离拖船不足平滑窗宽度的航迹部分进行平滑得到当前拖缆段阵形,从而实现转向机动过程中全阵阵形的实时估计。仿真结果表明:若拖线阵由间隔为5 m的81个阵元构成,所提出的方法与朴素water-pulley模型相比可以使转向机动过程中的平均阵增益提高约0.8 dB,平均方位估计偏差减小约4.7°。利用仿真结果分析算法的输入敏感性,对阵形估计方法进行简化使其更易于工程实现,海试数据验证表明简化的方法可行、有效。     

利用最小二乘支持向量机求解潜艇内外磁场映射模型

为提高潜艇磁隐身能力,应对潜艇固定磁场进行实时监测,提出利用最小二乘支持向量机的潜艇内外磁场映射方法。结合内外映射法和最小二乘支持向量机原理,通过交叉验证优化模型参数,建立由内到外的潜艇磁场映射模型。以潜艇外部垂向固定磁场变化量为分析对象,仿真和实验结果均与标准值吻合良好。与径向基神经网络算法相比,该方法的泛化能力和推算精度有明显提高,且更符合工程实际,对闭环消磁技术的研究具有指导意义。     

多碱光电阴极饱和机理研究

多碱光电阴极饱和机理的研究对于提高阴极电子发射能力具有重要意义。依据光电阴极三步电子发射理论,采用蒙特卡洛法研究了多碱光电阴极的电子发射过程。研究结果与相关文献中的实验数据进行了对比分析,光子能量临近光电阴极响应阈值附近时,得到的量子效率曲线以及电子能量分布曲线与实验数据吻合良好。基于上述模型,研究了光压效应和空间电荷效应对多碱光电阴极电子发射特性的影响。结果表明,多碱光电阴极在光压效应限制下的阈值饱和激光能量密度约为8μJ/cm~2,在空间电荷效应限制下的阈值饱和激光能量密度约为2. 23μJ/cm~2。开展了266 nm激光辐照多碱光电阴极实验,经测量,多碱光电阴极的阈值饱和激光能量密度约为2μJ/cm~2,这表明空间电荷效应是限制其光电子发射能力的主要因素。     

复合固体推进剂等效力学性能VCFEM细观预示方法

根据固体推进剂的细观结构特征,采用等圆最优装载方式生成代表性体积单元(Representative Volume Element,RVE)模型,并结合Voronoi单元有限元方法(Voronoi Cell Finite Element Method,VCFEM)和均匀化方法,发展了一种可预示固体推进剂等效力学性能的数值分析方法,从而得到体分比和组分材料对等效模量和等效泊松比的影响规律。为证明该方法的有效性,设计一个对称数值模型,通过对该方法和传统有限元方法的节点位移结果的比较,发现两者之间的相对误差小于5%,且VCFEM用少量单元就完成了分析,提高了计算效率。通过对不同细观结构下推进剂RVE模型的计算,发现随着夹杂体分比的增大,夹杂的颗粒增强效应越明显,基体材料的变化比夹杂材料对等效力学性能有着更加显著的影响。     

强爆轰驱动超高速碎片发射装置设计因素分析

为了得到发射装置设计因素和超高速碎片性能间的关系,考虑了药型罩的材料、炸药种类、装药长径比、药型罩的锥角、药型罩的厚度、药型罩顶部靠近装药侧的曲率半径等设计因素,采用AUTODYNTM,结合正交试验,对超高速碎片的发射过程进行数值模拟。结果表明,3种发射装置结构分别可以提供质量为1. 533 g的紫铜碎片、速度为11. 649 km/s的铝碎片、动能为85. 6 k J的铝碎片; 2种发射装置结构均可以提供质量大于1 g、速度高于11 km/s的密实结构圆柱状碎片。验证了仿真方法的可信性,对影响碎片性能的设计因素进行了分析、排序,并得到了这些设计因素与碎片质量、速度、动能的关系。     

结合全局与局部信息的主动轮廓分割模型

针对传统的基于区域的主动轮廓模型在分割灰度不均匀图像和噪声图像存在效果不佳的问题,提出结合全局项与局部项的主动轮廓分割模型。全局项由CV(Chan-Vese)模型的保真项构成,局部项的构建考虑局部区域信息的同时引入反映图像灰度特性的局部熵信息。依据图像灰度的特点,选择合理的全局项和局部项参数,并加入正则项保证曲线在演化过程中保持平滑,保障分割结果的可靠性。通过变分水平集方法最小化能量泛函,依据梯度下降流迭代更新水平集,完成曲线演化。采用模拟图像和实际图像进行实验分析,结果表明,所提出的结合全局项和局部项的主动轮廓模型可以高效地分割噪声严重以及灰度分布不均匀的图像。     

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.