Stochastic framework for partially degradation systems with continuous component degradation‐rate‐interactions

Many conventional models that characterize the reliability of multicomponent systems are developed on the premise that for a given system, the failures of its components are independent. Although this facilitates mathematical tractability, it may constitute a significant departure from what really takes place. In many real‐world applications, system components exhibit various degrees of interdependencies, which present significant challenges in predicting degradation performance and the remaining lifetimes of the individual components as well as the system at large. We focus on modeling the performance of interdependent components of networked systems that exhibit interactive degradation processes. Specifically, we focus on how the performance level of one component affects the degradation rates of other dependent components. This is achieved by using stochastic models to characterize how degradation‐based sensor signals associated with the components evolve over time. We consider “Continuous‐Type” component interactions that occur continuously over time. This type of degradation interaction exists in many applications, in which interdependencies occur on a continuum. We use a system of stochastic differential equations to capture such “Continuous‐Type” interaction. In addition, we utilize a Bayesian approach to update the proposed model using real‐time sensor signals observed in the field and provide more accurate estimation of component residual lifetimes. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 286–303, 2014     

The burglar problem with multiple options

We consider the burglar problem in which a burglar can either retire or choose among different types of burglaries, with each type having its own success probability and reward distribution. Some general structural results are established and, in the case of exponentially distributed reward distributions, a solution technique is presented. The burglar problem's relationship to a stochastic knapsack problem with a random exponentially distributed knapsack capacity is shown. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 359–364, 2014     

非相干背景光辐照二波耦合中的最佳匹配随机共振

针对非相干背景光辐照二波耦合中参数的最佳匹配设计问题,提出了一种基于随机共振理论的研究方法。首先,文章通过二波耦合过程进行物理机理分析和数值实验分析,证明了该问题在本质上可归结为一种随机共振现象。其次,从随机共振的角度,研究其中的最佳参数设计问题,给出了一种分布处理的最优参数设计流程。按照该方法,在给定增益要求的情况下,先根据信号光饱和与否来确定晶体长度,最后根据非相干光的比例对增益的影响来确定非相干光的比例。仿真实验表明,经过最佳参数设计后,信号的增益和输出信噪比上均有显著提高。     

A branch‐and‐price approach for the stochastic generalized assignment problem

In this article, we address a stochastic generalized assignment machine scheduling problem in which the processing times of jobs are assumed to be random variables. We develop a branch‐and‐price (B&P) approach for solving this problem wherein the pricing problem is separable with respect to each machine, and has the structure of a multidimensional knapsack problem. In addition, we explore two other extensions of this method—one that utilizes a dual‐stabilization technique and another that incorporates an advanced‐start procedure to obtain an initial feasible solution. We compare the performance of these methods with that of the branch‐and‐cut (B&C) method within CPLEX. Our results show that all B&P‐based approaches perform better than the B&C method, with the best performance obtained for the B&P procedure that includes both the extensions aforementioned. We also utilize a Monte Carlo method within the B&P scheme, which affords the use of a small subset of scenarios at a time to estimate the “true” optimal objective function value. Our experimental investigation reveals that this approach readily yields solutions lying within 5% of optimality, while providing more than a 10‐fold savings in CPU times in comparison with the best of the other proposed B&P procedures. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 131–143, 2014     

随机滤波模型在变速箱剩余寿命预测中的应用研究

摘要：基于变速箱加速寿命实验的振动信号,提取信号的多种特征参量．通过分析各特征参量的敏感性和稳定性,选择幅域裕度指标、峰值指标、波形指标和RMS（RootMeanSquare）作为特征参量,建立一种基于随机滤波的变速箱剩余寿命预测模型,给出剩余寿命后验概率密度的递推公式,设计了极大似然估计方法求解模型参数,并经实例验证模型的有效性和实用性．     

随机共振在微弱信号检测中的数值仿真

对基于非线性双稳系统随机共振的微弱信号检测技术进行数值研究,利用随机共振机制,浸入在噪声中的微弱信号可以得到有效的放大与增强。给出了基于Runge Kutta算法的双稳系统随机共振模型的求解方法,提出了利用随机共振检测微弱非周期信号的一种新思路。数值仿真结果表明,该方法不仅可以检测出强噪声极低频的微弱周期信号,而且可以对非周期信号进行有效的检测。     

具有变时滞的离散型随机BAM神经网络的稳定性

研究一类具有变时滞的离散型随机BAM神经网络。通过构造Lyapunov泛函以及线性矩阵不等式（LMI）,得出了离散系统全局渐近稳定的充分条件。     

基于随机网络的平均维修保障服务时间分析

利用随机网络建模方法在随机工程项目分析中的优越性,建立了不同保障方式下的维修保障过程模型。重点对网络活动中的维修等待时间和维修等待概率进行了分析,利用随机网络的解析算法,确定了维修力量的平均维修保障服务时间分析模型。最后将该方法应用于伴随修理过程,对其平均维修保障服务时间进行了案例分析。     

Approximating nondominated sets in continuous multiobjective optimization problems

Many important problems in Operations Research and Statistics require the computation of nondominated (or Pareto or efficient) sets. This task may be currently undertaken efficiently for discrete sets of alternatives or for continuous sets under special and fairly tight structural conditions. Under more general continuous settings, parametric characterisations of the nondominated set, for example through convex combinations of the objective functions or ε‐constrained problems, or discretizations‐based approaches, pose several problems. In this paper, the lack of a general approach to approximate the nondominated set in continuous multiobjective problems is addressed. Our simulation‐based procedure only requires to sample from the set of alternatives and check whether an alternative dominates another. Stopping rules, efficient sampling schemes, and procedures to check for dominance are proposed. A continuous approximation to the nondominated set is obtained by fitting a surface through the points of a discrete approximation, using a local (robust) regression method. Other actions like clustering and projecting points onto the frontier are required in nonconvex feasible regions and nonconnected Pareto sets. In a sense, our method may be seen as an evolutionary algorithm with a variable population size. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

A generalization of the weighted set covering problem

We study a generalization of the weighted set covering problem where every element needs to be covered multiple times. When no set contains more than two elements, we can solve the problem in polynomial time by solving a corresponding weighted perfect b‐matching problem. In general, we may use a polynomial‐time greedy heuristic similar to the one for the classical weighted set covering problem studied by D.S. Johnson [Approximation algorithms for combinatorial problems, J Comput Syst Sci 9 (1974), 256–278], L. Lovasz [On the ratio of optimal integral and fractional covers, Discrete Math 13 (1975), 383–390], and V. Chvatal [A greedy heuristic for the set‐covering problem, Math Oper Res 4(3) (1979), 233–235] to get an approximate solution for the problem. We find a worst‐case bound for the heuristic similar to that for the classical problem. In addition, we introduce a general type of probability distribution for the population of the problem instances and prove that the greedy heuristic is asymptotically optimal for instances drawn from such a distribution. We also conduct computational studies to compare solutions resulting from running the heuristic and from running the commercial integer programming solver CPLEX on problem instances drawn from a more specific type of distribution. The results clearly exemplify benefits of using the greedy heuristic when problem instances are large. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005