舰船机电系统非完备使用故障数据分析

舰船机电系统在使用维修过程中所记录的故障数据通常质量不高,信息记录不完整、不准确。针对这类不完备数据,利用图示法给出故障趋势的判定。在此基础上,分别利用齐次泊松过程、非齐次泊松过程和几何过程,对装备的历史故障数据进行分析。结果表明,几何过程产生的拟合误差最小,可预测装备的未来故障强度。     

基于区域定位重要度指标的GPS失效性分析

空间几何构型是决定GPS定位精度的关键因素之一。采用概率统计的思想,基于区域定位重要度指标算法,通过分析计算不同空间几何构型的几何精度系数,寻求对区域定位精度影响最大的卫星构型。在此基础上对GPS卫星进行重要度排序,并对GPS星座失效性进行分析。结果表明:此方法能有效找出对区域定位精度影响最大的卫星构型,并且避免了大规模仿真计算,快捷有效。     

几何分布定数截尾步加试验的最优设计

在逐步type-II结尾场合下,研究产品简单步进应力加速寿命试验的优化设计。假定产品服从几何分布,讨论了几何分布产品加速方程如何建立,利用次序统计量的大样本性质,得到相应的Fisher信息矩阵,以对数特征寿命极大似然估计的渐进方差最小为准则结合Fisher信息矩阵,给出了步进应力加速寿命试验的最优分配比例,通过模拟验证最优设计的有效性。     

新疆民俗数学文化探析

新疆民俗数学是具有鲜明民族特色、独特价值和丰富文化内涵的数学思想与思维方式的综合。新疆民俗数学较多地体现在用于造型和装饰的清真寺、民居、民族手工艺品等方面的几何纹饰上。对于民俗数学的研究,一方面是通过对这些集数学知识与传统文化于一体的“文化载体”的搜集、整理和分析,分析其蕴含的数学知识和数学思想;另一方面则关注民俗数学研究成果的教育学转化,在充分考虑新疆少数民族儿童数学认知思维特征以及数学双语教学原则、方法等的基础上,通过实现民俗数学的“课程化”,以弥补当前新疆少数民地区以“主流文化”为主导的数学课程对少数民族传统文化的“缺失”,进而推进本地区基础教育课程改革和数学教育质量的提升。     

An integral equation for the second moment function of a geometric process and its numerical solution

In this article, an integral equation satisfied by the second moment function M₂(t) of a geometric process is obtained. The numerical method based on the trapezoidal integration rule proposed by Tang and Lam for the geometric function M(t) is adapted to solve this integral equation. To illustrate the numerical method, the first interarrival time is assumed to be one of four common lifetime distributions, namely, exponential, gamma, Weibull, and lognormal. In addition to this method, a power series expansion is derived using the integral equation for the second moment function M₂(t), when the first interarrival time has an exponential distribution.     

MABAC method for multiple attribute group decision making under q-rung orthopair fuzzy environment

As the generalization of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), the q-rung orthopair fuzzy set (q-ROFS) has emerged as a more meaningful and effective tool to solve multiple attribute group decision making (MAGDM) problems in management and scientific domains. The MABAC (multi-attributive border approximation area comparison) model, which handles the complex and uncertain decision making issues by computing the distance between each alternative and the bored approximation area (BAA), has been investigated by an increasing number of researchers more recent years. In our article, consider the conventional MABAC model and some fundamental theories of q-rung orthopair fuzzy set (q-ROFS), we shall introduce the q-rung orthopair fuzzy MABAC model to solve MADM problems. at first, we briefly review some basic theories related to q-ROFS and conventional MABAC model. Furthermore, the q-rung orthopair fuzzy MABAC model is built and the decision making steps are described. In the end, An actual MADM application has been given to testify this new model and some comparisons between this novel MABAC model and two q-ROFNs aggregation operators are provided to further demonstrate the merits of the q-rung orthopair fuzzy MABAC model.     

高精度惯测组合标定误差分析

惯性测量组合(IMU)标定误差分析对于惯性导航系统性能评估、误差分配和器件设备选型具有重要意义,但目前关于高精度IMU标定误差的定量讨论很少。借助四元数旋转矢量理论建立了转台轴正交度误差和转角控制误差模型,结合IMU测量误差的表示,定量分析了一种典型多位置标定编排方式下的标定误差。仿真结果和捷联惯性导航系统的试验结果证实了标定误差分析的正确性。     

A bivariate optimal replacement policy for a cold standby repairable system with repair priority

In this article, an optimal replacement policy for a cold standby repairable system consisting of two dissimilar components with repair priority is studied. Assume that both Components 1 and 2, after repair, are not as good as new, and the main component (Component 1) has repair priority. Both the sequence of working times and that of the components'repair times are generated by geometric processes. We consider a bivariate replacement policy (T,N) in which the system is replaced when either cumulative working time of Component 1 reaches T, or the number of failures of Component 1 reaches N, whichever occurs first. The problem is to determine the optimal replacement policy (T,N)* such that the long run average loss per unit time (or simply the average loss rate) of the system is minimized. An explicit expression of this rate is derived, and then optimal policy (T,N)* can be numerically determined through a two‐dimensional‐search procedure. A numerical example is given to illustrate the model's applicability and procedure, and to illustrate some properties of the optimal solution. We also show that if replacements are made solely on the basis of the number of failures N, or solely on the basis of the cumulative working time T, the former class of policies performs better than the latter, albeit only under some mild conditions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Capacity expansion under a service‐level constraint for uncertain demand with lead times

For a service provider facing stochastic demand growth, expansion lead times and economies of scale complicate the expansion timing and sizing decisions. We formulate a model to minimize the infinite horizon expected discounted expansion cost under a service‐level constraint. The service level is defined as the proportion of demand over an expansion cycle that is satisfied by available capacity. For demand that follows a geometric Brownian motion process, we impose a stationary policy under which expansions are triggered by a fixed ratio of demand to the capacity position, i.e., the capacity that will be available when any current expansion project is completed, and each expansion increases capacity by the same proportion. The risk of capacity shortage during a cycle is estimated analytically using the value of an up‐and‐out partial barrier call option. A cutting plane procedure identifies the optimal values of the two expansion policy parameters simultaneously. Numerical instances illustrate that if demand grows slowly with low volatility and the expansion lead times are short, then it is optimal to delay the start of expansion beyond when demand exceeds the capacity position. Delays in initiating expansions are coupled with larger expansion sizes. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

微小型无人机遥感图像应用

通过给微小型无人机加装数码相机和微型INS姿态测量系统,可以同时获得对地面的遥感图像和当时无人机的姿态数据.根据传感器构像方程和几何畸变校正理论,对拍摄的图片进行几何校正.通过图像融合拼接,给出了目标地区的大面积数字影像图,最后给出了局部实验结果.