铁磁性设备补偿磁场的数学模型及其应用

研究用永磁体对铁磁性设备进行磁场补偿的问题,建立了补偿磁场的数学模型.将设备划分成若干个小长方体后,基于磁矩量法建立了数学模型,并对补偿磁场进行拟合.在计算模型中的耦合系数矩阵时,用多个点的平均值作为耦合系数的有效值,提高了计算结果的可靠性和稳定性.并且,针对永磁体距离设备很近时,设备呈现出的非线性磁化特性,通过优化方法求解各个单元的等效磁化率,这种方法不需要知道铁磁材料的磁化曲线和设备结构,便于计算和实际应用.最后,通过实验设计与数值计算,得到了永磁体对设备进行补偿的磁场分布,模型计算结果与实际测量数据误差11%以内,这说明该模型能够满足工业要求,具有实际应用价值.     

铁磁性设备补偿磁场的数学模型及其应用

研究用永磁体对铁磁性设备进行磁场补偿的问题,建立了补偿磁场的数学模型.将设备划分成若干个小长方体后,基于磁矩量法建立了数学模型,并对补偿磁场进行拟合.在计算模型中的耦合系数矩阵时,用多个点的平均值作为耦合系数的有效值,提高了计算结果的可靠性和稳定性.并且,针对永磁体距离设备很近时,设备呈现出的非线性磁化特性,通过优化方法求解各个单元的等效磁化率,这种方法不需要知道铁磁材料的磁化曲线和设备结构,便于计算和实际应用.最后,通过实验设计与数值计算,得到了永磁体对设备进行补偿的磁场分布,模型计算结果与实际测量数据误差在11%以内,这说明该模型能够满足工业要求,具有实际应用价值.     

黏性分层流中椭球体俯仰振荡研究

以黏性密度分层流下椭球体自由俯仰振荡衰减过程为研究内容,建立了密度连续分层流数值计算模型.通过对经典小球黏性绕流场的数值模拟和增阻系数的计算验证了数值模型的正确性.以初始45°攻角下的椭球体俯仰振荡过程为研究对象,采用基于Aitken亚松弛适应算法的双向流固耦合方法,数值模拟了不同内Froude(弗汝德)数Fri下椭球体俯仰衰减振荡的动态绕流场.数值研究结果表明,俯仰振荡将上下搅动周围流体,在椭球体上下两侧对称形成四个密度涡环,密度的垂向分层限制了涡环的垂向传播,也加速了涡环的消失,这种限制助长了水平运动的发展,远场尾涡流场将以水平波动的形式传播.在较高的内Froude数Fri和Reynolds(雷诺)数Re下,双向耦合抑制了数值震荡.研究还发现,随着来流速度的增加,阻力系数不增反降,这说明,对于自由俯仰振荡的椭球体,负阻尼现象仍然会出现.     

一种具有区间数信息的多目标指派方法

针对具有区间数信息的多目标指派问题,给出了一种指派方法。首先,将不同类型目标的区间数损益矩阵规范化为区间数成本矩阵,并应用区间数运算法则构建区间数多目标指派问题的总成本矩阵。然后,通过事先定义的任意两个区间数的序关系,将区间数指派问题优化模型转化为一个双目标优化模型,并采用线性加权法将其转化为单目标优化模型来进行求解,同时还考虑了如何处理人员数量与任务数量不相等的情形的指派问题;最后,通过一个实例分析说明了本文给出方法的可行性和有效性。本文的方法丰富了已有的求解方法,具有实际应用价值。     

基于动态遗传算法的共享配送模式研究

针对传统配送中配送车辆装载率低、车辆数量多及配送成本高等问题,提出不同类型零售商资源共享的城市配送优化方法,并考虑配送中的车辆油耗与不确定需求等问题。以总配送成本最低为目标建立模型,利用基于动态参数的改进遗传算法对模型进行求解。最后,通过算例对共享配送模式与算法进行测试。结果表明,共享配送模式能够有效减低车辆数量、提高装载率及降低配送成本,同时改进遗传算法能够高效、准确对模型求解。     

一种新的有杆抽油泵功图诊断模型及计算方法

通过对多级杆柱上的微元体进行动力学分析,对现有的Gibbs模型进行了改进,建立了一个新的有杆抽油泵功图诊断数学模型.采用隐式差分格式和变步长有限差分格式对模型进行求解,得到了接箍上、下分界面处和抽油杆均质段任意位置处的位移及载荷表达式,推导了等效阻尼系数的计算公式,建立了相应的迭代算法来计算井下泵功图.以某油井地面示功图为例,利用该模型进行了实例计算,与Gibbs方法对比结果表明,该模型及算法得到的泵功图更接近实际.     

建材中VOCs扩散系数和分配系数的模型研究

Bodala,运用静态双仓法建立的测定干建材中VOCs扩散系数和分配系数的数学模型是合理的,有一定的应用价值.但该模型假设低浓度仓中VOCs的初始浓度为零,限制了模型的应用范围.针对使用VOCs液体为污染源且建材透气性较好的条件,作出合理的假设,构建了VOCs在建材中扩散的数学模型.采用LaplaceCarson变换详细求解模型,得出计算VOCs扩散系数的方法,并运用两组数据对模型进行了比较分析,结果表明优化后的模型有一定的实用性和可行性.     

乘用车物流运输计划问题的建模研究

首先针对不同类型、数量乘用车的物流运输问题,构建整数线性规划模型,并对模型进行逐层优化求解,通过MATLAB编写通用程序实现计算;在此基础之上,为解决不同目的地的运输要求,采用启发式逐层优化算法进行求解;最后考虑多因素的实际问题,建立分层划分模型,提出构造型分层划分启发式算法求解.计算表明,所建模型计算结果良好,实现了对乘用车物流运输计划问题的优化.     

生鲜类物流配送网络选址-路径优化问题研究

为解决生鲜类物流配送网络选址-路径优化问题,构建了基于服务质量最优化、物流节点建造成本及物流运营服务成本最小化的多目标两层级物流配送网络选址-路径优化问题数学模型,并通过改进遗传算法求解最优方案.对遗传算法中的算子进行优化,解决了传统遗传算法求解过程中无法求得全局最优解以及易陷入局部最优解的现象.通过选取通州区部分区域为背景进行模型验证,得出优化后成本节约了15.71%,说明该模型具有良好的参考价值.     

航线联盟下航空货运网络枢纽点选址问题研究

本文研究航空联盟下航空货运网络的枢纽点选址问题(HLP),基于枢纽点的数量及位置随机与容量的限制。首先引入航线联盟选择概率函数,确定不同航段上的航线自营运输或外包运输的概率;其次根据选址中心法则,以网络总成本最小化为目标,建立枢纽点选址模型;再次采用改进的免疫混沌遗传算法求解模型;最后,以顺丰航空公司案例进行实例分析。结果表明:1)本文改进的算法较免疫混沌遗传算法并与免疫遗传算法及CPLEX结果对比,发现本文设计的算法有较强的收敛性和计算速度,且计算结果与CPLEX求解器求解结果相差不大;2)枢纽点数量不确定时,枢纽点的位置多集中在东部城市;3)航空公司选择联盟环境可以大大降低运营成本,航空公司为提高自身利润,应考虑加入联盟,从而降低自身成本。     

Pivot versus interior point methods: Pros and cons

Linear optimization (LO) is the fundamental problem of mathematical optimization. It admits an enormous number of applications in economics, engineering, science and many other fields. The three most significant classes of algorithms for solving LO problems are: pivot, ellipsoid and interior point methods. Because ellipsoid methods are not efficient in practice we will concentrate on the computationally successful simplex and primal–dual interior point methods only, and summarize the pros and cons of these algorithm classes.     

Automatic and adaptive calibration of 3D field sensors

Embedded sensors are an emerging trend in mobile consumer devices. Calibration of the sensors in this environment can be prohibitively difficult for the user. We propose an automatic calibration algorithm that can be used for any three-dimensional sensor sensing some external field. In particular, it is suitable for calibrating a three-axis magnetometer. The algorithm is based on recursive fitting of an ellipsoid to collected samples from the sensor. It can adaptively update the calibration parameters and is completely invisible to the user.     

Clustering intelligent transportation sensors using public transportation

Advanced transportation sensors use a wireless medium to communicate and use data fusion techniques to provide complete information. Large-scale use of intelligent transportation sensors can lead to data bottlenecks in an ad-hoc wireless sensor network, which needs to be reliable and should provide a framework to sensors that constantly join and leave the network. A possible solution is to use public transportation vehicles as data fusion nodes or cluster heads. This paper presents a mathematical programming approach to use public transportation vehicles as cluster heads. The mathematical programming solution seeks to maximize benefit achieved by covering both mobile and stationary sensors, while considering cost/penalty associated with changing cluster head locations. A simulation is developed to capture realistic considerations of a transportation network. This simulation is used to validate the solution provided by the mathematical model.     

A numerical model for magnetic chromatography

In this paper, we present details of a mathematical model for magnetic chromatography (MC) systems where strong distorted magnetic fields are used to separate particles from a colloidal mixture. The model simulates the effect of magnetic field gradients on particle motion, and includes calculation of the fluid flow, magnetic field, and particle concentration field. It is based on the finite-volume method (FVM) and uses an expanding-grid technique to handle domains with large aspect ratios. The model has been validated against the results from an analytical model. The numerical model has been used to simulate the performance of a real MC system under various operating conditions.     

An Iterative Exact Solution for the Dual Power Management Problem in Wireless Sensor Network

We study the dual power management problem in wireless sensor networks. Given a wireless sensor network with two possible power levels (heigh and low) for each sensor, the problem consists in minimizing the number of sensors assigned heigh power while ensuring the connectivity of the network. We formulate the problem by a binary integer programming model to minimize the total power consumption. Since the problem is NP-complete, we provide an iterative approximation based on iterative methods in combinatorial optimization. We solve the separation subproblem as a minimum spanning tree.     

基于遗传算法的多通道密集式移动货架订单拣选研究

密集式移动货架越来越多地应用到仓储实践中,提高了仓储空间利用率,但增加了订单拣选的时间成本。本文根据密集式移动货架的仓储布局特点,针对多条通道可同时打开的情况,将货架移动时间转换成通道移动距离进行计算,提出了多条通道依次移动的优化规则,以整批订单拣选所耗费的总时间最少为目标,建立了订单拣选顺序优化的数学模型。针对该模型的特点,设计了实数编码且全局寻优的遗传算法,并进行了不同规模的算例模拟。计算结果表明,该算法具有较强的适用性,针对不同规模的问题,均有显著的优化效果;货架数量、订单数量以及移动通道数量的小幅度增减,将会导致总拣选时间较大幅度的波动;多条移动通道初始位置居于中部或均匀分散,总拣选时间略优于其集中于仓储系统一端。     

Flow around an ellipsoid of revolution in a harmonic coaxial vector field

We give an integral equation defining a coaxial magnetic field near the surface of a superconductive axisymmetric body and the velocity of the liquid near the surface of an axisymmetric body situated coaxially to the flow of an ideal liquid. Using this equation in the case when the axisymmetric magnetic field before the placement of an ellipsoid of revolution coaxially to the field changed along the axis by a polynomial law, we analytically define the densities of the surface current and the force with which the magnetic field acts on the ellipsoid. Also the velocity of the liquid is determined near the surface of the ellipsoid of revolution and the force acting on the ellipsoid placed coaxially in the flow of an ideal liquid when the velocity of the liquid before the placement of the ellipsoid changed along the axis of symmetry by a polynomial law.     

Calculation of the magnetic field due to a bioelectric current dipole in an ellipsoid

The bioelectric current dipole model is important both theoretically and computationally in the study of electrical activity in the brain and stomach due to the resemblance of the shape of these two organs to an ellipsoid. To calculate the magnetic field B due to a dipole in an ellipsoid, one must evaluate truncated series expansions involving ellipsoidal harmonics , which are products of Lamé functions. In this article, we extend a strictly analytic model (G. Dassios and F. Kariotou, J. Math. Phys. 44 (2003), 220–241), where B was computed from an ellipsoidal harmonic expansion of order 2. The present derivations show how the field can be evaluated to arbitrary order using numerical procedures for evaluating the roots of Lamé polynomials of degree 5 or higher. This can be accomplished using an optimization technique for solving nonlinear systems of equations, which allows one to acquire an understanding of the truncation error associated with the harmonic series expansion used for the calculation. Funding was provided by the National Institute of Health, Grant No. 1RO1 DK 58697 and by the Veterans’ Affairs Research Service.     

Maximizing lifetime of a wireless sensor network via joint optimizing sink placement and sensor-to-sink routing

Wireless sensor networks typically contain hundreds of sensors. The sensors collect data and relay it to sinks through single hop or multiple hop paths. Sink deployment significantly influences the performance of a network. Since the energy capacity of each sensor is limited, optimizing sink deployment and sensor-to-sink routing is crucial. In this paper, this problem is modeled as a mixed integer optimization problem. Then, a novel layer-based diffusion particle swarm optimization method is proposed to solve this large-scaled optimization problem. In particular, two sensor-to-sink binding algorithms are combined as inner layer optimization to evaluate the fitness values of the solutions. Compared to existing methods that the sinks are selected from candidate positions, our method can achieve better performance since they can be placed freely within a geometrical plane. Several numerical examples are used to validate and demonstrate the performance of our method. The reported numerical results show that our method is superior to those existing. Furthermore, our method has good scalability which can be used to deploy a large-scaled sensor network.