基于形状法和伪谱法的小推力借力优化研究

小推力借力飞行轨道优化是一个多变量多约束的非线性优化问题,根据形状法和伪谱法,提出一种混合优化策略,分为全局优化和局部优化两个阶段进行。在全局优化阶段采用LT-PGA模型,即通过求解形状法小推力Lambert问题,搜索满足约束条件的小推力发射窗口,得到发射、借力和到达时间点。在局部优化阶段采用伪谱法得到推力控制率,用连接点设置解决借力行星处状态量的不连续问题。数值仿真结果表明,改进方法不用事先指定推力开关机序列,优化效率高,为初始设计阶段小推力借力飞行的轨道优化问题提供有益参考。     

多引力场小推力引力借力轨道设计与优化

采用序贯法设计优化小推力引力借力轨道(low-thrust gravity-assist,LTGA)时,设计步骤复杂且优化结果最优性条件难以保证.本文提出一种多引力场LTGA问题联立求解框架.首先对多引力场环境和探测器动力学模型进行统一描述和处理.设计初始化策略,利用Radau伪谱法将发射窗口、借力顺序、初始轨道搜索以及轨道优化联立求解,简化设计步骤.利用hp自适应网格精细化策略保证优化结果最优性条件.该联立框架用于求解地木转移任务,得到地球–火星–地球–木星的转移方案.本文提出的联立求解框架,简化了设计步骤,保证了优化结果的最优性条件,得到比序贯求解更优的转移方案.     

深空探测行星借力飞行轨道自动设计与仿真

深空探测任务中直接转移轨道一般需要较大的能量,借力飞行技术可以降低从地球的发射能量,经过多次天体借力到达目标星体,并可以一次探测多个天体.通过多天体的P-Rp图推测可能存在的多天体交会借力飞行方案,求解兰伯特问题,根据圆锥曲线拼接法搜索能量等高线图中匹配的C3,最后找出发射窗口.设计并研制了轨道方案与窗口自动搜索软件,通过EVEEJ的借力飞行方案,及其在STK软件中的仿真,验证设计方法的可行性及软件的正确、可靠性.给出了借力飞行技术的完整设计方法,为进行太阳系深空探测活动的行星借力飞行轨道设计提供参考.     

采用组合优化算法的深空探测轨迹优化

针对在2015年1月1日之后的10年期间,距地球三维轨迹1000万km内的1067颗行星进行探测,深空探测飞行器从地球出发,采用小推力控制,为了在10年时间内飞过的行星最多,给出了一种深空探测4-D飞行轨迹的全局优化算法,即采用静态参数＋动态参数的优化算法。经过长时间大规模的飞行数值仿真,飞行仿真出航天器的4-D最优飞行轨迹,在10年内路过了1067颗行星中的20颗行星。     

电动帆改进推力模型及深空探测性能分析

电动太阳风帆(简称电动帆)是一种利用太阳风动能冲力飞行的新兴无质损飞行器.针对电动帆传统推力模型中忽略了姿态对推力幅值影响的问题,本文推导得出了一种解析形式的改进推力模型,并与最新的多项式拟合改进推力模型进行了对比.对比结果显示两种改进推力模型数值结果很接近,但本文的解析改进推力模型形式更简单.为了重新评估电动帆在深空探测中的性能,以地球至火星的飞行任务为算例,分别采用传统推力模型和解析改进推力模型进行了电动帆轨迹优化仿真.仿真结果显示,在相同特征加速度情况下,采用改进解析推力模型完成任务所需时间,大于采用传统推力模型所用时间.上述现象的原因在于传统推力模型中忽略了姿态改变对推力加速度大小的影响,并高估了电动帆所能产生的最大推进角.     

小推力轨道转移快速优化设计

在研究电推进系统中,为满足小推力转移轨道高精度在线生成的要求,伪光谱方法在电推进小推力轨道转移优化设计中的应用。首先对小推力航天器轨道转移最优控制问题模型进行无量纲化处理,以提高优化算法求解精度。然后采用基于勒让德-高斯-兰伯特配置点的勒让德伪光谱方法,将最优控制问题离散成约束参数优化问题,再利用适于求解大尺度非线性规划问题的TOMLAB/SNOPT优化软件包进行求解。通过数值仿真计算,求解生成了满足各类约束条件的小推力转移轨道,并利用余向量映射定理及极小值原理验证了所得轨道转移控制量的最优性。结果表明,勒让德伪光谱优化算法具有对初始猜测值不敏感、收敛速度快、精度高等优点。     

遥感卫星小推力轨道转移控制

在太阳同步回归轨道遥感卫星的小推力轨道转移控制问题的研究中,小推力推进与化学推进方式有本质不同,不能再用速度脉冲的方法来设计轨道.针对推力方式不同的问题,采用了一组无奇点的春分点根数表示小推力卫星的动力学模型,从最优控制理论出发,给出了协态变量微分方程和最优推力方向,将轨道转移问题转化为非线性参数优化问题,利用非线性序列二次型规划法求解.对遥感卫星在1天回归和10天回归轨道之间的转移控制问题进行仿真,证明了方法的有效性.     

基于双模型直接配置法的航天器轨迹优化

针对有限推力航天器轨迹优化问题,提出一种HLDL双模型直接配置法将航天器的飞行轨迹划分为最大推力弧段和零推力弧段.在两种弧段上分别采用了两种不同的建模方法并利用埃尔米特插值法将最优化问题转化为非线性规划问题(NLP).给出了节点和配置点数目的选取与所在弧段的平均曲率大小成正比的法则,解决用于有限推力航天器轨迹优化所涉及的关键问题.仿真结果表明提出的方法能有效的解决飞行器轨迹优化问题并具备很强的鲁棒性.     

小推力火星探测器发射时机搜索方法

利用微分进化(DE)算法对小推力火星探测器发射时机进行搜索.首先建立了动力学方程,推导出最优化模型,然后使用两种策略采用DE算法与间接法相结合的方式对火星探测器发射机会进行了搜索,最后进行了仿真分析.研究结果表明:使用DE算法结合间接法的方式能够搜索到最优的发射机会;同时,针对所采用的发动机模型,小推力火星探测器发射机...     

弹道导弹弹道建模与仿真技术研究

在弹道导弹建模优化的研究中,针对弹道导弹防御技术仿真应用,建立了弹道导弹弹道仿真模型.首先基于最优能量椭圆弹道理论,采用优化迭代方法,考虑地球自转影响,建立了弹道导弹自由段模型,并根据导弹性能参数,建立了主动段和再入段弹道模型,从而得到从发射点到落点的包含不同飞行段特性的完整弹道模型.其次利用上述弹道模型开展仿真,得到了导弹飞行轨迹参数和二维和三维弹道演示效果.证明提出的弹道导弹仿真模型,弹道构建速度得到优化加快,能以较高的置信度反映弹道导弹运动特性,能够满足弹道导弹防御技术仿真应用要求.     

Using gravity models for the evaluation of new university site locations: A case study

A fundamental aspect of competitive spatial models is the choice behaviour of potential customers to patronize a facility. Most of the models used to describe this phenomenon are essentially based on the adaptation of Newton's law of gravitation to the economic case (gravity model).     

基于引力的孤立点检测算法

提出一种基于引力的孤立点检测算法.通过综合考虑数据对象周围的密度及数据对象之间的距离等因素对孤立点定义的影响来挖掘出数据集中隐含的孤立点.给出了与该算法相关的概念与技术,详细介绍了该算法,并用实际数据进行了实验.实验表明:该算法对数据集的维度具有很好的扩展性,能有效地识别孤立点,同时能反映出数据对象在数据集中的孤立程度.     

The effects of gravity inversion on exercise-induced spinal loading

Abstract

Changes in stature reflect the creep behaviour of the intervertebral discs when loaded and unloaded. Running, weight-training and bounding are exercises which load the spine and cause a loss in stature. Gravity-facilitated traction (inversion) has been shown to unload the spine and increase stature. This study examined the use of a gravity-inverted posture for attenuating the shrinkage induced by a bounding exercise regimen.

Eight male subjects, aged 20–26, performed the experimental protocol twice, at the same time of day (14·00 hours) with an alteration only to their 10min pre-exercise behaviour. The first occasion involved standing and the second involved gravity inversion at an angle of 50 degrees to the vertical. Prior to testing, each subject stood for a period of 20 min. Measurements of stature were taken at the beginning of the experiment, before and after the pre-exercise treatments, after the exercise period and at 5 min intervals during a 20 min standing recovery. A stadiometer, accurate to within 0·5 mm, was used to record alterations in stature. The exercise regimen consisted often sets of five standing broad jumps with 15 s recovery between each set.

Standing pre-exercise caused little change in stature, whereas, gravity inversion caused a mean increase in stature of 2·7mm (p<0·001). Exercise caused a mean shrinkage of 1·7 mm and 3·5 mm when it followed standing and gravity inversion, respectively (p<0·05). These results suggest that the benefits gained by unloading the spine are short-lived.     

Computation of gravity effects of two- and three-dimensional bodies with radial symmetry

A computer program in the form of a subroutine which computes the gravity effects of bodies with radial symmetry is described and presented. The program can be utilized in the situation of a circular disc, an infinite cylinder, a finite cylinder and for any arbitrary object which can be approximated into a set of circular discs about a common axis. The program has been applied to known situations and the results obtained are in excellent agreement with the previously known and reported ones.     

Computer programs for rapid computation of gravity effects of two-dimensional and three-dimensional bodies

A subroutine is presented which calculates the gravity effect of bodies of infinite strike length which have a polygonal cross section and uniform density. A second subroutine allows rapid calculation of end corrections, so approximating the effect of bodies of limited strike length. Modifications can be made which will allow the routines to be used for bodies asymmetrically positioned with respect to the line of observation.     

Prediction of future origin-destination matrix of air passengers by fratar and gravity models

This article presents the need to predict the future demand of the air traffic passengers for scheduled commercial airlines. To determine the passengers demand, we have proposed an algorithm for assigning the origin destination (OD) matrix of the passengers air traffic between different airports. In order to realize the problem, we assume two different circumstances. Firstly, we predicted the total air traffic passengers with the target year. Secondly, we distributed the air traffic passengers between airports according to geographic location using the gravity and fratar models. The effectiveness of proposed method was examined through an air transportation network in Sumatra island (in Indonesia) as a case study.     

A conditional p-hub location problem with attraction functions

We formulate the competitive hub location problem in which customers have gravity-like utility functions. In the resulting probabilistic model, customers choose an airline depending on a combination of functions of flying time and fare. The (conditional) follower's hub location problem is solved by means of a heuristic concentration method. Computational experience is obtained using the Australian data frequently used in the literature. The results demonstrate that the proposed method is viable even for problems of realistic size, and the results appear quite robust with respect to the leader's hub locations.     

一种基于引力的聚类方法

将万有引力的思想引入聚类分析中,提出了一种基于引力的聚类方法GCA(Gravitybased Clustering Approach),同时给出了一种计算聚类阈值的简单而有效的方法。GCA关于数据库的大小和属性个数具有近似线性时间复杂度,这使得聚类方法GCA具有好的扩展性。实验结果表明GCA可产生高质量的聚类结果。     

重力加速度计在倾斜度测量中的应用

从基本结构、测量原理、数值计算等方面论述了重力加速度计在倾斜度测量中的应用，并对测量系统结构误差的校正进行了分析。     

An interactive FORTRAN 77 program using GKS graphics for 2.5 D modeling of gravity and magnetic data

An interactive 2.5 D gravity and magnetics modeling program has been written for an ICL PERQ 2 workstation using FORTRAN 77 and GKS graphics. All of the available hardware and software input devices are utilized through GKS to produce an easy-to-use menu-driven program. A large number of functions are controlled by the software in order than the user can concentrate on the model. A range of options also are provided for manipulating the observed anomaly. The use of FORTRAN 77 and GKS should make the program easily portable to other computer systems and graphics devices. The modular form of the program should facilitate readily further development including optimization and real time modeling, given a more powerful computer with high-speed graphics.