A fast ellipsoid model for asteroids inverted from lightcurves

Research about asteroids has recently attracted more and more attention, especially focusing on their physical structures, such as their spin axis, rotation period and shape. The long distance between observers on Earth and asteroids makes it impossible to directly calculate the shape and other parameters of asteroids, with the exception of Near Earth Asteroids and others that have passed by some spacecrafts. Photometric measurements are still generally the main way to obtain research data on asteroids, i.e. the lightcurves recording the brightness and positions of asteroids. Supposing that the shape of the asteroid is a triaxial ellipsoid with a stable spin, a new method is presented in this article to reconstruct the shape models of asteroids from the lightcurves, together with other physical parameters. By applying a special curvature function, the method calculates the brightness integration on a unit sphere and Lebedev quadrature is employed for the discretization. Finally, the method searches for the optimal solution by the Levenberg-Marquardt algorithm to minimize the residual of the brightness. By adopting this method, not only can related physical parameters of asteroids be obtained at a reasonable accuracy, but also a simple shape model of an ellipsoid can be generated for reconstructing a more sophisticated shape model.

The forward and inverse problem of cardiac magnetic fields based on concentric ellipsoid torso-heart model

This paper constructs a concentric ellipsoid torso-heart model by boundary element method and investigates the impacts of model structures on the cardiac magnetic fields generated by both equivalent primary source—a current dipole and volume currents.Then by using the simulated magnetic fields based on the torso-heart model as input,the cardiac current sources—an array of current dipoles by optimal constrained linear inverse method are constructed.Next, the current dipole array reconstruction considering boundaries are compared with that in an unbounded homogeneous medium.Furthermore,the influence of random noise on reconstruction is also considered and the reconstructing effect is judged by several reconstructing parameters.

An Automated Model for Fitting a Hemi-Ellipsoid and Calculating Eigenvalues Using Matrices

Ellipsoid modeling is essential in a variety of fields, ranging from astronomy to medicine. Many response surfaces can be approximated by a hemi-ellipsoid, allowing estimation of shape, magnitude, and orientation via orthogonal vectors. If the shape of the ellipsoid under investigation changes over time, serial estimates of the orthogonal vectors allow time-sequence mapping of these complex response surfaces. We have developed a quantitative, analytic method that evaluates the dynamic changes of a hemi-ellipsoid over time that takes data points from a surface and transforms the data using a kernel function to matrix form. A least square analysis minimizes the difference between actual and calculated values and constructs the corresponding eigenvectors. With this method, it is possible to quantify the shape of a dynamic hemi-ellipsoid over time. Potential applications include modeling pressure surfaces in a variety of applications including medical.

General expression of double ellipsoidal heat source model and its error analysis

In order to analyze the maximum power density error with different heat flux distribution parameter values for double ellipsoidal heat source model,a general expression of double ellipsoidal heat source model was derived from Goldak double ellipsoidal heat source model,and the error of maximum power density was analyzed under this foundation. The calculation error of thermal cycling parameters caused by the maximum power density error was compared quantitatively by numerical simulation. The results show that for guarantee the accuracy of welding numerical simulation,it is better to introduce an error correction coefficient into the Goldak double ellipsoidal heat source model expression. And,heat flux distribution parameter should get higher value for the higher power density welding methods.

Modelling Orthometric Heights from a Combination of Ellipsoidal Heights and Gravimetric Geoid Model in Rivers State, Nigeria

Many applications in geodesy, hydrography and engineering require geoid-related heights. Spirit leveling which is the traditional means of obtaining geoid- or mean sea level-related heights is slow, time-consuming and costly. Global Navigation Satellite Systems (GNSS) offer faster and relatively cheaper way of obtaining geoid-related heights when geoidal undulation is applied to ellipsoidal heights. However, difficulties involved in determining acceptable geoid height have seriously hampered the application of GNSS for leveling in Rivers State, thus necessitating the need to develop an acceptable geoid model which will serve as a means of conversion of GNSS-delivered ellipsoidal heights to their orthometric heights equivalent. In pursuance of this objective, a detailed gravimetric geoid has been evaluated for Rivers State, Nigeria. The computation of the geoid was carried out by the traditional remove-restore procedure. The Earth Geopotential Model 2008 (EGM08) was applied as the reference field for both the remove and restore parts of the procedures;spherical Fast Fourier Transform (FFT) was employed for the evaluation of the Molodenskii’s integral formula for the height anomaly, (ζ) to yield the quasi-geoid;while the Residual Terrain Modelling (RTM) was done by prism integration. The classical gravimetric geoid over Rivers State was obtained from the rigorously evaluated quasi-geoid by adding the quasi-geoid to geoid (N?- ζ) correction it. The minimum and maximum geoid height values are 18.599 m and 20.114 m respectively with standard deviation of 0.345 m across the study area. Comparison of the gravimetric geoidal heights with the GPS/Leveling-derived geoidal heights of 13 stations across Rivers State, Nigeria showed that the absolute agreement with respect to the GPS/leveling datum is generally better than 7 cm root mean squares (r.m.s) error. Results also showed that combining both GPS heights and the computed Rivers State geoid model can give orthometric heights accurate to 3 cm post-fit using a 4-parameter empirical model. The geoid model can thus serve as a good alternative to traditional leveling when used with GPS leveling, particularly for third order leveling in the study area.

基于广义超椭球模型的结构非概率可靠性指标

非概率凸集合模型仅需获知结构不确定性的范围或界限来度量结构可靠性,因而适用于小样本不确定性结构工程问题.针对广义超椭球模型,对其非概率可靠性度量问题进行了研究.首先,提出了基于广义超椭球模型的简单非概率可靠性指标,定义为结构功能函数的均值与离差之比,并讨论了该可靠性指标的不一致性问题.其次,为克服上述不一致性问题,提出了一种比例因子非概率可靠性指标,定义为不确定域向外扩大或向内收缩时,失效面与不确定域接触的最小比例因子.最后,通过3个工程算例分析验证了所提非概率可靠性指标的有效性和可行性.

Q460C钢缺口板的疲劳裂纹萌生寿命计算模型和总疲劳寿命计算

基于位错随循环加载次数的增加加速移动、聚合形成疲劳裂纹的试验事实,假设疲劳裂纹萌生速率是循环加载次数的单调递增幂函数,通过积分推导出疲劳裂纹萌生寿命计算模型。Q460C钢缺口板的疲劳试验结果显示,疲劳裂纹萌生寿命、扩展寿命和总疲劳寿命均随应力幅和名义最大应力的降低而增加,疲劳裂纹形成寿命与总疲劳寿命的比值为0.82~0.90。我国《钢结构设计标准》建议的总疲劳寿命计算式的计算误差为-17.0%~+84.9%。以椭球面断裂模型作为裂尖开裂判据,对Q460C钢缺口板的疲劳裂纹扩展进行了理论计算和数值模拟。以疲劳裂纹萌生处应变溢出时裂纹长度0.05 mm作为疲劳裂纹萌生临界尺寸,标定的Q460C钢缺口板的疲劳裂纹萌生寿命计算式、扩展寿命计算式和总疲劳寿命计算式的计算误差分别为-15.0%~-1.2%、-12.4%~+2.8%和-12.1%~-1.4%。

基于椭球体建模的多机器人碰撞检测方法研究

多机器人协同工作共享的工作空间使得机器人彼此之间存在交互运动,这将不可避免地导致机器人在运动过程中发生碰撞现象,一旦碰撞发生就会造成严重的操作事故,所以碰撞检测是多机器人协作技术中重要的环节之一。针对多机器人碰撞检测问题,主要研究基于离散的碰撞检测,在规划的路径上划分时间步,反复地进行静态碰撞检测,从而完成机器人在运动过程中的碰撞检测。针对基于椭球体建模的多机器人碰撞检测问题,采用椭球体包围机器人连杆、关节等结构,获取空间椭球体间最短距离来判断机器人间是否有碰撞发生。针对椭球体间最短距离的求解,采用基于椭球坐标系的最短距离求解算法,以其中一椭球体中心为原点和椭球的半轴长建立局部椭球坐标系,利用等高面的概念来求解另一椭球体到椭球坐标系原点的最短距离,计算效率更快。对机器人结构参数进行初始化,并提取规划路径的空间位置参数,在路径上划分时间步,在每一个时间步上反复调用碰撞检测算法函数,从而获取机器人运动过程中各个离散点的最短距离,最终得到最短距离变化曲线,进行碰撞检测。并通过一个仿真算例验证了此方法的有效性。

基于超椭球Markov的列车控制中心剩余使用寿命预测

为研究设备可用度对列车控制中心(TCC,Train Control Center)的影响和预测TCC的剩余使用寿命(RUL,Remaining Useful Life),降低TCC的故障发生率,确保车辆安全运行,构建TCC动态故障树模型。通过引入Markov理论,将其转化为Markov模型,设计了TCC可用度评估与RUL预测方法;考虑了TCC的失效率和共因失效,利用D-S(Dempster-Shafer)证据理论对失效数据作数据融合处理,得到TCC设备初始故障区间概率;在此基础上,采用超椭球模型约束设备初始故障区间概率,得到更加精确的底事件故障区间概率;画出Markov状态转移图,用矩阵推导出TCC可用度和RUL的函数关系式,且对可用度的计算还考虑了维修因素。以兰州—乌鲁木齐客运专线某TCC数据作为分析案例,用该方法计算TCC及其各设备的可用度,并预测TCC的RUL。结果表明:与通用方法相比,评估结果相同,但评估信息更丰富。

工程结构椭球凸集模型可靠度的二次型计算方法研究

工程结构概率可靠度在理论上已经建立了完整的计算体系,但在实际工程应用中却停留在近似或半经验阶段。对于既有工程结构的可靠度评估,由于测试数据有限,采用椭球凸集模型可靠度进行评估有很高的工程价值和广泛的应用前景。椭球凸集模型可靠度有很多种不同的定义,但无论何种定义,如果完全脱离概率可靠度与失效概率的基本假定,则很难与现在基于概率可靠度评估方法的主流实现有效的衔接。从多维正态联合概率密度出发,推导了斜椭球方程及其标准化方法,同时结合极限状态方程,给出了椭球凸集模型可靠度与概率可靠度之间的数学关系。算例表明,得出的特殊简化情况下的椭球凸集模型可靠度计算方法和几何解释,可进一步推动该类可靠度在工程中的应用。

Comparison of Construction Method for DEM Simulation of Ellipsoidal Particles

Discrete element model was developed to simulate the ellipsoidal particles moving in the moving bed.Multi-element model was used to describe a ellipsoidal particle,the contact detection algorithm of ellipsoidal particle was developed,and both contact force and gravity force were considered in the models.The simulation results were validated by our experiment.Three algorithms for representing an ellipsoidal particle were compared in macro and micro aspects.The results show that there exists big difference in the microscopic parameters such as kinetic energy,rotational kinetic energy,deformation,contact force and collision number which leads to the difference of macroscopic parameters.The relative error in the discharge rate and tracer particle position is the largest between 3-tangent-element representation and experimental results.The flow pattern is similar for the 5-element and 3-intersection representations.The only difference is the discharge rate of 5-element representation is larger than the experimental value and that of the 3-intersection representation has the contrary result.Finally the 3-intersectionelement representation is chosen in the simulation due to less computing time than that of the 5-element representation.

Mathematical Model of Anisotropy of Magnetic Susceptibility (AMS)

Magnetic susceptibility of natural rocks and ores is important in many applications. In a few rock types magnetic susceptibility is independent of the direction in which a weak magnetic field is applied. Such rocks are magnetically isotropic. In most rock types, however, the magnitude of magnetic susceptibility in a constant weak field depends on the orientation of the magnetic field applied. Such rocks are magnetically anisotropic and such directional variation in magnetic susceptibility with these rocks is termed as anisotropy of magnetic susceptibility (AMS). Although attempts have been made on describing AMS using mathematical models, there is still a need to present a more consistent and united mathematical process for AMS. This paper presents a united AMS model by rationalizing the existing pieces of different AMS models through a consistent approach. A few examples of AMS from some types of natural rocks and ores are also presented to substantiate this united AMS model.

Continuum Constitutive Modeling for Isotropic Hyperelastic Materials

The partial differential equation for isotropic hyperelastic constitutive models has been postulated and derived from the balance between stored energy and stress work done. The partial differential equation as a function of three invariants has then been solved by Lie group methods. With geometric meanings of deformations, the general solution boils down to a particular three-term solution. The particular solution has been applied for several isotropic hyperelastic materials. For incompressible materials, vulcanized rubber containing 8% sulfur and Entec Enflex S4035A thermoplastic elastomer, three coefficients have been determined from uniaxial tension data and applied to predict the pure shear and equibiaxial tension modes. For a slightly compressible rubber material, the coefficients have also been extracted from the confined volumetric test data.

Numerical evaluation of overestimation of the interface thickness around ellipsoidal particle

When interfacial layers are viewed as a separate phase,the interface thickness plays an essential role in assessing physico-mechanical properties of particulate materials.However,the interface thickness from sectional analysis is often overestimated,due to the irregularity of surface textures of grains in opaque materials that gives rise to the normal of a cross-sectional plane non-perpendicular to the surface of grains.Hence,the determination of the overestimation degree is very critical to precisely obtain the interface thickness.This article develops a numerical model for the overestimation degree of the interface thickness around an ellipsoidal grain with an arbitrary aspect ratio,by applying an accurate sectional analysis algorithm,and quantitative stereology and geometrical probability theories.Furthermore,on the basis of the developed numerical model,the influence of ellipsoidal particle shape on the overestimation degree is quantitatively characterized.

沙尘气溶胶粒子多波长退偏振特性仿真研究

采用OPAC(Optical Properties of Aerosols and Clouds)模型提供的沙尘粒子谱分布和复折射率参数,结合多个入射波长,对群体沙尘气溶胶粒子的退偏振比进行了数值模拟计算。计算获得1064 nm、532 nm和355 nm入射波长下,不同轴比超椭球模型的沙尘气溶胶粒子群体的退偏振比分别为0.317,0.397和0.446,其中1064 nm波长的仿真结果与实际观测结果一致性最好,其次是532 nm波长的仿真结果,355 nm波长的仿真结果和实际观测结果有较大差异,其可能原因为采用了相同数目偶极子导致计算误差增大。本仿真研究中建立的非球形粒子散射模型和数值计算方法,为深入理解沙尘气溶胶光散射特性和研制多波长偏振激光雷达提供了理论基础。同时,多波长偏振探测也为气溶胶混合态和污染型气溶胶生成机理研究提供了重要的技术手段。

基于面磁矩分布的潜艇磁场计算

潜艇磁场的单个磁偶极子模型,在计算外空间磁场分布时与实际情况误差较大,为提高模型准确度,本文优化潜艇磁场的计算方法,将潜艇磁矩看作均匀分布于壳体上的无限个磁偶极子,提出并定义了面磁矩密度假设。通过求解潜艇表面上磁矩微分元在场点的磁场积分,得到基于面磁矩分布的潜艇磁场计算数学模型。经过对比分析表明,该模型能够更准确地描述潜艇磁场的空间分布特性,以及潜艇磁异常随着探测距离的变化情况。

基于多岛遗传算法的燃料电池汽车模糊控制策略优化

针对某款中型燃料电池物流车,基于MATLAB/SIMULINK搭建了整车前向仿真模型。根据功率跟随控制逻辑以及燃料电池汽车控制原则制定模糊规则,建立了双输入单输出Mamdani型模糊控制策略。为提高仿真效率,利用敏感性分析从23个设计变量中筛选出12个对结果影响较大的变量,建立了高精度椭球基神经网络近似模型作为优化的基础。针对模糊控制隶属函数的制定主观性较大的问题,采用多岛遗传算法优化隶属函数。仿真结果表明:优化后燃料电池系统输出功率更加平稳,百公里等效氢耗较优化前降低了8.4%,提高了整车经济性。

基于超高阶地球重力场模型的GNSS高程转化方法

为了将全球卫星导航系统(GNSS)得到的大地高直接应用于工程建设中,需要将大地高转换为正常高,基于5种超高阶地球重力场模型结合改进的“移去-拟合-恢复”法开展了GNSS高程转换方法研究,对实验结果的对比分析表明:在实验测区内,利用SGG-UGM-2地球重力场模型直接计算得出的高程异常值与真实高程异常的符合程度更高,中误差为±0.009 3 m.当采用“移去-拟合-恢复法”后,利用XGM2019e_2159地球重力场模型的高程异常拟合效果更优,中误差、极差、偏度值与峰度值最小,分别为±4.786 6 mm、18.875 7 mm、-0.648 8、0.887 8.

一种地球表面目标无源定位算法

基于WGS-84地球椭球体模型,研究并提出一种对流层散射效应下的超视距无源定位算法,能够对地球表面目标进行精确时差定位,并推导出相关计算公式。通过计算机仿真试验验证对比所提算法与现有技术在不同目标距离时的定位性能。仿真结果表明,所提算法的定位误差优于现有技术。

改进的非概率可靠度模型及应用

非概率可靠性指标本质上是一个用于评估结构安全的“指数”,缺乏概率化的解释,当非概率可靠性指标小于1时难以判断结构的安全性。非概率集合可靠度其本质是在非概率可靠性指标小于1的情况下对结构可靠性的度量,强调支撑区域与失效区域重叠的情况,并隐含均匀分布假设,这显然与实际不符合。本文进一步研究了非概率可靠性模型,考虑了基本变量在不确定域内部的分布情况,并改进了非概率可靠度模型。基于改进的非概率可靠度模型推导了非概率可靠度与概率可靠度的关系,基于此建立了非概率可靠性指标与概率可靠性指标的数学转换关系。最后,建立了基于改进的非概率可靠度模型非概率可靠性指标与概率可靠性指标的数学关系的可靠性评估方法。该方法提供了非概率可靠性指标小于1时,非概率凸模型的非概率可靠性分析的概率化评估结果,避免了在基本变量的原始样本数据不足情况下进行可靠性评估结果的不准确和非概率可靠性评估结果偏于保守而造成的工程浪费。