级数证明问题的几种处理方法

通过有关级数证明的几个例题，提出了思考和分析问题几种常用的方法。特别是对一般项为抽象形式的级数证明，更要思路开阔，根据所给的条件确定解决问题的不同方法。在级数的一般项中含有参数时，要对参数取值的不同情况进行讨论，才能得到完整的结果。最后介绍了一致收敛性质在证明问题中的应用，尤其当级数的一般项由定积分表示时，一致收敛级数的逐项微分、逐项积分的性质经常会用到。     

遥测数据时间序列滑动窗口动态分割技术

经由传感器采集的航天器遥测数据是产品验证、算法检验、数据挖掘等学科和方向重要的数据来源之一。由于原始测量数据采集密度高、信息量大,通常采用滑动窗口技术进行逐段处理和算法应用。但当滑动窗口的宽度固定时,数据的局部信息不能被充分提取出来;为此,提出遥测时序滑动窗口的动态分割流程。仿真结果表明:提出的时序分割和窗口宽度计算方法,可以根据数据自身的特点得到更加准确合理的非等长窗口集合;在保持曲线线段曲率的基础上,滑动窗口动态计算方法可以极大地提取拐点信息,合理地给出窗口宽度,对数据进行了简化与提纯,降低了建模难度,为下一步聚类分析、曲线匹配等工作提供了技术支持,提高了遥测数据的诊断与分析效率。     

Modeling Multifractality of the Solar Wind

The question of multifractality is of great importance because it allows us to investigate interplanetary hydromagnetic turbulence. The multifractal spectrum has been investigated with Voyager (magnetic field) data in the outer heliosphere and with Helios (plasma) data in the inner heliosphere. We use the Grassberger and Procaccia method that allows calculation of the generalized dimensions of the solar wind attractor in the phase space directly from the cleaned experimental signal. We analyze time series of plasma parameters of the low-speed streams of the solar wind measured in situ by Helios in the inner heliosphere. The resulting spectrum of dimensions shows a multifractal structure of the solar wind attractor. In order to quantify that multifractality, we use a simple analytical model of the dynamical system. Namely, we consider the generalized self-similar baker’s map with two parameters describing uniform compression and natural invariant measure on the attractor of the system. The action of this map exhibits stretching and folding properties leading to sensitive dependence on initial conditions. The obtained solar wind singularity spectrum is consistent with that for the multifractal measure on the weighted baker’s map.     

平面动力系统的ω（α）极限集的一些性质

本文论述了平面动力系统的ω(α)极限集在轨道有界时的一些性质，并对轨道无界情形下其极限集的结构做了一些初步研究。     

低轨卫星缺失时序数据的模式识别方法

在航天应用中，低轨卫星经常会由于原始数据缺失而影响卫星时序数据模式识别结果，降低准确率。针对该问题提出了一种新型MR-GRU模型，可有效处理缺失时序数据，并获得较好的模式识别准确率。区别于传统模型的补全缺失数据的方法，MR-GRU模型直接在缺失时序数据上运用循环神经网络进行训练，对传统门控循环单元结构进行了改进，增加了两个新变量：掩蔽项和衰减项。掩蔽项作用于输入，衰减项作用于输入和隐层单元输出。MR-GRU模型不仅能够保持时序数据固有的时间特性，还能有效提高模式识别精度。在卫星时序数据上的模式识别试验表明，MR-GRU模型准确率优于传统模型。     

基于有限Fourier级数的航天器转移轨迹设计

针对航天器小推力转移轨迹的初始设计问题，利用基于三阶Fourier级数的设计方法实现了航天器小推力的多圈转移。同时，基于有限Fourier级数的形状法，对具有多个约束条件的小推力多圈转移轨迹进行了优化设计。选取了共面同轴同偏心率的初始和末端轨道位置，对所提出的方法进行了仿真验证。结果表明：与改进逆五阶多项式形状法相比，所提出的方法虽然增加了转移时间，但当转移圈数为5圈、有限Fourier级数的项数为10时，可减少将近75%的转移速度增量，同时大大减小了所需的最大推力加速度的值。     

Evaluation of SARAL/AltiKa performance using GNSS/IMU equipped buoy in Sajafi,Imam Hassan and Kangan Ports

Performance of SARAL/AltiKa mission has been evaluated within 2016 altimeter calibration/validation framework in Persian Gulf through three campaigns conducted in the offshore waters of Sajafi, Imam Hassan and Kangan Ports, while the altimeter overflew the passes 470, 111 and 25 on 13 Feb, 7 March and 17 June 2016, respectively. As the preparation, a lightweight buoy was equipped with a GNSS receiver/choke-ring antenna and a MEMS-based IMU to measure independent datasets in the field operations. To obtain accurate sea surface height (SSH) time series, the offset of the onboard antenna from the equilibrium sea level was predetermined through surveying operations as the buoy was deploying in the onshore waters of Kangan Port. Accordingly, the double-difference carrier phase observations have been processed via the Bernese GPS Software v. 5.0 so as to provide the GNSS-derived time series at the comparison points of the calibration campaigns, once the disturbing effects due to the platform tilt and heave have been eliminated. Owing to comparing of the SSH time series and the associating altimetry 1?Hz GDR-T datasets, the calibration/validation of the SARAL/AltiKa has been performed in the both cases of radiometer and ECMWF wet troposphere corrections so as to identify potential land contamination. An agreement of the present findings in comparison with those attained in other international calibrations sites confirms the promising feasibility of Persian Gulf as a new dedicated site for calibration/validation of ongoing and future altimetry missions.     

风-雨耦合环境超高层三塔连体建筑雨压分布研究

以中国东南沿海某超高层三塔连体建筑为研究对象，以风-雨双向耦合算法为核心，基于计算流体动力学技术采用连续相和离散相模型进行风场和雨场的迭代模拟。首先基于9种风雨组合工况进行三塔连体建筑非定常脉动风场模拟，探讨超高层三塔连体建筑平均风压分布、表面速度流线和流场干扰机理。然后对比研究不同风雨组合工况下主塔表面雨滴附着数量、雨滴冲击力和雨压系数的分布规律，揭示风-雨耦合场中结构表面速度流线、雨滴运行轨迹和最终速度的作用机理。最后提炼出超高层三塔连体建筑最不利风-雨组合工况，并给出对应的雨压系数取值建议。研究表明：风-雨耦合环境下超高层连体建筑迎风面雨荷载作用最为显著，此时雨荷载与风荷载最大比值可达23.81%，局部测点最大雨压系数达到0.301，100 a重现期风速和强大暴雨组合为风-雨耦合作用的最不利组合工况。     

Shaping low-thrust trajectories with thrust-handling feature

Shape-based methods are becoming popular in low-thrust trajectory optimization due to their fast computation speeds. In existing shape-based methods constraints are treated at the acceleration level but not at the thrust level. These two constraint types are not equivalent since spacecraft mass decreases over time as fuel is expended. This paper develops a shape-based method based on a Fourier series approximation that is capable of representing trajectories defined in spherical coordinates and that enforces thrust constraints. An objective function can be incorporated to minimize overall mission cost, i.e., achieve minimum $\mathrm{\Delta }V$. A representative mission from Earth to Mars is studied. The proposed Fourier series technique is demonstrated capable of generating feasible and near-optimal trajectories. These attributes can facilitate future low-thrust mission designs where different trajectory alternatives must be rapidly constructed and evaluated.