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。     

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.     

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.     

求解具有多层试验数据成败型单元混联系统可靠性近似限的信息论方法

研究了求解具有多层成败型试验数据时,系统可靠性置信下限近似解的信息论方法,给出了各层试验数据综合的方法和步骤,推导了各层数据信息论方法折合及综合的计算公式。根据单元试验信息提供的信息量与系统折合试验应提供的信息量相等的原则,将多层试验数据逐级折合为系统的等效成败型数据,导出了等效成败型数据信息论方法折合的基本公式;结合可靠性工程的基本原理,根据单个成败型单元可靠性评定的经典精确置信限方法,给出了系统可靠性置信下限的近似解。并以实例形式说明了该方法的具体应用。     

纤维缠绕结构的一种可靠性优化设计方法研究

将纽曼级数展开的蒙特卡罗随机有限元应用于具有随机因素的纤维缠绕结构的应力求解;然后利用蒙特卡罗直接比较法和蔡希布（Ｔｓａｉ－Ｈｉｌｌ）失效判据给出该结构的可靠性算式,最后建立了此类结构的可靠性优化设计迭代法,并给出了一算例。     

基于支持向量机的航空发动机滑油监控分析

提出了一种基于支持向量机的航空发动机滑油金属含量预测方法。详细分析了支持向量机用于时间序列预测的理论基础,并给出了运用支持向量回归进行多步预测的一般公式,提出了用最终预报误差(FPE)准则优化选取嵌入维数。与传统的AR预测模型相比,支持向量机由于采用了新型的结构风险最小化准则表现出优秀的推广能力。经过数值仿真得出自回归(AR)模型仅适合于短期预测;支持向量机预测推广能力强、具有较强的鲁棒性和容错性,对较长区间预测仍具有较好的效果。最后,将其应用于某型发动机滑油的铁金属含量预测,取得了较好的效果。      

CHAMP卫星加速度计标校参数序列的谱分析

给出了利用能量守恒方法求定CHAMP卫星加速度计标校参数的基本原理和算法．对2001年8月-2003年12月共约两年半的CHAMP卫星加速度计数据进行了标校,导出了尺度、偏差和偏差漂移参数的时间序列,分别采用最小二乘谱分析和抗差谱分析对这些时间序列进行了分析．结果表明,尺度、偏差和偏差漂移参数都有明显的周期变化,但各主周期项略有差异．尺度的主周期是441d、220d、126d和13．4d的周期变化,其中220d和441d的周期变化的贡献相对较大．偏差中有明显的220d、126d和13．4d周期变化,各周期变化的贡献几乎相当;偏差漂移的主周期是220d、13．4d和9d的周期变化,其中13．4d的周期变化最为显著,几乎比其他周期项变化高出一个数量级．另外尺度和偏差参数还有明显的长期变化,而偏差漂移参数的长期变化不明显．     

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.