Geometric problem solving with strings and pins

Humans solve spatial and abstract problems more easily if these can be visualized and/or physically manipulated. We analyze the domain of geometric problem solving from a cognitive perspective and identify several levels of domain abstraction that interact in the problem solving process. We discuss the roles of physical manifestations of spatial configurations, their manipulation, and their perception for understanding problem solving processes. We propose an extension of the classical problem solving repertoire of constructive geometry to approach certain problems more directly than under the compass-and-straightedge paradigm. Specifically, we introduce strings and pins as helpful metaphors for a generalization of the constructive geometry approach. We present classical problems from spatial problem solving to illustrate the ‘strings and pins’ paradigm. Three case studies are discussed: strings-and-pins solutions to (i) the ellipse construction problem; (ii) the shortest path problem; and (iii) the angle trisection problem. Comparisons to formal solutions are drawn. Differences and similarities between the compass-and-straightedge paradigm and the strings-and-pins paradigm are analyzed. Features and limitations of constructive and depictive geometry as well as implications for computational approaches are discussed. The strings-and-pins domain is shown to be more general and less restrictive than the compass-and-straightedge domain.     

Study on UAV Path Planning Approach Based on Fuzzy Virtual Force

This article proposes a novel fuzzy virtual force (FVF) method for unmanned aerial vehicle (UAV) path planning in complicated environment. An integrated mathematical model of UAV path planning based on virtual force (VF) is constructed and the corresponding optimal solving method under the given indicators is presented. Specifically, a fixed step method is developed to reduce computational cost and the reachable condition of path planning is proved. The Bayesian belief network and fuzzy logic reasoning theories are applied to setting the path planning parameters adaptively, which can reflect the battlefield situation dynamically and precisely. A new way of combining threats is proposed to solve the local minima problem completely. Simulation results prove the feasibility and usefulness of using FVF for UAV path planning. Performance comparisons between the FVF method and the A* search algorithm demonstrate that the proposed approach is fast enough to meet the real-time requirements of the online path planning problems.     

顾及星像点分布的恒星相机在轨检校

由于卫星发射前后以及在轨运行过程中,环境因素的变化都可能引起恒星相机参数发生改变,从而导致星敏感器姿态测量精度下降.将多片空间后方交会方法应用于恒星相机的在轨检校.在利用该方法检校时,实验发现检校结果的精度受到参与检校的恒星影像上星像点分布的影响,由此进一步提出了凸包面积百分比准则,该方法自动选取分布较好的影像用于检校,有助于提高检校精度.实验结果证明:基于后方交会进行恒星相机在轨检校时,利用凸包法选取的影像片进行检校的精度明显优于未选片时检校的结果.      

基于压缩感知的频率和DOA联合估计算法

波达方向（DOA）估计是阵列信号处理的一个重要问题,针对信号的DOA估计问题,本文基于压缩感知理论,提出了一种新的频率和角度联合估计算法。首先利用方向波数的空间稀疏性,建立过完备稀疏字典,然后利用压缩采样阵列结构通过求解最优化问题得到方向波数的高分辨估计,最后利用最优空域滤波实现信号到达角度和频率的配对。相对于传统算法,该算法能够实现多信号DOA的高分辨估计,且经过压缩采样后降低了运算量,仿真验证了该算法的正确性与有效性。     

空间非编码标记特征点中心定位方法与比较

归纳总结了应用于可见光测量的空间标记非编码设计原则,例举了棋盘格型、栅格型、圆型等3种典型的非编码标记图案设计,分别阐述了各标记特征点中心定位方法和计算过程,开展了对比试验,结果表明：圆型非编码标记图案设计及其特征点中心定位精度明显高于其他两种图案,其图案设计简捷、特征点突出易于识别、在像平面中呈现各向同性、点中心定位精度高、计算速度快、噪声抑制能力强。     

A Qualitative Calculus for Three-Dimensional Rotations

We have developed a qualitative calculus for three-dimensional directions and rotations. A direction is characterized in terms of the signs of its components relative to an absolute coordinate system. A rotation is characterized in terms of the signs of the components of the associated 3 × 3 rotation matrix.

A system has been implemented that can solve the following problems: 1. Given the signs of direction and rotation matrix P, find the possible signs of the image of under P. Moreover, for each possible sign vector of · P, generate numerical instantiations of and P that yields that result.

2. Given the signs of rotation matrices P and Q, find the possible signs of the composition P · Q. Moreover, for each possible sign matrix for the composition, generate numerical instantiations of P and Q that yield that result.

We have also proved some related complexity and expressivity results. The satisfiability problem for a qualitative rotation constraint network is NP-complete in two dimensions and NP-hard in three dimensions. In three dimensions, any two directions are distinguishable by a qualitative rotation constraint network.     

基于可拓规则推理的故障诊断方法

针对产生式规则推理方法存在的推理效率低、知识获取困难以及难以用于多故障诊断等问题,研究基于可拓规则推理的故障诊断方法。首先将基元理论和产生式规则相结合,得到可拓规则的基元表示;然后给出可拓规则匹配度计算公式,并提出按前件基元类型和属性数据类型不同对可拓规则进行分层匹配,对所有匹配成功的可拓规则,提出先删减再排序的冲突消解策略,在算法分析中讨论可拓规则推理的时间复杂度;最后通过应用案例说明可拓规则表示、匹配、推理和冲突消解的全过程,结果表明该方法适用于机载设备的多故障诊断。      

基于多台站观测的中国区域地磁指数

利用中国14个地磁台站和全球23个地磁台站的H分量分钟值数据,分析单台站小时幅度指数r_H的时空分布特征,在此基础上结合台站之间r_H指数的相似度度量(残差指数Ra),采用K均值聚类算法将中国14个地磁台站划分为7个区域,根据加权法计算各区域的区域指数Rr.结果表明,r_H指数具有27天太阳自转周变化,季节变化不显著,但仍存在春秋季大而冬夏季小的特征;在空间变化上,r_H随纬度的增高而增大,并且在磁暴期间r_H指数的幅值和形态均表现出明显的经度差异,随地方时呈现晨-昏不对称现象;与Dst指数、SYM-H指数、Kp指数及各区域内台站的H分量观测数据对比分析发现,区域指数Rr能有效反映区域地磁扰动.      

CBR方法在液体火箭发动机推力室设计中的应用

液体火箭发动机推力室的设计和制造是一项极其复杂的系统工程,其性能参数、结构形式、组织方式、材料等的选择尤其依赖于设计人员丰富的经验和成功研制型号积累的设计知识。为实现对以往设计经验和知识的继承,在推力室的设计中引入了基于案例推理(CBR,case-based reasoning)的方法。基于案例推理的方法作为人工智能领域的一个重要分支,是指将过去对典型问题的求解事例,按一定的组织方式存储起来,积累成案例库,当用户求解某一新问题时,利用该案例库来指导进行求解的一种策略。根据液体火箭发动机推力室的设计内容、设计流程以及设计特点,得出推力室性能参数关系图,并基于案例推理的方法提出了推力室的案例表示方法和案例调整方案,并应用该调整技术实现了具体的案例调整。     

基于FDA-MIMO的距离欺骗干扰鉴别方法

提出了一种基于频率分集阵列多输入多输出(FDA-MIMO)的距离欺骗干扰鉴别方法。FDA-MIMO中,目标回波在阵元间产生的相位差及空间角频率与距离、角度呈线性关系,而假目标不满足该关系。本文对目标回波和多类假目标在FDA-MIMO接收端的相位差、空间角频率进行了理论推导,详细分析了上下变频、匹配滤波、信号混合、移频等因素的影响,给出了假目标鉴别的具体流程。理论分析及仿真结果表明,该方法能准确提取混合信号的相位差及空间角频率信息,有效对抗多种类型的转发式欺骗干扰。