Application of the restricted problem of three bodies to space mechanics

The most celebrated problem of dynamics, the problem of three bodies, is defined in the first chapter and it is shown how the problème restreint is obtained from the general formulation. This is followed by a historical review of the restricted problem from the point of view of space dynamics applications and the present state of the art is described in some detail. The third and final chapter reviews the major activities in the field of space mechanics and their relation to the restricted problem are pointed out.The purpose of this compte rendu is to demonstrate two theses. Firstly, based on the history of the restricted problem of three bodies, it will be shown that combining recent advances in computer technology and in analytical dynamics with modern topological techniques, a terra firma exists for a new attack on this classical problem.The second thesis is that the restricted problem of three bodies plays a central role in celestial mechanics and in space dynamics. From the second thesis it follows that progress in the solution of this problem will further the case of the entire field of space dynamics.An outline of a combined theoretical and experimental program, leading to possible significant contributions to this pièce de résistance of dynamics, completes the paper.     

舰艇编队防空火力分配问题的改进遗传算法

在建立舰艇编队防空火力分配模型的基础上,设计了求解该问题的改进遗传算法。实验结果表明,该算法可以有效求得舰艇编队防空火力分配问题的最优解或近似最优解,是求解舰艇编队防空火力分配问题的一个较好的方案。     

平均场网络在航迹关联中的应用

在多节点分布式多传感器融合系统中,航迹关联问题可以化为多维分配问题。多维分配问题是一个典型的组合优化问题,很难得到问题的最优解,而且其计算量会随着问题维数和目标数的增加容易呈现指数爆炸现象。在二维平均场人工神经网络的基础上提出了一种三维平均场网络模型用于解决此三维分配问题。仿真结果表明,该人工神经网络模型,能够有效解决多维分配问题,具有较高的关联正确率,当目标数不是很多时,可满足工程上的要求。另外,提出的三维网络模型可以推广到多维情况用于解决多维分配问题。     

编队卫星队形重构防碰撞最优轨迹规划

 针对编队卫星队形重构的轨迹规划问题,提出了直接配置混合整数线性规划(DCMILP)方法。首先将卫星编队飞行问题进行简化,整个过程使用线性化描述;继而将三阶Simpson方法扩展至编队卫星的队形重构过程中,将各卫星的状态量和控制量在各节点处离散化;然后根据目标函数及碰撞规避问题等各种约束条件,将整个过程转化为混合整数线性规划问题,从而可以找到该非凸问题的全局最优解。最后,通过对三维和二维两组编队卫星队形重构进行仿真,由结果可以看出,与传统方法相比该方法快速有效,能够满足实时性的要求,使得卫星编队的自主运行成为可能。     

Statistically Linearized Estimation of Reentry Trajectories

Several filters are applied to the problem of state estimation from inertial measurements of reentry drag. This is a highly nonlinear problem of practical significance. It is found that a filter based on the technique of statistical linearization performs better than the extended Kalman in this application. This is believed to be the first application of the statistically linearized filter to a practical dynamics problem. A sensitivity analysis is performed to demonstrate the relative insensitivity of this filter to modeling errors and approximations.     

基于神经网络的广义经典分配航迹关联算法

在序贯航迹关联算法的基础上提出了一种广义经典分配航迹关联算法。此算法实际上是求约束条件下的函数最小值问题,属于组合优化问题,其计算复杂度随着目标数的增加而发生爆炸现象。根据Hop field神经网络模型解决此类问题的能力对此广义经典问题进行了求解。仿真实验结果表明,广义经典分配算法能够有效地解决航迹关联问题,而且用神经网络求解此问题降低了计算复杂性,并具有很高的关联正确率。     

一类最佳飞行轨迹的计算

 本文给出了一种简化的直接多重打靶算法,并讨论了该算法在求解一类最佳飞行轨迹上的应用。数值计算结果表明,本文所给的算法收敛性好,对初值无很高要求,因而避免了在计算之前对问题进行冗繁的解析分析。     

人工智能在卫星任务规划中的应用

智能规划与调度是实现卫星自主规划其飞行任务的关键。将人工智能方法应用于卫星的任务规划,以执行对地观测任务为例,将任务规划问题归于组合优化问题,建立了相应的数学模型,并应用Hopfield神经网络算法进行求解,结果表明,该方法可用于单个仪器的任务规划。     

Conception of electronic wind tunnel and first results of its implementation

The problem of ensuring an ecological safety of modern civil and transport aircraft is directly related to the problem of aerodynamic efficiency. Ground-based tests have a wide spectrum of possibilities for investigations and for solution of the problems arising in these investigations. Ground-based aircraft tests are always characterized by the aspiration to test models of greater size in available transonic wind tunnels (TWT). In this situation, systematic errors caused by the influence of TWT test section Walls (TWTW) on a flowfield around model should be taken into account and excluded from the obtained results. This problem is extremely important for large transport aircraft models: in this case the requirements for the test data accuracy are especially stringent. Depending on the wind tunnel (WT) design peculiarities, this problem may be solved in different ways that are described in this article.     

基于混合遗传算法的中国旅行商问题满意解

针对组合优化中的旅行商问题 ,提出了贪心法与遗传算法相结合的混合遗传算法。文中给出了相应步骤并就中国旅行商问题得出满意解 ,该解优于已报道的结果。     

非稳态表面热流反演算法研究

表面热流的反演是一类典型的热传导逆问题。在采用有限体积法数值求解三维非稳态热传导问题的基础上,将该热传导逆问题转化为优化问题,建立了顺序函数法和共轭梯度法这两类反演算法。采用这两类算法对一个典型算例的计算结果表明:建立的两类反演算法都是有效的,具有较好的抗噪性能。顺序函数法的优势在于算法的推导和实现较为简便,但算法中存在人为确定的参数r,该参数的选取对反演结果有较大影响。共轭梯度法的算法中没有自由参数,但算法的推导和实现都较为复杂,其反演结果的精度和顺序函数法的反演结果精度基本相当。     

Uncertain multiobjective redundancy allocation problem of repairable systems based on artificial bee colony algorithm

Based on the uncertainty theory, this paper is devoted to the redundancy allocation problem in repairable parallel-series systems with uncertain factors, where the failure rate, repair rate and other relative coefficients involved are considered as uncertain variables. The availability of the system and the corresponding designing cost are considered as two optimization objectives. A crisp multiobjective optimization formulation is presented on the basis of uncertainty theory to solve this resultant problem. For solving this problem efficiently, a new multiobjective artificial bee colony algorithm is proposed to search the Pareto efficient set, which introduces rank value and crowding distance in the greedy selection strategy, applies fast non-dominated sort procedure in the exploitation search and inserts tournament selection in the onlooker bee phase. It shows that the proposed algorithm outperforms NSGA-II greatly and can solve multiobjective redundancy allocation problem efficiently. Finally, a numerical example is provided to illustrate this approach.     

Optimal measurement scheduling for state estimation

We consider the problem of optimal allocation of measurement resources, when: (1) the total measurement budget and time duration of measurements are fixed, and (2) the cost of an individual measurement varies inversely with the (controllable) measurement accuracy. The objective is to determine the time-distribution of measurement variances that minimizes a measure of error in estimating a discrete-time, vector stochastic process with known auto-correlation matrix using a linear estimator. The metric of estimation error is the trace of weighted sum of estimation error covariance matrices at various time indices. We show that this problem reduces to a nonlinear optimization problem with linear equality and inequality constraints. The solution to this problem is obtained via a variation of the projected Newton method. For the special case when the vector stochastic process is the state of a linear, finite-dimensional stochastic system, the problem reduces to the solution of a nonlinear optimal control problem. In this case, the gradient and Hessian with respect to the measurement costs are obtained via the solution of a two-point boundary value problem and the resulting optimization problem is solved via a variation of the projected Newton method. The proposed method is illustrated using four examples     

Iterative Optimal Orthogonalization of the Strapdown Matrix

This paper treats the problem of finding an orthogonal matrix which is the closest, in the Forbenius norm, to a given nonorthogonal matrix. This nonorthogonal matrix is the result of a fast but rather inaccurate computation of the well-known direction cosine matrix (DCM) of a strapdown inertial navigation system. The known closed-form solution to this problem is rederived using the directional derivative method, and the conditions for minimum distance are derived and discussed. A new iterative technique for solving this problem is derived as a result of the application of the gradient projection technique and the directional derivative method. The practical computational problems involved in this technique are discussed. The new technique is demonstrated by three examples. Although particular attention is given to the 3 X 3 direction cosine matrix, the conclusions are nonetheless valid higher order matries.     

Aerodynamic optimization of rotor airfoil based on multi-layer hierarchical constraint method

Rotor airfoil design is investigated in this paper. There are many difficulties for this high-dimensional multi-objective problem when traditional multi-objective optimization methods are used. Therefore, a multi-layer hierarchical constraint method is proposed by coupling principal component analysis (PCA) dimensionality reduction and e-constraint method to translate the orig-inal high-dimensional problem into a bi-objective problem. This paper selects the main design objectives by conducting PCA to the preliminary solution of original problem with consideration of the priority of design objectives. According to the e-constraint method, the design model is estab-lished by treating the two top-ranking design goals as objective and others as variable constraints. A series of bi-objective Pareto curves will be obtained by changing the variable constraints, and the favorable solution can be obtained by analyzing Pareto curve spectrum. This method is applied to the rotor airfoil design and makes great improvement in aerodynamic performance. It is shown that the method is convenient and efficient, beyond which, it facilitates decision-making of the high-dimensional multi-objective engineering problem.     

集合划分问题的蚁群算法

集合划分问题是一个典型的NP完全问题,建立了集合划分问题的优化数学模型,采用蚁群算法解决了此问题.对蚁群算法参数的合理选取进行了实验分析,给出了算法参数选取的基本原则.与贪心法作了比较,结果表明该方法比较有效.     

航天测控资源统一分配的多维遗传算法

对于航天器测控资源分配这一类时间窗受限的约束满足问题,国内外已有许多应用遗传算法的研究并取得了较好的成果。目前的研究主要针对的是低轨道航天器这类可见弧段较短、全弧段跟踪的问题,对于地球同步以及高轨道航天器这一类长弧段可见、非全弧段跟踪的资源分配问题,相关的应用研究较少。针对高低轨航天器测控资源统一分配问题的特点,经过对标准遗传算法的扩展,设计了一种能够描述高、低轨道航天器资源分配问题的多维编码方法,定义了相应的交叉算子、变异算子等算法要素,从而建立了一种能够解决航天测控资源统一分配问题的多维遗传算法。仿真计算表明,该算法能够有效解决目前我国航天测控网面临的"一网多星"管理模式下,高低轨航天器统一管理、统一分配测控资源的问题。     

吸气式空天飞行器闭环上升制导研究

闭环上升制导是吸气式空天飞行器达到快速优化、实时规划以及自主制导的必然要求。采用GHAME吸气式空天飞行器作为研究对象,提出了闭环上升制导最优控制方案,重点论证了该方案不存在关于节流阀值的奇异问题,并阐述了最优推力控制的Bang-Bang控制。引入有限差分法求解两点边值问题,并通过终端时刻调节算法求解终端时刻自由问题。仿真结果表明,所提出的闭环制导算法是有效、可行的,具有显著的优越性。     

神经网络在广义经典分配问题中的应用

在两节点分布式多传感器系统中,一些航迹关联算法可以化为广义经典分配问题。广义经典分配问题是一个组合优化问题。当目标数目较多时,很难得到问题的最优解,而且其计算量容易呈现指数爆炸现象。文章提出了用Hopfield神经网络和平均场网络解决此问题的方法。仿真结果表明,采用文章提出的人工神经网络模型求解广义经典分配问题,不仅使航迹关联具有较高的关联正确率,而且计算时间不会出现指数爆炸现象。仿真结果还表明,平均场网络相比Hopfield神经网络更易于得到问题的最优解。     

基于配点法的轨道在线优化方法研究

针对传统轨道优化方法无法应用于轨道在线优化的问题,提出了三阶辛普森配点法结合乘子法求解轨道在线优化问题的方法.首先建立变轨的最优化模型;然后,用三阶辛普森配点法将该最优控制问题转化为受约束的非线性规划问题;最后,采用增广拉格朗日乘子法对转化得来的受约束的非线性规划问题进行求解.仿真结果表明,所提出的方法可以得到高精度的轨道优化结果,并且对状态量和控制量的初值选取不敏感,且仿真具有实时性,计算速度快,可以达到在线进行轨道优化的要求.