广义奇异摄动降阶方法在控制器降阶中的应用

 首先推导了广义奇异摄动降阶和奇异摄动降阶的 Schur方法,解决了均衡变换可能出现病态的问题,并且算法具有较好的鲁棒性。然后,将其应用于控制器降阶,并同其它方法比较,认为原系统带宽附近的控制器降阶误差对降阶效果影响较大,而广义奇异摄动降阶法通过参数α的选择,能取得较好的降阶效果。可供工程设计参考。     

受限空间欠采样条件下航空发动机关键截面流场重构方法研究进展

由于受整机环境下几何特征对探针位置的限制以及3维流动等因素影响，通过有限的测点数据准确获取整机关键测试 截面参数非常困难。为解决这一难题，综合关键截面流场重构项目的研究成果，针对航空发动机内强3维、强不均匀流场，介绍了 一种受限空间欠采样条件下航空发动机复杂流场重构技术。基于航空发动机内流场近周期分布的特征，利用离散的探针数据通 过“多波束近似”的方法来精确重构发动机内部的周向流场。相关技术在重构多级压气机出口截面总压分布、燃烧室出口热斑分 布、高压涡轮出口截面总温分布的测试中进行了初步试验验证，结果表明：重构结果与真实试验结果的误差分别小于0.1%、0.5%、 0.3%。与传统均布或等节距探针布局方案及均值数据处理方法相比，采用新的探针布局方案及流场重构方法可以实现航空发动 机压气机出口总压场、燃烧室及高压涡轮出口总温场的精确重构。     

插值逼近结合FDTD法快速计算目标宽角度RCS

FDTD(Finite Difference Time Domain)法结合多项式插值逼近和样条函数插值逼近快速计算了三维目标的宽角度RCS(Radar Cross Section).引入插值逼近方法可以节省计算时间.在整个入射角度范围内选定若干个入射角,对不同的入射角,分别用FDTD法计算得到外推面上各点的切向电磁场值,进而得到这些场值随入射角度变化的插值函数,然后用插值函数计算出全入射角度范围内外推面上各点的切向电磁场值,最后通过近远场变换得到宽角度RCS.计算结果表明,在只有少数几个插值节点的情况下该方法就能很好地逼近FDTD法的精确计算结果,节省了计算时间.      

Second post-Newtonian approximation of scalar-tensor theory of gravity

Deep space laser ranging missions like ASTROD I (Single-Spacecraft Astrodynamical Space Test of Relativity using Optical Devices) and ASTROD, together with astrometry missions like GAIA and LATOR will be able to test relativistic gravity to an unprecedented level of accuracy. More precisely, these missions will enable us to test relativistic gravity to 10^-7–10^-9${10}^{-7}''–''{10}^{-9}$ of the size of relativistic (post-Newtonian) effects, and will require second post-Newtonian approximation of relevant theories of gravity. The first post-Newtonian approximation is valid to 10^-6${10}^{-6}$ and the second post-Newtonian approximation is valid to 10^-12${10}^{-12}$ in terms of post-Newtonian effects in the solar system. The scalar-tensor theory is widely discussed and used in tests of relativistic gravity, especially after the interests in inflation models and in dark energy models. In the Lagrangian, intermediate-range gravity term has a similar form as cosmological term. Here we present the full second post-Newtonian approximation of the scalar-tensor theory including viable examples of intermediate-range gravity. We use Chandrasekhar’s approach to derive the metric coefficients and the equation of the hydrodynamics governing a perfect fluid in the second post-Newtonian approximation in scalar-tensor theory; all terms inclusive of O(c^-4)$\mathrm{O}(c^{-4})$ are retained consistently in the equations of motion.     

一个时限信号采样定理及其在数据压缩中的应用

证明了一个时限信号采样定理，该定理指出：（１）对于一个带限信号，如果样点按照Ｎ阶Ｃｈｅｂｙｓｈｅｖ多项式的零点位置分布，则可在有限的时间长度之内获得信号的近似最佳一致逼近，在采样密度大于Ｎｙｑｕｉｓｔ率２．１３５倍的条件下，截断误差的上界随着样点个数的增加呈指数衰减；（２）若用Ｃｈｅｂｙｓｈｅｖ多项式的线性组合形式进行内插，内插过程稳定。将此结果用于数据压缩可得到一个结合非均匀采样的ＤＣＴ方法。计     

非均匀弹性地基上梁横向振动的渐近解法

研究非均匀弹性地基上梁的横向振动，提供了一种既能保证较高精度、计算又非常简单的固有频率的渐近解法，作为算例，给出了非均匀弹性地基上悬臂梁固有频率的一级近似计算公式并将计算结果与连续质量有限元素法的计算结果作了比较。     

置信分布的贝塔分布近似及其在可靠性统计中的应用

在复杂系统可靠性综合评估方法研究中,利用β分布来近似区间[0,1]上的各种概率分布是一种常用的工程方法,并被许多系统可靠性综合评估方法所采用。工程中常用的β分布近似方法有二阶矩法和点估计下限法。为了减少近似误差,本文在文献[1]的基础上,对文献[1]中提出的β分布近似的两点法进行了深入研究,证明了两点法解的存在性和唯一性,并在这一结果的基础上设计出有效的算法。通过模拟计算可以看出,两点法与目前普遍使用的二阶矩法和点估计下限法相比,近似的精确性明显提高,尤其在小子样情形下效果更为显著。     

Reachable set estimation for spacecraft relative motion based on bang-bang principle

For spacecraft formation flight, the information of relative motion reachable set is very important, which can be used to predict the operating boundary of adjacent spacecraft and thus to ensure the safety of spacecraft operation. In this paper, we aim at developing a numerical method to approximate the reachable set for spacecraft relative motion. In particular, we focus on the quality of the approximation and the computational cost. Based on the bang-bang control principle, a polyhedral approximation algorithm is proposed to compute the reachable set of a relative motion spacecraft system. An inner approximation and an outer approximation of the reachable set for the system can be obtained. We prove that the approximation quality measured in Hausdorff distance can be guaranteed. The method is easy to implement and has low computational cost. Finally, the effectiveness of the algorithm is demonstrated by experimental simulation.