基于KS函数的协同优化算法及其应用

多学科设计优化(MDO)是当前航空航天复杂系统设计研究中一个最新、最活跃的领域,针对多学科设计优化中协同算法优化过程中存在的收敛困难、计算量大、费时等问题,提出一种新的系统级约束处理方法,利用KS函数的凝聚特性,将系统级的多个学科约束凝聚成一个拥有光滑高阶可微的可行域单约束,来取代罚函数法中的多个约束,以缓解多约束之间的冲突并加速收敛速度.利用两个典型算例进行测试,结果表明改进方法有效.     

一类有理函数的不定积分

目的为了简单地求解有理函数P(x)/Q(x)的积分;方法对∫P(x)/(x-a)mdx∫,P(x)/(x-a)m(x-b)ndx型有理函数的积分给出一般计算公式;结果通过实例说明该公式简捷、对称,避免以往待定系数法带来的诸多不便;结论具有较强的实用性。     

基于加速度频响函数小波分解的模型修正方法

为提高模型修正效率，满足修正方法对于实测环境噪声的鲁棒性，将Kriging模型和小波分解引入加速度频响函数模型修正。首先，将加速度频响函数进行小波分解，用得到的第1层幅值较大的小波系数来表征原频响函数。其次，采用拉丁超立方抽样对初选待修正参数进行设计，根据设计结果对各参数进行灵敏度分析，从而确定模型修正的待修正参数，以待修正参数作为Kriging模型输入，所对应的小波系数作为Kriging模型输出，通过混合灰狼算法寻得最优Kriging模型相关系数，建立精确有效的Kriging模型。最后，以目标加速度频响函数小波分解的小波系数与Kriging模型输出的小波系数差值最小为目标，通过水循环算法求解模型待修正参数。数值算例表明，所提模型修正方法具有良好的修正效果，即使在加速度频响函数中加入信噪比为5 dB的高斯白噪声时，修正误差也低于4%，证明了该方法对于随机噪声的鲁棒性。     

基于多目标的飞行参数规划模型研究

分析了以飞机的飞行高度和速度为参数,以飞行总时间和燃油消耗为目标的飞行参数规划模型,并解算出此规划模型的最优解和目标函数的最优值。仿真分析结果表明目标函数选取不同,会对模型的最优解和最优值产生影响。此模型可为飞行参数规划研究提供参考。     

内压作用下的航空轮胎爆破碎片动力响应

航空轮胎爆破时受内压释放的影响,爆破碎片的速度会有明显增加,而非与适航标准规定的与轮胎降落时的胎速相同。利用Fluent中用户自定义函数编写动力响应程序,采用动网格和用户自定义函数相结合的方法,展开内压释放作用下的轮胎爆破碎片速度动力响应特性的数值模拟研究。假设轮胎爆破失效是存在先前缺陷造成的,将碎片受冲击后的动态过程分解为内压释放冲击加速阶段和以一定初速度在空气阻力下减速运动两个阶段,提出仅考虑碎片两侧实时压力差作为动力源的简化物理爆破模型,来分析碎片的速度受内压作用的响应和整个流场压力以及速度变化情况,弥补了数学模型未考虑内外压平衡过程的不足,为预测轮胎爆破后碎片获得能量和爆破气流能量等提供数值参考,以便提出相应的安全防范措施。     

The spatio-spectral localization approach to modeling VTEC over the western part of the USA using GPS observations

The precise ionosphere modeling is crucial and remains a challenge for GPS positioning and navigation, as well as many other Earth observation systems. In this research, two approaches have been proposed to model the vertical total electron content (VTEC) of the ionosphere using spherical slepian function. For the two-dimensional case, VTEC has been modeled in a sun-fixed reference frame and the three-dimensional approach based on the system of the three-dimensional base functions has been defined as the tensor product of the spherical slepian function for the longitude and latitude in an Earth-fixed reference frame, and the polynomial B-spline function for time. Rather than the spherical harmonics, the spherical slepian functions can be employed to produce the locally and globally orthogonal bases to optimally represent the data in any arbitrary region up to a given degree. The spherical slepian functions have been applied to the real data obtained from the ground-based GPS observation across the western part of the USA.     

Chaotic Characteristic Analysis of Air Traffic System

Chaotic characteristics of traffic flow time series is analyzed to further investigate nonlinear characteristics of air traffic system. Phase space is reconstructed both by time delay which is built through mutual information, and by embedding dimension which is based on false nearest neighbors method. In order to analyze chaotic characteristics of time series, correlation dimensions and the largest Lyapunov exponents are calculated through Grassberger-Procaccia （G-P） algorithm and small-data method. Five-day radar data from the control center in Guangzhou area are analyzed and the results show that saturated correlation dimensions with self-similar structures exist in time series, and the largest Lyapunov exponents are all equal to zero and not sensitive to initial conditions. Air traffic system is affected hy multiple factors, containing inherent randomness, which lead to chaos. Only grasping chaotic characteristics can air traffic be predicted and controlled accurately.     

Regional moment-independent sensitivity analysis with its applications in engineering

Traditional Global Sensitivity Analysis (GSA) focuses on ranking inputs according to their contributions to the output uncertainty.However,information about how the specific regions inside an input affect the output is beyond the traditional GSA techniques.To fully address this issue,in this work,two regional moment-independent importance measures,Regional Importance Measure based on Probability Density Function (RIMPDF) and Regional Importance Measure based on Cumula tive Distribution Function (RIMCDF),are introduced to find out the contributions of specific regions of an input to the whole output distribution.The two regional importance measures prove to be reasonable supplements of the traditional GSA techniques.The ideas of RIMPDF and RIMCDF are applied in two engineering examples to demonstrate that the regional moment-independent importance analysis can add more information concerning the contributions of model inputs.     

航材消耗件订货模型及解法

在分析航材消耗件需求规律的基础上，提出了一种基于多元函数的消耗件经济订货批量模型。结合实际数据定义模型参数，利用非线性约束下的广义拉格朗日乘数法即Kuhn-Tucker最优化条件求解模型极值，最终得到基于最佳订货周期和最小费用的最佳订货量。