基于多元极值Copula的尾流飞行风险概率评估

在尾流问题日益突出的背景之下，结合人-机-环复杂系统建模与多元极值理论，评估遭遇近距近地尾流情形下的飞行风险概率。基于蒙特卡罗法提取尾流极值参数，验证了一维极值参数符合广义极值（GEV）分布；在此基础上提出了二维极值参数的双参数变权重（DPAVW） Copula模型，利用自适应区间粒子群优化（ARPSO）算法对目标函数中的未知参数进行了辨识，拟合优度检验的结果表明DPAVW Copula模型具有比其他Copula模型更高的精度；在利用Copula模型对尾流三维空间中所有二维极值参数进行描述的基础上，求出了每个网格节点上对应的飞行风险概率值，构建了尾流场内二维及三维可视化风险概率图。所提方法是对飞机系统安全性评估理论与方法的有效补充，对于尾流场内的导航控制与风险规避、机场起降的尾流安全间隔改进、环境风险可视化等研究方向有一定的参考价值；同时也适用于不同状况下飞行风险概率的横向对比分析。

Flight Risk Probability Evaluation in Wakes Based on Multivariate Extremum Copula

Under the background of increasing wake vortex problems, risk probabilities in the situation of near-ground wake encounter are evaluated using complex human-machine-environment theory and multivariate extreme value theory. First, we extract extreme parameters through flight simulation based on Monte Carlo method, and verify the one-dimensional extreme parameters meet generalized extreme value (GEV) distribution; Second, we propose the double parameter & adaptive variable weight (DPAVW) Copula model for two-dimensional extreme parameters, then use ARPSO (Adaptive Range Particle Swarm Optimization) algorithm to identify unknown parameters of the one-dimensional and two-dimensional objective function, and the results of fitting test show DPAVW Copula model has higher accuracy than the other Copula models; Third, flight risk probability in each corresponding grid node is evaluated on the basis of using Copula model to describe all the extreme values in three-dimensional wake space, and then 2D and 3D visual maps of risk probability are built. The proposed methods are effective complements to the aircraft system safety assessment theory, and they have a certain reference value for research directions such as wake navigation control, wake risk aversion, airport safety interval improvement and environmental risks visualization. Moreover, they are also suitable for comparative analysis of flight risk probabilities under different circumstances.