Rapid prediction and rerouting planning method of suborbital debris hazard zones during high-density space launches
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摘要: 面对愈发频繁的商业亚轨道发射活动中可能出现的航空器潜在解体风险，利用协方差传播方法预测亚轨道解体事故中碎片的传播范围；将碎片运动方程转换为高斯马尔可夫过程，利用概率密度函数构造高斯马尔可夫过程在一定置信度下的概率椭球表征碎片分布；为避免亚轨道解体事故碎片对民航空域内的飞机造成碰撞风险，提出一种面向空管的亚轨道碎片危险区预测与路径规划方法；根据民航可接受的风险概率确定亚轨道碎片概率椭球的数学边界，计算概率椭球在水平方向的投影，利用几何方法将碎片危险区处理成凸多边形；通过改航点数量约束方法减少改航路径中改航点的数量，有利于飞机平稳改航。仿真结果表明：协方差传播方法在复杂大气环境中能够快速有效地预测出亚轨道解体事故碎片的传播过程，分别显示出置信度为99.999%和95.000%的椭球边界范围，置信度越高，概率椭球边界范围越大，越接近真实碎片下落传播范围；利用改航点数量约束方法优化后的改航路径距离相比约束前增加了0.13%，但改航点数量减少了50%。可见，利用协方差传播方法可及时、准确预测亚轨道解体事故碎片的传播范围，并在此基础上提出高效、安全的改航策略。Abstract: Considering the potential risk of aircraft disintegration that may occur in the increasingly frequent commercial suborbital launch activities, a covariance propagation method was used to predict the propagation range of debris from the suborbital disintegration accidents. The method converted the debris motion equation into a Gaussian-Markov process and used the probability density function to construct a probability ellipsoid of the Gaussian-Markov process at a certain confidence level for the characterization of debris distribution. To avoid the collision risk between debris from suborbital disintegration accidents and aircrafts within the civil airspace, a hazard zone prediction and routing planning method of suborbital debris for air traffic control was proposed. The mathematical boundary of the probability ellipsoid of suborbital debris was determined according to the acceptable risk probability of civil aviation, and the projection of the probability ellipsoid in the horizontal direction was calculated. The hazard zone of debris was processed into a convex polygon by a geometric method. The number of diversion points in the diversion path was reduced by the constrained method, which was conducive to the smooth diversion of aircraft. Simulation results reveal that the covariance propagation method can rapidly and effectively predict the propagation process of debris from suborbital disintegration accidents in a complex atmospheric environment, showing the ellipsoid boundary range of 99.999% and 95.000%, respectively. The higher the confidence degree, the larger the boundary range of the probability ellipsoid, and the closer it is to the real debris falling propagation range. By using the constrained method of number of diversion points, the optimized rerouting path distance increases by 0.13% compared with that before the constraint, but the number of diversion points reduces by 50%. Therefore, the covariance propagation method can timely and accurately predict the propagation range of debris from suborbital disintegration accidents, and on this basis, efficient and safe redirecting strategies can be presented. 1 tab, 7 figs, 30 refs.
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图 4 置信度为99.999%和95.000%时椭球边界
Figure 4. Ellipsoid boundaries at confidences of 99.999 % and 95.000%
图 5 民航空域初始飞行改航区划设计
Figure 5. Initial flight diversion area design in civil aviation domain
图 7 改航点数量约束条件下最终飞行改航区
Figure 7. Final flight diversion area under restriction of number of diversion points
表 1 改航路径距离和航路点数量
Table 1. Redirection path distance and number of waypoints
条件 路径 路径长度/km 改航点数量 改航路径 约束前 d1 368.88 10 qo→s′10→s′9→s′8→s′7→s′6→s′5→s′4→s′3→s′2→s′1→qf d2 360.92 8 qo→s′11→s′12→s′13→s′14→s′15→s′16→s′17→s′18→qf 约束后 d′1 372.27 4 qo→s″4→s″3→s″2→s″1→qf d′2 361.39 4 qo→s″5→s″6→s″7→s″8→qf 
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