Flexible arrival trajectory optimization at terminal airspace based on mixed integer programming
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摘要:
随着航空运输量持续增长和空域容量日渐饱和，固定进场程序对航班调配缺乏灵活性，潜在冲突多、调配困难、等待时间长、碳排放量大等问题日趋凸显。综合考虑多航班在终端区的进场、进近、排序、汇聚等运行过程，提出和描述了基于柔性进场航迹优化解决方案。基于终端区和航空器运行特征，设计终端区航班进场时空离散网络栅格。以航迹和总飞行长度最短为目标，建立柔性进场航迹的混合整数规划模型，分别考虑网络栅格规则、航空器转弯特性、飞行冲突、安全间隔、航迹连续性等限制条件，以天津机场终端区为例，基于不同的交通密度等级和终端区入口时间窗，设置多组典型实验案例，使用商业求解器Gurobi对所建模型进行求解验证。结果表明：柔性进场航迹较标准仪表进场程序(STAR)，航迹长度平均缩短127.375 km，飞行总长度平均降低534.75 km，航班进场时间平均减少6.24 min；且在相同交通密度等级，入口时间窗设置合理的情况下，柔性进场航迹对航班量的小幅波动具有一定的鲁棒性。
Abstract:Problems with flight conflicts, difficult deployment, lengthy wait times, and high carbon emissions are becoming more frequent as a result of the continuous growth in air traffic, the saturation of available airspace, and the rigidity of the conventional fixed approach procedure used in the terminal area. A solution based on flexible approach trajectory optimization is developed and detailed, taking into account the operating processes of multiple flights such as descent, approach, sequencing, and margining in the terminal area. A spatiotemporal discrete network grid of flight approaches in the terminal area is created based on the characteristics of the terminal and aircraft operation. A mixed integer programming model is developed with the objective of minimizing the trajectory and overall flight length, as well as being constrained by factors including grid regulations, airplane turning characteristics, flying conflicts, safety separation, and trajectory continuity. The model is solved and validated using the commercial solver Gurobi, and multiple sets of typical experimental scenarios are put up depending on different traffic density levels and the entrance time frame, using the Tianjin Airport terminal area as an example. The results show that the flexible approach trajectory length is decreased by an average of 127.375 km and the total flight length is reduced by 534.75 km compared with the standard instrument approach procedure (STAR), with an average reduction of 6.24 min in flight arrival times. Additionally, with the same traffic density level and a fair entrance time window setting, the flexible approach trajectory is resilient enough to handle slight variations in the number of flights.
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图 7 最终融合点栅格对应的3个可用对角航迹段
Figure 7. Three available diagonal trajectory segments in each final merge point grid
图 15 不同时间窗的进场航迹长度
Figure 15. Length of arrival trajectory based on different time window
图 18 中交通密度下不同测试的航迹
Figure 18. Trajectories for different tests in medium traffic density
图 19 高交通密度下不同测试的航迹
Figure 19. Trajectories for different tests in high traffic density
表 1 不同测试场景的案例数据
Table 1. Case data in different test scenarios
测试案例 密度 航班量 时间窗/min 三入口航班量 L-1 低 13 0 4-5-4 L-2 低 13 1 4-5-4 M-1 中 22 0 8-8-6 M-2 中 22 1 8-8-6 M-3 中 22 2 8-8-6 H-1 高 32 2 10-10-12 H-2 高 32 3 10-10-12 H-3 高 32 4 10-10-12 
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表 2 优化航迹相对原进场程序的长度变化
Table 2. Changes in the length of arrival trajectory
案例 航迹1
长度/km航迹2
长度/km航迹3
长度/km航迹4
长度/km总长度/
kmL-1 −37 +14 −67 −90 L-2 −31 +9 −82 −104 M-1 −11 +19 −13 −5 M-2 −31 +9 −67 −89 M-3 −31 +9 −82 −104 H-1 +3 +90 −47 −170 −124 H-2 −31 +19 −67 −170 −249 H-3 −31 +14 −67 −170 −254
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表 3 最后一架航班到达最终融合点的时间
Table 3. Time when the last flight arrived at the final merge point
min 测试场景 本文模型 STAR L-1 66 83 L-2 66 83 M-1 78 82 M-2 74 82 M-3 74 82 H-1 84 87 H-2 78 87 H-3 77 87
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表 4 不同测试案例的数据
Table 4. Data for different test cases
测试 密度 航班量 时间窗/min 三入口航班量 L-3 低 14 1 4-6-4 L-4 低 15 1 4-7-4 L-5 低 13 1 6-4-3 L-6 低 13 1 4-4-5 M-4 中 21 1 8-8-5 M-5 中 23 1 9-9-5 M-6 中 22 1 9-7-6 M-7 中 22 1 8-9-5 H-4 高 31 3 10-10-11 H-5 高 33 3 10-11-12 H-6 高 32 3 11-10-11 H-7 高 32 3 11-11-10
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