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基于混合整数规划的终端区柔性进场航迹优化

赵向领 周志亮

洪冠新, 庞健. 风切变场中直升机前飞状态动态响应[J]. 北京航空航天大学学报, 2005, 31(05): 524-528.
引用本文: 赵向领,周志亮. 基于混合整数规划的终端区柔性进场航迹优化[J]. 北京航空航天大学学报,2025,51(4):1127-1142 doi: 10.13700/j.bh.1001-5965.2023.0240
Hong Guanxin, Pang Jian. Helicopter dynamic response to wind shear in forward flight[J]. Journal of Beijing University of Aeronautics and Astronautics, 2005, 31(05): 524-528. (in Chinese)
Citation: ZHAO X L,ZHOU Z L. Flexible arrival trajectory optimization at terminal airspace based on mixed integer programming[J]. Journal of Beijing University of Aeronautics and Astronautics,2025,51(4):1127-1142 (in Chinese) doi: 10.13700/j.bh.1001-5965.2023.0240

基于混合整数规划的终端区柔性进场航迹优化

doi: 10.13700/j.bh.1001-5965.2023.0240
基金项目: 国家自然科学基金(52272356); 中国民航大学研究生科研创新资助项目(2022YJS087)
详细信息
    通讯作者:

    E-mail:zxl-llx@163.com

  • 中图分类号: V355

Flexible arrival trajectory optimization at terminal airspace based on mixed integer programming

Funds: National Natural Science Foundation of China (52272356); Graduate Research and Innovation Funding Project of Civil Aviation University of China (2022YJS087)
More Information
  • 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。

     

  • 图 1  水平方向上的进场航迹

    Figure 1.  Arrival trajectory form in horizontal direction

    图 2  改变航向时的航迹段选择

    Figure 2.  Trajectory selection during course change

    图 3  对头冲突限制示意图

    Figure 3.  Schematic diagram of head-on conflict constraints

    图 4  对头冲突的时空网络

    Figure 4.  Time-space network of head-on conflict

    图 5  顶点交叉冲突示意图

    Figure 5.  Schematic diagram of vertex cross-conflict

    图 6  单元格内的4个对角航迹段

    Figure 6.  Four diagonal trajectory segments for grid

    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 8  进场航迹结构示意图

    Figure 8.  Schematic diagram of arrival trajectory structure

    图 9  栅格化的进场程序

    Figure 9.  Rasterized arrival procedure

    图 10  不同场景的航班飞行总长度

    Figure 10.  Total flight length in different scenarios

    图 11  13架航班场景的进场航迹

    Figure 11.  Arrival trajectory of 13 aircraft scenario

    图 12  22架航班场景的进场航迹

    Figure 12.  Arrival trajectory of 22 aircraft scenario

    图 13  32架航班场景的进场航迹

    Figure 13.  Arrival trajectory of 32 aircraft scenario

    图 14  不同场景下的进场航迹长度

    Figure 14.  Length of arrival trajectory in different scenarios

    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 16  到达最终融合点的时间

    Figure 16.  Time to reach final merge point

    图 17  低交通密度下不同测试的航迹

    Figure 17.  Trajectories for different tests in low traffic density

    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

    图 20  不同权重系数下的结果

    Figure 20.  Results under different weight coefficients

    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 13 0 4-5-4
    L-2 13 1 4-5-4
    M-1 22 0 8-8-6
    M-2 22 1 8-8-6
    M-3 22 2 8-8-6
    H-1 32 2 10-10-12
    H-2 32 3 10-10-12
    H-3 32 4 10-10-12
    下载: 导出CSV

    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/
    km
    L-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
    下载: 导出CSV

    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
    下载: 导出CSV

    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 14 1 4-6-4
    L-4 15 1 4-7-4
    L-5 13 1 6-4-3
    L-6 13 1 4-4-5
    M-4 21 1 8-8-5
    M-5 23 1 9-9-5
    M-6 22 1 9-7-6
    M-7 22 1 8-9-5
    H-4 31 3 10-10-11
    H-5 33 3 10-11-12
    H-6 32 3 11-10-11
    H-7 32 3 11-11-10
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-05-11
  • 录用日期:  2023-10-13
  • 网络出版日期:  2023-11-17
  • 整期出版日期:  2025-04-30

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