Air Route Crossing Angles Optimization Model with Different Preferences
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摘要:为揭示交叉航路结构对空中交通影响的内部机理，有效打通航路节点运行瓶颈，研究了航路交叉角度优化问题. 首先，在分析航班飞行时间和航班油耗与航路基本相交结构角度关系的基础上，构建了交叉航路角度结构；其次，基于交叉航路交通量分布特征，建立了飞行时间和油耗偏好的交叉航路角度优化模型；最后，选取典型交叉航路进行了模型验证. 研究结果表明：航班飞行时间和油耗存在线性负相关关系；单一考虑时间优化时，航班总运行成本增加0.54%，仅考虑油耗优化时，总成本减少2.89%；无偏好优化时，航班总运行成本减少3.82%；考虑偏好时，在时间权重系数等于0.4处取得极小值，此时总运行成本降低5.26%，且空域内油耗密度、飞行冲突次数和管制员工作负荷3个指标的均值分别降低20.41%、56.12%、46.24%；优化后构型对原始空域结构的平均角度扰动为11.88%.Abstract:In order to investigate the internal mechanism of influence on air traffic posed by airspace structure and to clear bottlenecks of air traffic operation at air transit network nodes, the optimization of air route crossing angles was studied. After analysing the relationship between flight time, fuel consumption, and the angles of basic intersection route structure, an integrated crossing route angle structure was set up. Then, based on the air traffic flow distribution trait of the crossing routes, a preference mathematical model was developed to optimize the crossing angles in terms of flight time and fuel consumption. Finally, a representative crossing route was selected to verify the proposed model. The results show a negative linear correlation between flight time and fuel consumption and a 0.54% increase in total flight costs if flight time is solely considered versus a 2.89% decrease if only fuel consumption is taken into account. There is, however, a 3.82% reduction in total flight costs without preferences or 5.26% （the minimum value of total flight costs obtained when flight time coefficient equals 0.4） with preferences. The average amounts of fuel consumption density, flight conflicts, and controller workloads also declined 20.41%, 56.12%, and 46.24%, respectively, but the original airspace angle structure changed a mere 11.88% after the optimization.
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图 2单位航班飞行时间随角度变化关系及拟合结果
Figure 2.Relationships and fitting results of unit flight time change with angles
图 3单位航班飞行油耗随角度变化关系及拟合结果
Figure 3.Relationships and fitting results of unit flight fuel consumption change with angles
图 5总飞行时间、总油耗、总成本随时间权重变化关系
Figure 5.Relationship of total flight time，fuel and cost changes with time weight
图 6优化前后每架航班平均飞行时间比较
Figure 6.Comparison of mean flight time before and after optimization
图 7优化前后每架航班平均油耗比较
Figure 7.Comparison of mean flight fuel consumption before and after optimization
图 8优化前后油耗密度分布对比
Figure 8.Comparison of fuel consumption density before and after optimization
表 1各结构交通量均值和标准差
Table 1.Mean and standard deviation of flight numbers
计算项目 ${F_{{\rm R}_{(1,2)}}}$ ${F_{{\rm R}_{(3,4)}}}$ ${F_{{\rm R}_{(1,4)}}}$ ${F_{{\rm R}_{(2,3)}}}$ 均值/架次 636 682 7 40 标准差 7.456 0 5.148 4 1.324 2 2.225 3 
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表 2不同偏好对应的优化结果
Table 2.Optimization results for different preferences
优化指标 原始结构 仅优化时间 仅优化油耗 总飞行时间/h 541.6 468.0 592.8 总油耗/t 752.3 811.1 682.8 总成本/千元 5 695.4 5 726.2 5 530.6 时间变化率/% 0 –13.60 9.45 油耗变化率/% 0 7.81 –9.24 总成本变化率/% 0 0.54 –2.89 下载:
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表 3综合优化各结构对应角度
Table 3.Angles of each structure for comprehensive optimization
项目 汇聚 分散 转弯1 转弯2 优化前 54 51 33 72 优化后 61 57 50 68 下载:
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表 4综合优化结果
Table 4.Results of comprehensive optimization
项目 总时间/h 总油耗/t 总成本/千元 优化前 541.6 752.3 5 695.4 优化后 513.9 728.6 5 477.9 优化百分比/% –5.11 –3.15 –3.82 下载:
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表 5优化前后各评价指标结果
Table 5.Optimization results before and after optimization
项目 总时间/h 总油耗/t 总成本/千元 优化前 436.7 715.4 5 136.2 优化后 418.3 696.9 4 978.1 优化百分比/% –4.22 –2.58 –3.08 下载:
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