基于3种可视图的进场航班流量波动特性适应性评估

张勰; 肖恩媛; 刘宏志; 赵嶷飞; 王梦琦

doi:10.3963/j.jssn.1674-4861.2022.06.010

基于3种可视图的进场航班流量波动特性适应性评估

doi: 10.3963/j.jssn.1674-4861.2022.06.010

1.
中国民航大学空中交通管理学院天津 300300
2.
中国民航科学技术研究院民航发展规划研究院北京 100028

基金项目:

国家自然科学基金委员会与中国民用航空局联合资助项目 U1633112

详细信息

通讯作者:
张勰(1981—), 博士, 副研究员.研究方向: 交通信息工程及控制.E-mail: xiezhang@cauc.edu.cn

中图分类号: V355
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- 被引次数: 0
出版历程
- 收稿日期: 2022-04-23
- 网络出版日期: 2023-03-27

An Evaluation method for the Suitability of Three Visibility Graphs in Analyzing the Fluctuation Characteristics of Arrival Flight Flows

1.
College of Air Traffic Management, Civil Aviation University of China, Tianjin 300300, China
2.
Institute of Civil Aviation Development and Planning, China Academy of Civil Aviation Science and Technology, Beijing 100028, China

摘要

摘要: 在空域资源优化配置、运行效率提升、飞行安全保障等方面, 掌握空中交通流量波动规律发挥着先导性、基础性和关键性作用。为评估可视图、水平可视图、有限穿越可视图这3种图对航班流量波动特性及其演化的刻画能力, 针对同1个进场航班流的多尺度流量时间序列构建复杂网络, 分别从网络的整体结构和局部结构开展了适用性评估分析。针对网络整体结构特点, 提出了基于网络结构从属阵特点的网络细节损失率定义, 再通过k-core聚类分析考察了k阶核量化流量波动强度的适用性; 针对网络局部结构特点, 利用motif方法计算波动模式转移概率, 分析了不同长度序模体刻画波动演化的适应性水平。分析结果表明: ①当有限穿越可视图网络N值与节点数量占比在0.48%~1.442%区间时, N值的选择能够保证从属阵细节损失率在0.5范围内; ②可视图与有限穿越可视图(N=1~3)均能有效刻画航班流量时间序列的波动强度, 对时间序列波动的适应性评估值分别为2.665、4.810、6.973和9.883;③motifs序列长度过短, 将导致motifs类型数量少、不同motifs类型之间的转移概率趋于相同, 而在交通流混沌特性的影响下motifs序列过长对于预测没有意义, 因此, 可视图及N=1~3的有限穿越可视图motifs序列长度推荐使用选择4~7个节点长度。综上所述, 运用k-core聚类与motifs方法能有效分析整体网络与局部网络下波动模式的转移特征, 准确揭示空中交通时间维度的演变规律, 相关分析结果可以为航班延误预测提供依据, 能在航班实际运行管理中发挥先导性作用。
- 航班流量 /
- 时间序列 /
- 波动特性 /
- 可视图 /
- 网络结构 /
- 序模体 /
- k阶核算法
Abstract: Understanding the fluctuation characteristics of air traffic flows plays a leading, essential, and key role in many aspects of their control and management, such as airspace configuration optimization, efficiency promotion, and safety assurance. This paper aims to evaluate the suitability of the visibility graph(VG), horizontal visibility graph(HVG), and limited penetrable visibility graph(LPVG) in analyzing the fluctuation characteristics of air traffic flows. A complex network based on the multi-scale time series data extracted from the same arrival flow is developed and the suitability of three visibility graphs is evaluated from the global and local structure perspectives. From the global perspective, a concept of details loss rate is proposed by considering the characteristics of the network structure-dependent matrix. Then a k-core cluster is used to analyze the suitability of quantifying the strength of flight flow fluctuations. From the local perspective, a transfer probability of fluctuation patterns is calculated using the sequential motifs method, and the suitability of the sequential motif with different lengths in characterizing fluctuation characteristics of flight flows is evaluated. The results show that: ①the loss rate of detail can be limited within 0.5 when the proportion of N value of the LPVG in network nodes ranges from 0.48% to 1.442%;②VG and LPVG(N=1~3) can effectively describe the intensity of fluctuation of flight flow time series data and the suitability value is 2.665, 4.810, 6.973, and 9.883, respectively; ③a long sequential motif would reduce the number of sequential motifs and result in the similarity of transition probability among different types of the sequential motifs, while a short sequential motif is useless for prediction due the chaotic characteristics of traffic flow. Thus, it is recommended to use the sequential motif with the length of 4, 5, 6, and 7 for VG and LPVG(N=1~3). In conclusion, the k-core cluster and the motifs method provide an in-depth analysis of the transfer characteristics among the fluctuation modes and the evolution of time dimension in air traffic, which offers support for delay prediction and plays a leading role in the actual operation management of flights.
- flight flow /
- time series /
- fluctuation characteristic /
- visibility graph /
- network structure /
- sequential motif /
- k-core algorithm

HTML全文

图 1 天津滨海国际机场进场航班流量时间序列

Figure 1. The arrival flight flow volume time series of ZBTJ

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图 2 空中交通流量时间序列映射得到的可视图

Figure 2. Visibility graphs mapped from flight flow volume time series

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图 3 空中交通流量时间序列映射得到的水平可视图

Figure 3. Horizontal visibility graphs mapped from flight flow volume time series

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图 4 空中交通流量时间序列映射得到的有限穿越可视图

Figure 4. Limited penetrable visibility graphs mapped from flight flow volume time series

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图 5 3种可视图的网络矩阵结构图

Figure 5. Network matrix structure diagrams of three visibility graphs

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图 6 不同N取值的LPVG网络矩结构图

Figure 6. Limited penetrable visibility graph network matrix structure diagrams with different N values

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图 7 不同N取值的LPVG从属阵细节损失率

Figure 7. Limited penetrable visibility graph subordinate array detail loss rates with different N values

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图 8 3种可视图k-core网络图

Figure 8. Three visibility graphs k-core network graphs

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图 9 时间序列整体波动态势

Figure 9. Overall fluctuation trend of the time series

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图 10 方差评估波动适应性

Figure 10. Variance assessment fluctuation adaptability

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图 11 LPVG(N=1）流量时间序列中出现的序模体类型

Figure 11. Sequential motif types of limited penetrable visibility graph (N=1) presented in the flow time series

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图 12 序模体矩阵图

Figure 12. Sequential motif matrix diagram

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图 13 序模体转移概率图

Figure 13. Transition probability graphs of sequential motifs

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图 14 序模体转移概率分布图

Figure 14. Transition probability distribution curve of sequential motifs

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表 1 3种可视图从属阵可视线比率

Table 1. Subordinate array visibility lines ratios of three visibility graphs

时间粒度/min	可视线类型	1	2	3	4	5	6	7	8	9	图密度
	VG	0.276	0.253	0.342	0.533	0.304	0.573	0.213	0.143	0.600	0.038
5	LPVG（N=1）	0.456	0.447	0.537	0.867	0.520	0.702	0.406	0.280	0.800	0.071
	HVG	0.047	0.059	0.068	0.200	0.064	0.058	0.036	0.025	0.200	0.006
	VG	0.527	0.644	0.342	0.786	0.844	0.456	0.322	0.667		0.080
10	LPVG（N=1）	0.747	0.867	0.583	0.964	0.956	0.667	0.504	1.000		0.128
	HVG	0.088	0.089	0.075	0.036	0.067	0.047	0.047	0.000		0.009
	VG	0.905	0.455	0.600	0.800	0.711	0.822	0.667			0.137
20	LPVG（N=1）	1.000	0.673	0.800	1.000	0.889	0.956	1.000			0.211
	HVG	0.095	0.073	0.100	0.000	0.089	0.044	0.000			0.011

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表 2 不同N取值LPVG从属阵可视线比率

Table 2. Limited penetrable visibility graph subordinate array visibility lines ratios with different N values

时间粒度/min	N取值	1	2	3	4	5	6	7	8	9	图密度
	N=2	0.591	0.589	0.668	0.933	0.696	0.801	0.545	0.399	1.000	0.100
	N=3	0.717	0.688	0.758	1.000	0.789	0.901	0.647	0.513	1.000	0.125
5	N=4	0.815	0.779	0.816	1.000	0.871	0.977	0.721	0.597	1.000	0.149
	N=5	0.877	0.877	0.853	1.000	0.930	1.000	0.787	0.685	1.000	0.171
	N=6	0.909	0.945	0.884	1.000	0.988	1.000	0.853	0.759	1.000	0.191
	N=2	0.879	0.978	0.758	1.000	1.000	0.778	0.656	1.000		0.166
	N=3	0.967	1.000	0.892	1.000	1.000	0.848	0.772	1.000		0.203
10	N=4	1.000	1.000	0.967	1.000	1.000	0.924	0.873	1.000		0.238
	N=5	1.000	1.000	0.992	1.000	1.000	0.936	0.938	1.000		0.270
	N=6	1.000	1.000	1.000	1.000	1.000	0.982	0.975	1.000		0.310
	N=2	1.000	0.764	1.000	1.000	0.956	1.000	1.000			0.278
	N=3	1.000	0.927	1.000	1.000	1.000	1.000	1.000			0.347
20	N=4	1.000	1.000	1.000	1.000	1.000	1.000	1.000			0.406
	N=5	1.000	1.000	1.000	1.000	1.000	1.000	1.000			0.457
	N=6	1.000	1.000	1.000	1.000	1.000	1.000	1.000			0.516

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表 3 k-core统计特性

Table 3. The statistic characteristics of k-core

可视图	特征	数值
VG （core=8）	k-core分类	2	3	4	5	6	7	8
	频数	23	34	39	44	28	24	16
	累积频率	11.058	27.404	46.154	67.308	80.769	92.308	100
LPVG （core=13，N=1）	k-core分类	3	4	5	6	7	8	9	10	11	12	13
	频数	3	7	16	13	19	16	34	53	19	8	20
	累积频率	1.442	4.808	12.5	18.75	27.885	35.577	51.923	77.404	86.539	90.385	100
LPVG （core=17，N=2）	k-core分类	4	5	6	7	8	9	10	11	12	13	14	15	16	17
	频数	3	1	2	7	14	7	5	20	24	9	38	7	44	27
	累积频率	1.442	1.923	2.885	6.25	12.981	16.346	18.75	28.365	39.904	44.231	62.5	65.865	87.019	100
LPVG （core=20，N=3）	k-core分类	5	6	8	9	10	11	12	13	14	15	16	17	18	19	20
	频数	2	1	3	2	7	11	2	14	10	17	41	7	6	27	58
	累积频率	0.962	1.442	2.885	3.846	7.212	12.500	13.462	20.192	25.000	33.173	52.885	56.250	59.135	72.115	100

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表 4 序模体动态演化的统计特征

Table 4. Statistical characteristics of sequential motifs dynamic evolutions

可视图类型	窗口长度/min	序模体长度	转移次数/类型总数	序模体类型出现次数		序模体类型转移频次
可视图类型	窗口长度/min	序模体长度	转移次数/类型总数	μ₀	σ₀	μ_r	σ_r
VG	15	3	205/2	103.000	34.000	51.250	25.064
	20	4	204/5	41.000	38.838	17.000	19.240
	25	5	203/22	9.273	9.076	3.830	3.710
LPVG （N=1）	20	4	204/2	102.500	5.500	51.000	7.842
	25	5	203/6	34.000	25.344	11.278	12.197
	30	6	202/32	6.344	5.914	2.525	1.975
LPVG （N=2）	25	5	203/2	102.000	30.000	50.750	25.548
	30	6	202/6	33.833	23.954	10.632	11.645
	35	7	201/34	5.941	7.673	2.481	2.846
LPVG （N=3）	30	6	202/2	101.500	36.500	50.500	32.684
	35	7	201/6	33.667	29.998	10.579	15.901
	40	8	200/34	5.912	10.506	2.597	4.319

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