Integrated resilience of urban rail transit network with active passenger flow restriction under major public health disasters
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摘要: 分析了重大公共卫生灾害对城市轨道交通网络集成韧性的影响机理；基于韧性曲线模型对传统韧性测度方法进行了修正，构建了面向重大公共卫生灾害影响的城市轨道交通网络集成韧性测度方法；评估了城市轨道交通网络节点重要度水平，运用复杂网络构建了城市轨道交通网络拓扑模型，对节点客流进行了模拟分配；应用SEZIR传染病传播模型模拟了灾害传播过程，研究了城市轨道交通在重大公共卫生灾害背景下的集成韧性水平演化规律；以西安市疫情发展过程为研究对象，对主动客流限制下城市轨道交通网络的集成韧性水平进行了模拟和数值分析。研究结果表明：主动客流限制措施能够有效提高城市轨道交通网络对重大公共卫生灾害的阻断能力，当客流限制水平达到30%后，重大公共卫生灾害传播过程趋于平缓；主动客流限制措施会直接导致城市轨道交通网络运行效率降低，但能够提升城市轨道交通网络在重大公共卫生灾害影响下的集成韧性水平；当客流限制水平分别为70%、40%和20%时，城市轨道交通网络集成韧性水平的改善提升效果更加明显，累积改善效果分别可达到10.73%、46.87%和226.81%。Abstract: The influencing mechanism of major public health disasters on the integrated resilience of urban rail transit network was analyzed. The traditional resilience measurement method was modified by the resilience curve model, and an integrated resilience measurement method was constructed for the urban rail transit network affected by major public health disasters. The importance levels of urban rail transit network nodes were evaluated. A topological model of urban rail transit network was constructed by the complex network approach to simulate and assign the nodal passenger flow. The SEZIR infectious disease spread model was applied to simulate the spread process of disaster, and the evolution laws of the integrated resilience level of urban rail transit in the context of a major public health disaster were studied. The process of epidemic development in Xi'an was taken as the research object, the integrated resilience level of the urban rail transit network under active passenger flow constraints was simulated and numerically analyzed. Research results show that the ability of the urban rail transit network to interrupt the spread of major public health disasters can be effectively enhanced by active passenger flow restriction measures. The spread process of major public health disasters becomes gentle after the restriction level of passenger flow reaches 30%. Active passenger flow restriction measures are able to directly reduce the operational efficiency of the urban rail transit network, but the integrated resilience level of the urban rail transit network under the influence of major public health disasters can be improved. The improvement of integrated resilience level of the urban rail transit network is more significant when the passenger flow restriction level is 70%, 40%, and 20%, and the cumulative improvement is 10.73%, 46.87%, and 226.81%, respectively.
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图 1 自然灾害和重大公共卫生灾害对城市轨道交通网络韧性影响机理
Figure 1. Impact mechanisms of natural disasters and major public health disasters on urban rail network resilience
图 7 疫情发展期间城市轨道交通网络运行效率
Figure 7. Operation efficiency of urban rail transit network during development of epidemic
图 8 每日新增确诊病例变化趋势对比
Figure 8. Comparison of variation trends of new confirmed cases per day
图 9 60天模拟周期内不同ε下确诊病例变化
Figure 9. Changes of confirmed cases at different ε during 60-day simulation period
图 10 不同ε下城市轨道交通网络运行效率
Figure 10. Operation efficiencies of urban rail transit network at different ε
图 11 不同ε下疫情阻断能力与城市轨道交通网络韧性变化
Figure 11. Changes in epidemic interdiction capacity and urban rail transit network resilience at different ε
表 1 西安市城市交通主动限流措施
Table 1. Active traffic restriction measures in Xi'an
交通类型 主动限流措施 实现目标 城市轨道交通 风险车站“越站”运行 规避高风险区域 加开备用列车 控制列车满载率 调整线网运营服务时间 降低车站拥挤度，控制列车满载率 分批控制进站 降低车站拥挤度 关闭车站部分出入口 降低车站拥挤度 调整发车间隔 降低车站拥挤度，控制列车满载率 城市公交 车辆满载率不超过50% 控制车辆满载率 早晚高峰期间增加配车 控制车辆满载率 管控区域站点不停靠 规避高风险区域 客运站点关停 规避高风险区域 私家车 暂停机动车尾号限行措施 降低道路拥挤度，控制公共交通满载率 
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表 2 自然灾害与重大公共卫生灾害下城市轨道交通网络韧性研究对比
Table 2. Comparison of urban rail transit network resilience studies under major public health disasters and natural disasters
灾害类型 自然灾害 重大公共卫生灾害 结构层面影响 网络节点中断 网络结构未受到破坏 网络节点失效 网络线路中断 功能层面影响 城市轨道交通网络自身功能遭受灾害破坏，最大客流承载能力受损 城市轨道交通网络自身功能未遭到破坏，实际客流承载能力受到灾害防控措施限制 城市轨道交通网络运行影响 结构、功能受到灾害破坏，导致网络运行效率降低 灾害防控措施导致网络客流承载能力不能充分发挥，实际功能运行效率降低，对灾害的抵抗能力增加 城市轨道交通网络韧性内涵 网络遭受灾害干扰后，城市轨道交通网络系统性能受损-吸收干扰-系统性能恢复的过程 城市轨道交通网络在灾害干扰下引发实际客流承载功能、抵抗能力等综合系统运行性能恢复提升的过程
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表 3 西安城市轨道交通网络线路
Table 3. Urban rail transit network lines of Xi'an
线路编号 起点 终点 站点数 1 沣河森林公园 纺织城 23 2 韦曲南 北客站 21 3 保税区 鱼化寨 26 4 航天新城 北客站(北广场) 29 5 西安东站 创新港 34 6 西安国际医学中心 西北工业大学 13 9 秦陵西 纺织城 15 14(1期) 贺韶 北客站(北广场) 9
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表 4 西安城市轨道交通站点节点重要度分布
Table 4. Importance distribution of nodes at urban rail transit stations in Xi'an
节点编号 节点介数 节点度 重要度 节点编号 节点介数 节点度 重要度 0 0.000 0 0.25 0.500 0 78 0.182 6 0.50 0.889 7 1 0.030 9 0.50 0.738 0 79 0.184 3 0.50 0.891 4 2 0.061 4 0.50 0.768 5 80 0.151 1 0.50 0.858 2 3 0.091 5 0.50 0.798 6 81 0.126 4 0.50 0.833 5 4 0.121 2 0.50 0.828 3 82 0.103 6 0.50 0.810 7 5 0.150 5 0.50 0.857 6 83 0.082 2 0.50 0.789 3 6 0.179 4 0.50 0.886 5 84 0.061 7 0.50 0.768 8 7 0.207 9 0.50 0.915 0 85 0.041 7 0.50 0.748 8 8 0.236 0 0.50 0.943 1 86 0.028 0 0.50 0.735 1 9 0.263 7 0.50 0.970 8 87 0.033 3 0.50 0.740 4 10 0.291 0 0.50 0.998 1 88 0.191 5 0.50 0.898 6 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ 68 0.0309 0.50 0.738 0 146 0.317 9 0.50 1.025 0 69 0.061 4 0.50 0.768 5 147 0.344 4 0.50 1.051 5 70 0.091 5 0.50 0.798 6 148 0.370 5 0.50 1.077 6 71 0.121 2 0.50 0.828 3 149 0.000 0 0.25 0.500 0 72 0.150 5 0.50 0.857 6 150 0.030 9 0.50 0.738 0 73 0.179 4 0.50 0.886 5 151 0.061 4 0.50 0.768 5 74 0.207 9 0.50 0.915 0 152 0.073 4 0.50 0.780 5 75 0.236 0 0.50 0.943 1 153 0.068 4 0.50 0.775 5 76 0.087 4 0.50 0.794 5 154 0.074 9 0.50 0.782 0 77 0.211 4 1.00 1.211 4 155 0.085 4 0.50 0.792 5
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表 5 Pearson相关系数结果
Table 5. Results of Pearson correlation coefficient
数据 实际新增确诊病例 模型模拟新增确诊病例 实际新增确诊病例 1.000 0.933
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表 6 回归分析结果
Table 6. Regression analysis result
R2 F 自由度1 自由度2 显著性 0.870 294.935 1 44 0.000
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表 7 ε取值与情景设置
Table 7. ε values and scenarios setting
情景 ε/% 描述 1 100 未采取客流限制措施 2 90 实际承载客流不超过最大可承载客流的90% 3 80 实际承载客流不超过最大可承载客流的80% 4 70 实际承载客流不超过最大可承载客流的70% 5 60 实际承载客流不超过最大可承载客流的60% 6 50 实际承载客流不超过最大可承载客流的50% 7 40 实际承载客流不超过最大可承载客流的40% 8 30 实际承载客流不超过最大可承载客流的30% 9 20 实际承载客流不超过最大可承载客流的20%
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表 8 不同参数k下集成韧性模型效果分析
Table 8. Analysis of effect of integrated resilience model with different parameter k
k ε/% C C改善效率 R2 k=1 100 0.999 669 0.976 90 0.967 924 -0.031 756 80 0.928 448 -0.040 785 70 0.937 485 0.009 734 60 0.905 585 -0.034 028 50 0.870 427 -0.038 823 40 0.929 352 0.067 697 30 0.928 375 -0.001 051 20 1.213 994 0.307 655 k=2 100 0.999 669 0.987 90 1.006 206 0.006 539 80 0.999 405 -0.006 759 70 1.106 959 0.107 618 60 1.130 550 0.021 312 50 1.153 512 0.020 311 40 1.468 262 0.272 863 30 1.658 506 0.129 571 20 3.267 084 0.969 896 k=3 100 0.999 669 0.983 90 1.046 002 0.046 348 80 1.075 786 0.028 474 70 1.307 070 0.214 990 60 1.411 402 0.079 821 50 1.528 664 0.083 082 40 2.319 675 0.517 452 30 2.962 857 0.277 273 20 8.792 335 1.967 519 k=4 100 0.999 669 0.961 90 1.087 371 0.087 731 80 1.158 004 0.064 957 70 1.543 355 0.332 772 60 1.762 022 0.141 683 50 2.025 826 0.149 716 40 3.664 801 0.809 041 30 5.293 030 0.444 288 20 23.661 816 3.470 372
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表 9 不同ε下城市轨道交通网络集成韧性水平
Table 9. Integrated resilience levels of urban rail transit network under different ε
ε/% V T C累积改善效果 100 0.000 000 0.999 669 90 0.038 788 0.931 099 0.006 539 80 0.073 646 0.862 528 -0.000 264 70 0.166 171 0.793 957 0.107 325 60 0.221 879 0.725 384 0.130 924 50 0.281 583 0.656 814 0.153 894 40 0.457 347 0.588 243 0.468 748 30 0.580 237 0.519 673 0.659 055 20 0.989 982 0.451 100 2.268 166
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