A Method for Dynamic Coupling Coordination of High-speed Railway Node-line Passing Capacity Based on SEM
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摘要: 针对影响高铁点线系统通过能力动态因素众多且各动态因素间影响关系复杂、难以量化动态因素权重的问题，研究了基于结构方程模型（structural equation modeling，SEM）的高铁点线系统通过能力动态耦合协调方法。为探究高铁点线系统通过能力动态因素间的复杂影响关系，将影响高铁点线系统通过能力的动态因素分为点系统、线系统、运输组织、作业时间、延误及早点子系统，构建PLE-SEM的高铁点线系统通过能力动态协调模型。此基础上，引入上海西站—上海站区段的高铁点线系统数据对模型进行测量模型和结构模型检定，验证模型的有效性、科学性和拟合优度，揭示该区段高铁通过能力各子系统间的影响关系和影响方向，得到各子系统中各指标的权重，找出通过能力瓶颈。运用耦合协调度模型计算该区段点线通过能力系统和各子系统耦合协调度，识别关键环节。结果表明：①此模型方法适用于探究高铁点线系统通过能力动态因素间的复杂影响关系，能够识别判断出高铁点线系统通过能力各子系统中的重要动态因素，且能量化影响关系，指明影响方向；②经过实例模型计算，所提方法确定出各个子系统中的关键因素，并且能够反映因素之间的动态耦合关系，影响关系总计存在13条直接影响路径和9条间接影响路径，将各子系统间的影响可视化，可以依据所得结果选取合理计算能力参数及取值范围。Abstract: This study addresses the challenges posed by multiple dynamic factors affecting the passing capacity of high-speed railway node-line systems, particularly focusing on the complex interrelationships among these factors and the difficulty in quantifying their weights. A dynamic coupling coordination method based on structural equation modeling (SEM) is proposed to resolve these issues. The dynamic factors influencing high-speed railway node-line passing capacity are categorized into six subsystems: node system, line system, transportation organization, operational time, delays, and early arrivals. A PLE-SEM-based dynamic coordination model is subsequently constructed to analyze these subsystems. Operational data from the Shanghai West Station-Shanghai Station section are utilized to verify the model's validity, scientific rigor, and goodness-of-fit through measurement model and structural model validation. This process identifies interaction mechanisms, directional influences, and indicator weights across subsystems while detecting capacity bottlenecks. A coupling coordination degree model is further applied to assess system-level and subsystem-level coordination states, enabling the identification of key links. The results demonstrate: ①this model method is applicable for investigating the complex influence relationships among dynamic factors affecting the throughput capacity of high-speed railway node-line systems. It enables the identification of critical dynamic factors within subsystems of the system's throughput capacity, quantifies the influence relationships, and specifies the direction of impacts. ②Through comprehensive factor analysis and case study calculations, the proposed method effectively identifies key factors and reveals dynamic coupling relationships among them. A total of 13 direct influence paths and 9 indirect influence paths are established between subsystems, visualizing their interconnections. These results provide a basis for selecting appropriate capacity calculation parameters in practical applications.
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表 1 潜变量和观测变量表
Table 1. Table of latent and observed variables
潜变量 形态 观测变量 点系统（SS） 形成性 ss_1：上海站不同作业类型列车比 ss_2：上海西站不同作业类型列车比 ss_3：列车出发正点率 ss_4：旅客列车开行对数 线系统（LS） 形成性 1s_1：不同运行速度等级列车比 1s_2：列车发到比 1s_3：列车运行正点率 运输组织（TO） 形成性 to_1：停站基本扣除系数 to_2：列车运行图有效时间利用率 to_3：线间缓冲时间 to_4：流量分布 作业时间（OT） 形成性 to_1：发车占用时间 ot_2：接车占用时间 ot_3：追踪间隔时间 ot_4：额外占用时间 延误（DA） 反映性 da_1：出发晚点列车数及晚点率 da_2：到达晚点列车数及晚点率 da_3：平均初始晚点时间 da_4：平均初始晚点时间 早点（AE） 反映性 ae_1：平均初始早点时间 ae_2：平均连带早点时间 
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表 2 测量模型参数表
Table 2. Measurement Model Parameter Table
变量 形态 指标 因素负荷量/权重 Cronbach'$ \alpha $ CR值/VIF AVE值$ / t $值 SS 形成性 ss_1 0.687 6.453 3.841 ss_2 0.787 1.084 10.667 ss_3 0.602 1.256 6.976 ss_4 0.691 6.772 3.632 LS 形成性 ls_1 0.572 1.010 6.668 ls_2 0.559 1.027 9.060 ls_3 0.482 1.018 7.026 TO 形成性 to_1 0.478 1.237 6.456 to_2 0.440 1.094 8.061 to_3 0.424 1.090 7.219 to_4 0.489 1.249 6.187 OT 形成性 ot_1 0.589 1.111 5.904 ot_2 0.638 1.048 7.859 ot_3 0.390 1.034 4.374 ot_4 0.353 1.063 3.785 DA 反映性 da_1 0.955 0.977 0.914 da_2 0.960 da_3 0.964 0.969 da_4 0.946 AE 反映性 ae_1 0.984 0.970 0.985 0.971 ae_2 0.987 注：本表中因素负荷量、CR值和AVE值为反映性模型参数，权重、VIF和t值为形成性模型参数。
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表 3 假设检验结果表
Table 3. Hypothesis test results table
假设 路径 路径系数 t值 P值 检验结果 H1 SS $ \rightarrow $ LS 0.388 3.514 0.000 接受 H2 LS $ \rightarrow $ TO 0.487 2.963 0.003 接受 H3 $ \mathrm{SS} \rightarrow \mathrm{TO} $ 0.226 2.167 0.030 接受 H4 OT $ \rightarrow $ SS -0.503 6.155 0.000 接受 H5 OT $ \rightarrow $ LS -0.392 4.779 0.000 接受 H6 OT $ \rightarrow $ TO -0.067 0.783 0.434 拒绝 H7 $ \mathrm{DA} \rightarrow \mathrm{SS} $ -0.299 3.799 0.000 接受 H8 DA $ \rightarrow $ LS -0.163 2.776 0.006 接受 H9 DA $ \rightarrow $ OT 0.344 3.448 0.001 接受 H10 $ \mathrm{DA} \rightarrow \mathrm{TO} $ -0.167 2.428 0.015 接受 H11 $ \mathrm{AE} \rightarrow \mathrm{SS} $ -0.328 4.352 0.000 接受 H12 $ \mathrm{AE} \rightarrow \mathrm{LS} $ -0.184 2.668 0.008 接受 H13 $ \mathrm{AE} \rightarrow \mathrm{TO} $ -0.153 2.118 0.034 接受 H14 AE $ \rightarrow $ OT 0.445 4.493 0.000 接受
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表 4 间接路径表
Table 4. Indirectpath table
路径 路径系数 t值 P值 路径 路径系数 $ t $值 $ P $值 AE-OT-SS -0.224 3.399 0.001 DA-OT-SS -0.173 2.903 0.004 AE-SS-LS -0.127 3.256 0.001 DA-SS-LS -0.116 2.521 0.012 OT-LS-TO -0.191 2.633 0.008 SS-LS-TO 0.189 2.215 0.027 AE-OT-LS -0.175 3.176 0.002 DA-OT-LS -0.135 2.952 0.003 OT-SS-LS -0.195 2.627 0.009
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表 5 耦合协调度模型原始数据表
Table 5. Original data table of coupling coordination model
子系统 指标 组间权重 组内权重 子系统标准化值 指标标准化值 SS ss_1 0.15 0.24 0.697 0.687 ss_2 0.28 0.787 ss_3 0.22 0.602 ss_4 0.26 0.691 LS 1s_1 0.12 0.35 0.540 0.572 1s_2 0.35 0.559 1s_3 0.30 0.482 TO to_1 0.26 0.459 0.478 to_2 0.24 0.440 to_3 0.23 0.424 to_4 0.27 0.489 OT ot_1 0.22 0.30 0.522 0.589 ot_2 0.32 0.638 ot_3 0.20 0.390 ot_4 0.18 0.353 DA da_1 0.24 0.25 0.954 0.955 da_2 0.25 0.960 da_3 0.25 0.964 da_4 0.25 0.946 AE ae_1 0.27 0.5 0.988 0.987 ae_2 0.5 0.984
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表 6 子系统耦合协调度计算结果
Table 6. Calculation results of subsystem coupling coordination degree
指标 SS子系统 LS子系统 TO子系统 OT子系统 DA子系统 AE子系统 耦合度$ C $ 0.996 0.997 0.706 0.685 0.707 0.990 综合评价指数$ T $ 0.697 0.540 0.459 0.522 0.954 0.986 耦合协调度$ D $ 0.833 0.734 0.569 0.598 0.821 0.988
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表 7 耦合协调度等级划分表
Table 7. Coupling Coordination Level Classification Table
耦合协调度D范围 协调等级 等级划分 耦合协调度D范围 协调等级 等级划分 $ 0.00 \sim 0.09 $ 1 极度失调 $ 0.50 \sim 0.59 $ 6 勉强失调 $ 0.10 \sim 0.19 $ 2 严重失调 $ 0.60 \sim 0.69 $ 7 初级失调 $ 0.20 \sim 0.29 $ 3 中度失调 $ 0.70 \sim 0.79 $ 8 中级协调 $ 0.30 \sim 0.39 $ 4 轻度失调 $ 0.80 \sim 0.89 $ 9 良好协调 $ 0.40 \sim 0.49 $ 5 濒临失调 $ 0.90 \sim 1.00 $ 10 优质协调
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