中欧集装箱海铁复合运输网络脆弱性分析

中欧贸易运输涉及多个港口和车站，构成复杂的运输网络，网络枢纽节点受到自然灾害、安全事故等影响失效，导致网络仅局部连通，进而影响全局效率。为量化分析中欧集装箱运输网络在枢纽节点失效后的网络功能变化程度，基于中欧班列和海运航线网络构建海铁复合运输网络。在此基础上结合负荷-容量级联失效模型提出1种网络脆弱性仿真模型，模型考虑到节点容量、攻击方式及负载分配策略3类影响因素，并设定网络连通性及网络效率为脆弱性测度指标，仿真实验分析影响该网络脆弱性的因素与演化规律，并通过网络效率变化曲线判断了关键节点。结果显示，中欧集装箱海铁复合运输网络共计167个节点，网络具有无标度和小世界特性，度相关性系数为0.13，网络体现弱同配性，度值相近的节点倾向于互相连接；针对枢纽节点的蓄意攻击相比随机失效的网络更脆弱，失效节点数为3时，蓄意攻击下的网络连通性和效率对比随机失效时，分别下降20.15%和37.19%。从影响因素看，基于地理距离对失效节点负载进行重新分配的策略会加剧网络崩溃，节点容量的增加使网络更为鲁棒，当容量冗余系数增到0.2后，脆弱性指标达到临界阈值，外界干扰不再对整体网络产生影响；海港失效对网络效率的负面影响高于铁路站点，而欧洲港口的影响又高于中国港口。从关键节点识别看，欧洲港口中康斯坦萨港失效时网络效率降幅最大，达88%，中国区域为上海和宁波，降幅均为76%。研究结论有助于理解中欧集装箱海铁复合运输网络的脆弱性影响因素，在突发事件中优先保护关键节点，优化货流分配，从而提升部分枢纽节点失效时的运输网络鲁棒性。

Vulnerability Analysis of China-Europe Container Sea-rail Intermodal Transport Network

The China-Europe trade transportation involves multiple ports and rail stations, forming a complex transport network. The hub nodes of this network are vulnerable to various disruptions such as natural disasters and safety incidents, resulting in partial connectivity and consequently affecting the overall efficiency of the network. To quantitatively analyze the extent of functional changes in the China-Europe container intermodal transport network following the failure of hub nodes, a composite sea-rail transport network is developed based on the China-Europe rail services and shipping lines. On this basis, a simulation model is proposed to investigate the network vulnerability by integrating a load-capacity cascading failure model. The model considers three influencing factors: node capacity, attack methods, and load distribution strategies. The network connectivity and efficiency are set as the vulnerability indices. The simulation model is used to analyze the factors influencing the network vulnerability and its evolution, and to identify critical nodes by examining the change curve of network efficiency. The results reveal that the China-Europe container sea-rail intermodal transport network consists of 167 nodes, exhibiting scale-free and small-world characteristics, with a degree correlation coefficient of 0.13, indicating weak assortativity. The nodes with similar correlation degrees tend to be connected. Intentional attacks on hub nodes render the network more vulnerable compared to random failures. With 3 failed nodes, the intentional attacks result in a 20.15% decrease in network connectivity and a 37.19% decrease in efficiency compared to random failures. From the perspective of influential factors, strategies redistributing load based on geographic distance exacerbate network collapse. The increasing node capacity enhances network robustness, reaching a critical threshold when the capacity redundancy coefficient reaches 0.2, at which point external interference no longer affects the overall network. The negative impact of port failures on network efficiency surpasses that of railway stations, with European ports having a higher impact than Chinese ports. Regarding the critical node identification, the efficiency reduction is most substantial when the Constanta Port in Europe fails, decreasing by 88%. In the Chinese region, both Shanghai and Ningbo ports experience a reduction of 76%. These findings aid in understanding the vulnerability factors affecting the China-Europe container sea-rail intermodal transport network. It suggests the prioritization of protecting critical nodes during emergencies and optimizing cargo flow distribution to enhance robustness of the network in the event of partial hub node failures.