Vulnerability Analysis of China-Europe Railway Express Network Based on Improved Nonlinear Load-Capacity Model

The China-Europe Railway Express (C-ER Express) provides a transcontinental rail container service between China and Europe. As most C-ER Expresses are affected by frequent natural disasters and public health incidents, it faces the increasing risk of network vulnerability. When previous studies investigated the evolution of network vulnerability through local information, they often overlook the complexity of the network’s multidimensional characteristics. The nonlinear load-capacity (NLC) model proposed in this paper integrates local and global information of the network. This approach enables a detailed investigation into how condition thresholds and different types of nodes influence network vulnerability. Firstly, a feature matrix is constructed for C-ER Express based on the topological measures, freight information, and external environment scores. Then, the autoencoder is used to extract the low-dimensional dense information, and the DBSCAN is used to classify C-ER Express into distinct clusters. Secondly, The NLC model integrates feature coefficient to describe the initial capacity of nodes. Subsequently, the failure load is redistributed proportionally to neighboring nodes and remaining normal nodes based on time-varying load and initial capacity of nodes. Finally, the improved NLC model is applied to the C-ER Express under different simulation scenarios. Simulation results show that a reasonable condition threshold can mitigate the impact of small-scale node failures on the network. The DBSCAN attack strategy can effectively identify the node types and prevent the network from chain reactions brought by different types of node failures. This research study is expected to provide some reference value for relevant research about vulnerability analysis of the C-ER Express network.