Vulnerability assessment and evolution analysis of Beijing's Urban Rail Transit Network

With the development of urban rail transit system, the complexity of the network intensifies, and its vulnerability shifts correspondingly. Understanding the characteristics and evolution of network vulnerability, as well as identifying developmental patterns, enables more scientific network planning. Current researches on network vulnerability predominantly focus on the static vulnerability assessment of existing networks, with limited studies on vulnerability evolution. This paper divides the topological evolution of the Beijing Urban Rail Transit Network (BURTN) from 2000 to 2020 into Formation and Improvement stages using the K-means++ method. By constructing a multidimensional vulnerability assessment model that considers node degree uniformity, network efficiency, and connectivity, the vulnerability evolution characteristics and patterns of BURTN are explored in cases of both Single-station failures and Multi-station consecutive failures (including random and intentional failures). Furthermore, the evolutionary relationship between network vulnerability and network structure is explored using the Ridge regression model. Calculations reveal that in the case of Single-station failures, during the Formation stage, the proportion of highly vulnerable stations (HVS) and the impact of each station failure on network performance decrease significantly, by 69.36 % and 67.67 %, respectively. During the Improvement stage, the proportion of HVS decreases significantly, while the impact of each station failure on network performance decreases slightly, by 79.10 % and 37.04 %, respectively. In the case of Multi-station consecutive failures, during the Formation stage, the network’s ability to cope with both random and intentional failures decreases, with the percentage of network nodes removed at the collapse state decreasing by 24.95 % and 11.12 %, respectively. During the Improvement stage, the network’s ability to cope with random failures remains stable, while its ability to cope with intentional failures decreases. This study helps to understand vulnerability from an evolutionary perspective and provides practical strategies for reducing vulnerability.