Source node management in complex water network based on cascading failure and bidirectional risk transmission: The...

Water source nodes within water network are subject to dual pressures: the propagation of failure risks and reverse feedback from fluctuations in user demand. As the connectivity of water network and the relationship between water supply and consumption become increasingly complex, there is an urgent need to elucidate the patterns of bidirectional risk transmission in complex water network and to effectively manage water source nodes. Taking the water network of Henan Province as a case study, improved forward and reverse cascade failure models were established respectively. The criticality of water source nodes in forward risk propagation and their sensitivity to pressure in reverse feedback were comprehensively identified. Spearman correlation analysis and K-means clustering were employed to classify water source nodes into 'criticality+sensitivity' two-dimensional clusters. The results indicate that forward risk transmission exhibits distinct head-concentration characteristics, with a small number of critical reservoir nodes dominating cascade failure. Spatially, risk first propagates through the structural layer before permeating to the functional endpoints.Temporally, it follows a non-linear evolution pattern, initially intensifying and subsequently attenuating. Reverse risk propagation exhibits characteristics of 'source-proximity priority' and hierarchical feedback: as the degree of demand deviation and the number of affected users increase, reservoirs closest to the source are the first to reach their pressure limits and transmit pressure to secondary reservoirs. The two-dimensional classification criteria combining the criticality and sensitivity of reservoir nodes more comprehensively reflect the characteristics of reservoir nodes within the water network, enabling more precise, differentiated management of these nodes. This study broadens the research perspective on risk propagation in complex water network and provides theoretical support and decision-making guidance for the precise management of water source nodes to enhance the water supply security of water network.