Research on rapid equivalent simplification algorithm for complex underground mine ventilation networks

Mine ventilation network equivalent simplification technology is a powerful tool for analyzing fluid networks. However, with the increasing number of tunnels in mine ventilation networks, their complexity also rises, challenging the precision and computational speed of traditional equivalent simplification algorithms. To address these challenges, a rapid equivalent simplification algorithm for complex mine ventilation networks is proposed. This algorithm employs strong connectivity component algorithms from graph theory to swiftly detect unidirectional loops within the network. It improves the determination formula for equivalent simplification of subnets, thereby avoiding incorrect equivalent simplifications of unidirectional loops. The algorithm introduces a local series and parallel subnet equivalent simplification strategy based on the nodes' in-and-out degrees and the branches' inflow and outflow nodes. This strategy facilitates rapid equivalent simplification of series and parallel subnets in the network that do not contain angular connections. Furthermore, based on the principle of airflow balance in the in-and-out branches of subnet nodes, the paper proposes an optimization strategy for the set of node pairs requiring deep search within the network. This strategy improves the precision and efficiency of the simplification process by reducing unnecessary deep searches of node pairs. Initially, the algorithm's effectiveness is demonstrated through a specific mine ventilation network consisting of 100 branches and 71 nodes. Subsequent empirical tests on ten real mine ventilation networks show that the two optimization strategies proposed in this paper enhance the performance of traditional algorithms. For actual mine ventilation networks with 100 to 1001 branches, compared to traditional algorithms, the proposed algorithm not only increases the completeness of the equivalent simplification but also significantly reduces the network equivalent simplification time scale from (10¹, 10³) seconds to (10⁻², 1) seconds.