A novel homology-based framework for K-terminal network reliability estimation under mixed failure modes

Reliability analysis for large-scale critical infrastructure networks under mixed failure modes remains a challenging problem. This is mainly due to the combinatorial explosion of multiple failure scenarios, the lack of a unified treatment for mixed failures, and the need for many repeated evaluations when network topologies are changed. To address these challenges, this paper proposes a novel homology-based reliability analysis framework for the K-terminal network under mixed failures. This framework combines the respective advantages of homology theory, innovative graph algorithms, deep neural networks, and active learning strategies. First, a homology-based union-find (HUF) algorithm is proposed to verify K-terminal connectivity under mixed failures, where HUF serves as a subroutine for a homology-based bisection algorithm that efficiently identifies critical component-lifetime pairs. Furthermore, two methods for K-terminal network reliability estimation are proposed, one is the homology-based Monte Carlo sampling method, which can efficiently quantify survival-signature without path enumeration, and the other is the homology-based active learning method, which facilitates deep neural networks and uncertainty-guided adaptive sampling to improve the scalability under different topological structures. Numerical experiments on synthetic mixed-failure networks and several large-scale real-world networks illustrate the outstanding performance of the proposed homology-based framework for K-terminal reliability estimation.