A Vulnerability Identification Method for Distribution Networks Integrating Fuzzy Local Dimension and Topological Structure

As the scale of shipboard power systems expands, their vulnerability becomes increasingly prominent. Identifying vulnerable points in ship power grids is essential for enhancing system stability, optimizing overall performance, and ensuring safe navigation. To address this issue, this paper proposes an algorithm based on fuzzy local dimension and topology (FLDT). The algorithm distinguishes contributions from nodes at different radii and within the same radius to a central node using fuzzy sets, and then derives the final importance value of each node by combining the local dimension and topology. Experimental results on nine datasets demonstrate that the FLDT algorithm outperforms degree centrality (DC), closeness centrality (CC), local dimension (LD), fuzzy local dimension (FLD), local link similarity (LLS), and mixed degree decomposition (MDD) algorithms in three metrics: network efficiency (NE), largest connected component (LCC), and monotonicity. Furthermore, in a ship power grid experiment, when 40% of the most important nodes were removed, FLDT caused a network efficiency drop of 99.78% and reduced the LCC to 2.17%, significantly outperforming traditional methods. Additional experiments under topological perturbations—including edge addition, removal, and rewiring—also show that FLDT maintains superior performance, highlighting its robustness to structural changes. This indicates that the FLDT algorithm is more effective in identifying and evaluating vulnerable points and distinguishing nodes with varying levels of importance.