Analyzing Naval Ship Design with Graph Theory
Large ships are incredibly complex systems with many subsystems interacting at all levels. The performance and safe operation of ships is dependent on these systems running stably and not interfering with each other. This is especially true for naval vessels, which have the added challenge of having to consider these subsystems as active targets to disable the ship and harm the crew. As with all design processes, it is cheaper and quicker in the long run to catch design issues early in the process. With ship design this can be difficult as the multilevel layouts of these vessels can be hard to process before they are fully detailed with more intensive work later. Modeling all the subsystems as networks with information relating to their design criteria can make details of design intent and effectiveness far clearer. Once these networks are defined, graph optimization can drive further revisions in the early stages of design.
In the paper cited, examples of these analyses were carried out for the hypothetical schematic of a 108 m anti-piracy corvette with a 69 member crew. The most basic subsystem, passageways, was modeled with nodes at all doors and intersections of passageways. Edges, the passageways themselves, were weight with the real distance between nodes. The graph of 74 nodes and 194 edges had a diameter of 70.6 m. An important functionally is the crew members’ ability to evacuate the ship. Using the graph, the longest shortest path to an egress was 36.6 m from a storage area. To analyze dangerous congestion during evacuation, all nodes were evaluated with an adjusted betweenness metric weighting their distance to an exit by the number of shortest exit paths that pass through them. This allowed the flagging of a particularly high traffic ladder between decks, with the recommendation it be replaced with wider stairs. The electrical network was modeled with nodes in all spaces, intersections, and at notable machinery and weaponry. The edges were again distances, with an added weighting of the expected operating voltage. The resulting network showed a spoked wheel structure. The high betweenness nodes in the center were revealed as dangerous weaknesses to specific attacks on the electrical system. The fire suppression system had the same nodes and edges, and thus the centrality driven weaknesses, as the electrical graph, but with the edges weighted by a risk factor. To analyze the ship as one unit, the above systems were aggregated into a multiplex network. Using a multiplex quality function, the full ship showed very strong communities that could indicate further weakness due to the physical correlation of subsystems.
https://www.sciencedirect.com/science/article/pii/S2092678216303168