Enumeration and Identification of Unique 3D Spatial Topologies of Interconnected Engineering Systems Using Spatial Graphs

Systematic enumeration and identification of unique 3D spatial topologies complex engineering systems (such as automotive cooling systems, electric power trains, satellites, aero-engines) are essential to navigation these expansive design spaces with the goal identifying new configurations that can satisfy challenging system requirements. However, efficient through discrete topology (ST) options is a very problem due its combinatorial nature quickly exceed human cognitive abilities at even moderate complexity levels. This article presents new, efficient, scalable framework leverages mathematical graph theory represent, enumerate, identify distinctive topological classes for generic system, given architecture (SA) -- components their interconnections. First, diagrams (SGDs) generated SA from zero specified maximum number interconnect crossings. Then, corresponding Yamada polynomials all planar SGDs generated. categorized into classes, each which shares polynomial. Finally, within class, geometric models using having different numbers Selected case studies presented illustrate features our proposed framework, including an industrial application: ST fuel cell (AFCS). Design guidelines also provided practicing engineers aid application this types real-world problems such configuration packaging optimization.