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Systematic enumeration and identification of unique 3D spatial topologies ofcomplex engineering systems (such as automotive cooling systems, electric powertrains, satellites, and aero-engines) are essential to navigation of theseexpansive design spaces with the goal of identifying new spatial configurationsthat can satisfy challenging system requirements. However, efficient navigationthrough discrete 3D spatial topology (ST) options is a very challenging problemdue to its combinatorial nature and can quickly exceed human cognitiveabilities at even moderate complexity levels. This article presents a new,efficient, and scalable design framework that leverages mathematical spatialgraph theory to represent, enumerate, and identify distinctive 3D topologicalclasses for a generic 3D engineering system, given its system architecture (SA)-- its components and their interconnections. First, spatial graph diagrams(SGDs) are generated for a given SA from zero to a specified maximum number ofinterconnect crossings. Then, corresponding Yamada polynomials for all theplanar SGDs are generated. SGDs are categorized into topological classes, eachof which shares a unique Yamada polynomial. Finally, within each topologicalclass, 3D geometric models are generated using the spatial graph diagrams(SGDs) having different numbers of interconnect crossings. Selected casestudies are presented to illustrate the different features of our proposedframework, including an industrial engineering design application: STenumeration of a 3D automotive fuel cell cooling system (AFCS). Designguidelines are also provided for practicing engineers to aid the application ofthis framework to different types of real-world problems such as configurationdesign and spatial packaging optimization.

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