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

翻译：复杂工程系统（如汽车冷却系统、电力传动系统、卫星和航空发动机）独特三维空间拓扑的系统性枚举与识别，对于导航这些广阔设计空间、寻找能够满足严苛系统需求的新空间构型至关重要。然而，由于离散三维空间拓扑选项的组合特性，即使在中低复杂度层次，高效导航此类选项即构成极具挑战性的问题，并会迅速超出人类认知能力。本文提出一种新颖、高效且可扩展的设计框架，该框架利用数学空间图论，针对给定系统架构（即组件及其互连关系），对通用三维工程系统进行表征、枚举和辨识不同的三维拓扑类别。首先，针对给定系统架构，生成从零至指定最大互连交叉数的空间图示意图。随后，计算所有平面空间图示意图对应的Yamada多项式。空间图示意图被归类至拓扑类别中，每个类别共享唯一的Yamada多项式。最后，在每个拓扑类别内，利用具有不同互连交叉数的空间图示意图生成三维几何模型。通过选定的案例研究展示了所提框架的不同特性，包括一项工业工程设计应用：三维汽车燃料电池冷却系统的空间拓扑枚举。同时为实践工程师提供了设计指南，以辅助该框架应用于不同类型现实问题，如构型设计与空间布局优化。