A tensor-based formulation of hetero-functional graph theory

Amro M. Farid, Dakota J. Thompson, Wester Schoonenberg

    Research output: Contribution to journalArticlepeer-review

    3 Scopus citations

    Abstract

    Recently, hetero-functional graph theory (HFGT) has developed as a means to mathematically model the structure of large-scale complex flexible engineering systems. It does so by fusing concepts from network science and model-based systems engineering (MBSE). For the former, it utilizes multiple graph-based data structures to support a matrix-based quantitative analysis. For the latter, HFGT inherits the heterogeneity of conceptual and ontological constructs found in model-based systems engineering including system form, system function, and system concept. These diverse conceptual constructs indicate multi-dimensional rather than two-dimensional relationships. This paper provides the first tensor-based treatment of hetero-functional graph theory. In particular, it addresses the “system concept” and the hetero-functional adjacency matrix from the perspective of tensors and introduces the hetero-functional incidence tensor as a new data structure. The tensor-based formulation described in this work makes a stronger tie between HFGT and its ontological foundations in MBSE. Finally, the tensor-based formulation facilitates several analytical results that provide an understanding of the relationships between HFGT and multi-layer networks.

    Original languageEnglish
    Article number18805
    JournalScientific Reports
    Volume12
    Issue number1
    DOIs
    StatePublished - Dec 2022

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