Generalizing Linear Graphs and Bond Graph Models with Hetero-functional Graphs for System-of-Systems Engineering Applications

TL;DR

This paper demonstrates that hetero-functional graph theory is a comprehensive framework that generalizes linear graphs and bond graphs, enabling unified modeling of diverse complex engineering systems and systems-of-systems.

Contribution

It establishes a formal mathematical relationship showing hetero-functional graphs as a generalization of linear graphs and bond graphs, with comparative analysis across multiple system types.

Findings

Hetero-functional graphs unify modeling techniques across domains.

Mathematical proof of hetero-functional graphs as a generalization.

Comparison of modeling techniques on six diverse systems.

Abstract

In the 20th century, individual technology products like the generator, telephone, and automobile were connected to form many of the large-scale, complex, infrastructure networks we know today: the power grid, the communication infrastructure, and the transportation system. Progressively, these networked systems began interacting, forming what is now known as systems-of-systems. Because the component systems in the system-of-systems differ, modeling and analysis techniques with primitives applicable across multiple domains or disciplines are needed. For example, linear graphs and bond graphs have been used extensively in the electrical engineering, mechanical engineering, and mechatronic fields to design and analyze a wide variety of engineering systems. In contrast, hetero-functional graph theory (HFGT) has emerged to study many complex engineering systems and systems-of-systems (e.g. electric power, potable water, wastewater, natural gas, oil, coal, multi-modal transportation, mass-customized production, and personalized healthcare delivery systems). This paper seeks to relate hetero-functional graphs to linear graphs and bond graphs and demonstrate that the former is a generalization of the latter two. The contribution is relayed in three stages. First, the three modeling techniques are compared conceptually. Next, these techniques are contrasted on six example systems: (a) an electrical system, (b) a translational mechanical system, (c) a rotational mechanical system, (d) a fluidic system, (e) a thermal system, and (f) a multi-energy (electro-mechanical) system. Finally, this paper proves mathematically that hetero-functional graphs are a formal generalization of both linear graphs and bond graphs.