Abstract
The third chapter of this book orients the reader with hetero-functional graph theory preliminaries from the fields of ontological science, model-based systems engineering, and graph theory. The fundamental ontological concepts of soundness, completeness, lucidity, and laconicity are presented as means by which to formally assess the fidelity of a model. The ontological analysis finds that multi-layer networks maintain soundness and laconicity, but lack completeness and lucidity. The lack of completeness is caused by negligence of function in the modeling language, and the lack of lucidity is caused by the overload of mathematical concepts such as nodes and edges. The remainder of the chapter relates the model-based systems engineering foundations for hetero-functional graph theory as a means of addressing the heterogeneity of interdependent smart city infrastructure systems. In particular, it focuses on the concept of system architecture at the instantiated, reference, and meta levels of abstraction. This discussion sets up hetero-functional graph theory as a more ontologically appropriate domain conceptualization for interdependent infrastructures.
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Notes
- 1.
The original definition of large flexible engineering systems found in the Axiomatic Design literature [29] used the term functional requirements instead of system processes and the term design parameters instead of system resources. Recent works on hetero-functional graph theory [9, 11] have since adopted the definition revised as per the above for consistency of nomenclature.
- 2.
In certain cases the second condition can be relaxed so as to form a one-to-many mapping. However, the independence axiom explicitly prohibits many-to-many mappings of function to form.
- 3.
Power system test cases are often used to conduct power flow analysis studies. The underlying model neglects the lead lines from generators and loads to their associated buses. Other models of power systems such as transient stability models do include such lead lines. In such a case, the reference architecture would have no direct connection from the generators and loads to the buses. Furthermore, power flow analysis models usually do not differentiate between energy storage facilities and power generation facilities despite the former’s ability to both generate and consume power.
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Schoonenberg, W.C.H., Khayal, I.S., Farid, A.M. (2019). Hetero-functional Graph Theory Preliminaries. In: A Hetero-functional Graph Theory for Modeling Interdependent Smart City Infrastructure. Springer, Cham. https://doi.org/10.1007/978-3-319-99301-0_3
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