A Hetero-functional Graph Resilience Analysis for Convergent Systems-of-Systems

Our modern life has grown to depend on many and nearly ubiquitous large complex engineering systems. Many disciplines now seemingly ask the same question: ``In the face of assumed disruption, to what degree will these systems continue to perform and when will they be able to bounce back to normal operation"? Furthermore, there is a growing recognition that the greatest societal challenges of the Anthropocene era are intertwined, necessitating a convergent systems-of-systems modeling and analysis framework based upon reconciled ontologies, data, and theoretical methods. Consequently, this paper develops a methodology for hetero-functional graph resilience analysis and demonstrates it on a convergent system-of-systems. It uses the Systems Modeling Language, model-based systems engineering and Hetero-Functional Graph Theory (HFGT) to overcome the convergence research challenges when constructing models and measures from multiple disciplines for systems resilience. The paper includes both the ``survival" as well as ``recovery" components of resilience. It also strikes a middle ground between two disparate approaches to resilience measurement: structural measurement of formal graphs and detailed behavioral simulation. This paper also generalizes a previous resilience measure based on HFGT and benefits from recent theoretical and computational developments in HFGT. To demonstrate the methodological developments, the resilience analysis is conducted on a hypothetical energy-water nexus system of moderate size as a type of system-of-systems.