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 most significant societal challenges of the Anthropocene era are intertwined, necessitating a convergent systems-of-systems modelling 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 utilises the Systems Modelling Language, model-based systems engineering, and Hetero-Functional Graph Theory (HFGT) to address the convergence research challenges in constructing models and measures across multiple disciplines for systems resilience. The paper includes both the ‘survival’ as well as the ‘recovery’ components of resilience. It also strikes a middle ground between two disparate approaches to resilience measurement: structural measurement of formal graphs and detailed behavioural simulation. This paper also generalises a previous resilience measure based on HFGT, benefiting 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.