Category Theory Framework for System Engineering and Safety Assessment Model Synchronization Methodologies

Abstract

In recent decades, there has been a significant increase in systems’ complexity, leading to a rise in the need for more and more models. Models created with different intents are written using different formalisms and give diverse system representations. This work focuses on the system engineering domain and its models. It is crucial to assert a critical system’s compliance with its requirements. Thus, multiple models dedicated to these assertions are designed, such as safety or multi-physics models. As those models are independent of the architecture model, we need to provide means to assert and maintain consistency between them if we want the analyses to be relevant. The model synchronization methodologies give means to work on the consistency between the models through steps of abstraction to a common formalism, comparison, and concretization of the comparison results in the original models. This paper proposes a mathematical framework that allows for a formal definition of such a consistency relation and a mathematical description of the models. We use the context of category theory, as this is a mathematical theory providing great tools for taking into account different abstraction levels and composition of relations. Finally, we show how this mathematical framework can be applied to a specific synchronization methodology with a realistic study case.