To tackle the complexity of systems, engineers more and more on computer models and simulations. By designing these digital twins of the systems, they pursue two main objectives: first, to better understand the systems and to ensure that stakeholders share a common understanding of the problems at stake; second, to assess key performance indicators without having to perform physical experiments, which would be too costly, or simply impossible.
Models are already pervasive in most of the engineering disciplines like mechanical, electrical, or reliability engineering. As of today, their introduction into systems engineering is still an on going process and the subject of active researches and developments. Modeling technologies to be applied are still debated. One of the main difficulties is to capture the key features of the system under study while staying at the suitable level of abstraction. Another difficulty is to integrate in the models the heterogeneous characteristics of systems.
The Σ™ modeling framework aims at providing a generic, mathematically sound and computationally efficient, solution to these difficulties. It relies on two pillars.
- First, one describes the architecture of the system under study, i.e. the system is decomposed into subsystems. These subsystems can be themselves further decomposed until the suitable granularity is reached. The state of each subsystem is described by means of discrete (symbolic) and continuous variables.
- Second, one describes activities performed by subsystems. Activities are guarded, i.e. they are performed when a certain condition on the state of the system is satisfied. They take time. This time may be deterministic or stochastic.
Finally, they modify twice the state of the system. First at their beginning, to book the resources they need. Second at their completion, to release these resources and to describe their effect on the state of the system. Activities can not only modify the values of variables, but also create, move and delete components.
The Σ™ modeling language allows to specify the hierarchical structure and the behaviors, that is to say the business processes, of a given industrial system, but also the end-user interface with the business indicators & alerts that shall be computed and shown to the business users during the use of a systemic digital twin.
Σ is both a language and a method for describing and studying the dynamics of complex technical and socio-technical systems and their environment. It makes it possible to implement computer simulations, to assess key performance indicators by means of these simulations, to play “what-if” scenarios and to apply optimization techniques. In a word, the framework we propose here supports the design of systemic digital twins of complex technical systems. This article aims both at providing a guided tour of the Σ modeling framework and at illustrating its use by means of examples