Learn more about
WorldLab™ technology, Σ™ formal modeling language and Systemic Digital Twins
This section will be regularly updated
Σ™ Reference Manual
This manual presents Σ™, an object-oriented modeling language dedicated to the description and the simulation of the dynamics of complex industrial and socio-technical systems. Σ™ relies onto two pillars: first, the decomposition of the system into a hierarchy of subsystems, the state of each subsytems being described by means of variables. Second, the description of activities performed by subsystems and modifying their states. Although apparently simple, this way of describing complex systems dynamics turns out to be extremely powerful. Discrete event simulation performed on Σ™ models make it possible to play what-if scenarios, to assess key performance indicators, and to apply optimization techniques.
Σ™ is at the core of the WorldLab™ technology that aims at automatically developing systemic systemic digital twins of complex systems, thereby helping decision-makers to manage their strategic assets.
➤ This manual introduces Σ™ concepts and describes the syntax and the semantics of Σ™ constructs. It provides a reference for WorldLab™ users. Some of the constructs described here are not yet implemented in the Σ™ toolsuite and .we shall mention it explicitly, when it is the case.
A Guided Tour of the Systemic Modeling Language Σ™
Σ™ is both a language and a methodologic approach for describing and studying the dynamics of complex industrial 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, simulation & operational use 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
How to Simulate a MBSE System Model using Σ™ and WorldLab™?
The WorldLab™ technology allows to automatically produce systemic digital twins of an industrial system from a MBSE model through a specification designed in our Σ™ formal modeling language, supported by a standard development methodology.
The construction of a systemic digital twin based on WorldLab™ and Σ™ indeed follows a method in 3 steps, which is fully detailed in this document. This goes from the design of the systemic digital twin. then the software development of the systemic digital twin, until using the systemic digital twin for solving a business issue.
Managing the Systemic Digital Twin of an industrial Enterprise with WorldLab™ and Σ™
Using a systemic digital twin consists in creating & simulating evolution scenarios for an industrial system, executing the corresponding step-by-step and stochastic simulations and analyzing & optimizing their results, in order to manage continuous business improvements. The core deliverable of a systemic digital twin is indeed a set of key performance business indicators for various evolution scenarios, integrating volume & time hazards, of the considered industrial system, on which strategic or operational business decisions can be taken in the most relevant way.
➤ This white paper intends to present – through an example – our approach to behavorial digital twins which integrate all core features that we just sketched here above.