A Stochastic Approach to Maintaining the Operational Condition of Digital Twins

This thesis project is situated within the context of the fourth industrial revolution, where cyber-physical infrastructures (CPS) and digital twins (DT) play a central role in transforming operating systems. The digital twin, a virtual representation of a physical system, enables control, prediction, and improvement of production system maintenance. However, several scientific challenges hinder their large-scale deployment: loss of DT fidelity, lack of tools to monitor their lifecycle, and insufficient integration of humans in their evolution.
To address these challenges, this thesis proposes a stochastic approach to represent uncertainty and randomness in digital twin systems. The objective is to maintain their fidelity to the reference system by modeling data flows and system fluctuations using probabilistic distributions rather than deterministic values. This approach will differentiate between normal system evolutions, to which the DT must adapt, and random events requiring updates to the reference system.
The methodology is structured around two main axes. The first axis concerns stochastic modeling of digital twin dynamics: identification of random variables and their distributions, modeling of system dynamics through Markov processes or stochastic optimization models, and validation of the mathematical model. The second axis aims to develop a reflective digital twin capable of adapting its behavior according to changes in its reference system through a meta-model integrating notions of randomness, robustness indicators, and resilience.
The work program spans three years and includes: a state-of-the-art study, identification of a case study at the Festo training factory at IUT Lumière, mapping of modelable data and behaviors, modeling of the DT/reference system dynamics, definition of the stochastic model and reflective meta-model, as well as prototyping and experimentation.
Expected results include the development of a robust stochastic model based on Markov processes, implementation of a reflective meta-model enabling DT adaptation, and a functional prototype validated on an industrial case. This research aims to make digital twins more representative and practical for complex systems, thereby facilitating their updating and uncertainty management.