Ph. D. Project
Development of a digital twin integrating functional physical models, failures, ageing/degradation phenomena and control systems
2021/02/18 - 2024/06/30
This work is part of the "Digital Reactor" project, financed within the framework of the call for
"Structuring Projects for Competitiveness" (PSPC) of the Future Investment Program (PIA), and in which
the main actors of the French nuclear industry (EDF, Framatome, CEA, CORYS, ESI Group, Aneo, Axone,
BOOST, CRAN) participate. The objective of the "Digital Reactor" project is to build a reactor-scale
"digital twin", covering all life cycle phases, to simplify the design process and secure safety margins in
Objective of the project:
The work of Lot 2 " Operation Integration Bench" of the "Digital Reactor" project must develop, for a
given installation, a "digital twin" representative of the physical state of a system, such as a nuclear
reactor. The complex physical phenomena specific to a nuclear reactor are of a continuous nature and
are generally represented by differential equations, finite difference equations, ...
In order to be as representative as possible of the real-time status of the system, a "digital twin" must
also be able to integrate models of failures and equipment wear, and take them into account in the
management of operating and control modes. Whether for mode management or failure modeling,
their models are discrete models that evolve on the occurrence of events.
Moreover, if the continuous physical phenomena and the management of control modes evolve in a
rather deterministic way, the failure modes and the wear and tear of equipment are rather a stochastic
nature. Models of equipment ageing or degradation as a function of physical phenomena are necessary
to represent their evolution over time.
Thus, models able to take into account and integrate both continuous physical phenomena and discrete
functional and dysfunctional modes are hybrid models. To analyze, simulate and evaluate this type of
model, we develop at CRAN two types of approaches:
• an approach by Stochatic Hybrid Automata 5SHA) introduced and formally defined at CRAN [1, 2]
(modeling used in the framework of the preliminary projects APPRODYN [3] and CONNEXION in
collaboration with EDF);
• an approach by Colored Petri Nets (CPN) [4-6].
Whether the modeling approach (by SHA or CPN) and the type of model (aging or degradation), two
ways of resolution are possible: an exact analytical resolution of the equations and a resolution by
simulation. Among these two paths, we choose the simulation path for the following two reasons:
• the complexity of the physical phenomena taking into account in a nuclear reactor, but also the
complexity of the management of its functional and dysfunctional modes leads to an explosion in the
size of models that are incompatible with an exact analytical resolution;
• the objectives of the digital twin clearly fall within the field of simulation in order to, on the one
hand, train human operators according to different control strategies and the type of encountered
situation and, on the other hand, facilitate the understanding of complex physical phenomena and their
impacts in order to be able to assist operations at any time.
The following numerical tools for simulation could be used:
• for SHA modeling: PyCATSHOO (software developed by EDF) [7];
• for CPN modeling: CPNTools (free software) [8].
CRAN's contribution on this subject will focus on the definition and implementation of a simulation of
the reactor's operating modes integrating physical models and failures. Work will begin in January
Scientific objectives and phases of work:
The scientific objectives and the main phases of work identified are as follows:
1) Definition and formalization of requirements and scientific issues to be solved
a. What granularity for the integration of the physical models of continuous nature issued from Lot 1?
b. What are the needs of the operator and the data available to perform the integration of the
ageing/degradation models on the digital twin (link with task 2.2. of LOT 2)?
c. Definition of specific requirements for the test case (cold run) by integrating the answers to the
first two questions for future use as a proof of concept on the results of the CRAN work.
d. Analysis of the scientific and technical state of the art.

2) Specification of the approach/formalisms/tools for the integration of functional, dysfunctional,
ageing/degradation and control models for their simulation in the digital twin
a. Definition of a temporal execution semantics to be able to perform simulations integrating both
continuous/discrete and deterministic/stochastic aspects,
b. Integration of physical models of a continuous nature (from Lot 1) into discrete models by
proposing possible mechanisms for abstraction/transformation of the models according to the retained
tool (SHA, CPN),
c. Definition of the mutual dependency relationships between ageing/degradation phenomena and
the dynamic behaviour of the physical system
d. Integration of the "Aging/Deterioration - Physical System" dependencies defined in c) into the
control models.

3) Development of a "proof of concept" prototype
a. Implementation of the results of 2) within the available numerical tools and possible adaptation to
the context of use
b. Implementation of the "cold run" test case
c. Analysis of results and possible feedback on 2).
digital twin, discrete event systems, system dependability, stochastic processes, degradation, aging
Modeling and Control of Industrial Systems