Thesis context

At the IRT SystemX, located at the heart of the Paris-Saclay international science campus, you will play an active role in the dynamic development of a research center in the various scientific fields involved in the digital transformation of systems. SystemX is backed by France’s leading research institutions and universities and brings together a range of industrial and academic partners. Its main mission is to generate new knowledge and innovative solutions based on the new digital engineering and to push/dispatch its skills across all economic sectors. More specifically, the PhD candidate will be a part of the scientific domain 4 “Optimization”. The PhD thesis topic is identified based on the ambition and objectives of JNI3 project (Predictive Maintenance and health indicators for Digital
Twins) which addresses the predictive maintenance of complex systems in the era of Digital Twins. The PhD candidate will be supervised by Dr. Makhlouf Hadji, expert researcher at SystemX institute and Prof. Miguel Anjos from Edinburg University.
Hence, the PhD student will be based at SystemX Institute (Palaiseau, France) with regular travels to Edinburg University

Thesis topic

Context & Objectives

Regarding a given physical asset or complex industrial system, a digital twin (DT) consists in linking, using virtualization techniques, the models of the various physical components, their flows and the environments in which they evolve. This DT will rely on the use of different and heterogeneous data collected from a large number of deployed sensors, to propose data-driven modeling (see [1]) in order to achieve precise operational objectives when implementing the physical system using this feedback provided by the DT. Then, for such a system and its associated DT, we plan to control and evaluate its predictive maintenance planning (see [2], for example). Two particular points will be taken into account in this work:

  • it is very commonly the case that the data collected and used as input to our DT is affected by numerous biases (missing data, errors, unstable sensors, etc.). To better manage these uncertainties, this thesis is part of the stochastic optimization approach to propose predictive and scalable maintenance plannings in this uncertain environment.
  • for the implementation of these stochastic optimizations, a set of constraints will be built, containing among others, resource limitation considered in the same description of the convex hull than production cost or safety cost. We use existing key indicators (such as Remaining Useful Life) to evaluate the degradation level of a given physical asset or complex system.

The optimization solution that will be obtained in the digital twin, will be used as feedback to the physical asset (built on a given use-case) to reconfigure, actuate or modify the maintenance planning accordingly. After validating the theoretical approach mentioned above, we propose to illustrate it on an industrial use case of the JNI3 project that will demonstrate the interest of DT for data-driven, constrained predictive maintenance of a complex system.

Scientific challenges

The role of the collected data and measurements are key for predictive maintenance planning and optimization. Indeed, we will use data-driven optimization techniques to establish efficient predictive maintenance planning that meets the above-mentioned constraints. To reach this first objective, the thesis will investigate exact mathematical models for small and medium problem instances. These exact formulations will be provided using chance constraints [6] with a given risk level. Equivalent deterministic formulations will be investigated to approximate the chance constraints and to provide near optimal solutions of the constrained predictive maintenance optimization problem. This former will be used as a new service adjunct to the DT capable of providing rational feedback (in terms of maintenance planning, for instance) to the physical asset. To go beyond state of the art, this thesis will explore new data driven optimization approaches to be able to improve considerably the accuracy of the decision. Hence, we will investigate predict-then-optimize approaches [4] [5] allowing to i) consume the near real time collected data from the physical asset to provide more health state predictions using modified machine learning algorithms with a loss function totally correlated to the output of optimization engine, ii) an optimization algorithm able to handle with maintenance cost minimization under several constraints. So, these approaches are looking to minimize the decision error instead of a classical loss function such as MSE (Mean Square Error), for example


The whole results of the thesis will be considered in illustrations on a technological DT pipeline covering the data collection, data-driven models (stochastic optimization under constraints, predict then optimize, etc.) and visualization of the data and decisions. We can rely on the deployment of open-source DT solutions and technologies [3].


[1] Towards Model-Driven Digital Twin Engineering: Current Opportunities and Future Challenges, F. Bordeleau, et al., International Conference on Systems Modelling and Management, pp 43-54, 2020
[2] Digital Twin for maintenance: A literature review: I. Errandonea et al., Computers in Industry, Volume 123, 2020, 103316, ISSN 0166-3615 2020
[3] DT tools :
[4] Toon Vanderschueren, Tim Verdonck, Bart Baesens, Wouter Verbeke, Predict-then-optimize or predict-and-optimize? An empirical evaluation of cost-sensitive learning strategies, Information Sciences, Volume 594, 2022, Pages 400-415, ISSN 0020-0255,
[5] A.N., Elmachtoub et al, Smart “Predict, then Optimize”, Management Science Volume 68 Issue 101, January 2022, pp 9–26
[6] On probabilistic constrained programming. Prékopa, A. In Kuhn H.W. (ed) Proc. Of the Princeton Symposium on Math. Programming, pages 113-138, Princeton University Press, Princeton, New-Jersey (1970).

Candidate profile

Applying candidates should have a Master 2 or Engineering diploma in applied mathematics and optimization, with the following expected skills:
– Strong skills in mathematical modelling, optimization
– Strong skills in python language development

Informations clés

Type de contrat : IRT SystemX

Localisation du poste : SystemX Institute (Palaiseau, France)

Référence de l’offre : DIT-03-2023

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