Trainee Project
Markovian and Semi-Markovian Input-Output models for prognosis.
2022/03/01 - 2022/07/31
Within the framework of the Factory of futur (FoF), and more specifically of predictive maintenance (CBM+), it is necessary to
exploit tools able of predicting the remaining useful life of components or systems. The models that can be used are based on
models or data. We will focus here on data-based approaches and more particularly on stochastic models of the Hidden Markovian
Model (HMM) type.
Hidden Markovian models are models of interest for residual life prognosis. Degradation, which is generally not measurable because
it is a complex notion, is modeled by a Markovian process. Several other random processes are associated and produce observable
signals conditioned by the hidden state of a Markovian process. These signals are measured and provide information on the hidden
The physical degradation of a component or a system is dependent on the operating conditions. It seems rational to condition the
Hidden Markovian process by exogenous variables conditioning the evolution speed of this process towards the final state and thus
the remaining useful life (RUL). These models are IOHMM (Input/Output HMM) type models, very close to Artificial Intelligence
As HMM and IOHMM models are based on a Markovian process, they are memoryless, i.e. the future state depends only on the
current state. In fact, the duration of stay in a hidden state is not considered, which implies a poorly estimated residual life. It exists
Hidden Semi-Markovian Models (HsMM) where the lifetime is taken into account but they are not conditioned by exogenous
processes (operational conditions). To take benefits of these two types of models, it is necessary to develop IOHsMMs. This is the
purpose of this project.
For this purpose, the schedule of the work is as follows:
1. Learning of HMM, IOHMM, HsMM models via the available tools
2. Benchmarking of the models
3. Transformation of HsMM model into IOHsMM
4. Validation on Benchmark data.

SHAHIN K.I., Dynamic probabilistic graphical model applied to the system health diagnosis,
prognosis, and the remains useful life estimation, PHD of the University of Lorraine, 2020
Factory of Future, Pronostic, Degradation
Duration :5 Months,
Employer: Université de Lorraine,
Place: Faculté des Sciences de Nancy, CRAN
Expected Profil : Second Year Master Student in Control Theory or Applied Mathematics or Computer Science having a good
knowledge of probabilistic models, skills in programming under MatLab, and having knowledge of physical modeling.
Eco-Technic systems engineering
ISET Departement, Legal funds defined by the French Government (573,30 ¬/month)