Dans cette présentation, je proposerai une introduction à certains outils fondamentaux de la géométrie différentielle — en particulier les formes différentielles, la dérivée de Lie et le crochet de Lie — appliqués à l’analyse des systèmes dynamiques. Ces notions permettront d’aborder plusieurs aspects essentiels : l’étude de la stabilité, la linéarisation par retour d’état, ainsi que la linéarisation des systèmes observables modulo des termes dépendant de la sortie.

The degradation of industrial systems is a natural and often unavoidable process. Hidden Markov Models (HMMs) are used for state-based bearing degradation analysis. A challenge arises because bearings can deteriorate in multiple ways, depending on crack locations. To address this, a Multi-Branch Hidden Markov Model (MB-HMM) was developed to handle multiple deteriorations. However, MB-HMM primarily uses simulated data where deterioration is known in advance. In contrast, real-world sensors collect data with uncertainties, potentially causing false alarms and impacting the First Predicting Time. We used the FEMTO-bearing dataset, which includes continuous monitoring until failure, with unknown fault locations and varying degradation levels. This study presents a comprehensive preprocessing framework and employs the Extended Multi-Branch HMM . Our experimental analysis shows that the proposed strategy significantly enhances the Signal-to-Noise Ratio. The active branch is defined based on prior and posterior probabilities, with the branch's prior probability and topology linked to the four fault frequencies of the bearing. The EMB-HMM outperforms other models in state prediction, featuring four branches and five hidden states. It improves state sequence accuracy, predicts degradation levels and FPT, and achieves zero false alarms for Fake Fault.

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2. Notre recherche pour des réponses sociétales et environnementales. Proposition d’un thème complémentaire de nos activités concernant le Maintien en Condition Opérationnelle des systèmes.