Applied research internship offer for 2nd-year Master or 3rd-year engineering school students – Signal processing and optimal transport techniques for anomaly detection – 5 months

Project description

Predictive maintenance, essential for the industry 4.0, allows for the prevention of costly breakdowns by anticipating malfunctions. One way of planning maintenance operations is by detecting anomalies based on historical and realtime data. However, the scarcity of data related to anomalies limits the effectiveness of supervised approaches, highlighting the relevance of unsupervised methods. Time-frequency analysis [2, 5], which decomposes non-stationary signals into temporal and spectral components, provides the opportunity to detect subtle variations in industrial systems. The objective of this internship is to leverage time-frequency characteristics to formulate a regularized optimal transport problem, leading to the development of an unsupervised anomaly detection algorithm. Indeed, optimal transport [1, 6] is known for its sensitivity to anomalies, and the idea is to exploit this sensitivity in the time-frequency domain to identify the types of considered anomalies [4]. The data for this study will be generated from a real industrial environment using the IT’m Factory platform [3].

To implement our unsupervised algorithm for anomaly detection, we will focus on the following tasks:

• Modeling the behavior of coefficients in the time-frequency plane.

• Mathematical formulation of the anomaly detection as an optimization problem.

• Definition of a decision threshold based on optimal transport distance.

Keywords: anomaly detection, time-frequency analysis, time series, optimal transport, machine learning.

Basic information

• Internship duration : 5 months

• Starting date : as soon as possible and no later than March 31, 2024

• Location : École des Mines de Saint-Étienne (EMSE), Institut Henri Fayol, Saint-Étienne, France

• Indemnities : Legal amount (https://www.service-public.fr/particuliers/vosdroits/F32131)

• Supervisors : Marina Krémé marina.kreme@emse.fr, Arthur Kramer arthur.kramer@emse.fr, Thomas Galtier thomas.galtier@emse.fr

Candidate profile

• 2nd-year of MSc and/or 3rd-year of an engineering school,

• Strong background in applied mathematics,

• Strong programming skills in Python

• Proficiency in the English language

• Skills in signal processing will be highly appreciated.

Requirements

Application

To apply, candidates must send, their CV and a cover letter to the supervisors.

References

[1] Amina Alaoui-Belghiti, Sylvain Chevallier, and Eric Monacelli. Unsupervised anomaly detection using optimal transport for predictive maintenance. In Artificial Neural Networks and Machine Learning.ICANN. Springer, 2019.

[2] François Auger and Franz Hlawatsch. Time-frequency analysis: concepts and methods. ISTE, 2008.

[3] Institut Mines-Télécom. Itm factory, 2018.

[4] Imad Anis Kheffache. Optimal transport theory for anomaly detection, 2024.

[5] A Marina Krémé, Valentin Emiya, Caroline Chaux, and Bruno Torrésani. Time-frequency fading algorithms based on gabor multipliers. IEEE Journal of Selected Topics in Signal Processing, 15(1):65–77, 2020.

[6] Gabriel Peyré, Marco Cuturi, et al. Computational optimal transport: With applications to data science. Foundations and Trends® in Machine Learning, 11(5-6):355–607, 2019.