Ifsttar PhD subject

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Title : Imaging of 3D elastic waveguides – Application to rails

Main host Laboratory - Referent Advisor GERS - GeoEND  -  TREYSSEDE Fabien      tél. : +33 240845932

Director of the main host Laboratory DEROBERT Xavier  -

PhD Speciality Acoustique, Mécanique, Génie Civil

Axis of the performance contract 2 - COP2017 - More efficient and resilient infrastructure

Main location Nantes

Doctoral affiliation ECOLE CENTRALE NANTES

PhD school Sciences de l'Ingénierie et des Systèmes (SIS)

Planned PhD supervisor TREYSSEDE Fabien  -  Université Gustave Eiffel  -  GERS - GeoEND

Planned PhD co-supervisor LAGUERRE Laurent  -  Université Gustave Eiffel  -  GERS - GeoEND

Planned financing Contrat doctoral 01-2B  - Université Gustave Eiffel

Abstract

Context:

Guided waves have the advantage of propagating over long distances with little energy loss. They offer a promising avenue for non-destructive testing (NDT) and structural health monitoring of slender structures. In the railway industry, detecting and locating defects in rails, particularly in the foot, is a major challenge to ensure safety and optimize transport network maintenance. This PhD topic is part of the ANR Ultratrail project, a collaboration between Université Gustave Eiffel (UGE), the University of Bordeaux, and SNCF (the national company of the French railways), in which the PhD candidate will be actively involved.

However, the development of robust NDT methods faces several challenges:
- instrumentation constraints: the number of sensors must be limited for cost and accessibility reasons,
- complex wave propagation: the multimodal and dispersive nature of guided waves complicates measurement interpretation, requiring advanced propagation models.

In the field of modeling, UGE has developed state-of-the-art numerical tools [1], based on the following finite element methods dedicated to 3D guided waves:
- SAFE (Semi-Analytical Finite Element) for healthy structures [2-4]
- hybrid FE-SAFE (Finite Element – SAFE) for damaged structures [5-6].

Project:

The objective of this PhD research is to develop and optimize innovative imaging methods adapted to 3D elastic waveguides, with a specific application to rails. These methods must account for instrumentation constraints (limited number of transducers) and the particular characteristics of guided waves (dispersion, multimodality).

Based on the mathematical framework of inverse problems in elastodynamics, the proposed approach will rely on evaluating a gradient that reveals the sensitivity of a cost function to the medium’s parameters. This approach, based on the adjoint state and the modal formalism of waveguides, will enable rapid defect localization (imaging) without requiring iterative computations.

Already applied to 2D elastic waveguides (plates) [7], this methodology will need to be extended to 3D waveguides (rails), raising several questions about:
- the influence of measurement and excitation configurations (frequencies, sensor positions and numbers...)
- sensitivity to uncertainties under realistic conditions (noise, sources...)
- the selection of an appropriate gradient (imaging function) depending on the nature of the defects being investigated.

The PhD candidate will exploit UGE’s modeling tools [1] to:
- develop digital twins to simulate elastic wave propagation in rails, with and without defects, to
- implement and test various imaging algorithms, using synthetic data,
- validate the results using laboratory experimental measurements.

Workplace:

The PhD will take place at the GeoEND Laboratory (Geophysics and Non-Destructive Evaluation) at Université Gustave Eiffel, located in Nantes, France. The candidate will benefit from multidisciplinary supervision and have access to cutting-edge experimental and computational facilities.

Desired Profile:

We are looking for an engineer or Master's graduate in acoustics, mechanics, or applied mathematics.

Required skills:
• Numerical modeling and finite elements
• Wave propagation or structural dynamics
• Programming (Python, Matlab, or C++)
Preferred skills:
• Inverse problems and signal processing

Application Process:

Interested candidates are invited to submit the following documents before May 15th, 2025:
• Detailed CV
• Cover letter
• Master’s (or final year of engineering school) transcripts (including, if possible, class ranking)
• Recommendation letter(s) (optional but recommended)

Keywords : acoustics, wave, guide, mode, finite element, modeling, simulation, imaging, experimental, inverse problem, adjoint state, time reversal

Main host Laboratory - Referent Advisor	GERS - GeoEND - TREYSSEDE Fabien tél. : +33 240845932
Director of the main host Laboratory	DEROBERT Xavier -
PhD Speciality	Acoustique, Mécanique, Génie Civil
Axis of the performance contract	2 - COP2017 - More efficient and resilient infrastructure
Main location	Nantes
Doctoral affiliation	ECOLE CENTRALE NANTES
PhD school	Sciences de l'Ingénierie et des Systèmes (SIS)
Planned PhD supervisor	TREYSSEDE Fabien - Université Gustave Eiffel - GERS - GeoEND
Planned PhD co-supervisor	LAGUERRE Laurent - Université Gustave Eiffel - GERS - GeoEND
Planned financing	Contrat doctoral 01-2B - Université Gustave Eiffel
Abstract Context: Guided waves have the advantage of propagating over long distances with little energy loss. They offer a promising avenue for non-destructive testing (NDT) and structural health monitoring of slender structures. In the railway industry, detecting and locating defects in rails, particularly in the foot, is a major challenge to ensure safety and optimize transport network maintenance. This PhD topic is part of the ANR Ultratrail project, a collaboration between Université Gustave Eiffel (UGE), the University of Bordeaux, and SNCF (the national company of the French railways), in which the PhD candidate will be actively involved. However, the development of robust NDT methods faces several challenges: - instrumentation constraints: the number of sensors must be limited for cost and accessibility reasons, - complex wave propagation: the multimodal and dispersive nature of guided waves complicates measurement interpretation, requiring advanced propagation models. In the field of modeling, UGE has developed state-of-the-art numerical tools [1], based on the following finite element methods dedicated to 3D guided waves: - SAFE (Semi-Analytical Finite Element) for healthy structures [2-4] - hybrid FE-SAFE (Finite Element – SAFE) for damaged structures [5-6]. Project: The objective of this PhD research is to develop and optimize innovative imaging methods adapted to 3D elastic waveguides, with a specific application to rails. These methods must account for instrumentation constraints (limited number of transducers) and the particular characteristics of guided waves (dispersion, multimodality). Based on the mathematical framework of inverse problems in elastodynamics, the proposed approach will rely on evaluating a gradient that reveals the sensitivity of a cost function to the medium’s parameters. This approach, based on the adjoint state and the modal formalism of waveguides, will enable rapid defect localization (imaging) without requiring iterative computations. Already applied to 2D elastic waveguides (plates) [7], this methodology will need to be extended to 3D waveguides (rails), raising several questions about: - the influence of measurement and excitation configurations (frequencies, sensor positions and numbers...) - sensitivity to uncertainties under realistic conditions (noise, sources...) - the selection of an appropriate gradient (imaging function) depending on the nature of the defects being investigated. The PhD candidate will exploit UGE’s modeling tools [1] to: - develop digital twins to simulate elastic wave propagation in rails, with and without defects, to - implement and test various imaging algorithms, using synthetic data, - validate the results using laboratory experimental measurements. Workplace: The PhD will take place at the GeoEND Laboratory (Geophysics and Non-Destructive Evaluation) at Université Gustave Eiffel, located in Nantes, France. The candidate will benefit from multidisciplinary supervision and have access to cutting-edge experimental and computational facilities. Desired Profile: We are looking for an engineer or Master's graduate in acoustics, mechanics, or applied mathematics. Required skills: • Numerical modeling and finite elements • Wave propagation or structural dynamics • Programming (Python, Matlab, or C++) Preferred skills: • Inverse problems and signal processing Application Process: Interested candidates are invited to submit the following documents before May 15th, 2025: • Detailed CV • Cover letter • Master’s (or final year of engineering school) transcripts (including, if possible, class ranking) • Recommendation letter(s) (optional but recommended)
Keywords :	acoustics, wave, guide, mode, finite element, modeling, simulation, imaging, experimental, inverse problem, adjoint state, time reversal

List of topics

Applications closed