DESCRIPTION :
You will numerically analyze how damage, such as cracks, material fatigue, etc, alters these basins and affects the system's global
stability [1]. This work will involve exploring how damage reshapes the basins' boundaries and assessing the system's resilience to
external perturbations, providing insights beyond traditional analyses.
Your work will bridge applied mathematics and mechanical engineering, combining theoretical insights with computational tech-
niques. You will combine computational tools and explore and develop metrics [2, 3, 4, 5] to tackle questions like: How does damage
shift a system's behavior? Can we predict when a damaged structure might fail to recover from a disturbance? The project involves
numerical simulation and theoretical developments. Depending on progress and interests, there will also be an opportunity to
contribute to algorithmic and code development aimed at improving the computation of basins of attraction. Beyond the tech-
nical skills, you will gain experience in interdisciplinary research, working alongside experts to address challenges with real-world
implications, such as improving the safety and reliability of mechanical systems.
This project is ideal for students in applied mathematics or mechanical engineering, with interests in nonlinear dynamics, stability
theory, statistics and/or computational methods.
[1] M. Stender and N. Hoffmann, "bstab: An open-source software for computing the basin stability of multi-stable dynamical systems,"
Nonlinear Dynamics, vol. 107, pp. 1451-1468, 2022. [Online]. Available: https://link.springer.com/article/10.1007/s11071-021-06786-5
[2] P. Menck, J. Heitzig, N. Marwan, and J. Kurths, "How basin stability complements the linear-stability paradigm," Nature Physics, vol. 9, pp.
89-92, 2013. [Online]. Available: https://www.nature.com/articles/nphys2516
[3] M. Soliman and J. Thompson, "Integrity measures quantifying the erosion of smooth and fractal basins of attraction," Journal of Sound and
Vibration, vol. 135, pp. 453-475, 1989. [Online]. Available: https://www.sciencedirect.com/science/article/pii/0022460X89906998
[4] G. Habib, "Dynamical integrity assessment of stable equilibria: a new rapid iterative procedure," Nonlinear Dynamics, vol. 106, pp.
2073-2096, November 2021. [Online]. Available: https://link.springer.com/article/10.1007/s11071-021-06936-9
[5] O. Avci, O. Abdeljaber, S. Kiranyaz, M. Hussein, M. Gabbouj, and D. J. Inman, "A review of vibration-based damage detection in civil
structures: From traditional methods to machine learning and deep learning applications," Mechanical Systems and Signal Processing, vol.
147, p. 107077, Jan. 2021. [Online]. Available: https://doi.org/10.1016/j.ymssp.2020.107077
Principales activités
* Implementing models of nonlinear systems that include damage evolution laws,
* Study multistability and basins of attraction in nonlinear mechanical systems,
* Analyze the evolution of the topology of these basins as a function of the damage level,
* Develop metrics to quantify global stability and system robustness,
* Contribute to research that bridges mathematical/statistical modeling with engineering applications.
Niveau de formation : Bac+5
Temps partiel / Temps plein : Plein temps
Type de contrat : Stage/Jeune diplômé
Compétences : Simulation Informatique, Programmation Informatique, Systèmes Dynamiques, MATLAB, Machine Learning, Traitement de Signal, Deep Learning, Free and Open Source Software, Persévérance, Fiabilité, Algorithmes, Mathématiques Appliquées, Vibrations, Érosions, Génie Mécanique, Mathématiques, Systèmes Mécaniques, Sciences Physiques, Etudes et Statistiques, Dynamique des Structures, Métrique, Applications des Règles et Consignes de Sécurité
Courriel :
adrien.melot@inria.fr
Téléphone :
0299847100
Type d'annonceur : Employeur direct