Open AccessAn alternative to Lyapunov Exponent as Damage Sensitive Feature
Author(s) -
Antoine Clément,
Stéphane Laurens
Publication year - 2011
Publication title -
hal (le centre pour la communication scientifique directe)
Language(s) - English
DOI - 10.1088/0964-1726/20/2/02501
Subject(s) - lyapunov exponent , jacobian matrix and determinant , computation , lyapunov function , feature (linguistics) , control theory (sociology) , lyapunov equation , mathematics , computer science , nonlinear system , algorithm , physics , artificial intelligence , chaotic , control (management) , quantum mechanics , linguistics , philosophy
International audienceWhen using Lyapunov exponents as damage sensitive feature (DSF) in vibration based structural health monitoring, the computation time represents an important issue for real time applications. To overcome this problem, a new feature, the Jacobian Feature Vector (JFV), is proposed based on the same algorithm but allowing faster computation. Whereas for Lyapunov exponents calculation, the trajectories in the state space are followed for more than a thousand time steps, the new feature is formed by the Jacobian matrix of the dynamics after few time steps. The new feature and the Lyapunov exponents are tested on two case studies : a mass/spring/damper model and a laboratory three story structure. Both the DSF are showing a good performance in detecting damage for the numerical study, even if the Lyapunov exponents present a slightly better ability. Regarding the experimental data, Lyapunov exponents failed to detect damage while the JFV is clearly able to reveal structural changes. Therefore, the JFV offers a robust alternative to Lyapunov exponents allowing to save computation time