An alternative to Lyapunov Exponent as Damage Sensitive Feature

Antoine Clément (1) , S. Laurens (1)

1 LMDC - Laboratoire Matériaux et Durabilité des constructions

When 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.

Mots clés: SHM; damage detection; Lyapunov Exponents

Domaines: Vibrations [physics.class-ph]; Vibrations [physics.class-ph]; Dynamique Chaotique [nlin.CD]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Antoine Clément, S. Laurens. An alternative to Lyapunov Exponent as Damage Sensitive Feature. Smart Materials and Structures, 2011, 20 (2), pp.025017. ⟨10.1088/0964-1726/20/2/02501⟩. ⟨hal-00557282⟩