Identification of cascade of Hammerstein models for the description of non-linearities in vibrating devices

Marc Rébillat (1, 2) , Romain Hennequin (3) , Etienne Corteel (4) , Brian F.G. Katz (1)

1 LIMSI - Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur
2 LMS - Laboratoire de mécanique des solides
3 TSI - Département Traitement du Signal et des Images
4 sonic emotion - sonic emotion

In a number of vibration applications, systems under study are slightly nonlinear. It is thus of great importance to have a way to model and to measure these nonlinearities in the frequency range of use. Cascade of Hammerstein models conveniently allows one to describe a large class of nonlinearities. A simple method based on a phase property of exponential sine sweeps is proposed to identify the structural elements of such a model from only one measured response of the system. Mathematical foundations and practical implementation of the method are discussed. The method is afterwards validated on simulated and real systems. Vibrating devices such as acoustical transducers are well approximated by cascade of Hammerstein models. The harmonic distortion generated by those transducers can be predicted by the model over the entire audio frequency range for any desired input amplitude. Agreement with more time consuming classical distortion measurement methods was found to be good.

Mots clés: vibro-acoustic systems; nonlinearities estimation

Domaines: Acoustique [physics.class-ph]; Acoustique [physics.class-ph]

Marc Rébillat, Romain Hennequin, Etienne Corteel, Brian F.G. Katz. Identification of cascade of Hammerstein models for the description of non-linearities in vibrating devices. Journal of Sound and Vibration, 2010, 330 (5), pp.1018-1038. ⟨10.1016/j.jsv.2010.09.012⟩. ⟨hal-00619301⟩