A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control

Bart Besselink (1) , Umut Tabak (2) , Agnieszka Lutowska (3) , Nathan van de Wouw (4) , H. Nijmeijer (4) , Daniel J. Rixen (5, 6) , Michiel Hochstenbach (3) , Wil Schilders (3)

1 Department of Electromagnetic Engineering [Stockholm]
2 Department of Precision and Microsystems Engineering (PME)
3 Department of Mathematics and Computer Science [Eindhoven]
4 Department of Mechanical Engineering [Eindhoven]
5 Department of Precision and Microsystems Engineering
6 Institute of Applied Mechanics [Garching]

In this paper, popular model reduction techniques from the fields of structural dynamics, numerical mathematics and systems and control are reviewed and compared. The motivation for such a comparison stems from the fact that the model reduction techniques in these fields have been developed fairly independently. In addition, the insight obtained by the comparison allows for making a motivated choice for a particular model reduction technique, on the basis of the desired objectives and properties of the model reduction problem. In particular, a detailed review is given on mode displacement techniques, moment matching methods and balanced truncation, whereas important extensions are outlined briefly. In addition, a qualitative comparison of these methods is presented, hereby focusing both on theoretical and computational aspects. Finally, the differences are illustrated on a quantitative level by means of application of the model reduction techniques to a common example.

Domaines: Mécanique [physics.med-ph]; Mécanique des solides [physics.class-ph]

Bart Besselink, Umut Tabak, Agnieszka Lutowska, Nathan van de Wouw, H. Nijmeijer, et al.. A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control. Journal of Sound and Vibration, 2013, 332 (19), pp.4403-4422. ⟨10.1016/j.jsv.2013.03.025⟩. ⟨hal-01711355⟩