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

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 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 focussing 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.