A Critical Exposition of Model Order Reduction Techniques: Application to a Slewing Flexible Beam

Complexity of dynamical systems are increasing more and more as well as their mathematical models. At the same time, simulation of system behaviour assumes a key role to assure the fulfillment of requirements as performances, quality, safety, and robustness. Therefore, due to model complexity, it is often very complex to assess a system behaviour but a reduction of model complexity could enhance the simulation aimed to specific characteristics of the system. Several useful model order reduction (MOR) techniques exist but each of them is often powerful for specific applications. This review paper deals with MOR by critically comparing the most popular MOR techniques from the fields of structural dynamics, numerical mathematics and systems and control. In particular, after different reduction techniques have been presented, a table summarizing their most important features is proposed, for comparison purpose. The motivation for such comparison stems from the fact that the insight obtained by the comparison allows to make a motivated choice for a particular model reduction technique, on the basis of the desired properties retained in the reduced model. Particular attention is paid on reduction techniques from the area of structural dynamics. Finally, the differences among some of the presented reduction techniques are illustrated, on a quantitative level, by means of their application to the case of a slewing flexible beam. In particular, in the application of the different reduction techniques, a consistent-mass finite element model, with only translational degrees of freedom, is employed as beam full model.