Comparison of CMS, Krylov and Balanced Truncation Based Model Reduction from a Mechanical Application Engineer’s Perspective

Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


Component Mode Synthesis (CMS) is a well known and established method for order reduction of Finite Element (FE) models. One advantage of CMS is a clear physical interpretability and another, more practical one, is the availability in common FE packages. In the last years a lot of research has been done, in order to adapt reduction methods, which are based on Krylov subspaces and balanced truncation for FE models. Several recent publications denote mode based reduction methods, like CMS, as out-dated while the latter ones are so called ‘modern methods’. For a mechanical application engineer the question arises, whether these methods are really so advantageous, that the reliable CMS should be exchanged against one of the two other methods.

This paper is devoted to a numerical and qualitative comparison of these three methods with respect to each other. The contribution starts with an introduction, where the ‘mechanical application engineer’s perspective’ is explained in terms of requirements and boundary conditions of the reduction process. Next, all three approaches will be briefly outlined and representative literature will be cited. In the next chapter, all three methods will be demonstrated by a simple three mass example, so that some basic characteristics can easily be seen and first conclusions can be drawn. In the subsequent section the different methods will be applied to simple FE structures and the quality of the reduced models will be examined. Finally a conclusion will be drawn whether one of the three methods is clear better (or worse) with respect to the other ones.


Vibration Mode Model Reduction Model Order Reduction Krylov Subspace Trial Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Stiffness matrix


Stiffness matrix

B, B1

Input matrix

C, C1

Output matrix

E, A

System matrices for LTI system


State space vector

\( {{ \tilde{\mathbf M}}} \)

Quantity M in reduced model


Force vector


Nodal DOF vector of FE model


Output vector


Number of DOF of FE model


Number of external forces


Number of outputs


Number of DOF in reduced model


Number of considered modes


Number of static trial vectors

V, W

Subspace for reduction


Modes gained by an eigenvalue problem


Static deformation shapes


Boundary DOF


Inner DOF


Number of boundary DOF


Complex laplace variable


Transfer function matrix




Eigenfrequency of the i-th mode


Eigenfrequency limit

\( {{\mathbf T}}_j^{{{s_0}}} \)

j-th moment around s0


Controllability Gramian matrix


Observability Gramian matrix




Particular time instant


Hankel Singular Value


Number of considered trial vectors


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© Springer Science+Buisness Media, LLC 2012

Authors and Affiliations

  1. 1.University of Applied Sciences Upper AustriaWelsAustria

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