Dominant Modes via Model Error

Abstract

This paper deals with obtaining a reduced model of a stable mechanical system with proportional damping. Such systems can be conveniently represented in modal coordinates. Two popular schemes, namely the modal cost analysis and the balancing method, offer simple means of identifying dominant modes for retention in the reduced model. The dominance is measured via the modal costs in the case of MCA, and via the singular values of the gramian-product in the case of balancing. Though these measures do not exactly reflect the more appropriate model error which is the H2 norm of the output-error between the full and the reduced models, they do lead to simple computations. Normally, the model error is computed after the reduced model is obtained, since it is believed that, in general, the model error cannot be easily computed a priori. The main thrust of this paper is to point out that the model error can also be calculated a priori, just as easily as the above measures. Hence the model error itself can be used to determine the dominant modes. Moreover, the simplicity of the computations do not presume any special properties of the system, such as small damping, orthogonal-symmetry, etc.