Krylov and Modal Subspace based Model Order Reduction with A-Priori Error Estimation

Abstract

Versatile model order reduction techniques for the reduction of dynamic systems have been presented in the last decades. Krylov subspace based methods are considered as efficient in terms of computational effort and reduction order and can be used in order to match the transfer function locally. However, they lack of a simple and efficient automatisation and error estimation. On the other hand, modal reduction is popular because it leads to exactly matching eigenfrequencies. The static behaviour and the overall accuracy of the frequency response, though, are poor. In this paper, a combination of both methods is presented and discussed. In order to characterise a method for the reduction of mechanical models for the simulation of machine tools and similar mechatronic systems, first, the requirements on the model reduction method are derived. Criteria for the relative error of the frequency response function, the transmission zeros, and the poles are defined and the idea of defining a frequency range of interest is established. Subsequently, a combination of Krylov and modal subspaces for the reduction of dynamic systems with second-order structure and proportional damping is presented. It is shown that the combination of the bases of the two methods leads to a combination of the advantages and an elimination of the drawbacks of them both. Moreover, an estimation for the upper bound of the defined error criteria is developed and verified with numerical results. The result of this paper is an a priori parametrisable and numerically efficient model reduction method, which leads to reduced systems of low order with a definable error limit within a definable frequency range.