Surrogate model reduction for linear dynamic systems based on a frequency domain modal analysis

Abstract

A novel model reduction methodology for linear dynamic systems with parameter variations is presented based on a frequency domain formulation and use of the proper orthogonal decomposition. For an efficient treatment of parameter variations, the system matrices are divided into a nominal and an incremental part. It is shown that the perturbed part is modally equivalent to a new system where the incremental matrices are isolated into the forcing term. To account for the continuous changes in the parameters, the single-composite-input is invoked with a finite number of predetermined incremental matrices. The frequency-domain Karhunen---Loeve procedure is used to calculate a rich set of basis modes accounting for the variations. For demonstration, the new procedure is applied to a finite element model of the Goland wing undergoing oscillations and shown to produce extremely accurate reduced-order surrogate model for a wide range of parameter variations.