A hybrid adaptive sampling algorithm for obtaining reduced order models for systems with frequency dependent state‐space matrices

Abstract

SummaryThis paper proposes a hybrid adaptive sampling algorithm to automate the generation of reduced order models for systems described by large‐scale frequency dependent state‐space models. The evaluation of the frequency dependent state‐space model for each frequency sample can be computationally expensive. The distribution of frequency samples must be optimized to avoid oversampling and undersampling. In order to have an optimum number of frequency samples, the proposed algorithm uses the reflective exploration technique for the adaptive selection of samples, and the sampling is further refined using a binary search to validate the frequency dependent reduced order models. Projection‐based model order reduction techniques are used for obtaining the reduced order model. The projection matrix for each frequency sample is merged to obtain a common projection matrix for all samples. However, in certain cases when the number of sample points increases, the merged projection matrix also increases in dimension and might fail to provide a satisfactory reduction in model size. Thus, the merged projection matrix is truncated based on its singular values to obtain a compact common projection matrix. Then, the reduced order state‐space matrices per frequency are interpolated over the frequency range of interest to obtain the system response. Pertinent examples validate the proposed hybrid adaptive sampling algorithm. Copyright © 2015 John Wiley & Sons, Ltd.