A hybrid adaptive sampling algorithm for obtaining reduced ordermodels for systems with frequency dependent state-space matrices

This paper proposes a hybrid adaptive sampling algorithm to automate the generation of reduced order modelsfor systems described by large-scale frequency dependent state-space models. The evaluation of the frequencydependent state-space model for each frequency sample can be computationally expensive. The distribution offrequency samples must be optimized to avoid oversampling and undersampling. In order to have an optimumnumber of frequency samples, the proposed algorithm uses the reflective exploration technique for the adaptiveselection of samples, and the sampling is further refined using a binary search to validate the frequency dependentreduced order models. Projection-based model order reduction techniques are used for obtaining the reduced ordermodel. The projection matrix for each frequency sample is merged to obtain a common projection matrix for allsamples. However, in certain cases when the number of sample points increases, the merged projection matrixalso increases in dimension and might fail to provide a satisfactory reduction in model size. Thus, the mergedprojection 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 obtainthe system response. Pertinent examples validate the proposed hybrid adaptive sampling algorithm.