Resampling Plans for Sample Point Selection in Multipoint Model-Order Reduction

Abstract

Multipoint projection methods have gained much notoriety in model-order reduction of linear, nonlinear, and parameter-varying systems. A well-known difficulty with such methods lies in the need for clever point selection to attain model compactness and accuracy. In this paper, the authors present a method for sample point selection in multipoint projection-based model-order reduction. The proposed technique, which is borrowed from the statistical modeling area, is based on resampling schemes to estimate error and can be coupled with recently proposed order reduction schemes to efficiently produce accurate models. Two alternative implementations are presented: 1) a rigorous linear-matrix-inequality-based technique and 2) a simpler, more efficient, heuristic search. The goal of this paper is to answer two questions. First, can this alternative metric be effective in selecting sample points in the sense of placing points in regions of high error without recourse to evaluation of the larger system? Second, if the metric is effective in this sense, under what conditions are substantial improvements in the model reduction efficiency achieved? Results are shown that indicate that the metric is indeed effective in a variety of settings, therefore opening the possibility for performing adaptive error control