Model order reduction based on low-rank approximation for parameterized eigenvalue problems in structural dynamics

Abstract

This study introduces a novel reduced -order modeling approach for parameterized eigenvalue problems. The proposed framework represents eigenvectors as a low -rank approximation and is implemented using an offline -online strategy. In the offline stage, nonlinear equations are formulated by imposing a stationary condition on the weighted Rayleigh quotient over sampled points and eigenvalues of interest. A variant of the Krylov subspace approach is applied to progressively identify the dominant response characteristics at sampled points. In the online stage, a reduced -order model is obtained through Galerkin projection, and eigensolutions at unsampled points are determined. The performance of the proposed framework is validated through numerical examples, where perturbation, least -angle regression, and Gaussian process are considered for comparison. The obtained results demonstrate that the proposed framework can accurately estimate eigensolutions, even when eigenvalues are adjacent to each other. In terms of efficiency, the a priori construction of the low -dimensional basis is possible without solving the full -order model, resulting in substantial CPU time savings during the offline computation process. Lastly, the applicability of the proposed framework is investigated through an uncertainty quantification example using numerical and experimental results.