Reduced-order modeling via proper generalized decomposition for uncertainty quantification of frequency response functions

This paper presents a new reduced-order modeling methodology for frequency response analysis of linear dynamical systems with parametric uncertainty. The proposed framework consists of offline and online stages in the computation process. The offline stage introduces a variant of proper generalization decomposition (PGD), which approximates the solution of the full-order model (FOM) as a low-rank separated representation. A key feature of the proposed PGD is the collocation representation equipped with the Dirac-delta function, which handles non-smooth characteristics of frequency responses point-wisely. This strategy replaces direct computations of FOM on a large number of samples and frequencies with iterative solving of the subproblems formulated by the progressive Galerkin approach. In the online stage, the PGD modes acquired from the offline stage are used to generate a reduced-order model (ROM). Solutions for unsampled points are evaluated through ROM, which is further utilized to estimate the statistics of the frequency response function. Numerical examples demonstrate that the proposed methodology accelerates computational efficiency while maintaining accuracy over the frequency range including resonance.