Sparse polynomial chaos expansions of frequency response functions using stochastic frequency transformation

TL;DR

This paper introduces a novel approach combining frequency transformation and sparse polynomial chaos expansions to efficiently and accurately approximate frequency response functions in stochastic dynamic systems, reducing computational cost.

Contribution

It proposes a frequency transformation strategy to improve PCE efficiency for FRFs and employs principal component analysis for output reduction, enhancing surrogate modeling accuracy.

Findings

Accurate prediction of single FRFs achieved

Faster convergence of moments compared to Monte Carlo methods

Effective for systems with multiple random inputs

Abstract

Frequency response functions (FRFs) are important for assessing the behavior of stochastic linear dynamic systems. For large systems, their evaluations are time-consuming even for a single simulation. In such cases, uncertainty quantification by crude Monte-Carlo simulation is not feasible. In this paper, we propose the use of sparse adaptive polynomial chaos expansions (PCE) as a surrogate of the full model. To overcome known limitations of PCE when applied to FRF simulation, we propose a frequency transformation strategy that maximizes the similarity between FRFs prior to the calculation of the PCE surrogate. This strategy results in lower-order PCEs for each frequency. Principal component analysis is then employed to reduce the number of random outputs. The proposed approach is applied to two case studies: a simple 2-DOF system and a 6-DOF system with 16 random inputs. The accuracy assessment of the results indicates that the proposed approach can predict single FRFs accurately. Besides, it is shown that the first two moments of the FRFs obtained by the PCE converge to the reference results faster than with the Monte-Carlo (MC) methods.