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

V. Yaghoubi (1) , S. Marelli (2) , B. Sudret (3, 2) , T. Abrahamsson, (1)

1 Department of Applied Mechanics
2 ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

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 (MC) 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-Degree Of Freedom (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 MC methods.

Mots clés: Frequency response functions; Stochastic frequencytransformation; Uncertainty quantification; Principal component analysis; Polynomial chaos expansions

Domaines: Calcul [stat.CO]; Méthodologie [stat.ME]

V. Yaghoubi, S. Marelli, B. Sudret, T. Abrahamsson,. Sparse polynomial chaos expansions of frequency response functions using stochastic frequency transformation. 2017. ⟨hal-01428958⟩