Global sensitivity analysis: A Bayesian learning based polynomial chaos approach

JOURNAL OF COMPUTATIONAL PHYSICS

卷:415

Article

Bhattacharyya, Biswarup¹ 

[1] Univ Claude Bernard Lyon 1, Univ Lyon, IFSTTAR, LBMC UMR T9406, F-69622 Villeurbanne, France

关键词: Sparse polynomial chaos expansion;    Global sensitivity analysis;    Bayesian approach;    Automatic relevance determination;    Sobol' indices;   

DOI  :  10.1016/j.jcp.2020.109539

来源: Elsevier

【 摘 要 】

A novel sparse polynomial chaos expansion (PCE) is proposed in this paper for global sensitivity analysis (GSA). The proposed model combines variational Bayesian (VB) inference and automatic relevance determination (ARD) with the PCE model. The VB inference is utilized to compute the PCE coefficients. The PCE coefficients are obtained through a simple optimization procedure in the VB framework. On the other hand, the curse of dimensionality issue of PCE model is tackled using the ARD which reduces the number of polynomial bases significantly. The applicability of the proposed approach is illustrated by performing GSA on five numerical examples. The results show that the proposed approach outperforms a similar state-of-art surrogate model in obtaining an accurate sensitivity index using limited number of model evaluations. For all the examples, the PCE models are highly sparse, which require very few polynomial bases to assess an accurate sensitivity index. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free