Global sensitivity analysis using low-rank tensor approximations

Abstract : In the context of global sensitivity analysis, the Sobol’ indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these indices at low computational cost, by post-processing the coefficients of polynomial meta-models belonging to the class of low-rank tensor approximations. Meta-models of this class can be particularly efficient in representing responses of high-dimensional models, because the number of unknowns in their general functional form grows only linearly with the input dimension. The proposed approach is validated in example applications, where the Sobol’ indices derived from the meta-model coefficients are compared to reference indices, the latter obtained by exact analytical solutions or Monte-Carlo simulation with extremely large samples. Moreover, low-rank tensor approximations are confronted to the popular polynomial chaos expansion meta-models in case studies that involve analytical rank-one functions and finite-element models pertinent to structural mechanics and heat conduction. In the examined applications, indices based on the novel approach tend to converge faster to the reference solution with increasing size of the experimental design used to build the meta-model.
Document type :
Journal articles
Liste complète des métadonnées

Cited literature [74 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01428988
Contributor : Noura Fajraoui <>
Submitted on : Wednesday, January 11, 2017 - 5:51:50 PM
Last modification on : Tuesday, March 5, 2019 - 9:30:11 AM
Document(s) archivé(s) le : Wednesday, April 12, 2017 - 12:18:46 PM

File

RSUQ-2016-004.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

K. Konakli, B. Sudret. Global sensitivity analysis using low-rank tensor approximations. Reliability Engineering and System Safety, Elsevier, 2016, ⟨10.1016/j.ress.2016.07.012⟩. ⟨hal-01428988⟩

Share

Metrics

Record views

58

Files downloads

108