Global sensitivity analysis using low-rank tensor approximations.
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| Title: | Global sensitivity analysis using low-rank tensor approximations. |
|---|---|
| Authors: | Konakli, Katerina1 konakli@ibk.baug.ethz.ch, Sudret, Bruno1 |
| Source: | Reliability Engineering & System Safety. Dec2016, Vol. 156, p64-83. 20p. |
| Subjects: | Approximation theory, Polynomial chaos, Coefficients (Statistics), Sensitivity analysis, Monte Carlo method |
| 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. [ABSTRACT FROM AUTHOR] |
| Copyright of Reliability Engineering & System Safety is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 118157225 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Global sensitivity analysis using low-rank tensor approximations. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Konakli%2C+Katerina%22">Konakli, Katerina</searchLink><relatesTo>1</relatesTo><i> konakli@ibk.baug.ethz.ch</i><br /><searchLink fieldCode="AR" term="%22Sudret%2C+Bruno%22">Sudret, Bruno</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Reliability+Engineering+%26+System+Safety%22">Reliability Engineering & System Safety</searchLink>. Dec2016, Vol. 156, p64-83. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomial+chaos%22">Polynomial chaos</searchLink><br /><searchLink fieldCode="DE" term="%22Coefficients+%28Statistics%29%22">Coefficients (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Sensitivity+analysis%22">Sensitivity analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Reliability Engineering & System Safety is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.ress.2016.07.012 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 64 Subjects: – SubjectFull: Approximation theory Type: general – SubjectFull: Polynomial chaos Type: general – SubjectFull: Coefficients (Statistics) Type: general – SubjectFull: Sensitivity analysis Type: general – SubjectFull: Monte Carlo method Type: general Titles: – TitleFull: Global sensitivity analysis using low-rank tensor approximations. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Konakli, Katerina – PersonEntity: Name: NameFull: Sudret, Bruno IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2016 Type: published Y: 2016 Identifiers: – Type: issn-print Value: 09518320 Numbering: – Type: volume Value: 156 Titles: – TitleFull: Reliability Engineering & System Safety Type: main |
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