Data-Driven Method to Quantify Correlated Uncertainties
Polynomial chaos (PC) has been proven to be an efficient method for uncertainty quantification, but its applicability is limited by two strong assumptions: the mutual independence of random variables and the requirement of exact knowledge about the distribution of the random variables. We describe a...
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10129195/ |
| _version_ | 1827935761266114560 |
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| author | Jeahan Jung Minseok Choi |
| author_facet | Jeahan Jung Minseok Choi |
| author_sort | Jeahan Jung |
| collection | DOAJ |
| description | Polynomial chaos (PC) has been proven to be an efficient method for uncertainty quantification, but its applicability is limited by two strong assumptions: the mutual independence of random variables and the requirement of exact knowledge about the distribution of the random variables. We describe a new data-driven method for dealing with correlated multivariate random variables for uncertainty quantification that requires only observed data of the random variables. It is based on the transformation of correlated random variables into independent random variables. We use singular value decomposition as a transformation strategy that does not require information about the probability distribution. For the transformed random variables, we can construct the PC basis to build a surrogate model. This approach provides an additional benefit of quantifying high-dimensional uncertainties by combining our method with the analysis-of-variance (ANOVA) method. We demonstrate in several numerical examples that our proposed approach leads to accurate solutions with a much smaller number of simulations compared to the Monte Carlo method. |
| first_indexed | 2024-03-13T07:59:29Z |
| format | Article |
| id | doaj.art-b99f60329ff3422f9f4d719ad9d64fa2 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-13T07:59:29Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-b99f60329ff3422f9f4d719ad9d64fa22023-06-01T23:00:34ZengIEEEIEEE Access2169-35362023-01-0111506055061810.1109/ACCESS.2023.327752110129195Data-Driven Method to Quantify Correlated UncertaintiesJeahan Jung0https://orcid.org/0000-0001-6430-4087Minseok Choi1https://orcid.org/0000-0002-7245-0823Department of Mathematics, Pohang University of Science and Technology (POSTECH), Pohang, Gyeongbuk, Republic of KoreaDepartment of Mathematics, Pohang University of Science and Technology (POSTECH), Pohang, Gyeongbuk, Republic of KoreaPolynomial chaos (PC) has been proven to be an efficient method for uncertainty quantification, but its applicability is limited by two strong assumptions: the mutual independence of random variables and the requirement of exact knowledge about the distribution of the random variables. We describe a new data-driven method for dealing with correlated multivariate random variables for uncertainty quantification that requires only observed data of the random variables. It is based on the transformation of correlated random variables into independent random variables. We use singular value decomposition as a transformation strategy that does not require information about the probability distribution. For the transformed random variables, we can construct the PC basis to build a surrogate model. This approach provides an additional benefit of quantifying high-dimensional uncertainties by combining our method with the analysis-of-variance (ANOVA) method. We demonstrate in several numerical examples that our proposed approach leads to accurate solutions with a much smaller number of simulations compared to the Monte Carlo method.https://ieeexplore.ieee.org/document/10129195/Correlated random variableshigh dimensionpolynomial chaos expansionuncertainty quantification |
| spellingShingle | Jeahan Jung Minseok Choi Data-Driven Method to Quantify Correlated Uncertainties IEEE Access Correlated random variables high dimension polynomial chaos expansion uncertainty quantification |
| title | Data-Driven Method to Quantify Correlated Uncertainties |
| title_full | Data-Driven Method to Quantify Correlated Uncertainties |
| title_fullStr | Data-Driven Method to Quantify Correlated Uncertainties |
| title_full_unstemmed | Data-Driven Method to Quantify Correlated Uncertainties |
| title_short | Data-Driven Method to Quantify Correlated Uncertainties |
| title_sort | data driven method to quantify correlated uncertainties |
| topic | Correlated random variables high dimension polynomial chaos expansion uncertainty quantification |
| url | https://ieeexplore.ieee.org/document/10129195/ |
| work_keys_str_mv | AT jeahanjung datadrivenmethodtoquantifycorrelateduncertainties AT minseokchoi datadrivenmethodtoquantifycorrelateduncertainties |