HYPAD-UQ: A Derivative-Based Uncertainty Quantification Method Using a Hypercomplex Finite Element MethodSource: Journal of Verification, Validation and Uncertainty Quantification:;2023:;volume( 008 ):;issue: 002::page 21002-1Author:Balcer, Matthew
,
Aristizabal, Mauricio
,
Rincon-Tabares, Juan-Sebastian
,
Montoya, Arturo
,
Restrepo, David
,
Millwater, Harry
DOI: 10.1115/1.4062459Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: A derivative-based uncertainty quantification (UQ) method called HYPAD-UQ that utilizes sensitivities from a computational model was developed to approximate the statistical moments and Sobol' indices of the model output. Hypercomplex automatic differentiation (HYPAD) was used as a means to obtain accurate high-order partial derivatives from computational models such as finite element analyses. These sensitivities are used to construct a surrogate model of the output using a Taylor series expansion and subsequently used to estimate statistical moments (mean, variance, skewness, and kurtosis) and Sobol' indices using algebraic expansions. The uncertainty in a transient linear heat transfer analysis was quantified with HYPAD-UQ using first-order through seventh-order partial derivatives with respect to seven random variables encompassing material properties, geometry, and boundary conditions. Random sampling of the analytical solution and the regression-based stochastic perturbation finite element method were also conducted to compare accuracy and computational cost. The results indicate that HYPAD-UQ has superior accuracy for the same computational effort compared to the regression-based stochastic perturbation finite element method. Sensitivities calculated with HYPAD can allow higher-order Taylor series expansions to be an effective and practical UQ method.
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contributor author | Balcer, Matthew | |
contributor author | Aristizabal, Mauricio | |
contributor author | Rincon-Tabares, Juan-Sebastian | |
contributor author | Montoya, Arturo | |
contributor author | Restrepo, David | |
contributor author | Millwater, Harry | |
date accessioned | 2023-11-29T19:49:31Z | |
date available | 2023-11-29T19:49:31Z | |
date copyright | 6/13/2023 12:00:00 AM | |
date issued | 6/13/2023 12:00:00 AM | |
date issued | 2023-06-13 | |
identifier issn | 2377-2158 | |
identifier other | vvuq_008_02_021002.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl1/handle/yetl/4295054 | |
description abstract | A derivative-based uncertainty quantification (UQ) method called HYPAD-UQ that utilizes sensitivities from a computational model was developed to approximate the statistical moments and Sobol' indices of the model output. Hypercomplex automatic differentiation (HYPAD) was used as a means to obtain accurate high-order partial derivatives from computational models such as finite element analyses. These sensitivities are used to construct a surrogate model of the output using a Taylor series expansion and subsequently used to estimate statistical moments (mean, variance, skewness, and kurtosis) and Sobol' indices using algebraic expansions. The uncertainty in a transient linear heat transfer analysis was quantified with HYPAD-UQ using first-order through seventh-order partial derivatives with respect to seven random variables encompassing material properties, geometry, and boundary conditions. Random sampling of the analytical solution and the regression-based stochastic perturbation finite element method were also conducted to compare accuracy and computational cost. The results indicate that HYPAD-UQ has superior accuracy for the same computational effort compared to the regression-based stochastic perturbation finite element method. Sensitivities calculated with HYPAD can allow higher-order Taylor series expansions to be an effective and practical UQ method. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | HYPAD-UQ: A Derivative-Based Uncertainty Quantification Method Using a Hypercomplex Finite Element Method | |
type | Journal Paper | |
journal volume | 8 | |
journal issue | 2 | |
journal title | Journal of Verification, Validation and Uncertainty Quantification | |
identifier doi | 10.1115/1.4062459 | |
journal fristpage | 21002-1 | |
journal lastpage | 21002-20 | |
page | 20 | |
tree | Journal of Verification, Validation and Uncertainty Quantification:;2023:;volume( 008 ):;issue: 002 | |
contenttype | Fulltext |