HYPAD-UQ:一种基于导数的超复杂有限元不确定度量化方法

IF 0.5 Q4 ENGINEERING, MECHANICAL Journal of Verification, Validation and Uncertainty Quantification Pub Date : 2023-05-03 DOI:10.1115/1.4062459
Matthew R. Balcer, M. Aristizábal, Juan Sebastian Rincon Tabares, Arturo Montoya, David Restrepo, H. Millwater
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引用次数: 0

摘要

开发了一种称为HYPAD-UQ的基于导数的不确定性量化(UQ)方法,该方法利用计算模型的灵敏度来近似模型输出的统计矩和Sobol指数。HYPAD是一种从有限元分析等计算模型中获得精确高阶偏导数的方法。这些灵敏度用于使用泰勒级数展开构建输出的代理模型,随后用于使用代数展开估计统计矩(均值、方差、偏度和峰度)和Sobol指数。瞬态线性传热分析中的不确定性使用HYPAD-UQ进行量化,使用一阶至七阶偏导数对包括材料特性、几何形状和边界条件在内的七个随机变量进行量化。分析解的随机抽样和基于回归的随机扰动有限元方法也进行了比较,以比较精度和计算成本。结果表明,与基于回归的随机扰动有限元方法相比,HYPAD-UQ在相同的计算工作量下具有更高的精度。用HYPAD计算的灵敏度可以使高阶泰勒级数展开成为一种有效而实用的UQ方法。
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HYPAD-UQ: A Derivative-based Uncertainty Quantification Method Using a Hypercomplex Finite Element Method
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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CiteScore
1.60
自引率
16.70%
发文量
12
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