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A generalized active subspace for dimension reduction in mixed aleatory-epistemic uncertainty quantification

机译:混合杀菌性不确定性量化的尺寸降低的广义活性子空间

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Aleatory and epistemic uncertainties are being increasingly incorporated in verification, validation, and uncertainty quantification (UQ). However, the crucial UQ of high efficiency and confidence remains challenging for mixed multidimensional uncertainties. In this study, a generalized active subspace (GAS) for dimension reduction is presented and the characteristics of GAS are investigated by interval analysis. An7 adaptive response surface model can then be employed for uncertainty propagation. Since the precise eigenvalues of interval matrix are difficult to solve in mathematics, three alternative estimate methods, i.e. interval eigenvalue analysis (IEA), empirical distribution function (EDF), and Taylor expansions, are developed for the GAS computation and practical use. The efficacy of the GAS and the estimate methods is demonstrated on three test examples: a three-dimensional response function, a standard NASA test of six-dimensional mixed uncertainties, and a NACA0012 airfoil design case of ten epistemic uncertainties. The IEA estimate is comparatively more suitable, but needs more computational cost due to the requirement of bound matrices. When the uncertainty level is small, the three methods are all applicable and the estimate based on EDF can be more efficient. The methodology exhibits high accuracy and strong adaptability in dimension reduction, thus providing a potential template for tackling a wide variety of multidimensional mixed aleatory-epistemic UQ problems. (C) 2020 Elsevier B.V. All rights reserved.
机译:阶段性和认知的不确定性越来越多地纳入验证,验证和不确定性量化(UQ)。但是,高效率和信心的关键UQ对混合多维不确定因素仍然挑战。在该研究中,提出了一种尺寸减少的通用活性子空间(气体),并且通过间隔分析研究了气体的特性。然后可以采用AN7自适应响应表面模型以用于不确定传播。由于间隔基质的精确特征值难以在数学中难以解决,因此三种替代估计方法,即间隔特征值分析(IEA),经验分布函数(EDF)和泰勒扩展是用于气体计算和实际使用的。在三个测试实施例中证明了气体和估计方法的功效:三维响应函数,六维混合不确定性的标准NASA试验,以及NACA0012翼型设计案例为十个认知不确定性。 IEA估计比结合矩阵的要求相对更合适,但需要更多的计算成本。当不确定性水平小时,这三种方法都适用,基于EDF的估计可以更有效。该方法表现出高精度和尺寸减少的强烈适应性,从而提供了解决各种多维混合蛋白认知UQ问题的潜在模板。 (c)2020 Elsevier B.v.保留所有权利。

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