图书馆订阅: Guest
Begell Digital Portal Begell 数字图书馆 电子图书 期刊 参考文献及会议录 研究收集
国际不确定性的量化期刊
影响因子: 3.259 5年影响因子: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

ISSN 打印: 2152-5080
ISSN 在线: 2152-5099

Open Access

国际不确定性的量化期刊

DOI: 10.1615/Int.J.UncertaintyQuantification.v1.i2.20
pages 119-146

DESIGN UNDER UNCERTAINTY EMPLOYING STOCHASTIC EXPANSION METHODS

Michael S. Eldred
Sandia National Laboratories, P. O. Box 5800, Mail Stop: 1318, Org: 01411, Albuquerque, NM 87185-1318, USA
Howard C. Elman
Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, USA

ABSTRACT

Nonintrusive polynomial chaos expansion (PCE) and stochastic collocation (SC) methods are attractive techniques for uncertainty quantification due to their fast convergence properties and ability to produce functional representations of stochastic variability. PCE estimates coefficients for known orthogonal polynomial basis functions based on a set of response function evaluations, using sampling, linear regression, tensor-product quadrature, cubature, or Smolyak sparse grid approaches. SC, on the other hand, forms interpolation functions for known coefficients and requires the use of structured collocation point sets derived from tensor product or sparse grids. Once PCE or SC representations have been obtained for a response metric of interest, analytic expressions can be derived for the moments of the expansion and for the design derivatives of these moments, allowing for efficient design under uncertainty formulations involving moment control (e.g., robust design). This paper presents two approaches for moment design sensitivities, one involving a single response function expansion over the full range of both the design and uncertain variables and one involving response function and derivative expansions over only the uncertain variables for each instance of the design variables. These two approaches present trade-offs involving expansion dimensionality, global versus local validity, collocation point data requirements, and L2 (mean, variance, probability) versus L (minima, maxima) interrogation requirements. Given this capability for analytic moments and moment sensitivities, bilevel, sequential, and multifidelity formulations for design under uncertainty are explored. Computational results are presented for a set of algebraic benchmark test problems, with attention to design formulation, stochastic expansion type, stochastic sensitivity approach, and numerical integration method.


Articles with similar content:

POLYNOMIAL CHAOS FOR SEMIEXPLICIT DIFFERENTIAL ALGEBRAIC EQUATIONS OF INDEX 1
International Journal for Uncertainty Quantification, Vol.3, 2013, issue 1
Roland Pulch
STOCHASTIC DYNAMIC RESPONSE ANALYSIS OF NONLINEAR STRUCTURES WITH GENERAL NONUNIFORM RANDOM PARAMETERS BY MINIMIZING GL2-DISCREPANCY
International Journal for Multiscale Computational Engineering, Vol.14, 2016, issue 3
Jianbing Chen, Pengyan Song, Xiaodan Ren
POLYNOMIAL-CHAOS-BASED KRIGING
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 2
Joe Wiart, Bruno Sudret, Roland Schobi
OPTIMAL DESIGN UNDER UNCERTAINTY OF REINFORCED CONCRETE STRUCTURES USING SYSTEM RELIABILITY APPROACH
International Journal for Uncertainty Quantification, Vol.3, 2013, issue 6
Abdelkhalak El-Hami, Didier Lemosse, Younes Aoues, Alaa Chateauneuf
SPARSE MULTIRESOLUTION REGRESSION FOR UNCERTAINTY PROPAGATION
International Journal for Uncertainty Quantification, Vol.4, 2014, issue 4
Daniele Schiavazzi, Gianluca Iaccarino, Alireza Doostan