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International Journal for Uncertainty Quantification

Published 6 issues per year

ISSN Print: 2152-5080

ISSN Online: 2152-5099

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.7 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.9 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.5 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.0007 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.5 SJR: 0.584 SNIP: 0.676 CiteScore™:: 3 H-Index: 25

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DESIGN UNDER UNCERTAINTY EMPLOYING STOCHASTIC EXPANSION METHODS

Volume 1, Issue 2, 2011, pp. 119-146
DOI: 10.1615/Int.J.UncertaintyQuantification.v1.i2.20
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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.

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