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Sensitivity analysis using anchored ANOVA expansion and high order moments computation

Kunkun Tang 1, * Pietro Marco Congedo 1 Rémi Abgrall 1
* Corresponding author
1 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems
CNRS - Centre National de la Recherche Scientifique : UMR5800, UB - Université de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : An anchored ANOVA method is proposed in this paper to decompose statistical moments. Compared to standard ANOVA with mutually orthogonal components, anchored ANOVA, with arbitrary anchor point, loses orthogonality if employing the same measure. However, an advantage consists in the considerably reduced number of deterministic solver's computations, which renders uncertainty quantification of real engineering problems much easier. Different from existing methods, covariance decomposition of output variance is used in this paper to take account of interactions between non-orthogonal components, yielding an exact variance expansion, and thus, with a suitable numerical integration method, provides a strategy that converges. This convergence is verified by studying academic tests. In particular, sensitivity problem of existing method to anchor point is analyzed via Ishigami case, and we point out covariance decomposition survives from it. Covariance-based sensitivity indices (SI) are also used, compared to variance-based SI. Furthermore, we emphasize covariance decomposition can be generalized in a straightforward way to decompose high order moments. For academic problems, results show the method converges to exact solution regarding both skewness and kurtosis. Finally, the proposed method is applied on a realistic case, i.e. estimating chemical reactions uncertainties in a hypersonic flow around a space vehicle during an atmospheric reentry.
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https://hal.inria.fr/hal-00987189
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Submitted on : Monday, May 5, 2014 - 4:02:38 PM
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Kunkun Tang, Pietro Marco Congedo, Rémi Abgrall. Sensitivity analysis using anchored ANOVA expansion and high order moments computation. [Research Report] RR-8531, 2014. ⟨hal-00987189⟩

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