Application of the control variate technique to estimation of total sensitivity indices

Kucherenko, Sergei; Delpuech, B.; Iooss, Bertrand; Tarantola, Stefano

doi:10.1016/j.ress.2014.07.008

Cited by 39 publications

(11 citation statements)

References 17 publications

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“…Evaluation of Sobol' main effect indices remains to be an active area of research: we could mention application of RBD [13], various metamodelling methods [14,15,16] and some other attempts to improve direct formulas [17]. We also note that a new method for improving the efficiency of the Monte Carlo estimates for the Sobol' total sensitivity indices was developed in [18]. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Different numerical estimators for main effect global sensitivity indices

Kucherenko

Song

2017

Reliability Engineering & System Safety

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The variance-based method of global sensitivity indices based on Sobol' sensitivity indices became very popular among practitioners due to its easiness of interpretation. For complex practical problems computation of Sobol' indices generally requires a large number of function evaluations to achieve reasonable convergence. Four different direct formulas for computing Sobol’ main effect sensitivity indices are compared on a set of test models for which there are analytical results. Considered test functions represent various types of models that are found in practice. Formulas are based on high-dimensional integrals which are evaluated using Monte Carlo (MC) and Quasi Monte Carlo (QMC) techniques. Direct formulas are also compared with a different approach based on the so-called “double loop reordering” formula. It is found that the “double loop reordering” (DLR) approach shows a superior performance among all methods both for models with independent and dependent variables

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Section: Introductionmentioning

confidence: 99%

Different numerical estimators for main effect global sensitivity indices

Kucherenko

Song

2017

Reliability Engineering & System Safety

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“…Various methods have been investigated for computing the Sobol' indices based on Monte Carlo simulation (Archer et al, 1997;Sobol', 2001;Saltelli, 2002;Sobol' and Kucherenko, 2005;Saltelli et al, 2010); because of the large number of model evaluations required, these methods are not affordable for computationally costly models. To overcome this limitation, more efficient estimators have recently been proposed (Sobol et al, 2007;Janon et al, 2013;Kucherenko et al, 2015;Owen, 2013). A different approach is to substitute a complex model by a meta-model, which has similar statistical properties while maintaining a simple functional form (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Global sensitivity analysis using low-rank tensor approximations

Konakli

Sudret

2016

Reliability Engineering & System Safety

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In the context of global sensitivity analysis, the Sobol' indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these indices at low computational cost, by postprocessing the coefficients of polynomial meta-models belonging to the class of low-rank tensor approximations. Meta-models of this class can be particularly efficient in representing responses of high-dimensional models, because the number of unknowns in their general functional form grows only linearly with the input dimension. The proposed approach is validated in example applications, where the Sobol' indices derived from the meta-model coefficients are compared to reference indices, the latter obtained by exact analytical solutions or Monte-Carlo simulation with extremely large samples. Moreover, low-rank tensor approximations are confronted to the popular polynomial chaos expansion meta-models in case studies that involve analytical rank-one functions and finite-element models pertinent to structural mechanics and heat conduction. In the examined applications, indices based on the novel approach tend to converge faster to the reference solution with increasing size of the experimental design used to build the meta-model.

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