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This page links some uncertainties-related publications relevant to the Opus community.

Polynomial chaos expansion for sensitivity analysis.

Thierry Crestaux (CEA-DM2S), Olivier Le Maitre (LIMSI-CNRS), Jean-Marc Martinez (CEA-DM2S)

In this paper, the computation of Sobol’s sensitivity indices from the polynomial chaos expansion of a model output involving uncertain inputs is investigated. It is shown that when the model output is smooth with regards to the inputs, a spectral convergence of the computed sensitivity indices is achieved. However, even for smooth outputs the method is limited to a moderate number of inputs, say 10 – 20, as it becomes computationally too demanding to reach the convergence domain. Alternative methods (such as sampling strategies) are then more attractive. The method is also challenged when the output is non-smooth even when the number of inputs is limited.

Controlled stratification for quantile estimation,

C. Cannamela, J. Garnier, and B. Iooss, Ann. Appl. Stat., Vol. 2, pp. 1554-1580 (2008).

In this paper we propose and discuss variance reduction techniques for the estimation of quantiles of the output of a complex model with random input parameters. These techniques are based on the use of a reduced model, such as a metamodel or a response surface. The reduced model can be used as a control variate; or a rejection method can be implemented to sample the realizations of the input parameters in prescribed relevant strata; or the reduced model can be used to determine a good biased distribution of the input parameters for the implementation of an importance sampling strategy. The different strategies are analyzed and the asymptotic variances are computed, which shows the benefit of an adaptive controlled stratification method. This method is finally applied to a real example (computation of the peak cladding temperature during a large-break loss of coolant accident in a nuclear reactor).

Adaptive sparse polynomial chaos expansions for uncertainty propagation and sensitivity analysis.

G. Blatman, PhD Thesis, Université Blaise Pascal - Clermont-Ferrand II.

This thesis takes place in the context of uncertainty propagation and sensitivity analysis of computer simulation codes for industrial application. It is aimed at carrying out such probabilistic studies while minimizing the number of model evaluations which may reveal time consuming. The present work relies upon the expansion of the model response onto the polynomial chaos (PC) basis, which allows the analyst to perform post-processing at a negligible cost. However fitting the PC expansion may require a high number of calls to the model if the latter depends on a large number of input parameters, say more than 10. To circumvent this problem, two algorithms are proposed in order to select only a low number of significant terms in the PC approximation, namely a stepwise regression scheme and a procedure based on Least Angle Regression (LAR). Both approaches eventually provide PC representations with a small number of coefficients which may be computed using a reduced number of model evaluations. The methods are first tested and compared on various academic examples. Then they are applied to the industrial problem of the assessment of a pressure vessel of a nuclear powerplant. The obtained results show the efficiency of the proposed procedures to carry out uncertainty and sensitivity analysis of high-dimensional problems.

Quantifying uncertainty in an industrial approach : an emerging consensus in an old epistemological debate

E. de Rocquigny, S.A.P.I.EN.S, 2.1 | 2009

Uncertainty is ubiquitous in modern decision-making supported by quantitative modeling. While uncertainty treatment has been initially largely developed in risk or environmental assessment, it is gaining large-spread interest in many industrial fields generating knowledge and practices going beyond the classical risk versus uncertainty or epistemic versus aleatory debates. On the basis of years of applied research in different sectors at the European scale, this paper discusses the emergence of a methodological consensus throughout a number of fields of engineering and applied science such as metrology, safety and reliability, protection against natural risk, manufacturing statistics, numerical design and scientific computing etc. In relation with the applicable regula-tion and standards and a relevant quantity of interest for decision-making, this approach involves in particular the proper identification of key steps such as : the quantification (or modeling) of the sources of uncertainty, possibly involving an inverse approach ; their propagation through a pre-existing physical-industrial model; the ranking of importance or sensitivity analysis and sometimes a subsequent optimisation step. It aims at giving a consistent and industrially-realistic framework for practical mathematical modeling, assumingly restricted to quantitative and quantifiable uncertainty, and illustrated on three typical examples. Axes of further research proving critical for the environmental or industrial issues are outlined: the information challenges posed by uncertainty modeling in the context of data scarcity, and the corresponding calibration and inverse probabilistic techniques, bound to be developed to best value industrial or environmental monitoring and data acquisition systems under uncertainty; the numerical challenges entailing considerable development of high-performance computing in the field; the acceptability challenges in the context of the precautionary principle.